xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision b45e3bf4ff73d80a20c3202b6cd9f79d2f2d3efe)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
4           C = A * B
5 */
6 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
7 #include <../src/mat/utils/freespace.h>
8 #include <../src/mat/impls/aij/mpi/mpiaij.h>
9 #include <petscbt.h>
10 #include <../src/mat/impls/dense/mpi/mpidense.h>
11 #include <petsc/private/vecimpl.h>
12 #include <petsc/private/sfimpl.h>
13 
14 #if defined(PETSC_HAVE_HYPRE)
15 PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat);
16 #endif
17 
18 PETSC_INTERN PetscErrorCode MatProductSymbolic_AB_MPIAIJ_MPIAIJ(Mat C)
19 {
20   PetscErrorCode      ierr;
21   Mat_Product         *product = C->product;
22   Mat                 A=product->A,B=product->B;
23   MatProductAlgorithm alg=product->alg;
24   PetscReal           fill=product->fill;
25   PetscBool           flg;
26 
27   PetscFunctionBegin;
28   /* scalable */
29   ierr = PetscStrcmp(alg,"scalable",&flg);CHKERRQ(ierr);
30   if (flg) {
31     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
32     PetscFunctionReturn(0);
33   }
34 
35   /* nonscalable */
36   ierr = PetscStrcmp(alg,"nonscalable",&flg);CHKERRQ(ierr);
37   if (flg) {
38     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr);
39     PetscFunctionReturn(0);
40   }
41 
42   /* seqmpi */
43   ierr = PetscStrcmp(alg,"seqmpi",&flg);CHKERRQ(ierr);
44   if (flg) {
45     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C);CHKERRQ(ierr);
46     PetscFunctionReturn(0);
47   }
48 
49   /* backend general code */
50   ierr = PetscStrcmp(alg,"backend",&flg);CHKERRQ(ierr);
51   if (flg) {
52     ierr = MatProductSymbolic_MPIAIJBACKEND(C);CHKERRQ(ierr);
53     PetscFunctionReturn(0);
54   }
55 
56 #if defined(PETSC_HAVE_HYPRE)
57   ierr = PetscStrcmp(alg,"hypre",&flg);CHKERRQ(ierr);
58   if (flg) {
59     ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr);
60     PetscFunctionReturn(0);
61   }
62 #endif
63   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
64 }
65 
66 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
67 {
68   PetscErrorCode ierr;
69   Mat_APMPI      *ptap = (Mat_APMPI*)data;
70 
71   PetscFunctionBegin;
72   ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr);
73   ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
74   ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
75   ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
76   ierr = MatDestroy(&ptap->Pt);CHKERRQ(ierr);
77   ierr = PetscFree(ptap->api);CHKERRQ(ierr);
78   ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
79   ierr = PetscFree(ptap->apa);CHKERRQ(ierr);
80   ierr = PetscFree(ptap);CHKERRQ(ierr);
81   PetscFunctionReturn(0);
82 }
83 
84 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
85 {
86   PetscErrorCode    ierr;
87   Mat_MPIAIJ        *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
88   Mat_SeqAIJ        *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
89   Mat_SeqAIJ        *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
90   PetscScalar       *cda=cd->a,*coa=co->a;
91   Mat_SeqAIJ        *p_loc,*p_oth;
92   PetscScalar       *apa,*ca;
93   PetscInt          cm =C->rmap->n;
94   Mat_APMPI         *ptap;
95   PetscInt          *api,*apj,*apJ,i,k;
96   PetscInt          cstart=C->cmap->rstart;
97   PetscInt          cdnz,conz,k0,k1;
98   const PetscScalar *dummy;
99   MPI_Comm          comm;
100   PetscMPIInt       size;
101 
102   PetscFunctionBegin;
103   MatCheckProduct(C,3);
104   ptap = (Mat_APMPI*)C->product->data;
105   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
106   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
107   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
108 
109   PetscCheckFalse(!ptap->P_oth && size>1,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
110 
111   /* flag CPU mask for C */
112 #if defined(PETSC_HAVE_DEVICE)
113   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
114   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
115   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
116 #endif
117 
118   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
119   /*-----------------------------------------------------*/
120   /* update numerical values of P_oth and P_loc */
121   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
122   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
123 
124   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
125   /*----------------------------------------------------------*/
126   /* get data from symbolic products */
127   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
128   p_oth = NULL;
129   if (size >1) {
130     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
131   }
132 
133   /* get apa for storing dense row A[i,:]*P */
134   apa = ptap->apa;
135 
136   api = ptap->api;
137   apj = ptap->apj;
138   /* trigger copy to CPU */
139   ierr = MatSeqAIJGetArrayRead(a->A,&dummy);CHKERRQ(ierr);
140   ierr = MatSeqAIJRestoreArrayRead(a->A,&dummy);CHKERRQ(ierr);
141   ierr = MatSeqAIJGetArrayRead(a->B,&dummy);CHKERRQ(ierr);
142   ierr = MatSeqAIJRestoreArrayRead(a->B,&dummy);CHKERRQ(ierr);
143   for (i=0; i<cm; i++) {
144     /* compute apa = A[i,:]*P */
145     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
146 
147     /* set values in C */
148     apJ  = apj + api[i];
149     cdnz = cd->i[i+1] - cd->i[i];
150     conz = co->i[i+1] - co->i[i];
151 
152     /* 1st off-diagonal part of C */
153     ca = coa + co->i[i];
154     k  = 0;
155     for (k0=0; k0<conz; k0++) {
156       if (apJ[k] >= cstart) break;
157       ca[k0]      = apa[apJ[k]];
158       apa[apJ[k++]] = 0.0;
159     }
160 
161     /* diagonal part of C */
162     ca = cda + cd->i[i];
163     for (k1=0; k1<cdnz; k1++) {
164       ca[k1]      = apa[apJ[k]];
165       apa[apJ[k++]] = 0.0;
166     }
167 
168     /* 2nd off-diagonal part of C */
169     ca = coa + co->i[i];
170     for (; k0<conz; k0++) {
171       ca[k0]      = apa[apJ[k]];
172       apa[apJ[k++]] = 0.0;
173     }
174   }
175   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
176   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
177   PetscFunctionReturn(0);
178 }
179 
180 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
181 {
182   PetscErrorCode     ierr;
183   MPI_Comm           comm;
184   PetscMPIInt        size;
185   Mat_APMPI          *ptap;
186   PetscFreeSpaceList free_space=NULL,current_space=NULL;
187   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
188   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
189   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
190   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
191   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
192   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
193   PetscBT            lnkbt;
194   PetscReal          afill;
195   MatType            mtype;
196 
197   PetscFunctionBegin;
198   MatCheckProduct(C,4);
199   PetscCheckFalse(C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
200   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
201   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
202 
203   /* create struct Mat_APMPI and attached it to C later */
204   ierr = PetscNew(&ptap);CHKERRQ(ierr);
205 
206   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
207   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
208 
209   /* get P_loc by taking all local rows of P */
210   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
211 
212   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
213   pi_loc = p_loc->i; pj_loc = p_loc->j;
214   if (size > 1) {
215     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
216     pi_oth = p_oth->i; pj_oth = p_oth->j;
217   } else {
218     p_oth = NULL;
219     pi_oth = NULL; pj_oth = NULL;
220   }
221 
222   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
223   /*-------------------------------------------------------------------*/
224   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
225   ptap->api = api;
226   api[0]    = 0;
227 
228   /* create and initialize a linked list */
229   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
230 
231   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
232   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
233   current_space = free_space;
234 
235   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
236   for (i=0; i<am; i++) {
237     /* diagonal portion of A */
238     nzi = adi[i+1] - adi[i];
239     for (j=0; j<nzi; j++) {
240       row  = *adj++;
241       pnz  = pi_loc[row+1] - pi_loc[row];
242       Jptr = pj_loc + pi_loc[row];
243       /* add non-zero cols of P into the sorted linked list lnk */
244       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
245     }
246     /* off-diagonal portion of A */
247     nzi = aoi[i+1] - aoi[i];
248     for (j=0; j<nzi; j++) {
249       row  = *aoj++;
250       pnz  = pi_oth[row+1] - pi_oth[row];
251       Jptr = pj_oth + pi_oth[row];
252       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
253     }
254     /* add possible missing diagonal entry */
255     if (C->force_diagonals) {
256       j = i + rstart; /* column index */
257       ierr = PetscLLCondensedAddSorted(1,&j,lnk,lnkbt);CHKERRQ(ierr);
258     }
259 
260     apnz     = lnk[0];
261     api[i+1] = api[i] + apnz;
262 
263     /* if free space is not available, double the total space in the list */
264     if (current_space->local_remaining<apnz) {
265       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
266       nspacedouble++;
267     }
268 
269     /* Copy data into free space, then initialize lnk */
270     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
271     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
272 
273     current_space->array           += apnz;
274     current_space->local_used      += apnz;
275     current_space->local_remaining -= apnz;
276   }
277 
278   /* Allocate space for apj, initialize apj, and */
279   /* destroy list of free space and other temporary array(s) */
280   ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr);
281   apj  = ptap->apj;
282   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
283   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
284 
285   /* malloc apa to store dense row A[i,:]*P */
286   ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
287 
288   /* set and assemble symbolic parallel matrix C */
289   /*---------------------------------------------*/
290   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
291   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
292 
293   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
294   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
295   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
296   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
297 
298   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
299   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
300   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
301   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
302 
303   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
304   C->ops->productnumeric = MatProductNumeric_AB;
305 
306   /* attach the supporting struct to C for reuse */
307   C->product->data    = ptap;
308   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
309 
310   /* set MatInfo */
311   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
312   if (afill < 1.0) afill = 1.0;
313   C->info.mallocs           = nspacedouble;
314   C->info.fill_ratio_given  = fill;
315   C->info.fill_ratio_needed = afill;
316 
317 #if defined(PETSC_USE_INFO)
318   if (api[am]) {
319     ierr = PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
320     ierr = PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
321   } else {
322     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
323   }
324 #endif
325   PetscFunctionReturn(0);
326 }
327 
328 /* ------------------------------------------------------- */
329 static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
330 static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);
331 
332 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
333 {
334   Mat_Product *product = C->product;
335   Mat         A = product->A,B=product->B;
336 
337   PetscFunctionBegin;
338   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
339     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
340 
341   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
342   C->ops->productsymbolic = MatProductSymbolic_AB;
343   PetscFunctionReturn(0);
344 }
345 /* -------------------------------------------------------------------- */
346 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
347 {
348   Mat_Product *product = C->product;
349   Mat         A = product->A,B=product->B;
350 
351   PetscFunctionBegin;
352   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
353     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);
354 
355   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
356   C->ops->productsymbolic          = MatProductSymbolic_AtB;
357   PetscFunctionReturn(0);
358 }
359 
360 /* --------------------------------------------------------------------- */
361 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
362 {
363   PetscErrorCode ierr;
364   Mat_Product    *product = C->product;
365 
366   PetscFunctionBegin;
367   switch (product->type) {
368   case MATPRODUCT_AB:
369     ierr = MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);CHKERRQ(ierr);
370     break;
371   case MATPRODUCT_AtB:
372     ierr = MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);CHKERRQ(ierr);
373     break;
374   default:
375     break;
376   }
377   PetscFunctionReturn(0);
378 }
379 /* ------------------------------------------------------- */
380 
381 typedef struct {
382   Mat          workB,workB1;
383   MPI_Request  *rwaits,*swaits;
384   PetscInt     nsends,nrecvs;
385   MPI_Datatype *stype,*rtype;
386   PetscInt     blda;
387 } MPIAIJ_MPIDense;
388 
389 PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
390 {
391   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
392   PetscErrorCode  ierr;
393   PetscInt        i;
394 
395   PetscFunctionBegin;
396   ierr = MatDestroy(&contents->workB);CHKERRQ(ierr);
397   ierr = MatDestroy(&contents->workB1);CHKERRQ(ierr);
398   for (i=0; i<contents->nsends; i++) {
399     ierr = MPI_Type_free(&contents->stype[i]);CHKERRMPI(ierr);
400   }
401   for (i=0; i<contents->nrecvs; i++) {
402     ierr = MPI_Type_free(&contents->rtype[i]);CHKERRMPI(ierr);
403   }
404   ierr = PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);CHKERRQ(ierr);
405   ierr = PetscFree(contents);CHKERRQ(ierr);
406   PetscFunctionReturn(0);
407 }
408 
409 static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
410 {
411   PetscErrorCode  ierr;
412   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
413   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,m,M,n,N;
414   MPIAIJ_MPIDense *contents;
415   VecScatter      ctx=aij->Mvctx;
416   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
417   MPI_Comm        comm;
418   MPI_Datatype    type1,*stype,*rtype;
419   const PetscInt  *sindices,*sstarts,*rstarts;
420   PetscMPIInt     *disp;
421   PetscBool       cisdense;
422 
423   PetscFunctionBegin;
424   MatCheckProduct(C,4);
425   PetscCheckFalse(C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
426   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
427   ierr = PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);CHKERRQ(ierr);
428   if (!cisdense) {
429     ierr = MatSetType(C,((PetscObject)B)->type_name);CHKERRQ(ierr);
430   }
431   ierr = MatGetLocalSize(C,&m,&n);CHKERRQ(ierr);
432   ierr = MatGetSize(C,&M,&N);CHKERRQ(ierr);
433   if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) {
434     ierr = MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);CHKERRQ(ierr);
435   }
436   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
437   ierr = MatSetUp(C);CHKERRQ(ierr);
438   ierr = MatDenseGetLDA(B,&blda);CHKERRQ(ierr);
439   ierr = PetscNew(&contents);CHKERRQ(ierr);
440 
441   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);CHKERRQ(ierr);
442   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);CHKERRQ(ierr);
443 
444   /* Create column block of B and C for memory scalability when BN is too large */
445   /* Estimate Bbn, column size of Bb */
446   if (nz) {
447     Bbn1 = 2*Am*BN/nz;
448     if (!Bbn1) Bbn1 = 1;
449   } else Bbn1 = BN;
450 
451   bs = PetscAbs(B->cmap->bs);
452   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
453   if (Bbn1 > BN) Bbn1 = BN;
454   ierr = MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);CHKERRMPI(ierr);
455 
456   /* Enable runtime option for Bbn */
457   ierr = PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
458   ierr = PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);CHKERRQ(ierr);
459   ierr = PetscOptionsEnd();CHKERRQ(ierr);
460   Bbn  = PetscMin(Bbn,BN);
461 
462   if (Bbn > 0 && Bbn < BN) {
463     numBb = BN/Bbn;
464     Bbn1 = BN - numBb*Bbn;
465   } else numBb = 0;
466 
467   if (numBb) {
468     ierr = PetscInfo(C,"use Bb, BN=%" PetscInt_FMT ", Bbn=%" PetscInt_FMT "; numBb=%" PetscInt_FMT "\n",BN,Bbn,numBb);CHKERRQ(ierr);
469     if (Bbn1) { /* Create workB1 for the remaining columns */
470       ierr = PetscInfo(C,"use Bb1, BN=%" PetscInt_FMT ", Bbn1=%" PetscInt_FMT "\n",BN,Bbn1);CHKERRQ(ierr);
471       /* Create work matrix used to store off processor rows of B needed for local product */
472       ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);CHKERRQ(ierr);
473     } else contents->workB1 = NULL;
474   }
475 
476   /* Create work matrix used to store off processor rows of B needed for local product */
477   ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB);CHKERRQ(ierr);
478 
479   /* Use MPI derived data type to reduce memory required by the send/recv buffers */
480   ierr = PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits);CHKERRQ(ierr);
481   contents->stype  = stype;
482   contents->nsends = nsends;
483 
484   contents->rtype  = rtype;
485   contents->nrecvs = nrecvs;
486   contents->blda   = blda;
487 
488   ierr = PetscMalloc1(Bm+1,&disp);CHKERRQ(ierr);
489   for (i=0; i<nsends; i++) {
490     nrows_to = sstarts[i+1]-sstarts[i];
491     for (j=0; j<nrows_to; j++) disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
492     ierr = MPI_Type_create_indexed_block(nrows_to,1,disp,MPIU_SCALAR,&type1);CHKERRMPI(ierr);
493     ierr = MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);CHKERRMPI(ierr);
494     ierr = MPI_Type_commit(&stype[i]);CHKERRMPI(ierr);
495     ierr = MPI_Type_free(&type1);CHKERRMPI(ierr);
496   }
497 
498   for (i=0; i<nrecvs; i++) {
499     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
500     nrows_from = rstarts[i+1]-rstarts[i];
501     disp[0] = 0;
502     ierr = MPI_Type_create_indexed_block(1,nrows_from,disp,MPIU_SCALAR,&type1);CHKERRMPI(ierr);
503     ierr = MPI_Type_create_resized(type1,0,nz*sizeof(PetscScalar),&rtype[i]);CHKERRMPI(ierr);
504     ierr = MPI_Type_commit(&rtype[i]);CHKERRMPI(ierr);
505     ierr = MPI_Type_free(&type1);CHKERRMPI(ierr);
506   }
507 
508   ierr = PetscFree(disp);CHKERRQ(ierr);
509   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);CHKERRQ(ierr);
510   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);CHKERRQ(ierr);
511   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
512   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
513   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
514   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
515 
516   C->product->data = contents;
517   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
518   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
519   PetscFunctionReturn(0);
520 }
521 
522 PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
523 /*
524     Performs an efficient scatter on the rows of B needed by this process; this is
525     a modification of the VecScatterBegin_() routines.
526 
527     Input: Bbidx = 0: B = Bb
528                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
529 */
530 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
531 {
532   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
533   PetscErrorCode    ierr;
534   const PetscScalar *b;
535   PetscScalar       *rvalues;
536   VecScatter        ctx = aij->Mvctx;
537   const PetscInt    *sindices,*sstarts,*rstarts;
538   const PetscMPIInt *sprocs,*rprocs;
539   PetscInt          i,nsends,nrecvs;
540   MPI_Request       *swaits,*rwaits;
541   MPI_Comm          comm;
542   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
543   MPIAIJ_MPIDense   *contents;
544   Mat               workB;
545   MPI_Datatype      *stype,*rtype;
546   PetscInt          blda;
547 
548   PetscFunctionBegin;
549   MatCheckProduct(C,4);
550   PetscCheckFalse(!C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
551   contents = (MPIAIJ_MPIDense*)C->product->data;
552   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);CHKERRQ(ierr);
553   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);CHKERRQ(ierr);
554   ierr = PetscMPIIntCast(nsends,&nsends_mpi);CHKERRQ(ierr);
555   ierr = PetscMPIIntCast(nrecvs,&nrecvs_mpi);CHKERRQ(ierr);
556   if (Bbidx == 0) workB = *outworkB = contents->workB;
557   else workB = *outworkB = contents->workB1;
558   PetscCheckFalse(nrows != workB->rmap->n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of rows of workB %" PetscInt_FMT " not equal to columns of aij->B %d",workB->cmap->n,nrows);
559   swaits = contents->swaits;
560   rwaits = contents->rwaits;
561 
562   ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr);
563   ierr = MatDenseGetLDA(B,&blda);CHKERRQ(ierr);
564   PetscCheckFalse(blda != contents->blda,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot reuse an input matrix with lda %" PetscInt_FMT " != %" PetscInt_FMT,blda,contents->blda);
565   ierr = MatDenseGetArray(workB,&rvalues);CHKERRQ(ierr);
566 
567   /* Post recv, use MPI derived data type to save memory */
568   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
569   rtype = contents->rtype;
570   for (i=0; i<nrecvs; i++) {
571     ierr = MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);CHKERRMPI(ierr);
572   }
573 
574   stype = contents->stype;
575   for (i=0; i<nsends; i++) {
576     ierr = MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);CHKERRMPI(ierr);
577   }
578 
579   if (nrecvs) { ierr = MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE);CHKERRMPI(ierr); }
580   if (nsends) { ierr = MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);CHKERRMPI(ierr); }
581 
582   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);CHKERRQ(ierr);
583   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);CHKERRQ(ierr);
584   ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr);
585   ierr = MatDenseRestoreArray(workB,&rvalues);CHKERRQ(ierr);
586   PetscFunctionReturn(0);
587 }
588 
589 static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
590 {
591   PetscErrorCode  ierr;
592   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
593   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
594   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
595   Mat             workB;
596   MPIAIJ_MPIDense *contents;
597 
598   PetscFunctionBegin;
599   MatCheckProduct(C,3);
600   PetscCheckFalse(!C->product->data,PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
601   contents = (MPIAIJ_MPIDense*)C->product->data;
602   /* diagonal block of A times all local rows of B */
603   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
604   ierr = MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);CHKERRQ(ierr);
605   if (contents->workB->cmap->n == B->cmap->N) {
606     /* get off processor parts of B needed to complete C=A*B */
607     ierr = MatMPIDenseScatter(A,B,0,C,&workB);CHKERRQ(ierr);
608 
609     /* off-diagonal block of A times nonlocal rows of B */
610     ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);CHKERRQ(ierr);
611   } else {
612     Mat      Bb,Cb;
613     PetscInt BN=B->cmap->N,n=contents->workB->cmap->n,i;
614     PetscCheckFalse(n <= 0,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Column block size %" PetscInt_FMT " must be positive",n);
615 
616     for (i=0; i<BN; i+=n) {
617       ierr = MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);CHKERRQ(ierr);
618       ierr = MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);CHKERRQ(ierr);
619 
620       /* get off processor parts of B needed to complete C=A*B */
621       ierr = MatMPIDenseScatter(A,Bb,i+n>BN,C,&workB);CHKERRQ(ierr);
622 
623       /* off-diagonal block of A times nonlocal rows of B */
624       cdense = (Mat_MPIDense*)Cb->data;
625       ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);CHKERRQ(ierr);
626 
627       ierr = MatDenseRestoreSubMatrix(B,&Bb);CHKERRQ(ierr);
628       ierr = MatDenseRestoreSubMatrix(C,&Cb);CHKERRQ(ierr);
629     }
630   }
631   PetscFunctionReturn(0);
632 }
633 
634 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
635 {
636   PetscErrorCode    ierr;
637   Mat_MPIAIJ        *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
638   Mat_SeqAIJ        *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
639   Mat_SeqAIJ        *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
640   PetscInt          *adi = ad->i,*adj,*aoi=ao->i,*aoj;
641   PetscScalar       *ada,*aoa,*cda=cd->a,*coa=co->a;
642   Mat_SeqAIJ        *p_loc,*p_oth;
643   PetscInt          *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
644   PetscScalar       *pa_loc,*pa_oth,*pa,valtmp,*ca;
645   PetscInt          cm    = C->rmap->n,anz,pnz;
646   Mat_APMPI         *ptap;
647   PetscScalar       *apa_sparse;
648   const PetscScalar *dummy;
649   PetscInt          *api,*apj,*apJ,i,j,k,row;
650   PetscInt          cstart = C->cmap->rstart;
651   PetscInt          cdnz,conz,k0,k1,nextp;
652   MPI_Comm          comm;
653   PetscMPIInt       size;
654 
655   PetscFunctionBegin;
656   MatCheckProduct(C,3);
657   ptap = (Mat_APMPI*)C->product->data;
658   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
659   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
660   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
661   PetscCheckFalse(!ptap->P_oth && size>1,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");
662 
663   /* flag CPU mask for C */
664 #if defined(PETSC_HAVE_DEVICE)
665   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
666   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
667   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
668 #endif
669   apa_sparse = ptap->apa;
670 
671   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
672   /*-----------------------------------------------------*/
673   /* update numerical values of P_oth and P_loc */
674   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
675   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
676 
677   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
678   /*----------------------------------------------------------*/
679   /* get data from symbolic products */
680   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
681   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
682   if (size >1) {
683     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
684     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
685   } else {
686     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
687   }
688 
689   /* trigger copy to CPU */
690   ierr = MatSeqAIJGetArrayRead(a->A,&dummy);CHKERRQ(ierr);
691   ierr = MatSeqAIJRestoreArrayRead(a->A,&dummy);CHKERRQ(ierr);
692   ierr = MatSeqAIJGetArrayRead(a->B,&dummy);CHKERRQ(ierr);
693   ierr = MatSeqAIJRestoreArrayRead(a->B,&dummy);CHKERRQ(ierr);
694   api = ptap->api;
695   apj = ptap->apj;
696   for (i=0; i<cm; i++) {
697     apJ = apj + api[i];
698 
699     /* diagonal portion of A */
700     anz = adi[i+1] - adi[i];
701     adj = ad->j + adi[i];
702     ada = ad->a + adi[i];
703     for (j=0; j<anz; j++) {
704       row = adj[j];
705       pnz = pi_loc[row+1] - pi_loc[row];
706       pj  = pj_loc + pi_loc[row];
707       pa  = pa_loc + pi_loc[row];
708       /* perform sparse axpy */
709       valtmp = ada[j];
710       nextp  = 0;
711       for (k=0; nextp<pnz; k++) {
712         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
713           apa_sparse[k] += valtmp*pa[nextp++];
714         }
715       }
716       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
717     }
718 
719     /* off-diagonal portion of A */
720     anz = aoi[i+1] - aoi[i];
721     aoj = ao->j + aoi[i];
722     aoa = ao->a + aoi[i];
723     for (j=0; j<anz; j++) {
724       row = aoj[j];
725       pnz = pi_oth[row+1] - pi_oth[row];
726       pj  = pj_oth + pi_oth[row];
727       pa  = pa_oth + pi_oth[row];
728       /* perform sparse axpy */
729       valtmp = aoa[j];
730       nextp  = 0;
731       for (k=0; nextp<pnz; k++) {
732         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
733           apa_sparse[k] += valtmp*pa[nextp++];
734         }
735       }
736       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
737     }
738 
739     /* set values in C */
740     cdnz = cd->i[i+1] - cd->i[i];
741     conz = co->i[i+1] - co->i[i];
742 
743     /* 1st off-diagonal part of C */
744     ca = coa + co->i[i];
745     k  = 0;
746     for (k0=0; k0<conz; k0++) {
747       if (apJ[k] >= cstart) break;
748       ca[k0]        = apa_sparse[k];
749       apa_sparse[k] = 0.0;
750       k++;
751     }
752 
753     /* diagonal part of C */
754     ca = cda + cd->i[i];
755     for (k1=0; k1<cdnz; k1++) {
756       ca[k1]        = apa_sparse[k];
757       apa_sparse[k] = 0.0;
758       k++;
759     }
760 
761     /* 2nd off-diagonal part of C */
762     ca = coa + co->i[i];
763     for (; k0<conz; k0++) {
764       ca[k0]        = apa_sparse[k];
765       apa_sparse[k] = 0.0;
766       k++;
767     }
768   }
769   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
770   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
771   PetscFunctionReturn(0);
772 }
773 
774 /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
775 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
776 {
777   PetscErrorCode     ierr;
778   MPI_Comm           comm;
779   PetscMPIInt        size;
780   Mat_APMPI          *ptap;
781   PetscFreeSpaceList free_space = NULL,current_space=NULL;
782   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
783   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
784   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
785   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
786   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
787   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
788   PetscReal          afill;
789   MatType            mtype;
790 
791   PetscFunctionBegin;
792   MatCheckProduct(C,4);
793   PetscCheckFalse(C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
794   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
795   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
796 
797   /* create struct Mat_APMPI and attached it to C later */
798   ierr = PetscNew(&ptap);CHKERRQ(ierr);
799 
800   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
801   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
802 
803   /* get P_loc by taking all local rows of P */
804   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
805 
806   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
807   pi_loc = p_loc->i; pj_loc = p_loc->j;
808   if (size > 1) {
809     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
810     pi_oth = p_oth->i; pj_oth = p_oth->j;
811   } else {
812     p_oth  = NULL;
813     pi_oth = NULL; pj_oth = NULL;
814   }
815 
816   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
817   /*-------------------------------------------------------------------*/
818   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
819   ptap->api = api;
820   api[0]    = 0;
821 
822   ierr = PetscLLCondensedCreate_Scalable(lsize,&lnk);CHKERRQ(ierr);
823 
824   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
825   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
826   current_space = free_space;
827   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
828   for (i=0; i<am; i++) {
829     /* diagonal portion of A */
830     nzi = adi[i+1] - adi[i];
831     for (j=0; j<nzi; j++) {
832       row  = *adj++;
833       pnz  = pi_loc[row+1] - pi_loc[row];
834       Jptr = pj_loc + pi_loc[row];
835       /* Expand list if it is not long enough */
836       if (pnz+apnz_max > lsize) {
837         lsize = pnz+apnz_max;
838         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
839       }
840       /* add non-zero cols of P into the sorted linked list lnk */
841       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
842       apnz     = *lnk; /* The first element in the list is the number of items in the list */
843       api[i+1] = api[i] + apnz;
844       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
845     }
846     /* off-diagonal portion of A */
847     nzi = aoi[i+1] - aoi[i];
848     for (j=0; j<nzi; j++) {
849       row  = *aoj++;
850       pnz  = pi_oth[row+1] - pi_oth[row];
851       Jptr = pj_oth + pi_oth[row];
852       /* Expand list if it is not long enough */
853       if (pnz+apnz_max > lsize) {
854         lsize = pnz + apnz_max;
855         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
856       }
857       /* add non-zero cols of P into the sorted linked list lnk */
858       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
859       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
860       api[i+1] = api[i] + apnz;
861       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
862     }
863 
864     /* add missing diagonal entry */
865     if (C->force_diagonals) {
866       j = i + rstart; /* column index */
867       ierr = PetscLLCondensedAddSorted_Scalable(1,&j,lnk);CHKERRQ(ierr);
868     }
869 
870     apnz     = *lnk;
871     api[i+1] = api[i] + apnz;
872     if (apnz > apnz_max) apnz_max = apnz;
873 
874     /* if free space is not available, double the total space in the list */
875     if (current_space->local_remaining<apnz) {
876       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
877       nspacedouble++;
878     }
879 
880     /* Copy data into free space, then initialize lnk */
881     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
882     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
883 
884     current_space->array           += apnz;
885     current_space->local_used      += apnz;
886     current_space->local_remaining -= apnz;
887   }
888 
889   /* Allocate space for apj, initialize apj, and */
890   /* destroy list of free space and other temporary array(s) */
891   ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr);
892   apj  = ptap->apj;
893   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
894   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
895 
896   /* create and assemble symbolic parallel matrix C */
897   /*----------------------------------------------------*/
898   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
899   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
900   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
901   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
902   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
903   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
904 
905   /* malloc apa for assembly C */
906   ierr = PetscCalloc1(apnz_max,&ptap->apa);CHKERRQ(ierr);
907 
908   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
909   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
910   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
911   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
912 
913   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
914   C->ops->productnumeric = MatProductNumeric_AB;
915 
916   /* attach the supporting struct to C for reuse */
917   C->product->data    = ptap;
918   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
919 
920   /* set MatInfo */
921   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
922   if (afill < 1.0) afill = 1.0;
923   C->info.mallocs           = nspacedouble;
924   C->info.fill_ratio_given  = fill;
925   C->info.fill_ratio_needed = afill;
926 
927 #if defined(PETSC_USE_INFO)
928   if (api[am]) {
929     ierr = PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
930     ierr = PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
931   } else {
932     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
933   }
934 #endif
935   PetscFunctionReturn(0);
936 }
937 
938 /* This function is needed for the seqMPI matrix-matrix multiplication.  */
939 /* Three input arrays are merged to one output array. The size of the    */
940 /* output array is also output. Duplicate entries only show up once.     */
941 static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
942                                PetscInt  size2, PetscInt *in2,
943                                PetscInt  size3, PetscInt *in3,
944                                PetscInt *size4, PetscInt *out)
945 {
946   int i = 0, j = 0, k = 0, l = 0;
947 
948   /* Traverse all three arrays */
949   while (i<size1 && j<size2 && k<size3) {
950     if (in1[i] < in2[j] && in1[i] < in3[k]) {
951       out[l++] = in1[i++];
952     }
953     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
954       out[l++] = in2[j++];
955     }
956     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
957       out[l++] = in3[k++];
958     }
959     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
960       out[l++] = in1[i];
961       i++, j++;
962     }
963     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
964       out[l++] = in1[i];
965       i++, k++;
966     }
967     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
968       out[l++] = in2[j];
969       k++, j++;
970     }
971     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
972       out[l++] = in1[i];
973       i++, j++, k++;
974     }
975   }
976 
977   /* Traverse two remaining arrays */
978   while (i<size1 && j<size2) {
979     if (in1[i] < in2[j]) {
980       out[l++] = in1[i++];
981     }
982     else if (in1[i] > in2[j]) {
983       out[l++] = in2[j++];
984     }
985     else {
986       out[l++] = in1[i];
987       i++, j++;
988     }
989   }
990 
991   while (i<size1 && k<size3) {
992     if (in1[i] < in3[k]) {
993       out[l++] = in1[i++];
994     }
995     else if (in1[i] > in3[k]) {
996       out[l++] = in3[k++];
997     }
998     else {
999       out[l++] = in1[i];
1000       i++, k++;
1001     }
1002   }
1003 
1004   while (k<size3 && j<size2)  {
1005     if (in3[k] < in2[j]) {
1006       out[l++] = in3[k++];
1007     }
1008     else if (in3[k] > in2[j]) {
1009       out[l++] = in2[j++];
1010     }
1011     else {
1012       out[l++] = in3[k];
1013       k++, j++;
1014     }
1015   }
1016 
1017   /* Traverse one remaining array */
1018   while (i<size1) out[l++] = in1[i++];
1019   while (j<size2) out[l++] = in2[j++];
1020   while (k<size3) out[l++] = in3[k++];
1021 
1022   *size4 = l;
1023 }
1024 
1025 /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1026 /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1027 /* matrix-matrix multiplications.  */
1028 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1029 {
1030   PetscErrorCode     ierr;
1031   MPI_Comm           comm;
1032   PetscMPIInt        size;
1033   Mat_APMPI          *ptap;
1034   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
1035   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
1036   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
1037   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
1038   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
1039   PetscInt           adponz, adpdnz;
1040   PetscInt           *pi_loc,*dnz,*onz;
1041   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
1042   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1043                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1044   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1045   PetscBT            lnkbt;
1046   PetscReal          afill;
1047   PetscMPIInt        rank;
1048   Mat                adpd, aopoth;
1049   MatType            mtype;
1050   const char         *prefix;
1051 
1052   PetscFunctionBegin;
1053   MatCheckProduct(C,4);
1054   PetscCheckFalse(C->product->data,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1055   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1056   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1057   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
1058   ierr = MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);CHKERRQ(ierr);
1059 
1060   /* create struct Mat_APMPI and attached it to C later */
1061   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1062 
1063   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1064   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1065 
1066   /* get P_loc by taking all local rows of P */
1067   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1068 
1069   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1070   pi_loc = p_loc->i;
1071 
1072   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1073   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
1074   ierr      = PetscMalloc1(am+2,&adpoi);CHKERRQ(ierr);
1075 
1076   adpoi[0]    = 0;
1077   ptap->api = api;
1078   api[0] = 0;
1079 
1080   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1081   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1082   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
1083 
1084   /* Symbolic calc of A_loc_diag * P_loc_diag */
1085   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1086   ierr = MatProductCreate(a->A,p->A,NULL,&adpd);CHKERRQ(ierr);
1087   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1088   ierr = MatSetOptionsPrefix(adpd,prefix);CHKERRQ(ierr);
1089   ierr = MatAppendOptionsPrefix(adpd,"inner_diag_");CHKERRQ(ierr);
1090 
1091   ierr = MatProductSetType(adpd,MATPRODUCT_AB);CHKERRQ(ierr);
1092   ierr = MatProductSetAlgorithm(adpd,"sorted");CHKERRQ(ierr);
1093   ierr = MatProductSetFill(adpd,fill);CHKERRQ(ierr);
1094   ierr = MatProductSetFromOptions(adpd);CHKERRQ(ierr);
1095 
1096   adpd->force_diagonals = C->force_diagonals;
1097   ierr = MatProductSymbolic(adpd);CHKERRQ(ierr);
1098 
1099   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1100   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1101   p_off = (Mat_SeqAIJ*)((p->B)->data);
1102   poff_i = p_off->i; poff_j = p_off->j;
1103 
1104   /* j_temp stores indices of a result row before they are added to the linked list */
1105   ierr = PetscMalloc1(pN+2,&j_temp);CHKERRQ(ierr);
1106 
1107   /* Symbolic calc of the A_diag * p_loc_off */
1108   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1109   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);CHKERRQ(ierr);
1110   current_space = free_space_diag;
1111 
1112   for (i=0; i<am; i++) {
1113     /* A_diag * P_loc_off */
1114     nzi = adi[i+1] - adi[i];
1115     for (j=0; j<nzi; j++) {
1116       row  = *adj++;
1117       pnz  = poff_i[row+1] - poff_i[row];
1118       Jptr = poff_j + poff_i[row];
1119       for (i1 = 0; i1 < pnz; i1++) {
1120         j_temp[i1] = p->garray[Jptr[i1]];
1121       }
1122       /* add non-zero cols of P into the sorted linked list lnk */
1123       ierr = PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);CHKERRQ(ierr);
1124     }
1125 
1126     adponz     = lnk[0];
1127     adpoi[i+1] = adpoi[i] + adponz;
1128 
1129     /* if free space is not available, double the total space in the list */
1130     if (current_space->local_remaining<adponz) {
1131       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1132       nspacedouble++;
1133     }
1134 
1135     /* Copy data into free space, then initialize lnk */
1136     ierr = PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1137 
1138     current_space->array           += adponz;
1139     current_space->local_used      += adponz;
1140     current_space->local_remaining -= adponz;
1141   }
1142 
1143   /* Symbolic calc of A_off * P_oth */
1144   ierr = MatSetOptionsPrefix(a->B,prefix);CHKERRQ(ierr);
1145   ierr = MatAppendOptionsPrefix(a->B,"inner_offdiag_");CHKERRQ(ierr);
1146   ierr = MatCreate(PETSC_COMM_SELF,&aopoth);CHKERRQ(ierr);
1147   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);CHKERRQ(ierr);
1148   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1149   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;
1150 
1151   /* Allocate space for apj, adpj, aopj, ... */
1152   /* destroy lists of free space and other temporary array(s) */
1153 
1154   ierr = PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);CHKERRQ(ierr);
1155   ierr = PetscMalloc1(adpoi[am]+2, &adpoj);CHKERRQ(ierr);
1156 
1157   /* Copy from linked list to j-array */
1158   ierr = PetscFreeSpaceContiguous(&free_space_diag,adpoj);CHKERRQ(ierr);
1159   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1160 
1161   adpoJ = adpoj;
1162   adpdJ = adpdj;
1163   aopJ = aopothj;
1164   apj  = ptap->apj;
1165   apJ = apj; /* still empty */
1166 
1167   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1168   /* A_diag * P_loc_diag to get A*P */
1169   for (i = 0; i < am; i++) {
1170     aopnz  =  aopothi[i+1] -  aopothi[i];
1171     adponz = adpoi[i+1] - adpoi[i];
1172     adpdnz = adpdi[i+1] - adpdi[i];
1173 
1174     /* Correct indices from A_diag*P_diag */
1175     for (i1 = 0; i1 < adpdnz; i1++) {
1176       adpdJ[i1] += p_colstart;
1177     }
1178     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1179     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1180     ierr = MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);CHKERRQ(ierr);
1181 
1182     aopJ += aopnz;
1183     adpoJ += adponz;
1184     adpdJ += adpdnz;
1185     apJ += apnz;
1186     api[i+1] = api[i] + apnz;
1187   }
1188 
1189   /* malloc apa to store dense row A[i,:]*P */
1190   ierr = PetscCalloc1(pN+2,&ptap->apa);CHKERRQ(ierr);
1191 
1192   /* create and assemble symbolic parallel matrix C */
1193   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1194   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
1195   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1196   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1197   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1198   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1199 
1200   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
1201   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1202   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1203   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1204 
1205   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1206   C->ops->productnumeric = MatProductNumeric_AB;
1207 
1208   /* attach the supporting struct to C for reuse */
1209   C->product->data    = ptap;
1210   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;
1211 
1212   /* set MatInfo */
1213   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1214   if (afill < 1.0) afill = 1.0;
1215   C->info.mallocs           = nspacedouble;
1216   C->info.fill_ratio_given  = fill;
1217   C->info.fill_ratio_needed = afill;
1218 
1219 #if defined(PETSC_USE_INFO)
1220   if (api[am]) {
1221     ierr = PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1222     ierr = PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1223   } else {
1224     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1225   }
1226 #endif
1227 
1228   ierr = MatDestroy(&aopoth);CHKERRQ(ierr);
1229   ierr = MatDestroy(&adpd);CHKERRQ(ierr);
1230   ierr = PetscFree(j_temp);CHKERRQ(ierr);
1231   ierr = PetscFree(adpoj);CHKERRQ(ierr);
1232   ierr = PetscFree(adpoi);CHKERRQ(ierr);
1233   PetscFunctionReturn(0);
1234 }
1235 
1236 /*-------------------------------------------------------------------------*/
1237 /* This routine only works when scall=MAT_REUSE_MATRIX! */
1238 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1239 {
1240   PetscErrorCode ierr;
1241   Mat_APMPI      *ptap;
1242   Mat            Pt;
1243 
1244   PetscFunctionBegin;
1245   MatCheckProduct(C,3);
1246   ptap = (Mat_APMPI*)C->product->data;
1247   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1248   PetscCheckFalse(!ptap->Pt,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1249 
1250   Pt   = ptap->Pt;
1251   ierr = MatTranspose(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr);
1252   ierr = MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);CHKERRQ(ierr);
1253   PetscFunctionReturn(0);
1254 }
1255 
1256 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1257 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1258 {
1259   PetscErrorCode      ierr;
1260   Mat_APMPI           *ptap;
1261   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
1262   MPI_Comm            comm;
1263   PetscMPIInt         size,rank;
1264   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1265   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1266   PetscInt            *lnk,i,k,nsend,rstart;
1267   PetscBT             lnkbt;
1268   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
1269   PETSC_UNUSED PetscMPIInt icompleted=0;
1270   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
1271   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1272   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1273   MPI_Request         *swaits,*rwaits;
1274   MPI_Status          *sstatus,rstatus;
1275   PetscLayout         rowmap;
1276   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1277   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1278   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1279   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1280   PetscTable          ta;
1281   MatType             mtype;
1282   const char          *prefix;
1283 
1284   PetscFunctionBegin;
1285   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1286   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1287   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1288 
1289   /* create symbolic parallel matrix C */
1290   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1291   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1292 
1293   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1294 
1295   /* create struct Mat_APMPI and attached it to C later */
1296   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1297   ptap->reuse = MAT_INITIAL_MATRIX;
1298 
1299   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1300   /* --------------------------------- */
1301   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1302   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1303 
1304   /* (1) compute symbolic A_loc */
1305   /* ---------------------------*/
1306   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1307 
1308   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1309   /* ------------------------------------ */
1310   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1311   ierr = MatSetOptionsPrefix(ptap->Ro,prefix);CHKERRQ(ierr);
1312   ierr = MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");CHKERRQ(ierr);
1313   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_oth);CHKERRQ(ierr);
1314   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);CHKERRQ(ierr);
1315 
1316   /* (3) send coj of C_oth to other processors  */
1317   /* ------------------------------------------ */
1318   /* determine row ownership */
1319   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
1320   rowmap->n  = pn;
1321   rowmap->bs = 1;
1322   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
1323   owners = rowmap->range;
1324 
1325   /* determine the number of messages to send, their lengths */
1326   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
1327   ierr = PetscArrayzero(len_s,size);CHKERRQ(ierr);
1328   ierr = PetscArrayzero(len_si,size);CHKERRQ(ierr);
1329 
1330   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1331   coi   = c_oth->i; coj = c_oth->j;
1332   con   = ptap->C_oth->rmap->n;
1333   proc  = 0;
1334   for (i=0; i<con; i++) {
1335     while (prmap[i] >= owners[proc+1]) proc++;
1336     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1337     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1338   }
1339 
1340   len          = 0; /* max length of buf_si[], see (4) */
1341   owners_co[0] = 0;
1342   nsend        = 0;
1343   for (proc=0; proc<size; proc++) {
1344     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1345     if (len_s[proc]) {
1346       nsend++;
1347       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1348       len         += len_si[proc];
1349     }
1350   }
1351 
1352   /* determine the number and length of messages to receive for coi and coj  */
1353   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
1354   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
1355 
1356   /* post the Irecv and Isend of coj */
1357   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1358   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1359   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
1360   for (proc=0, k=0; proc<size; proc++) {
1361     if (!len_s[proc]) continue;
1362     i    = owners_co[proc];
1363     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRMPI(ierr);
1364     k++;
1365   }
1366 
1367   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1368   /* ---------------------------------------- */
1369   ierr = MatSetOptionsPrefix(ptap->Rd,prefix);CHKERRQ(ierr);
1370   ierr = MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");CHKERRQ(ierr);
1371   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_loc);CHKERRQ(ierr);
1372   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);CHKERRQ(ierr);
1373   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1374 
1375   /* receives coj are complete */
1376   for (i=0; i<nrecv; i++) {
1377     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1378   }
1379   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1380   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRMPI(ierr);}
1381 
1382   /* add received column indices into ta to update Crmax */
1383   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1384 
1385   /* create and initialize a linked list */
1386   ierr = PetscTableCreate(an,aN,&ta);CHKERRQ(ierr); /* for compute Crmax */
1387   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1388 
1389   for (k=0; k<nrecv; k++) {/* k-th received message */
1390     Jptr = buf_rj[k];
1391     for (j=0; j<len_r[k]; j++) {
1392       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1393     }
1394   }
1395   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
1396   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
1397 
1398   /* (4) send and recv coi */
1399   /*-----------------------*/
1400   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1401   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1402   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1403   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1404   for (proc=0,k=0; proc<size; proc++) {
1405     if (!len_s[proc]) continue;
1406     /* form outgoing message for i-structure:
1407          buf_si[0]:                 nrows to be sent
1408                [1:nrows]:           row index (global)
1409                [nrows+1:2*nrows+1]: i-structure index
1410     */
1411     /*-------------------------------------------*/
1412     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1413     buf_si_i    = buf_si + nrows+1;
1414     buf_si[0]   = nrows;
1415     buf_si_i[0] = 0;
1416     nrows       = 0;
1417     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1418       nzi = coi[i+1] - coi[i];
1419       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1420       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1421       nrows++;
1422     }
1423     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRMPI(ierr);
1424     k++;
1425     buf_si += len_si[proc];
1426   }
1427   for (i=0; i<nrecv; i++) {
1428     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1429   }
1430   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1431   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRMPI(ierr);}
1432 
1433   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
1434   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1435   ierr = PetscFree(swaits);CHKERRQ(ierr);
1436   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1437 
1438   /* (5) compute the local portion of C      */
1439   /* ------------------------------------------ */
1440   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1441   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
1442   current_space = free_space;
1443 
1444   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
1445   for (k=0; k<nrecv; k++) {
1446     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1447     nrows       = *buf_ri_k[k];
1448     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1449     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1450   }
1451 
1452   ierr = MatPreallocateInitialize(comm,pn,an,dnz,onz);CHKERRQ(ierr);
1453   ierr = PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);CHKERRQ(ierr);
1454   for (i=0; i<pn; i++) { /* for each local row of C */
1455     /* add C_loc into C */
1456     nzi  = c_loc->i[i+1] - c_loc->i[i];
1457     Jptr = c_loc->j + c_loc->i[i];
1458     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1459 
1460     /* add received col data into lnk */
1461     for (k=0; k<nrecv; k++) { /* k-th received message */
1462       if (i == *nextrow[k]) { /* i-th row */
1463         nzi  = *(nextci[k]+1) - *nextci[k];
1464         Jptr = buf_rj[k] + *nextci[k];
1465         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1466         nextrow[k]++; nextci[k]++;
1467       }
1468     }
1469 
1470     /* add missing diagonal entry */
1471     if (C->force_diagonals) {
1472       k = i + owners[rank]; /* column index */
1473       ierr = PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);CHKERRQ(ierr);
1474     }
1475 
1476     nzi = lnk[0];
1477 
1478     /* copy data into free space, then initialize lnk */
1479     ierr = PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1480     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
1481   }
1482   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1483   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1484   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
1485 
1486   /* local sizes and preallocation */
1487   ierr = MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1488   if (P->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);CHKERRQ(ierr);}
1489   if (A->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);CHKERRQ(ierr);}
1490   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1491   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1492 
1493   /* add C_loc and C_oth to C */
1494   ierr = MatGetOwnershipRange(C,&rstart,NULL);CHKERRQ(ierr);
1495   for (i=0; i<pn; i++) {
1496     ncols = c_loc->i[i+1] - c_loc->i[i];
1497     cols  = c_loc->j + c_loc->i[i];
1498     row   = rstart + i;
1499     ierr = MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);CHKERRQ(ierr);
1500 
1501     if (C->force_diagonals) {
1502       ierr = MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);CHKERRQ(ierr);
1503     }
1504   }
1505   for (i=0; i<con; i++) {
1506     ncols = c_oth->i[i+1] - c_oth->i[i];
1507     cols  = c_oth->j + c_oth->i[i];
1508     row   = prmap[i];
1509     ierr = MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);CHKERRQ(ierr);
1510   }
1511   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1512   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1513   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1514 
1515   /* members in merge */
1516   ierr = PetscFree(id_r);CHKERRQ(ierr);
1517   ierr = PetscFree(len_r);CHKERRQ(ierr);
1518   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
1519   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
1520   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
1521   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
1522   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
1523 
1524   /* attach the supporting struct to C for reuse */
1525   C->product->data    = ptap;
1526   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1527   PetscFunctionReturn(0);
1528 }
1529 
1530 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1531 {
1532   PetscErrorCode    ierr;
1533   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
1534   Mat_SeqAIJ        *c_seq;
1535   Mat_APMPI         *ptap;
1536   Mat               A_loc,C_loc,C_oth;
1537   PetscInt          i,rstart,rend,cm,ncols,row;
1538   const PetscInt    *cols;
1539   const PetscScalar *vals;
1540 
1541   PetscFunctionBegin;
1542   MatCheckProduct(C,3);
1543   ptap = (Mat_APMPI*)C->product->data;
1544   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1545   PetscCheckFalse(!ptap->A_loc,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1546   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1547 
1548   if (ptap->reuse == MAT_REUSE_MATRIX) {
1549     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1550     /* 1) get R = Pd^T, Ro = Po^T */
1551     /*----------------------------*/
1552     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1553     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1554 
1555     /* 2) compute numeric A_loc */
1556     /*--------------------------*/
1557     ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1558   }
1559 
1560   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1561   A_loc = ptap->A_loc;
1562   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);CHKERRQ(ierr);
1563   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);CHKERRQ(ierr);
1564   C_loc = ptap->C_loc;
1565   C_oth = ptap->C_oth;
1566 
1567   /* add C_loc and C_oth to C */
1568   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1569 
1570   /* C_loc -> C */
1571   cm    = C_loc->rmap->N;
1572   c_seq = (Mat_SeqAIJ*)C_loc->data;
1573   cols = c_seq->j;
1574   vals = c_seq->a;
1575   for (i=0; i<cm; i++) {
1576     ncols = c_seq->i[i+1] - c_seq->i[i];
1577     row = rstart + i;
1578     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1579     cols += ncols; vals += ncols;
1580   }
1581 
1582   /* Co -> C, off-processor part */
1583   cm    = C_oth->rmap->N;
1584   c_seq = (Mat_SeqAIJ*)C_oth->data;
1585   cols  = c_seq->j;
1586   vals  = c_seq->a;
1587   for (i=0; i<cm; i++) {
1588     ncols = c_seq->i[i+1] - c_seq->i[i];
1589     row = p->garray[i];
1590     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1591     cols += ncols; vals += ncols;
1592   }
1593   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1594   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1595   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1596 
1597   ptap->reuse = MAT_REUSE_MATRIX;
1598   PetscFunctionReturn(0);
1599 }
1600 
1601 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1602 {
1603   PetscErrorCode      ierr;
1604   Mat_Merge_SeqsToMPI *merge;
1605   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
1606   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1607   Mat_APMPI           *ptap;
1608   PetscInt            *adj;
1609   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1610   MatScalar           *ada,*ca,valtmp;
1611   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1612   MPI_Comm            comm;
1613   PetscMPIInt         size,rank,taga,*len_s;
1614   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1615   PetscInt            **buf_ri,**buf_rj;
1616   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1617   MPI_Request         *s_waits,*r_waits;
1618   MPI_Status          *status;
1619   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1620   const PetscScalar   *dummy;
1621   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1622   Mat                 A_loc;
1623   Mat_SeqAIJ          *a_loc;
1624 
1625   PetscFunctionBegin;
1626   MatCheckProduct(C,3);
1627   ptap = (Mat_APMPI*)C->product->data;
1628   PetscCheckFalse(!ptap,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1629   PetscCheckFalse(!ptap->A_loc,PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1630   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1631   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1632   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1633 
1634   merge = ptap->merge;
1635 
1636   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1637   /*------------------------------------------*/
1638   /* get data from symbolic products */
1639   coi    = merge->coi; coj = merge->coj;
1640   ierr   = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
1641   bi     = merge->bi; bj = merge->bj;
1642   owners = merge->rowmap->range;
1643   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);
1644 
1645   /* get A_loc by taking all local rows of A */
1646   A_loc = ptap->A_loc;
1647   ierr  = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr);
1648   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1649   ai    = a_loc->i;
1650   aj    = a_loc->j;
1651 
1652   /* trigger copy to CPU */
1653   ierr = MatSeqAIJGetArrayRead(p->A,&dummy);CHKERRQ(ierr);
1654   ierr = MatSeqAIJRestoreArrayRead(p->A,&dummy);CHKERRQ(ierr);
1655   ierr = MatSeqAIJGetArrayRead(p->B,&dummy);CHKERRQ(ierr);
1656   ierr = MatSeqAIJRestoreArrayRead(p->B,&dummy);CHKERRQ(ierr);
1657   for (i=0; i<am; i++) {
1658     anz = ai[i+1] - ai[i];
1659     adj = aj + ai[i];
1660     ada = a_loc->a + ai[i];
1661 
1662     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1663     /*-------------------------------------------------------------*/
1664     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1665     pnz = po->i[i+1] - po->i[i];
1666     poJ = po->j + po->i[i];
1667     pA  = po->a + po->i[i];
1668     for (j=0; j<pnz; j++) {
1669       row = poJ[j];
1670       cj  = coj + coi[row];
1671       ca  = coa + coi[row];
1672       /* perform sparse axpy */
1673       nexta  = 0;
1674       valtmp = pA[j];
1675       for (k=0; nexta<anz; k++) {
1676         if (cj[k] == adj[nexta]) {
1677           ca[k] += valtmp*ada[nexta];
1678           nexta++;
1679         }
1680       }
1681       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1682     }
1683 
1684     /* put the value into Cd (diagonal part) */
1685     pnz = pd->i[i+1] - pd->i[i];
1686     pdJ = pd->j + pd->i[i];
1687     pA  = pd->a + pd->i[i];
1688     for (j=0; j<pnz; j++) {
1689       row = pdJ[j];
1690       cj  = bj + bi[row];
1691       ca  = ba + bi[row];
1692       /* perform sparse axpy */
1693       nexta  = 0;
1694       valtmp = pA[j];
1695       for (k=0; nexta<anz; k++) {
1696         if (cj[k] == adj[nexta]) {
1697           ca[k] += valtmp*ada[nexta];
1698           nexta++;
1699         }
1700       }
1701       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1702     }
1703   }
1704 
1705   /* 3) send and recv matrix values coa */
1706   /*------------------------------------*/
1707   buf_ri = merge->buf_ri;
1708   buf_rj = merge->buf_rj;
1709   len_s  = merge->len_s;
1710   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1711   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1712 
1713   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
1714   for (proc=0,k=0; proc<size; proc++) {
1715     if (!len_s[proc]) continue;
1716     i    = merge->owners_co[proc];
1717     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRMPI(ierr);
1718     k++;
1719   }
1720   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRMPI(ierr);}
1721   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRMPI(ierr);}
1722 
1723   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1724   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1725   ierr = PetscFree(coa);CHKERRQ(ierr);
1726 
1727   /* 4) insert local Cseq and received values into Cmpi */
1728   /*----------------------------------------------------*/
1729   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1730   for (k=0; k<merge->nrecv; k++) {
1731     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1732     nrows       = *(buf_ri_k[k]);
1733     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1734     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1735   }
1736 
1737   for (i=0; i<cm; i++) {
1738     row  = owners[rank] + i; /* global row index of C_seq */
1739     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1740     ba_i = ba + bi[i];
1741     bnz  = bi[i+1] - bi[i];
1742     /* add received vals into ba */
1743     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1744       /* i-th row */
1745       if (i == *nextrow[k]) {
1746         cnz    = *(nextci[k]+1) - *nextci[k];
1747         cj     = buf_rj[k] + *(nextci[k]);
1748         ca     = abuf_r[k] + *(nextci[k]);
1749         nextcj = 0;
1750         for (j=0; nextcj<cnz; j++) {
1751           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1752             ba_i[j] += ca[nextcj++];
1753           }
1754         }
1755         nextrow[k]++; nextci[k]++;
1756         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1757       }
1758     }
1759     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1760   }
1761   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1762   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1763 
1764   ierr = PetscFree(ba);CHKERRQ(ierr);
1765   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1766   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1767   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1768   PetscFunctionReturn(0);
1769 }
1770 
1771 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1772 {
1773   PetscErrorCode      ierr;
1774   Mat                 A_loc;
1775   Mat_APMPI           *ptap;
1776   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1777   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1778   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1779   PetscInt            nnz;
1780   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1781   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1782   MPI_Comm            comm;
1783   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1784   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1785   PetscInt            len,proc,*dnz,*onz,*owners;
1786   PetscInt            nzi,*bi,*bj;
1787   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1788   MPI_Request         *swaits,*rwaits;
1789   MPI_Status          *sstatus,rstatus;
1790   Mat_Merge_SeqsToMPI *merge;
1791   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1792   PetscReal           afill  =1.0,afill_tmp;
1793   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1794   Mat_SeqAIJ          *a_loc;
1795   PetscTable          ta;
1796   MatType             mtype;
1797 
1798   PetscFunctionBegin;
1799   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1800   /* check if matrix local sizes are compatible */
1801   PetscCheckFalse(A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend,comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != P (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
1802 
1803   ierr = MPI_Comm_size(comm,&size);CHKERRMPI(ierr);
1804   ierr = MPI_Comm_rank(comm,&rank);CHKERRMPI(ierr);
1805 
1806   /* create struct Mat_APMPI and attached it to C later */
1807   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1808 
1809   /* get A_loc by taking all local rows of A */
1810   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr);
1811 
1812   ptap->A_loc = A_loc;
1813   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1814   ai          = a_loc->i;
1815   aj          = a_loc->j;
1816 
1817   /* determine symbolic Co=(p->B)^T*A - send to others */
1818   /*----------------------------------------------------*/
1819   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
1820   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
1821   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1822                          >= (num of nonzero rows of C_seq) - pn */
1823   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
1824   coi[0] = 0;
1825 
1826   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1827   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1828   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1829   current_space = free_space;
1830 
1831   /* create and initialize a linked list */
1832   ierr = PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);CHKERRQ(ierr);
1833   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1834   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1835 
1836   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
1837 
1838   for (i=0; i<pon; i++) {
1839     pnz = poti[i+1] - poti[i];
1840     ptJ = potj + poti[i];
1841     for (j=0; j<pnz; j++) {
1842       row  = ptJ[j]; /* row of A_loc == col of Pot */
1843       anz  = ai[row+1] - ai[row];
1844       Jptr = aj + ai[row];
1845       /* add non-zero cols of AP into the sorted linked list lnk */
1846       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
1847     }
1848     nnz = lnk[0];
1849 
1850     /* If free space is not available, double the total space in the list */
1851     if (current_space->local_remaining<nnz) {
1852       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1853       nspacedouble++;
1854     }
1855 
1856     /* Copy data into free space, and zero out denserows */
1857     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
1858 
1859     current_space->array           += nnz;
1860     current_space->local_used      += nnz;
1861     current_space->local_remaining -= nnz;
1862 
1863     coi[i+1] = coi[i] + nnz;
1864   }
1865 
1866   ierr = PetscMalloc1(coi[pon]+1,&coj);CHKERRQ(ierr);
1867   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1868   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); /* must destroy to get a new one for C */
1869 
1870   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1871   if (afill_tmp > afill) afill = afill_tmp;
1872 
1873   /* send j-array (coj) of Co to other processors */
1874   /*----------------------------------------------*/
1875   /* determine row ownership */
1876   ierr = PetscNew(&merge);CHKERRQ(ierr);
1877   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1878 
1879   merge->rowmap->n  = pn;
1880   merge->rowmap->bs = 1;
1881 
1882   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1883   owners = merge->rowmap->range;
1884 
1885   /* determine the number of messages to send, their lengths */
1886   ierr = PetscCalloc1(size,&len_si);CHKERRQ(ierr);
1887   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
1888 
1889   len_s        = merge->len_s;
1890   merge->nsend = 0;
1891 
1892   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
1893 
1894   proc = 0;
1895   for (i=0; i<pon; i++) {
1896     while (prmap[i] >= owners[proc+1]) proc++;
1897     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1898     len_s[proc] += coi[i+1] - coi[i];
1899   }
1900 
1901   len          = 0; /* max length of buf_si[] */
1902   owners_co[0] = 0;
1903   for (proc=0; proc<size; proc++) {
1904     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1905     if (len_si[proc]) {
1906       merge->nsend++;
1907       len_si[proc] = 2*(len_si[proc] + 1);
1908       len         += len_si[proc];
1909     }
1910   }
1911 
1912   /* determine the number and length of messages to receive for coi and coj  */
1913   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1914   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1915 
1916   /* post the Irecv and Isend of coj */
1917   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1918   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1919   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
1920   for (proc=0, k=0; proc<size; proc++) {
1921     if (!len_s[proc]) continue;
1922     i    = owners_co[proc];
1923     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRMPI(ierr);
1924     k++;
1925   }
1926 
1927   /* receives and sends of coj are complete */
1928   ierr = PetscMalloc1(size,&sstatus);CHKERRQ(ierr);
1929   for (i=0; i<merge->nrecv; i++) {
1930     PETSC_UNUSED PetscMPIInt icompleted;
1931     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1932   }
1933   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1934   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRMPI(ierr);}
1935 
1936   /* add received column indices into table to update Armax */
1937   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1938   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1939     Jptr = buf_rj[k];
1940     for (j=0; j<merge->len_r[k]; j++) {
1941       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1942     }
1943   }
1944   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1945 
1946   /* send and recv coi */
1947   /*-------------------*/
1948   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1949   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1950   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1951   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1952   for (proc=0,k=0; proc<size; proc++) {
1953     if (!len_s[proc]) continue;
1954     /* form outgoing message for i-structure:
1955          buf_si[0]:                 nrows to be sent
1956                [1:nrows]:           row index (global)
1957                [nrows+1:2*nrows+1]: i-structure index
1958     */
1959     /*-------------------------------------------*/
1960     nrows       = len_si[proc]/2 - 1;
1961     buf_si_i    = buf_si + nrows+1;
1962     buf_si[0]   = nrows;
1963     buf_si_i[0] = 0;
1964     nrows       = 0;
1965     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1966       nzi               = coi[i+1] - coi[i];
1967       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1968       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1969       nrows++;
1970     }
1971     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRMPI(ierr);
1972     k++;
1973     buf_si += len_si[proc];
1974   }
1975   i = merge->nrecv;
1976   while (i--) {
1977     PETSC_UNUSED PetscMPIInt icompleted;
1978     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRMPI(ierr);
1979   }
1980   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1981   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRMPI(ierr);}
1982   ierr = PetscFree(len_si);CHKERRQ(ierr);
1983   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1984   ierr = PetscFree(swaits);CHKERRQ(ierr);
1985   ierr = PetscFree(sstatus);CHKERRQ(ierr);
1986   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1987 
1988   /* compute the local portion of C (mpi mat) */
1989   /*------------------------------------------*/
1990   /* allocate bi array and free space for accumulating nonzero column info */
1991   ierr  = PetscMalloc1(pn+1,&bi);CHKERRQ(ierr);
1992   bi[0] = 0;
1993 
1994   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1995   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
1996   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1997   current_space = free_space;
1998 
1999   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
2000   for (k=0; k<merge->nrecv; k++) {
2001     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2002     nrows       = *buf_ri_k[k];
2003     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
2004     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
2005   }
2006 
2007   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
2008   ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr);
2009   rmax = 0;
2010   for (i=0; i<pn; i++) {
2011     /* add pdt[i,:]*AP into lnk */
2012     pnz = pdti[i+1] - pdti[i];
2013     ptJ = pdtj + pdti[i];
2014     for (j=0; j<pnz; j++) {
2015       row  = ptJ[j];  /* row of AP == col of Pt */
2016       anz  = ai[row+1] - ai[row];
2017       Jptr = aj + ai[row];
2018       /* add non-zero cols of AP into the sorted linked list lnk */
2019       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
2020     }
2021 
2022     /* add received col data into lnk */
2023     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2024       if (i == *nextrow[k]) { /* i-th row */
2025         nzi  = *(nextci[k]+1) - *nextci[k];
2026         Jptr = buf_rj[k] + *nextci[k];
2027         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
2028         nextrow[k]++; nextci[k]++;
2029       }
2030     }
2031 
2032     /* add missing diagonal entry */
2033     if (C->force_diagonals) {
2034       k = i + owners[rank]; /* column index */
2035       ierr = PetscLLCondensedAddSorted_Scalable(1,&k,lnk);CHKERRQ(ierr);
2036     }
2037 
2038     nnz = lnk[0];
2039 
2040     /* if free space is not available, make more free space */
2041     if (current_space->local_remaining<nnz) {
2042       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
2043       nspacedouble++;
2044     }
2045     /* copy data into free space, then initialize lnk */
2046     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
2047     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
2048 
2049     current_space->array           += nnz;
2050     current_space->local_used      += nnz;
2051     current_space->local_remaining -= nnz;
2052 
2053     bi[i+1] = bi[i] + nnz;
2054     if (nnz > rmax) rmax = nnz;
2055   }
2056   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
2057 
2058   ierr      = PetscMalloc1(bi[pn]+1,&bj);CHKERRQ(ierr);
2059   ierr      = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
2060   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2061   if (afill_tmp > afill) afill = afill_tmp;
2062   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
2063   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
2064   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
2065   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
2066 
2067   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2068   /*-------------------------------------------------------------------------------*/
2069   ierr = MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2070   ierr = MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));CHKERRQ(ierr);
2071   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
2072   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
2073   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
2074   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
2075   ierr = MatSetBlockSize(C,1);CHKERRQ(ierr);
2076   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
2077   for (i=0; i<pn; i++) {
2078     row  = i + rstart;
2079     nnz  = bi[i+1] - bi[i];
2080     Jptr = bj + bi[i];
2081     ierr = MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);CHKERRQ(ierr);
2082   }
2083   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2084   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2085   ierr = MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
2086   merge->bi        = bi;
2087   merge->bj        = bj;
2088   merge->coi       = coi;
2089   merge->coj       = coj;
2090   merge->buf_ri    = buf_ri;
2091   merge->buf_rj    = buf_rj;
2092   merge->owners_co = owners_co;
2093 
2094   /* attach the supporting struct to C for reuse */
2095   C->product->data    = ptap;
2096   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2097   ptap->merge         = merge;
2098 
2099   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2100 
2101 #if defined(PETSC_USE_INFO)
2102   if (bi[pn] != 0) {
2103     ierr = PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
2104     ierr = PetscInfo(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
2105   } else {
2106     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
2107   }
2108 #endif
2109   PetscFunctionReturn(0);
2110 }
2111 
2112 /* ---------------------------------------------------------------- */
2113 static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2114 {
2115   PetscErrorCode ierr;
2116   Mat_Product    *product = C->product;
2117   Mat            A=product->A,B=product->B;
2118   PetscReal      fill=product->fill;
2119   PetscBool      flg;
2120 
2121   PetscFunctionBegin;
2122   /* scalable */
2123   ierr = PetscStrcmp(product->alg,"scalable",&flg);CHKERRQ(ierr);
2124   if (flg) {
2125     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
2126     goto next;
2127   }
2128 
2129   /* nonscalable */
2130   ierr = PetscStrcmp(product->alg,"nonscalable",&flg);CHKERRQ(ierr);
2131   if (flg) {
2132     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr);
2133     goto next;
2134   }
2135 
2136   /* matmatmult */
2137   ierr = PetscStrcmp(product->alg,"at*b",&flg);CHKERRQ(ierr);
2138   if (flg) {
2139     Mat       At;
2140     Mat_APMPI *ptap;
2141 
2142     ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
2143     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);CHKERRQ(ierr);
2144     ptap = (Mat_APMPI*)C->product->data;
2145     if (ptap) {
2146       ptap->Pt = At;
2147       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2148     }
2149     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2150     goto next;
2151   }
2152 
2153   /* backend general code */
2154   ierr = PetscStrcmp(product->alg,"backend",&flg);CHKERRQ(ierr);
2155   if (flg) {
2156     ierr = MatProductSymbolic_MPIAIJBACKEND(C);CHKERRQ(ierr);
2157     PetscFunctionReturn(0);
2158   }
2159 
2160   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2161 
2162 next:
2163   C->ops->productnumeric = MatProductNumeric_AtB;
2164   PetscFunctionReturn(0);
2165 }
2166 
2167 /* ---------------------------------------------------------------- */
2168 /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2169 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2170 {
2171   PetscErrorCode ierr;
2172   Mat_Product    *product = C->product;
2173   Mat            A=product->A,B=product->B;
2174 #if defined(PETSC_HAVE_HYPRE)
2175   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
2176   PetscInt       nalg = 5;
2177 #else
2178   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
2179   PetscInt       nalg = 4;
2180 #endif
2181   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2182   PetscBool      flg;
2183   MPI_Comm       comm;
2184 
2185   PetscFunctionBegin;
2186   /* Check matrix local sizes */
2187   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2188   PetscCheckFalse(A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
2189 
2190   /* Set "nonscalable" as default algorithm */
2191   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2192   if (flg) {
2193     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2194 
2195     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2196     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2197       MatInfo     Ainfo,Binfo;
2198       PetscInt    nz_local;
2199       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2200 
2201       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2202       ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2203       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2204 
2205       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2206       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2207 
2208       if (alg_scalable) {
2209         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2210         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2211         ierr = PetscInfo(B,"Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n",B->cmap->N,(double)(product->fill*nz_local));CHKERRQ(ierr);
2212       }
2213     }
2214   }
2215 
2216   /* Get runtime option */
2217   if (product->api_user) {
2218     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
2219     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2220     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2221   } else {
2222     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");CHKERRQ(ierr);
2223     ierr = PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2224     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2225   }
2226   if (flg) {
2227     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2228   }
2229 
2230   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2231   PetscFunctionReturn(0);
2232 }
2233 
2234 /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2235 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2236 {
2237   PetscErrorCode ierr;
2238   Mat_Product    *product = C->product;
2239   Mat            A=product->A,B=product->B;
2240   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
2241   PetscInt       nalg = 4;
2242   PetscInt       alg = 1; /* set default algorithm  */
2243   PetscBool      flg;
2244   MPI_Comm       comm;
2245 
2246   PetscFunctionBegin;
2247   /* Check matrix local sizes */
2248   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2249   PetscCheckFalse(A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != B (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);
2250 
2251   /* Set default algorithm */
2252   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2253   if (flg) {
2254     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2255   }
2256 
2257   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2258   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2259     MatInfo     Ainfo,Binfo;
2260     PetscInt    nz_local;
2261     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2262 
2263     ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2264     ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2265     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2266 
2267     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2268     ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2269 
2270     if (alg_scalable) {
2271       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2272       ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2273       ierr = PetscInfo(B,"Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n",B->cmap->N,(double)(product->fill*nz_local));CHKERRQ(ierr);
2274     }
2275   }
2276 
2277   /* Get runtime option */
2278   if (product->api_user) {
2279     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");CHKERRQ(ierr);
2280     ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2281     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2282   } else {
2283     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");CHKERRQ(ierr);
2284     ierr = PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2285     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2286   }
2287   if (flg) {
2288     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2289   }
2290 
2291   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2292   PetscFunctionReturn(0);
2293 }
2294 
2295 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2296 {
2297   PetscErrorCode ierr;
2298   Mat_Product    *product = C->product;
2299   Mat            A=product->A,P=product->B;
2300   MPI_Comm       comm;
2301   PetscBool      flg;
2302   PetscInt       alg=1; /* set default algorithm */
2303 #if !defined(PETSC_HAVE_HYPRE)
2304   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
2305   PetscInt       nalg=5;
2306 #else
2307   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
2308   PetscInt       nalg=6;
2309 #endif
2310   PetscInt       pN=P->cmap->N;
2311 
2312   PetscFunctionBegin;
2313   /* Check matrix local sizes */
2314   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2315   PetscCheckFalse(A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%" PetscInt_FMT ", %" PetscInt_FMT ") != Prow (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
2316   PetscCheckFalse(A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%" PetscInt_FMT ", %" PetscInt_FMT ") != Prow (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
2317 
2318   /* Set "nonscalable" as default algorithm */
2319   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2320   if (flg) {
2321     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2322 
2323     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2324     if (pN > 100000) {
2325       MatInfo     Ainfo,Pinfo;
2326       PetscInt    nz_local;
2327       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2328 
2329       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2330       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
2331       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2332 
2333       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2334       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRMPI(ierr);
2335 
2336       if (alg_scalable) {
2337         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2338         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2339       }
2340     }
2341   }
2342 
2343   /* Get runtime option */
2344   if (product->api_user) {
2345     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
2346     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2347     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2348   } else {
2349     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");CHKERRQ(ierr);
2350     ierr = PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2351     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2352   }
2353   if (flg) {
2354     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2355   }
2356 
2357   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2358   PetscFunctionReturn(0);
2359 }
2360 
2361 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2362 {
2363   Mat_Product *product = C->product;
2364   Mat         A = product->A,R=product->B;
2365 
2366   PetscFunctionBegin;
2367   /* Check matrix local sizes */
2368   PetscCheckFalse(A->cmap->n != R->cmap->n || A->rmap->n != R->cmap->n,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A local (%" PetscInt_FMT ", %" PetscInt_FMT "), R local (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->rmap->n,A->rmap->n,R->rmap->n,R->cmap->n);
2369 
2370   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2371   PetscFunctionReturn(0);
2372 }
2373 
2374 /*
2375  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2376 */
2377 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2378 {
2379   PetscErrorCode ierr;
2380   Mat_Product    *product = C->product;
2381   PetscBool      flg = PETSC_FALSE;
2382   PetscInt       alg = 1; /* default algorithm */
2383   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2384   PetscInt       nalg = 3;
2385 
2386   PetscFunctionBegin;
2387   /* Set default algorithm */
2388   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2389   if (flg) {
2390     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2391   }
2392 
2393   /* Get runtime option */
2394   if (product->api_user) {
2395     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");CHKERRQ(ierr);
2396     ierr = PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2397     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2398   } else {
2399     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");CHKERRQ(ierr);
2400     ierr = PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2401     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2402   }
2403   if (flg) {
2404     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2405   }
2406 
2407   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2408   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2409   PetscFunctionReturn(0);
2410 }
2411 
2412 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2413 {
2414   PetscErrorCode ierr;
2415   Mat_Product    *product = C->product;
2416 
2417   PetscFunctionBegin;
2418   switch (product->type) {
2419   case MATPRODUCT_AB:
2420     ierr = MatProductSetFromOptions_MPIAIJ_AB(C);CHKERRQ(ierr);
2421     break;
2422   case MATPRODUCT_AtB:
2423     ierr = MatProductSetFromOptions_MPIAIJ_AtB(C);CHKERRQ(ierr);
2424     break;
2425   case MATPRODUCT_PtAP:
2426     ierr = MatProductSetFromOptions_MPIAIJ_PtAP(C);CHKERRQ(ierr);
2427     break;
2428   case MATPRODUCT_RARt:
2429     ierr = MatProductSetFromOptions_MPIAIJ_RARt(C);CHKERRQ(ierr);
2430     break;
2431   case MATPRODUCT_ABC:
2432     ierr = MatProductSetFromOptions_MPIAIJ_ABC(C);CHKERRQ(ierr);
2433     break;
2434   default:
2435     break;
2436   }
2437   PetscFunctionReturn(0);
2438 }
2439