xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision 967582eba84cc53dc1fbf6b54d6aa49b7d83bae6)
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/vecscatterimpl.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     goto next;
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     goto next;
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     goto next;
47   }
48 
49 #if defined(PETSC_HAVE_HYPRE)
50   ierr = PetscStrcmp(alg,"hypre",&flg);CHKERRQ(ierr);
51   if (flg) {
52     ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr);
53     PetscFunctionReturn(0);
54   }
55 #endif
56   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
57 
58 next:
59   {
60     Mat_MPIAIJ *c  = (Mat_MPIAIJ*)C->data;
61     Mat_APMPI  *ap = c->ap;
62     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatFreeIntermediateDataStructures","Mat");CHKERRQ(ierr);
63     ap->freestruct = PETSC_FALSE;
64     ierr = PetscOptionsBool("-mat_freeintermediatedatastructures","Free intermediate data structures", "MatFreeIntermediateDataStructures",ap->freestruct,&ap->freestruct, NULL);CHKERRQ(ierr);
65     ierr = PetscOptionsEnd();CHKERRQ(ierr);
66   }
67   PetscFunctionReturn(0);
68 }
69 
70 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
71 {
72   PetscErrorCode ierr;
73   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
74   Mat_APMPI      *ptap = a->ap;
75 
76   PetscFunctionBegin;
77   ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr);
78   ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
79   ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
80   ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
81   ierr = MatDestroy(&ptap->Pt);CHKERRQ(ierr);
82   ierr = PetscFree(ptap->api);CHKERRQ(ierr);
83   ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
84   ierr = PetscFree(ptap->apa);CHKERRQ(ierr);
85   ierr = ptap->destroy(A);CHKERRQ(ierr);
86   ierr = PetscFree(ptap);CHKERRQ(ierr);
87   PetscFunctionReturn(0);
88 }
89 
90 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
91 {
92   PetscErrorCode ierr;
93   Mat_MPIAIJ     *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
94   Mat_SeqAIJ     *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
95   Mat_SeqAIJ     *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
96   PetscScalar    *cda=cd->a,*coa=co->a;
97   Mat_SeqAIJ     *p_loc,*p_oth;
98   PetscScalar    *apa,*ca;
99   PetscInt       cm   =C->rmap->n;
100   Mat_APMPI      *ptap=c->ap;
101   PetscInt       *api,*apj,*apJ,i,k;
102   PetscInt       cstart=C->cmap->rstart;
103   PetscInt       cdnz,conz,k0,k1;
104   MPI_Comm       comm;
105   PetscMPIInt    size;
106 
107   PetscFunctionBegin;
108   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
109   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
110 
111   if (!ptap->P_oth && size>1) SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
112 
113   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
114   /*-----------------------------------------------------*/
115   /* update numerical values of P_oth and P_loc */
116   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
117   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
118 
119   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
120   /*----------------------------------------------------------*/
121   /* get data from symbolic products */
122   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
123   p_oth = NULL;
124   if (size >1) {
125     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
126   }
127 
128   /* get apa for storing dense row A[i,:]*P */
129   apa = ptap->apa;
130 
131   api = ptap->api;
132   apj = ptap->apj;
133   for (i=0; i<cm; i++) {
134     /* compute apa = A[i,:]*P */
135     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
136 
137     /* set values in C */
138     apJ  = apj + api[i];
139     cdnz = cd->i[i+1] - cd->i[i];
140     conz = co->i[i+1] - co->i[i];
141 
142     /* 1st off-diagonal part of C */
143     ca = coa + co->i[i];
144     k  = 0;
145     for (k0=0; k0<conz; k0++) {
146       if (apJ[k] >= cstart) break;
147       ca[k0]      = apa[apJ[k]];
148       apa[apJ[k++]] = 0.0;
149     }
150 
151     /* diagonal part of C */
152     ca = cda + cd->i[i];
153     for (k1=0; k1<cdnz; k1++) {
154       ca[k1]      = apa[apJ[k]];
155       apa[apJ[k++]] = 0.0;
156     }
157 
158     /* 2nd off-diagonal part of C */
159     ca = coa + co->i[i];
160     for (; k0<conz; k0++) {
161       ca[k0]      = apa[apJ[k]];
162       apa[apJ[k++]] = 0.0;
163     }
164   }
165   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
166   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
167 
168   if (ptap->freestruct) {
169     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
170   }
171   PetscFunctionReturn(0);
172 }
173 
174 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
175 {
176   PetscErrorCode     ierr;
177   MPI_Comm           comm;
178   PetscMPIInt        size;
179   Mat_APMPI          *ptap;
180   PetscFreeSpaceList free_space=NULL,current_space=NULL;
181   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data,*c;
182   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
183   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
184   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
185   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
186   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
187   PetscBT            lnkbt;
188   PetscReal          afill;
189   MatType            mtype;
190 
191   PetscFunctionBegin;
192   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
193   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
194 
195   /* create struct Mat_APMPI and attached it to C later */
196   ierr = PetscNew(&ptap);CHKERRQ(ierr);
197 
198   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
199   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
200 
201   /* get P_loc by taking all local rows of P */
202   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
203 
204   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
205   pi_loc = p_loc->i; pj_loc = p_loc->j;
206   if (size > 1) {
207     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
208     pi_oth = p_oth->i; pj_oth = p_oth->j;
209   } else {
210     p_oth = NULL;
211     pi_oth = NULL; pj_oth = NULL;
212   }
213 
214   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
215   /*-------------------------------------------------------------------*/
216   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
217   ptap->api = api;
218   api[0]    = 0;
219 
220   /* create and initialize a linked list */
221   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
222 
223   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
224   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
225   current_space = free_space;
226 
227   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
228   for (i=0; i<am; i++) {
229     /* diagonal portion of A */
230     nzi = adi[i+1] - adi[i];
231     for (j=0; j<nzi; j++) {
232       row  = *adj++;
233       pnz  = pi_loc[row+1] - pi_loc[row];
234       Jptr = pj_loc + pi_loc[row];
235       /* add non-zero cols of P into the sorted linked list lnk */
236       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
237     }
238     /* off-diagonal portion of A */
239     nzi = aoi[i+1] - aoi[i];
240     for (j=0; j<nzi; j++) {
241       row  = *aoj++;
242       pnz  = pi_oth[row+1] - pi_oth[row];
243       Jptr = pj_oth + pi_oth[row];
244       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
245     }
246 
247     apnz     = lnk[0];
248     api[i+1] = api[i] + apnz;
249 
250     /* if free space is not available, double the total space in the list */
251     if (current_space->local_remaining<apnz) {
252       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
253       nspacedouble++;
254     }
255 
256     /* Copy data into free space, then initialize lnk */
257     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
258     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
259 
260     current_space->array           += apnz;
261     current_space->local_used      += apnz;
262     current_space->local_remaining -= apnz;
263   }
264 
265   /* Allocate space for apj, initialize apj, and */
266   /* destroy list of free space and other temporary array(s) */
267   ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr);
268   apj  = ptap->apj;
269   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
270   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
271 
272   /* malloc apa to store dense row A[i,:]*P */
273   ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
274 
275   /* set and assemble symbolic parallel matrix C */
276   /*---------------------------------------------*/
277   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
278   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
279 
280   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
281   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
282   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
283 
284   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
285   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
286   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
287   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
288 
289   ptap->destroy        = C->ops->destroy;
290   ptap->duplicate      = C->ops->duplicate;
291   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
292   C->ops->productnumeric = MatProductNumeric_AB;
293   C->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
294   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
295 
296   /* attach the supporting struct to C for reuse */
297   c     = (Mat_MPIAIJ*)C->data;
298   c->ap = ptap;
299 
300   /* set MatInfo */
301   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
302   if (afill < 1.0) afill = 1.0;
303   C->info.mallocs           = nspacedouble;
304   C->info.fill_ratio_given  = fill;
305   C->info.fill_ratio_needed = afill;
306 
307 #if defined(PETSC_USE_INFO)
308   if (api[am]) {
309     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
310     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
311   } else {
312     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
313   }
314 #endif
315   PetscFunctionReturn(0);
316 }
317 
318 /* ------------------------------------------------------- */
319 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
320 {
321   Mat_Product *product = C->product;
322   Mat         A = product->A,B=product->B;
323 
324   PetscFunctionBegin;
325   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
326     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
327 
328   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
329   C->ops->productsymbolic = MatProductSymbolic_AB;
330   C->ops->productnumeric  = MatProductNumeric_AB;
331   PetscFunctionReturn(0);
332 }
333 /* -------------------------------------------------------------------- */
334 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
335 {
336   Mat_Product *product = C->product;
337   Mat         A = product->A,B=product->B;
338 
339   PetscFunctionBegin;
340   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
341     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);
342 
343   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
344   C->ops->productsymbolic          = MatProductSymbolic_AtB;
345   PetscFunctionReturn(0);
346 }
347 
348 /* --------------------------------------------------------------------- */
349 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
350 {
351   PetscErrorCode ierr;
352   Mat_Product    *product = C->product;
353 
354   PetscFunctionBegin;
355   switch (product->type) {
356   case MATPRODUCT_AB:
357     ierr = MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);CHKERRQ(ierr);
358     break;
359   case MATPRODUCT_AtB:
360     ierr = MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);CHKERRQ(ierr);
361     break;
362   default:
363     /* Use MatProduct_Basic() if there is no specific implementation */
364     C->ops->productsymbolic = MatProductSymbolic_Basic;
365   }
366   PetscFunctionReturn(0);
367 }
368 /* ------------------------------------------------------- */
369 
370 typedef struct {
371   Mat          workB,Bb,Cb,workB1,Bb1,Cb1;
372   MPI_Request  *rwaits,*swaits;
373   PetscInt     numBb;  /* num of Bb matrices */
374   PetscInt     nsends,nrecvs;
375   MPI_Datatype *stype,*rtype;
376 } MPIAIJ_MPIDense;
377 
378 PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
379 {
380   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
381   PetscErrorCode  ierr;
382   PetscInt        i;
383 
384   PetscFunctionBegin;
385   ierr = MatDestroy(&contents->workB);CHKERRQ(ierr);
386 
387   if (contents->numBb) {
388     ierr = MatDestroy(&contents->Bb);CHKERRQ(ierr);
389     ierr = MatDestroy(&contents->Cb);CHKERRQ(ierr);
390 
391     ierr = MatDestroy(&contents->workB1);CHKERRQ(ierr);
392     ierr = MatDestroy(&contents->Bb1);CHKERRQ(ierr);
393     ierr = MatDestroy(&contents->Cb1);CHKERRQ(ierr);
394   }
395   for (i=0; i<contents->nsends; i++) {
396     ierr = MPI_Type_free(&contents->stype[i]);CHKERRQ(ierr);
397   }
398   for (i=0; i<contents->nrecvs; i++) {
399     ierr = MPI_Type_free(&contents->rtype[i]);CHKERRQ(ierr);
400   }
401   ierr = PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);CHKERRQ(ierr);
402   ierr = PetscFree(contents);CHKERRQ(ierr);
403   PetscFunctionReturn(0);
404 }
405 
406 /*
407     This is a "dummy function" that handles the case where matrix C was created as a dense matrix
408   directly by the user and passed to MatMatMult() with the MAT_REUSE_MATRIX option
409 
410   It is the same as MatMatMultSymbolic_MPIAIJ_MPIDense() except does not create C
411 */
412 PETSC_INTERN PetscErrorCode MatMatMultNumeric_MPIDense(Mat A,Mat B,Mat C)
413 {
414   PetscBool      flg;
415   PetscErrorCode ierr;
416 
417   PetscFunctionBegin;
418   ierr = PetscObjectTypeCompare((PetscObject)A,MATNEST,&flg);CHKERRQ(ierr);
419   if (flg) {
420     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
421     ierr = MatMatMultSymbolic_Nest_Dense(A,B,PETSC_DEFAULT,&C);CHKERRQ(ierr);
422     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
423     C->ops->matmultnumeric = MatMatMultNumeric_Nest_Dense;
424   } else {
425     ierr = MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,PETSC_DEFAULT,C);CHKERRQ(ierr);
426   }
427   ierr = (*C->ops->matmultnumeric)(A,B,C);CHKERRQ(ierr);
428   PetscFunctionReturn(0);
429 }
430 
431 /*
432   Create Bb, Cb, Bb1 and Cb1 matrices to be used by MatMatMultSymbolic_MPIAIJ_MPIDense().
433   These matrices are used as wrappers for sub-columns of B and C, thus their own matrix operations are not used.
434   Modified from MatCreateDense().
435 */
436 PETSC_STATIC_INLINE PetscErrorCode MatCreateSubMPIDense_private(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt rbs,PetscInt cbs,PetscScalar *data,Mat *A)
437 {
438   PetscErrorCode ierr;
439 
440   PetscFunctionBegin;
441   ierr = MatCreate(comm,A);CHKERRQ(ierr);
442   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
443   ierr = MatSetBlockSizes(*A,rbs,cbs);CHKERRQ(ierr);
444   ierr = MatSetType(*A,MATMPIDENSE);CHKERRQ(ierr);
445   ierr = MatMPIDenseSetPreallocation(*A,data);CHKERRQ(ierr);
446   (*A)->assembled = PETSC_TRUE;
447   PetscFunctionReturn(0);
448 }
449 
450 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
451 {
452   PetscErrorCode  ierr;
453   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
454   Mat_MPIDense    *b=(Mat_MPIDense*)B->data;
455   Mat_SeqDense    *bseq=(Mat_SeqDense*)(b->A)->data;
456   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,lda=bseq->lda;
457   PetscContainer  container;
458   MPIAIJ_MPIDense *contents;
459   VecScatter      ctx=aij->Mvctx;
460   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from;
461   MPI_Comm        comm;
462   MPI_Datatype    type1,*stype,*rtype;
463   const PetscInt  *sindices,*sstarts,*rstarts;
464   PetscMPIInt     *disp;
465 
466   PetscFunctionBegin;
467   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
468   if (!C->preallocated) {
469     ierr = MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);CHKERRQ(ierr);
470     ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
471     ierr = MatSetType(C,MATMPIDENSE);CHKERRQ(ierr);
472     ierr = MatMPIDenseSetPreallocation(C,NULL);CHKERRQ(ierr);
473   }
474 
475   ierr = PetscNew(&contents);CHKERRQ(ierr);
476   contents->numBb = 0;
477 
478   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);CHKERRQ(ierr);
479   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);CHKERRQ(ierr);
480 
481   /* Create column block of B and C for memory scalability when BN is too large */
482   /* Estimate Bbn, column size of Bb */
483   if (nz) {
484     Bbn1 = 2*Am*BN/nz;
485   } else Bbn1 = BN;
486 
487   bs = PetscAbs(B->cmap->bs);
488   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
489   if (Bbn1 > BN) Bbn1 = BN;
490   ierr = MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
491 
492   /* Enable runtime option for Bbn */
493   ierr = PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
494   ierr = PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);CHKERRQ(ierr);
495   if (Bbn > BN) SETERRQ2(comm,PETSC_ERR_ARG_SIZ,"Bbn=%D cannot be larger than %D, column size of B",Bbn,BN);
496   ierr = PetscOptionsEnd();CHKERRQ(ierr);
497 
498   if (Bbn < BN) {
499     contents->numBb = BN/Bbn;
500     Bbn1 = BN - contents->numBb*Bbn;
501   }
502 
503   if (contents->numBb) {
504     PetscScalar data[1]; /* fake array for Bb and Cb */
505     ierr = PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,contents->numBb);CHKERRQ(ierr);
506     ierr = MatCreateSubMPIDense_private(comm,B->rmap->n,PETSC_DECIDE,A->rmap->N,Bbn,B->rmap->bs,B->cmap->bs,data,&contents->Bb);CHKERRQ(ierr);
507     ierr = MatCreateSubMPIDense_private(comm,Am,PETSC_DECIDE,A->rmap->N,Bbn,C->rmap->bs,C->cmap->bs,data,&contents->Cb);CHKERRQ(ierr);
508 
509     if (Bbn1) { /* Create Bb1 and Cb1 for the remaining columns */
510       ierr = PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);CHKERRQ(ierr);
511       ierr = MatCreateSubMPIDense_private(comm,B->rmap->n,PETSC_DECIDE,A->rmap->N,Bbn1,B->rmap->bs,B->cmap->bs,data,&contents->Bb1);CHKERRQ(ierr);
512       ierr = MatCreateSubMPIDense_private(comm,Am,PETSC_DECIDE,A->rmap->N,Bbn1,C->rmap->bs,C->cmap->bs,data,&contents->Cb1);CHKERRQ(ierr);
513 
514       /* Create work matrix used to store off processor rows of B needed for local product */
515       ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);CHKERRQ(ierr);
516     }
517   }
518 
519   /* Create work matrix used to store off processor rows of B needed for local product */
520   ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB);CHKERRQ(ierr);
521 
522   /* Use MPI derived data type to reduce memory required by the send/recv buffers */
523   ierr = PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits);CHKERRQ(ierr);
524   contents->stype  = stype;
525   contents->nsends = nsends;
526 
527   contents->rtype  = rtype;
528   contents->nrecvs = nrecvs;
529 
530   ierr = PetscMalloc1(Bm+1,&disp);CHKERRQ(ierr);
531   for (i=0; i<nsends; i++) {
532     nrows_to = sstarts[i+1]-sstarts[i];
533     for (j=0; j<nrows_to; j++){
534       disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
535     }
536     ierr = MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);CHKERRQ(ierr);
537 
538     ierr = MPI_Type_create_resized(type1,0,lda*sizeof(PetscScalar),&stype[i]);CHKERRQ(ierr);
539     ierr = MPI_Type_commit(&stype[i]);CHKERRQ(ierr);
540     ierr = MPI_Type_free(&type1);CHKERRQ(ierr);
541   }
542 
543   for (i=0; i<nrecvs; i++) {
544     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
545     nrows_from = rstarts[i+1]-rstarts[i];
546     disp[0] = 0;
547     ierr = MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);CHKERRQ(ierr);
548     ierr = MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);CHKERRQ(ierr);
549     ierr = MPI_Type_commit(&rtype[i]);CHKERRQ(ierr);
550     ierr = MPI_Type_free(&type1);CHKERRQ(ierr);
551   }
552 
553   ierr = PetscFree(disp);CHKERRQ(ierr);
554   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);CHKERRQ(ierr);
555   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);CHKERRQ(ierr);
556 
557   ierr = PetscContainerCreate(comm,&container);CHKERRQ(ierr);
558   ierr = PetscContainerSetPointer(container,contents);CHKERRQ(ierr);
559   ierr = PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);CHKERRQ(ierr);
560   ierr = PetscObjectCompose((PetscObject)C,"workB",(PetscObject)container);CHKERRQ(ierr);
561   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
562   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
563   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
564   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
565   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
566   PetscFunctionReturn(0);
567 }
568 
569 extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);
570 /*
571     Performs an efficient scatter on the rows of B needed by this process; this is
572     a modification of the VecScatterBegin_() routines.
573 
574     Input: Bbidx = 0: B = Bb
575                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
576 */
577 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
578 {
579   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
580   PetscErrorCode    ierr;
581   const PetscScalar *b;
582   PetscScalar       *rvalues;
583   VecScatter        ctx = aij->Mvctx;
584   const PetscInt    *sindices,*sstarts,*rstarts;
585   const PetscMPIInt *sprocs,*rprocs;
586   PetscInt          i,nsends,nrecvs,nrecvs2;
587   MPI_Request       *swaits,*rwaits;
588   MPI_Comm          comm;
589   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,imdex,nsends_mpi,nrecvs_mpi;
590   MPI_Status        status;
591   MPIAIJ_MPIDense   *contents;
592   PetscContainer    container;
593   Mat               workB;
594   MPI_Datatype      *stype,*rtype;
595 
596   PetscFunctionBegin;
597   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
598   ierr = PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);CHKERRQ(ierr);
599   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
600   ierr = PetscContainerGetPointer(container,(void**)&contents);CHKERRQ(ierr);
601 
602   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);CHKERRQ(ierr);
603   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);CHKERRQ(ierr);
604   ierr = PetscMPIIntCast(nsends,&nsends_mpi);CHKERRQ(ierr);
605   ierr = PetscMPIIntCast(nrecvs,&nrecvs_mpi);CHKERRQ(ierr);
606   if (Bbidx == 0) {
607     workB = *outworkB = contents->workB;
608   } else {
609     workB = *outworkB = contents->workB1;
610   }
611   if (nrows != workB->rmap->n) SETERRQ2(comm,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",workB->cmap->n,nrows);
612   swaits  = contents->swaits;
613   rwaits  = contents->rwaits;
614 
615   ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr);
616   ierr = MatDenseGetArray(workB,&rvalues);CHKERRQ(ierr);
617 
618   /* Post recv, use MPI derived data type to save memory */
619   rtype = contents->rtype;
620   for (i=0; i<nrecvs; i++) {
621     ierr = MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
622   }
623 
624   stype = contents->stype;
625   for (i=0; i<nsends; i++) {
626     ierr = MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
627   }
628 
629   nrecvs2 = nrecvs;
630   while (nrecvs2) {
631     ierr = MPI_Waitany(nrecvs_mpi,rwaits,&imdex,&status);CHKERRQ(ierr);
632     nrecvs2--;
633   }
634   if (nsends) {ierr = MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);CHKERRQ(ierr);}
635 
636   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);CHKERRQ(ierr);
637   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);CHKERRQ(ierr);
638   ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr);
639   ierr = MatDenseRestoreArray(workB,&rvalues);CHKERRQ(ierr);
640   ierr = MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
641   ierr = MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
642   PetscFunctionReturn(0);
643 }
644 
645 /*
646   Compute Cb = A*Bb
647 */
648 PETSC_STATIC_INLINE PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense_private(Mat A,Mat Bb,PetscInt Bbidx,PetscInt start,Mat C,const PetscScalar *barray,PetscScalar *carray,Mat Cb)
649 {
650   PetscErrorCode  ierr;
651   PetscInt        start1;
652   Mat             workB;
653   Mat_MPIAIJ      *aij = (Mat_MPIAIJ*)A->data;
654   Mat_MPIDense    *cbdense = (Mat_MPIDense*)Cb->data;
655 
656   PetscFunctionBegin;
657   /* Place barray to Bb */
658   start1 = start*Bb->rmap->n;
659   ierr = MatDensePlaceArray(Bb,barray+start1);CHKERRQ(ierr);
660 
661   /* get off processor parts of Bb needed to complete Cb=A*Bb */
662   ierr = MatMPIDenseScatter(A,Bb,Bbidx,C,&workB);CHKERRQ(ierr);
663   ierr = MatDenseResetArray(Bb);CHKERRQ(ierr);
664 
665   /* off-diagonal block of A times nonlocal rows of Bb */
666   /* Place carray to Cb */
667   start1 = start*Cb->rmap->n;
668   ierr = MatDensePlaceArray(Cb,carray+start1);CHKERRQ(ierr);
669   ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cbdense->A);CHKERRQ(ierr);
670   ierr = MatDenseResetArray(Cb);CHKERRQ(ierr);
671   PetscFunctionReturn(0);
672 }
673 
674 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
675 {
676   PetscErrorCode  ierr;
677   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
678   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
679   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
680   Mat             workB;
681   MPIAIJ_MPIDense *contents;
682   PetscContainer  container;
683   MPI_Comm        comm;
684   PetscInt        numBb;
685 
686   PetscFunctionBegin;
687   /* diagonal block of A times all local rows of B*/
688   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(aij->A,bdense->A,cdense->A);CHKERRQ(ierr);
689 
690   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
691   ierr = PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);CHKERRQ(ierr);
692   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
693   ierr = PetscContainerGetPointer(container,(void**)&contents);CHKERRQ(ierr);
694   numBb = contents->numBb;
695 
696   if (!numBb) {
697     /* get off processor parts of B needed to complete C=A*B */
698     ierr = MatMPIDenseScatter(A,B,0,C,&workB);CHKERRQ(ierr);
699 
700     /* off-diagonal block of A times nonlocal rows of B */
701     ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);CHKERRQ(ierr);
702 
703   } else {
704     const PetscScalar *barray;
705     PetscScalar       *carray;
706     Mat               Bb=contents->Bb,Cb=contents->Cb;
707     PetscInt          BbN=Bb->cmap->N,start,i;
708 
709     ierr = MatDenseGetArrayRead(B,&barray);CHKERRQ(ierr);
710     ierr = MatDenseGetArray(C,&carray);CHKERRQ(ierr);
711     for (i=0; i<numBb; i++) {
712       start = i*BbN;
713       ierr = MatMatMultNumeric_MPIAIJ_MPIDense_private(A,Bb,0,start,C,barray,carray,Cb);CHKERRQ(ierr);
714     }
715 
716     if (contents->Bb1) {
717       Bb = contents->Bb1; Cb = contents->Cb1;
718       start = i*BbN;
719       ierr = MatMatMultNumeric_MPIAIJ_MPIDense_private(A,Bb,1,start,C,barray,carray,Cb);CHKERRQ(ierr);
720     }
721     ierr = MatDenseRestoreArrayRead(B,&barray);CHKERRQ(ierr);
722     ierr = MatDenseRestoreArray(C,&carray);CHKERRQ(ierr);
723   }
724   PetscFunctionReturn(0);
725 }
726 
727 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
728 {
729   PetscErrorCode ierr;
730   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
731   Mat_SeqAIJ     *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
732   Mat_SeqAIJ     *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
733   PetscInt       *adi = ad->i,*adj,*aoi=ao->i,*aoj;
734   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
735   Mat_SeqAIJ     *p_loc,*p_oth;
736   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
737   PetscScalar    *pa_loc,*pa_oth,*pa,valtmp,*ca;
738   PetscInt       cm    = C->rmap->n,anz,pnz;
739   Mat_APMPI      *ptap = c->ap;
740   PetscScalar    *apa_sparse;
741   PetscInt       *api,*apj,*apJ,i,j,k,row;
742   PetscInt       cstart = C->cmap->rstart;
743   PetscInt       cdnz,conz,k0,k1,nextp;
744   MPI_Comm       comm;
745   PetscMPIInt    size;
746 
747   PetscFunctionBegin;
748   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
749   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
750 
751   if (!ptap->P_oth && size>1) {
752     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
753   }
754   apa_sparse = ptap->apa;
755 
756   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
757   /*-----------------------------------------------------*/
758   /* update numerical values of P_oth and P_loc */
759   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
760   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
761 
762   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
763   /*----------------------------------------------------------*/
764   /* get data from symbolic products */
765   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
766   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
767   if (size >1) {
768     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
769     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
770   } else {
771     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
772   }
773 
774   api = ptap->api;
775   apj = ptap->apj;
776   for (i=0; i<cm; i++) {
777     apJ = apj + api[i];
778 
779     /* diagonal portion of A */
780     anz = adi[i+1] - adi[i];
781     adj = ad->j + adi[i];
782     ada = ad->a + adi[i];
783     for (j=0; j<anz; j++) {
784       row = adj[j];
785       pnz = pi_loc[row+1] - pi_loc[row];
786       pj  = pj_loc + pi_loc[row];
787       pa  = pa_loc + pi_loc[row];
788       /* perform sparse axpy */
789       valtmp = ada[j];
790       nextp  = 0;
791       for (k=0; nextp<pnz; k++) {
792         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
793           apa_sparse[k] += valtmp*pa[nextp++];
794         }
795       }
796       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
797     }
798 
799     /* off-diagonal portion of A */
800     anz = aoi[i+1] - aoi[i];
801     aoj = ao->j + aoi[i];
802     aoa = ao->a + aoi[i];
803     for (j=0; j<anz; j++) {
804       row = aoj[j];
805       pnz = pi_oth[row+1] - pi_oth[row];
806       pj  = pj_oth + pi_oth[row];
807       pa  = pa_oth + pi_oth[row];
808       /* perform sparse axpy */
809       valtmp = aoa[j];
810       nextp  = 0;
811       for (k=0; nextp<pnz; k++) {
812         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
813           apa_sparse[k] += valtmp*pa[nextp++];
814         }
815       }
816       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
817     }
818 
819     /* set values in C */
820     cdnz = cd->i[i+1] - cd->i[i];
821     conz = co->i[i+1] - co->i[i];
822 
823     /* 1st off-diagonal part of C */
824     ca = coa + co->i[i];
825     k  = 0;
826     for (k0=0; k0<conz; k0++) {
827       if (apJ[k] >= cstart) break;
828       ca[k0]        = apa_sparse[k];
829       apa_sparse[k] = 0.0;
830       k++;
831     }
832 
833     /* diagonal part of C */
834     ca = cda + cd->i[i];
835     for (k1=0; k1<cdnz; k1++) {
836       ca[k1]        = apa_sparse[k];
837       apa_sparse[k] = 0.0;
838       k++;
839     }
840 
841     /* 2nd off-diagonal part of C */
842     ca = coa + co->i[i];
843     for (; k0<conz; k0++) {
844       ca[k0]        = apa_sparse[k];
845       apa_sparse[k] = 0.0;
846       k++;
847     }
848   }
849   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
850   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
851 
852   if (ptap->freestruct) {
853     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
854   }
855   PetscFunctionReturn(0);
856 }
857 
858 /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
859 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
860 {
861   PetscErrorCode     ierr;
862   MPI_Comm           comm;
863   PetscMPIInt        size;
864   Mat_APMPI          *ptap;
865   PetscFreeSpaceList free_space = NULL,current_space=NULL;
866   Mat_MPIAIJ         *a         = (Mat_MPIAIJ*)A->data,*c;
867   Mat_SeqAIJ         *ad        = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
868   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
869   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
870   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
871   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
872   PetscReal          afill;
873   MatType            mtype;
874 
875   PetscFunctionBegin;
876   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
877   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
878 
879   /* create struct Mat_APMPI and attached it to C later */
880   ierr = PetscNew(&ptap);CHKERRQ(ierr);
881 
882   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
883   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
884 
885   /* get P_loc by taking all local rows of P */
886   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
887 
888   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
889   pi_loc = p_loc->i; pj_loc = p_loc->j;
890   if (size > 1) {
891     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
892     pi_oth = p_oth->i; pj_oth = p_oth->j;
893   } else {
894     p_oth  = NULL;
895     pi_oth = NULL; pj_oth = NULL;
896   }
897 
898   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
899   /*-------------------------------------------------------------------*/
900   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
901   ptap->api = api;
902   api[0]    = 0;
903 
904   ierr = PetscLLCondensedCreate_Scalable(lsize,&lnk);CHKERRQ(ierr);
905 
906   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
907   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
908   current_space = free_space;
909   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
910   for (i=0; i<am; i++) {
911     /* diagonal portion of A */
912     nzi = adi[i+1] - adi[i];
913     for (j=0; j<nzi; j++) {
914       row  = *adj++;
915       pnz  = pi_loc[row+1] - pi_loc[row];
916       Jptr = pj_loc + pi_loc[row];
917       /* Expand list if it is not long enough */
918       if (pnz+apnz_max > lsize) {
919         lsize = pnz+apnz_max;
920         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
921       }
922       /* add non-zero cols of P into the sorted linked list lnk */
923       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
924       apnz     = *lnk; /* The first element in the list is the number of items in the list */
925       api[i+1] = api[i] + apnz;
926       if (apnz > apnz_max) apnz_max = apnz;
927     }
928     /* off-diagonal portion of A */
929     nzi = aoi[i+1] - aoi[i];
930     for (j=0; j<nzi; j++) {
931       row  = *aoj++;
932       pnz  = pi_oth[row+1] - pi_oth[row];
933       Jptr = pj_oth + pi_oth[row];
934       /* Expand list if it is not long enough */
935       if (pnz+apnz_max > lsize) {
936         lsize = pnz + apnz_max;
937         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
938       }
939       /* add non-zero cols of P into the sorted linked list lnk */
940       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
941       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
942       api[i+1] = api[i] + apnz;
943       if (apnz > apnz_max) apnz_max = apnz;
944     }
945     apnz     = *lnk;
946     api[i+1] = api[i] + apnz;
947     if (apnz > apnz_max) apnz_max = apnz;
948 
949     /* if free space is not available, double the total space in the list */
950     if (current_space->local_remaining<apnz) {
951       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
952       nspacedouble++;
953     }
954 
955     /* Copy data into free space, then initialize lnk */
956     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
957     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
958 
959     current_space->array           += apnz;
960     current_space->local_used      += apnz;
961     current_space->local_remaining -= apnz;
962   }
963 
964   /* Allocate space for apj, initialize apj, and */
965   /* destroy list of free space and other temporary array(s) */
966   ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr);
967   apj  = ptap->apj;
968   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
969   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
970 
971   /* create and assemble symbolic parallel matrix C */
972   /*----------------------------------------------------*/
973   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
974   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
975   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
976   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
977   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
978 
979   /* malloc apa for assembly C */
980   ierr = PetscCalloc1(apnz_max,&ptap->apa);CHKERRQ(ierr);
981 
982   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
983   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
984   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
985   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
986 
987   ptap->destroy             = C->ops->destroy;
988   ptap->duplicate           = C->ops->duplicate;
989   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
990   C->ops->productnumeric = MatProductNumeric_AB;
991   C->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
992   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
993 
994   /* attach the supporting struct to C for reuse */
995   c     = (Mat_MPIAIJ*)C->data;
996   c->ap = ptap;
997 
998   /* set MatInfo */
999   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1000   if (afill < 1.0) afill = 1.0;
1001   C->info.mallocs           = nspacedouble;
1002   C->info.fill_ratio_given  = fill;
1003   C->info.fill_ratio_needed = afill;
1004 
1005 #if defined(PETSC_USE_INFO)
1006   if (api[am]) {
1007     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1008     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1009   } else {
1010     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1011   }
1012 #endif
1013   PetscFunctionReturn(0);
1014 }
1015 
1016 /* This function is needed for the seqMPI matrix-matrix multiplication.  */
1017 /* Three input arrays are merged to one output array. The size of the    */
1018 /* output array is also output. Duplicate entries only show up once.     */
1019 static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
1020                                PetscInt  size2, PetscInt *in2,
1021                                PetscInt  size3, PetscInt *in3,
1022                                PetscInt *size4, PetscInt *out)
1023 {
1024   int i = 0, j = 0, k = 0, l = 0;
1025 
1026   /* Traverse all three arrays */
1027   while (i<size1 && j<size2 && k<size3) {
1028     if (in1[i] < in2[j] && in1[i] < in3[k]) {
1029       out[l++] = in1[i++];
1030     }
1031     else if(in2[j] < in1[i] && in2[j] < in3[k]) {
1032       out[l++] = in2[j++];
1033     }
1034     else if(in3[k] < in1[i] && in3[k] < in2[j]) {
1035       out[l++] = in3[k++];
1036     }
1037     else if(in1[i] == in2[j] && in1[i] < in3[k]) {
1038       out[l++] = in1[i];
1039       i++, j++;
1040     }
1041     else if(in1[i] == in3[k] && in1[i] < in2[j]) {
1042       out[l++] = in1[i];
1043       i++, k++;
1044     }
1045     else if(in3[k] == in2[j] && in2[j] < in1[i])  {
1046       out[l++] = in2[j];
1047       k++, j++;
1048     }
1049     else if(in1[i] == in2[j] && in1[i] == in3[k]) {
1050       out[l++] = in1[i];
1051       i++, j++, k++;
1052     }
1053   }
1054 
1055   /* Traverse two remaining arrays */
1056   while (i<size1 && j<size2) {
1057     if (in1[i] < in2[j]) {
1058       out[l++] = in1[i++];
1059     }
1060     else if(in1[i] > in2[j]) {
1061       out[l++] = in2[j++];
1062     }
1063     else {
1064       out[l++] = in1[i];
1065       i++, j++;
1066     }
1067   }
1068 
1069   while (i<size1 && k<size3) {
1070     if (in1[i] < in3[k]) {
1071       out[l++] = in1[i++];
1072     }
1073     else if(in1[i] > in3[k]) {
1074       out[l++] = in3[k++];
1075     }
1076     else {
1077       out[l++] = in1[i];
1078       i++, k++;
1079     }
1080   }
1081 
1082   while (k<size3 && j<size2)  {
1083     if (in3[k] < in2[j]) {
1084       out[l++] = in3[k++];
1085     }
1086     else if(in3[k] > in2[j]) {
1087       out[l++] = in2[j++];
1088     }
1089     else {
1090       out[l++] = in3[k];
1091       k++, j++;
1092     }
1093   }
1094 
1095   /* Traverse one remaining array */
1096   while (i<size1) out[l++] = in1[i++];
1097   while (j<size2) out[l++] = in2[j++];
1098   while (k<size3) out[l++] = in3[k++];
1099 
1100   *size4 = l;
1101 }
1102 
1103 /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1104 /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1105 /* matrix-matrix multiplications.  */
1106 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1107 {
1108   PetscErrorCode     ierr;
1109   MPI_Comm           comm;
1110   PetscMPIInt        size;
1111   Mat_APMPI          *ptap;
1112   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
1113   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data;
1114   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
1115   Mat_MPIAIJ         *p        =(Mat_MPIAIJ*)P->data;
1116   Mat_MPIAIJ         *c;
1117   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
1118   PetscInt           adponz, adpdnz;
1119   PetscInt           *pi_loc,*dnz,*onz;
1120   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
1121   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1122                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1123   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1124   PetscBT            lnkbt;
1125   PetscReal          afill;
1126   PetscMPIInt        rank;
1127   Mat                adpd, aopoth;
1128   MatType            mtype;
1129   const char         *prefix;
1130 
1131   PetscFunctionBegin;
1132   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1133   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1134   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1135   ierr = MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend); CHKERRQ(ierr);
1136 
1137   /* create struct Mat_APMPI and attached it to C later */
1138   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1139 
1140   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1141   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1142 
1143   /* get P_loc by taking all local rows of P */
1144   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1145 
1146 
1147   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1148   pi_loc = p_loc->i;
1149 
1150   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1151   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
1152   ierr      = PetscMalloc1(am+2,&adpoi);CHKERRQ(ierr);
1153 
1154   adpoi[0]    = 0;
1155   ptap->api = api;
1156   api[0] = 0;
1157 
1158   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1159   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1160   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
1161 
1162   /* Symbolic calc of A_loc_diag * P_loc_diag */
1163   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1164   ierr = MatProductCreate(a->A,p->A,NULL,&adpd);CHKERRQ(ierr);
1165   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1166   ierr = MatSetOptionsPrefix(adpd,prefix);CHKERRQ(ierr);
1167   ierr = MatAppendOptionsPrefix(adpd,"inner_diag_");CHKERRQ(ierr);
1168 
1169   ierr = MatProductSetType(adpd,MATPRODUCT_AB);CHKERRQ(ierr);
1170   ierr = MatProductSetAlgorithm(adpd,"sorted");CHKERRQ(ierr);
1171   ierr = MatProductSetFill(adpd,fill);CHKERRQ(ierr);
1172   ierr = MatProductSetFromOptions(adpd);CHKERRQ(ierr);
1173   ierr = MatProductSymbolic(adpd);CHKERRQ(ierr);
1174 
1175   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1176   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1177   p_off = (Mat_SeqAIJ*)((p->B)->data);
1178   poff_i = p_off->i; poff_j = p_off->j;
1179 
1180   /* j_temp stores indices of a result row before they are added to the linked list */
1181   ierr = PetscMalloc1(pN+2,&j_temp);CHKERRQ(ierr);
1182 
1183 
1184   /* Symbolic calc of the A_diag * p_loc_off */
1185   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1186   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);CHKERRQ(ierr);
1187   current_space = free_space_diag;
1188 
1189   for (i=0; i<am; i++) {
1190     /* A_diag * P_loc_off */
1191     nzi = adi[i+1] - adi[i];
1192     for (j=0; j<nzi; j++) {
1193       row  = *adj++;
1194       pnz  = poff_i[row+1] - poff_i[row];
1195       Jptr = poff_j + poff_i[row];
1196       for(i1 = 0; i1 < pnz; i1++) {
1197         j_temp[i1] = p->garray[Jptr[i1]];
1198       }
1199       /* add non-zero cols of P into the sorted linked list lnk */
1200       ierr = PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);CHKERRQ(ierr);
1201     }
1202 
1203     adponz     = lnk[0];
1204     adpoi[i+1] = adpoi[i] + adponz;
1205 
1206     /* if free space is not available, double the total space in the list */
1207     if (current_space->local_remaining<adponz) {
1208       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1209       nspacedouble++;
1210     }
1211 
1212     /* Copy data into free space, then initialize lnk */
1213     ierr = PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1214 
1215     current_space->array           += adponz;
1216     current_space->local_used      += adponz;
1217     current_space->local_remaining -= adponz;
1218   }
1219 
1220   /* Symbolic calc of A_off * P_oth */
1221   ierr = MatSetOptionsPrefix(a->B,prefix);CHKERRQ(ierr);
1222   ierr = MatAppendOptionsPrefix(a->B,"inner_offdiag_");CHKERRQ(ierr);
1223   ierr = MatCreate(PETSC_COMM_SELF,&aopoth);CHKERRQ(ierr);
1224   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);CHKERRQ(ierr);
1225   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1226   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;
1227 
1228   /* Allocate space for apj, adpj, aopj, ... */
1229   /* destroy lists of free space and other temporary array(s) */
1230 
1231   ierr = PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);CHKERRQ(ierr);
1232   ierr = PetscMalloc1(adpoi[am]+2, &adpoj);CHKERRQ(ierr);
1233 
1234   /* Copy from linked list to j-array */
1235   ierr = PetscFreeSpaceContiguous(&free_space_diag,adpoj);CHKERRQ(ierr);
1236   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1237 
1238   adpoJ = adpoj;
1239   adpdJ = adpdj;
1240   aopJ = aopothj;
1241   apj  = ptap->apj;
1242   apJ = apj; /* still empty */
1243 
1244   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1245   /* A_diag * P_loc_diag to get A*P */
1246   for (i = 0; i < am; i++) {
1247     aopnz  =  aopothi[i+1] -  aopothi[i];
1248     adponz = adpoi[i+1] - adpoi[i];
1249     adpdnz = adpdi[i+1] - adpdi[i];
1250 
1251     /* Correct indices from A_diag*P_diag */
1252     for(i1 = 0; i1 < adpdnz; i1++) {
1253       adpdJ[i1] += p_colstart;
1254     }
1255     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1256     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1257     ierr = MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz); CHKERRQ(ierr);
1258 
1259     aopJ += aopnz;
1260     adpoJ += adponz;
1261     adpdJ += adpdnz;
1262     apJ += apnz;
1263     api[i+1] = api[i] + apnz;
1264   }
1265 
1266   /* malloc apa to store dense row A[i,:]*P */
1267   ierr = PetscCalloc1(pN+2,&ptap->apa);CHKERRQ(ierr);
1268 
1269   /* create and assemble symbolic parallel matrix C */
1270   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1271   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
1272   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1273   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1274   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1275 
1276 
1277   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
1278   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1279   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1280   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1281 
1282 
1283   ptap->destroy        = C->ops->destroy;
1284   ptap->duplicate      = C->ops->duplicate;
1285   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1286   C->ops->productnumeric = MatProductNumeric_AB;
1287   C->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
1288 
1289   /* attach the supporting struct to C for reuse */
1290   c       = (Mat_MPIAIJ*)C->data;
1291   c->ap = ptap;
1292 
1293   /* set MatInfo */
1294   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1295   if (afill < 1.0) afill = 1.0;
1296   C->info.mallocs           = nspacedouble;
1297   C->info.fill_ratio_given  = fill;
1298   C->info.fill_ratio_needed = afill;
1299 
1300 #if defined(PETSC_USE_INFO)
1301   if (api[am]) {
1302     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1303     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1304   } else {
1305     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1306   }
1307 #endif
1308 
1309   ierr = MatDestroy(&aopoth);CHKERRQ(ierr);
1310   ierr = MatDestroy(&adpd);CHKERRQ(ierr);
1311   ierr = PetscFree(j_temp);CHKERRQ(ierr);
1312   ierr = PetscFree(adpoj);CHKERRQ(ierr);
1313   ierr = PetscFree(adpoi);CHKERRQ(ierr);
1314   PetscFunctionReturn(0);
1315 }
1316 
1317 /*-------------------------------------------------------------------------*/
1318 /* This routine only works when scall=MAT_REUSE_MATRIX! */
1319 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1320 {
1321   PetscErrorCode ierr;
1322   Mat_MPIAIJ     *c=(Mat_MPIAIJ*)C->data;
1323   Mat_APMPI      *ptap= c->ap;
1324   Mat            Pt;
1325 
1326   PetscFunctionBegin;
1327   if (!ptap->Pt) {
1328     MPI_Comm comm;
1329     ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1330     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
1331   }
1332 
1333   Pt = ptap->Pt;
1334   ierr = MatTranspose(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr);
1335   ierr = MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);CHKERRQ(ierr);
1336 
1337   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
1338   if (ptap->freestruct) {
1339     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
1340   }
1341   PetscFunctionReturn(0);
1342 }
1343 
1344 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1345 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1346 {
1347   PetscErrorCode      ierr;
1348   Mat_APMPI           *ptap;
1349   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*c;
1350   MPI_Comm            comm;
1351   PetscMPIInt         size,rank;
1352   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1353   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1354   PetscInt            *lnk,i,k,nsend;
1355   PetscBT             lnkbt;
1356   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
1357   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1358   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1359   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1360   MPI_Request         *swaits,*rwaits;
1361   MPI_Status          *sstatus,rstatus;
1362   PetscLayout         rowmap;
1363   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1364   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1365   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1366   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1367   PetscTable          ta;
1368   MatType             mtype;
1369   const char          *prefix;
1370 
1371   PetscFunctionBegin;
1372   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1373   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1374   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1375 
1376   /* create symbolic parallel matrix C */
1377   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1378   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1379 
1380   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1381 
1382   /* create struct Mat_APMPI and attached it to C later */
1383   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1384   ptap->reuse = MAT_INITIAL_MATRIX;
1385 
1386   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1387   /* --------------------------------- */
1388   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1389   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1390 
1391   /* (1) compute symbolic A_loc */
1392   /* ---------------------------*/
1393   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1394 
1395   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1396   /* ------------------------------------ */
1397   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1398   ierr = MatSetOptionsPrefix(ptap->Ro,prefix);CHKERRQ(ierr);
1399   ierr = MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");CHKERRQ(ierr);
1400   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_oth);CHKERRQ(ierr);
1401   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);CHKERRQ(ierr);
1402 
1403   /* (3) send coj of C_oth to other processors  */
1404   /* ------------------------------------------ */
1405   /* determine row ownership */
1406   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
1407   rowmap->n  = pn;
1408   rowmap->bs = 1;
1409   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
1410   owners = rowmap->range;
1411 
1412   /* determine the number of messages to send, their lengths */
1413   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
1414   ierr = PetscArrayzero(len_s,size);CHKERRQ(ierr);
1415   ierr = PetscArrayzero(len_si,size);CHKERRQ(ierr);
1416 
1417   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1418   coi   = c_oth->i; coj = c_oth->j;
1419   con   = ptap->C_oth->rmap->n;
1420   proc  = 0;
1421   for (i=0; i<con; i++) {
1422     while (prmap[i] >= owners[proc+1]) proc++;
1423     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1424     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1425   }
1426 
1427   len          = 0; /* max length of buf_si[], see (4) */
1428   owners_co[0] = 0;
1429   nsend        = 0;
1430   for (proc=0; proc<size; proc++) {
1431     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1432     if (len_s[proc]) {
1433       nsend++;
1434       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1435       len         += len_si[proc];
1436     }
1437   }
1438 
1439   /* determine the number and length of messages to receive for coi and coj  */
1440   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
1441   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
1442 
1443   /* post the Irecv and Isend of coj */
1444   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1445   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1446   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
1447   for (proc=0, k=0; proc<size; proc++) {
1448     if (!len_s[proc]) continue;
1449     i    = owners_co[proc];
1450     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
1451     k++;
1452   }
1453 
1454   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1455   /* ---------------------------------------- */
1456   ierr = MatSetOptionsPrefix(ptap->Rd,prefix);CHKERRQ(ierr);
1457   ierr = MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");CHKERRQ(ierr);
1458   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_loc);CHKERRQ(ierr);
1459   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);CHKERRQ(ierr);
1460   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1461 
1462   /* receives coj are complete */
1463   for (i=0; i<nrecv; i++) {
1464     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1465   }
1466   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1467   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
1468 
1469   /* add received column indices into ta to update Crmax */
1470   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1471 
1472   /* create and initialize a linked list */
1473   ierr = PetscTableCreate(an,aN,&ta);CHKERRQ(ierr); /* for compute Crmax */
1474   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1475 
1476   for (k=0; k<nrecv; k++) {/* k-th received message */
1477     Jptr = buf_rj[k];
1478     for (j=0; j<len_r[k]; j++) {
1479       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1480     }
1481   }
1482   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
1483   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
1484 
1485   /* (4) send and recv coi */
1486   /*-----------------------*/
1487   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1488   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1489   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1490   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1491   for (proc=0,k=0; proc<size; proc++) {
1492     if (!len_s[proc]) continue;
1493     /* form outgoing message for i-structure:
1494          buf_si[0]:                 nrows to be sent
1495                [1:nrows]:           row index (global)
1496                [nrows+1:2*nrows+1]: i-structure index
1497     */
1498     /*-------------------------------------------*/
1499     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1500     buf_si_i    = buf_si + nrows+1;
1501     buf_si[0]   = nrows;
1502     buf_si_i[0] = 0;
1503     nrows       = 0;
1504     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1505       nzi = coi[i+1] - coi[i];
1506       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1507       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1508       nrows++;
1509     }
1510     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
1511     k++;
1512     buf_si += len_si[proc];
1513   }
1514   for (i=0; i<nrecv; i++) {
1515     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1516   }
1517   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1518   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
1519 
1520   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
1521   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1522   ierr = PetscFree(swaits);CHKERRQ(ierr);
1523   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1524 
1525   /* (5) compute the local portion of C      */
1526   /* ------------------------------------------ */
1527   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1528   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
1529   current_space = free_space;
1530 
1531   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
1532   for (k=0; k<nrecv; k++) {
1533     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1534     nrows       = *buf_ri_k[k];
1535     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1536     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1537   }
1538 
1539   ierr = MatPreallocateInitialize(comm,pn,an,dnz,onz);CHKERRQ(ierr);
1540   ierr = PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);CHKERRQ(ierr);
1541   for (i=0; i<pn; i++) {
1542     /* add C_loc into C */
1543     nzi  = c_loc->i[i+1] - c_loc->i[i];
1544     Jptr = c_loc->j + c_loc->i[i];
1545     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1546 
1547     /* add received col data into lnk */
1548     for (k=0; k<nrecv; k++) { /* k-th received message */
1549       if (i == *nextrow[k]) { /* i-th row */
1550         nzi  = *(nextci[k]+1) - *nextci[k];
1551         Jptr = buf_rj[k] + *nextci[k];
1552         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1553         nextrow[k]++; nextci[k]++;
1554       }
1555     }
1556     nzi = lnk[0];
1557 
1558     /* copy data into free space, then initialize lnk */
1559     ierr = PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1560     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
1561   }
1562   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1563   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1564   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
1565 
1566   /* local sizes and preallocation */
1567   ierr = MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1568   if (P->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);CHKERRQ(ierr);}
1569   if (A->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);CHKERRQ(ierr);}
1570   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1571   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1572 
1573   /* members in merge */
1574   ierr = PetscFree(id_r);CHKERRQ(ierr);
1575   ierr = PetscFree(len_r);CHKERRQ(ierr);
1576   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
1577   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
1578   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
1579   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
1580   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
1581 
1582   /* attach the supporting struct to C for reuse */
1583   c = (Mat_MPIAIJ*)C->data;
1584   c->ap         = ptap;
1585   ptap->destroy = C->ops->destroy;
1586 
1587   /* C is not ready for use - assembly will be done by MatPtAPNumeric() */
1588   C->assembled        = PETSC_FALSE;
1589   C->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
1590   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
1591   PetscFunctionReturn(0);
1592 }
1593 
1594 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1595 {
1596   PetscErrorCode    ierr;
1597   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1598   Mat_SeqAIJ        *c_seq;
1599   Mat_APMPI         *ptap = c->ap;
1600   Mat               A_loc,C_loc,C_oth;
1601   PetscInt          i,rstart,rend,cm,ncols,row;
1602   const PetscInt    *cols;
1603   const PetscScalar *vals;
1604 
1605   PetscFunctionBegin;
1606   if (!ptap->A_loc) {
1607     MPI_Comm comm;
1608     ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1609     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
1610   }
1611 
1612   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1613 
1614   if (ptap->reuse == MAT_REUSE_MATRIX) {
1615     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1616     /* 1) get R = Pd^T, Ro = Po^T */
1617     /*----------------------------*/
1618     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1619     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1620 
1621     /* 2) compute numeric A_loc */
1622     /*--------------------------*/
1623     ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1624   }
1625 
1626   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1627   A_loc = ptap->A_loc;
1628   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);CHKERRQ(ierr);
1629   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);CHKERRQ(ierr);
1630   C_loc = ptap->C_loc;
1631   C_oth = ptap->C_oth;
1632 
1633   /* add C_loc and Co to to C */
1634   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1635 
1636   /* C_loc -> C */
1637   cm    = C_loc->rmap->N;
1638   c_seq = (Mat_SeqAIJ*)C_loc->data;
1639   cols = c_seq->j;
1640   vals = c_seq->a;
1641   for (i=0; i<cm; i++) {
1642     ncols = c_seq->i[i+1] - c_seq->i[i];
1643     row = rstart + i;
1644     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1645     cols += ncols; vals += ncols;
1646   }
1647 
1648   /* Co -> C, off-processor part */
1649   cm    = C_oth->rmap->N;
1650   c_seq = (Mat_SeqAIJ*)C_oth->data;
1651   cols  = c_seq->j;
1652   vals  = c_seq->a;
1653   for (i=0; i<cm; i++) {
1654     ncols = c_seq->i[i+1] - c_seq->i[i];
1655     row = p->garray[i];
1656     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1657     cols += ncols; vals += ncols;
1658   }
1659   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1660   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1661 
1662   ptap->reuse = MAT_REUSE_MATRIX;
1663 
1664   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
1665   if (ptap->freestruct) {
1666     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
1667   }
1668   PetscFunctionReturn(0);
1669 }
1670 
1671 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1672 {
1673   PetscErrorCode      ierr;
1674   Mat_Merge_SeqsToMPI *merge;
1675   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1676   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1677   Mat_APMPI           *ptap;
1678   PetscInt            *adj;
1679   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1680   MatScalar           *ada,*ca,valtmp;
1681   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1682   MPI_Comm            comm;
1683   PetscMPIInt         size,rank,taga,*len_s;
1684   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1685   PetscInt            **buf_ri,**buf_rj;
1686   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1687   MPI_Request         *s_waits,*r_waits;
1688   MPI_Status          *status;
1689   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1690   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1691   Mat                 A_loc;
1692   Mat_SeqAIJ          *a_loc;
1693 
1694   PetscFunctionBegin;
1695   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1696   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1697   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1698 
1699   ptap  = c->ap;
1700   if (!ptap->A_loc) SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
1701   merge = ptap->merge;
1702 
1703   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1704   /*------------------------------------------*/
1705   /* get data from symbolic products */
1706   coi    = merge->coi; coj = merge->coj;
1707   ierr   = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
1708   bi     = merge->bi; bj = merge->bj;
1709   owners = merge->rowmap->range;
1710   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);
1711 
1712   /* get A_loc by taking all local rows of A */
1713   A_loc = ptap->A_loc;
1714   ierr  = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr);
1715   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1716   ai    = a_loc->i;
1717   aj    = a_loc->j;
1718 
1719   for (i=0; i<am; i++) {
1720     anz = ai[i+1] - ai[i];
1721     adj = aj + ai[i];
1722     ada = a_loc->a + ai[i];
1723 
1724     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1725     /*-------------------------------------------------------------*/
1726     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1727     pnz = po->i[i+1] - po->i[i];
1728     poJ = po->j + po->i[i];
1729     pA  = po->a + po->i[i];
1730     for (j=0; j<pnz; j++) {
1731       row = poJ[j];
1732       cj  = coj + coi[row];
1733       ca  = coa + coi[row];
1734       /* perform sparse axpy */
1735       nexta  = 0;
1736       valtmp = pA[j];
1737       for (k=0; nexta<anz; k++) {
1738         if (cj[k] == adj[nexta]) {
1739           ca[k] += valtmp*ada[nexta];
1740           nexta++;
1741         }
1742       }
1743       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1744     }
1745 
1746     /* put the value into Cd (diagonal part) */
1747     pnz = pd->i[i+1] - pd->i[i];
1748     pdJ = pd->j + pd->i[i];
1749     pA  = pd->a + pd->i[i];
1750     for (j=0; j<pnz; j++) {
1751       row = pdJ[j];
1752       cj  = bj + bi[row];
1753       ca  = ba + bi[row];
1754       /* perform sparse axpy */
1755       nexta  = 0;
1756       valtmp = pA[j];
1757       for (k=0; nexta<anz; k++) {
1758         if (cj[k] == adj[nexta]) {
1759           ca[k] += valtmp*ada[nexta];
1760           nexta++;
1761         }
1762       }
1763       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1764     }
1765   }
1766 
1767   /* 3) send and recv matrix values coa */
1768   /*------------------------------------*/
1769   buf_ri = merge->buf_ri;
1770   buf_rj = merge->buf_rj;
1771   len_s  = merge->len_s;
1772   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1773   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1774 
1775   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
1776   for (proc=0,k=0; proc<size; proc++) {
1777     if (!len_s[proc]) continue;
1778     i    = merge->owners_co[proc];
1779     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
1780     k++;
1781   }
1782   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
1783   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
1784 
1785   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1786   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1787   ierr = PetscFree(coa);CHKERRQ(ierr);
1788 
1789   /* 4) insert local Cseq and received values into Cmpi */
1790   /*----------------------------------------------------*/
1791   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1792   for (k=0; k<merge->nrecv; k++) {
1793     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1794     nrows       = *(buf_ri_k[k]);
1795     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1796     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1797   }
1798 
1799   for (i=0; i<cm; i++) {
1800     row  = owners[rank] + i; /* global row index of C_seq */
1801     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1802     ba_i = ba + bi[i];
1803     bnz  = bi[i+1] - bi[i];
1804     /* add received vals into ba */
1805     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1806       /* i-th row */
1807       if (i == *nextrow[k]) {
1808         cnz    = *(nextci[k]+1) - *nextci[k];
1809         cj     = buf_rj[k] + *(nextci[k]);
1810         ca     = abuf_r[k] + *(nextci[k]);
1811         nextcj = 0;
1812         for (j=0; nextcj<cnz; j++) {
1813           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1814             ba_i[j] += ca[nextcj++];
1815           }
1816         }
1817         nextrow[k]++; nextci[k]++;
1818         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1819       }
1820     }
1821     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1822   }
1823   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1824   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1825 
1826   ierr = PetscFree(ba);CHKERRQ(ierr);
1827   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1828   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1829   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1830 
1831   if (ptap->freestruct) {
1832     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
1833   }
1834   PetscFunctionReturn(0);
1835 }
1836 
1837 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1838 {
1839   PetscErrorCode      ierr;
1840   Mat                 A_loc,POt,PDt;
1841   Mat_APMPI           *ptap;
1842   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1843   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data,*c;
1844   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1845   PetscInt            nnz;
1846   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1847   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1848   MPI_Comm            comm;
1849   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1850   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1851   PetscInt            len,proc,*dnz,*onz,*owners;
1852   PetscInt            nzi,*bi,*bj;
1853   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1854   MPI_Request         *swaits,*rwaits;
1855   MPI_Status          *sstatus,rstatus;
1856   Mat_Merge_SeqsToMPI *merge;
1857   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1858   PetscReal           afill  =1.0,afill_tmp;
1859   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1860   Mat_SeqAIJ          *a_loc,*pdt,*pot;
1861   PetscTable          ta;
1862   MatType             mtype;
1863 
1864   PetscFunctionBegin;
1865   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1866   /* check if matrix local sizes are compatible */
1867   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != P (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
1868 
1869   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1870   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1871 
1872   /* create struct Mat_APMPI and attached it to C later */
1873   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1874 
1875   /* get A_loc by taking all local rows of A */
1876   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr);
1877 
1878   ptap->A_loc = A_loc;
1879   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1880   ai          = a_loc->i;
1881   aj          = a_loc->j;
1882 
1883   /* determine symbolic Co=(p->B)^T*A - send to others */
1884   /*----------------------------------------------------*/
1885   ierr = MatTransposeSymbolic_SeqAIJ(p->A,&PDt);CHKERRQ(ierr);
1886   pdt  = (Mat_SeqAIJ*)PDt->data;
1887   pdti = pdt->i; pdtj = pdt->j;
1888 
1889   ierr = MatTransposeSymbolic_SeqAIJ(p->B,&POt);CHKERRQ(ierr);
1890   pot  = (Mat_SeqAIJ*)POt->data;
1891   poti = pot->i; potj = pot->j;
1892 
1893   /* then, compute symbolic Co = (p->B)^T*A */
1894   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1895                          >= (num of nonzero rows of C_seq) - pn */
1896   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
1897   coi[0] = 0;
1898 
1899   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1900   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1901   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1902   current_space = free_space;
1903 
1904   /* create and initialize a linked list */
1905   ierr = PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);CHKERRQ(ierr);
1906   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1907   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1908 
1909   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
1910 
1911   for (i=0; i<pon; i++) {
1912     pnz = poti[i+1] - poti[i];
1913     ptJ = potj + poti[i];
1914     for (j=0; j<pnz; j++) {
1915       row  = ptJ[j]; /* row of A_loc == col of Pot */
1916       anz  = ai[row+1] - ai[row];
1917       Jptr = aj + ai[row];
1918       /* add non-zero cols of AP into the sorted linked list lnk */
1919       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
1920     }
1921     nnz = lnk[0];
1922 
1923     /* If free space is not available, double the total space in the list */
1924     if (current_space->local_remaining<nnz) {
1925       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1926       nspacedouble++;
1927     }
1928 
1929     /* Copy data into free space, and zero out denserows */
1930     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
1931 
1932     current_space->array           += nnz;
1933     current_space->local_used      += nnz;
1934     current_space->local_remaining -= nnz;
1935 
1936     coi[i+1] = coi[i] + nnz;
1937   }
1938 
1939   ierr = PetscMalloc1(coi[pon]+1,&coj);CHKERRQ(ierr);
1940   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1941   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); /* must destroy to get a new one for C */
1942 
1943   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1944   if (afill_tmp > afill) afill = afill_tmp;
1945 
1946   /* send j-array (coj) of Co to other processors */
1947   /*----------------------------------------------*/
1948   /* determine row ownership */
1949   ierr = PetscNew(&merge);CHKERRQ(ierr);
1950   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1951 
1952   merge->rowmap->n  = pn;
1953   merge->rowmap->bs = 1;
1954 
1955   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1956   owners = merge->rowmap->range;
1957 
1958   /* determine the number of messages to send, their lengths */
1959   ierr = PetscCalloc1(size,&len_si);CHKERRQ(ierr);
1960   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
1961 
1962   len_s        = merge->len_s;
1963   merge->nsend = 0;
1964 
1965   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
1966 
1967   proc = 0;
1968   for (i=0; i<pon; i++) {
1969     while (prmap[i] >= owners[proc+1]) proc++;
1970     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1971     len_s[proc] += coi[i+1] - coi[i];
1972   }
1973 
1974   len          = 0; /* max length of buf_si[] */
1975   owners_co[0] = 0;
1976   for (proc=0; proc<size; proc++) {
1977     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1978     if (len_si[proc]) {
1979       merge->nsend++;
1980       len_si[proc] = 2*(len_si[proc] + 1);
1981       len         += len_si[proc];
1982     }
1983   }
1984 
1985   /* determine the number and length of messages to receive for coi and coj  */
1986   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1987   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1988 
1989   /* post the Irecv and Isend of coj */
1990   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1991   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1992   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
1993   for (proc=0, k=0; proc<size; proc++) {
1994     if (!len_s[proc]) continue;
1995     i    = owners_co[proc];
1996     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
1997     k++;
1998   }
1999 
2000   /* receives and sends of coj are complete */
2001   ierr = PetscMalloc1(size,&sstatus);CHKERRQ(ierr);
2002   for (i=0; i<merge->nrecv; i++) {
2003     PetscMPIInt icompleted;
2004     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
2005   }
2006   ierr = PetscFree(rwaits);CHKERRQ(ierr);
2007   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
2008 
2009   /* add received column indices into table to update Armax */
2010   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
2011   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
2012     Jptr = buf_rj[k];
2013     for (j=0; j<merge->len_r[k]; j++) {
2014       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
2015     }
2016   }
2017   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
2018   /* printf("Armax %d, an %d + Bn %d = %d, aN %d\n",Armax,A->cmap->n,a->B->cmap->N,A->cmap->n+a->B->cmap->N,aN); */
2019 
2020   /* send and recv coi */
2021   /*-------------------*/
2022   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
2023   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
2024   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
2025   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
2026   for (proc=0,k=0; proc<size; proc++) {
2027     if (!len_s[proc]) continue;
2028     /* form outgoing message for i-structure:
2029          buf_si[0]:                 nrows to be sent
2030                [1:nrows]:           row index (global)
2031                [nrows+1:2*nrows+1]: i-structure index
2032     */
2033     /*-------------------------------------------*/
2034     nrows       = len_si[proc]/2 - 1;
2035     buf_si_i    = buf_si + nrows+1;
2036     buf_si[0]   = nrows;
2037     buf_si_i[0] = 0;
2038     nrows       = 0;
2039     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
2040       nzi               = coi[i+1] - coi[i];
2041       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
2042       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
2043       nrows++;
2044     }
2045     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
2046     k++;
2047     buf_si += len_si[proc];
2048   }
2049   i = merge->nrecv;
2050   while (i--) {
2051     PetscMPIInt icompleted;
2052     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
2053   }
2054   ierr = PetscFree(rwaits);CHKERRQ(ierr);
2055   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
2056   ierr = PetscFree(len_si);CHKERRQ(ierr);
2057   ierr = PetscFree(len_ri);CHKERRQ(ierr);
2058   ierr = PetscFree(swaits);CHKERRQ(ierr);
2059   ierr = PetscFree(sstatus);CHKERRQ(ierr);
2060   ierr = PetscFree(buf_s);CHKERRQ(ierr);
2061 
2062   /* compute the local portion of C (mpi mat) */
2063   /*------------------------------------------*/
2064   /* allocate bi array and free space for accumulating nonzero column info */
2065   ierr  = PetscMalloc1(pn+1,&bi);CHKERRQ(ierr);
2066   bi[0] = 0;
2067 
2068   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
2069   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
2070   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
2071   current_space = free_space;
2072 
2073   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
2074   for (k=0; k<merge->nrecv; k++) {
2075     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2076     nrows       = *buf_ri_k[k];
2077     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
2078     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
2079   }
2080 
2081   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
2082   ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr);
2083   rmax = 0;
2084   for (i=0; i<pn; i++) {
2085     /* add pdt[i,:]*AP into lnk */
2086     pnz = pdti[i+1] - pdti[i];
2087     ptJ = pdtj + pdti[i];
2088     for (j=0; j<pnz; j++) {
2089       row  = ptJ[j];  /* row of AP == col of Pt */
2090       anz  = ai[row+1] - ai[row];
2091       Jptr = aj + ai[row];
2092       /* add non-zero cols of AP into the sorted linked list lnk */
2093       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
2094     }
2095 
2096     /* add received col data into lnk */
2097     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2098       if (i == *nextrow[k]) { /* i-th row */
2099         nzi  = *(nextci[k]+1) - *nextci[k];
2100         Jptr = buf_rj[k] + *nextci[k];
2101         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
2102         nextrow[k]++; nextci[k]++;
2103       }
2104     }
2105     nnz = lnk[0];
2106 
2107     /* if free space is not available, make more free space */
2108     if (current_space->local_remaining<nnz) {
2109       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
2110       nspacedouble++;
2111     }
2112     /* copy data into free space, then initialize lnk */
2113     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
2114     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
2115 
2116     current_space->array           += nnz;
2117     current_space->local_used      += nnz;
2118     current_space->local_remaining -= nnz;
2119 
2120     bi[i+1] = bi[i] + nnz;
2121     if (nnz > rmax) rmax = nnz;
2122   }
2123   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
2124 
2125   ierr      = PetscMalloc1(bi[pn]+1,&bj);CHKERRQ(ierr);
2126   ierr      = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
2127   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2128   if (afill_tmp > afill) afill = afill_tmp;
2129   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
2130   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
2131 
2132   ierr = MatDestroy(&POt);CHKERRQ(ierr);
2133   ierr = MatDestroy(&PDt);CHKERRQ(ierr);
2134 
2135   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2136   /*-------------------------------------------------------------------------------*/
2137   ierr = MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2138   ierr = MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));CHKERRQ(ierr);
2139   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
2140   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
2141   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
2142   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
2143   ierr = MatSetBlockSize(C,1);CHKERRQ(ierr);
2144   for (i=0; i<pn; i++) {
2145     row  = i + rstart;
2146     nnz  = bi[i+1] - bi[i];
2147     Jptr = bj + bi[i];
2148     ierr = MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);CHKERRQ(ierr);
2149   }
2150   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2151   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2152   merge->bi        = bi;
2153   merge->bj        = bj;
2154   merge->coi       = coi;
2155   merge->coj       = coj;
2156   merge->buf_ri    = buf_ri;
2157   merge->buf_rj    = buf_rj;
2158   merge->owners_co = owners_co;
2159 
2160   /* attach the supporting struct to C for reuse */
2161   c = (Mat_MPIAIJ*)C->data;
2162 
2163   c->ap       = ptap;
2164   ptap->api   = NULL;
2165   ptap->apj   = NULL;
2166   ptap->merge = merge;
2167   ptap->apa   = NULL;
2168   ptap->destroy   = C->ops->destroy;
2169   ptap->duplicate = C->ops->duplicate;
2170 
2171   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2172   C->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
2173   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
2174 
2175 #if defined(PETSC_USE_INFO)
2176   if (bi[pn] != 0) {
2177     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
2178     ierr = PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
2179   } else {
2180     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
2181   }
2182 #endif
2183   PetscFunctionReturn(0);
2184 }
2185 
2186 /* ---------------------------------------------------------------- */
2187 static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2188 {
2189   PetscErrorCode ierr;
2190   Mat_Product    *product = C->product;
2191   Mat            A=product->A,B=product->B;
2192   PetscReal      fill=product->fill;
2193   PetscBool      flg;
2194 
2195   PetscFunctionBegin;
2196   /* scalable */
2197   ierr = PetscStrcmp(product->alg,"scalable",&flg);CHKERRQ(ierr);
2198   if (flg) {
2199     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
2200     goto next;
2201   }
2202 
2203   /* nonscalable */
2204   ierr = PetscStrcmp(product->alg,"nonscalable",&flg);CHKERRQ(ierr);
2205   if (flg) {
2206     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr);
2207     goto next;
2208   }
2209 
2210   /* matmatmult */
2211   ierr = PetscStrcmp(product->alg,"at*b",&flg);CHKERRQ(ierr);
2212   if (flg) {
2213     Mat         At;
2214     Mat_APMPI   *ptap;
2215     Mat_MPIAIJ  *c;
2216     ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
2217 
2218     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);CHKERRQ(ierr);
2219     c    = (Mat_MPIAIJ*)C->data;
2220     ptap = c->ap;
2221     if (ptap) {
2222       ptap->Pt = At;
2223       C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
2224     }
2225     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2226     goto next;
2227   }
2228 
2229   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2230 
2231 next:
2232   C->ops->productnumeric = MatProductNumeric_AtB;
2233 
2234   {
2235     Mat_MPIAIJ *c  = (Mat_MPIAIJ*)C->data;
2236     Mat_APMPI  *ap = c->ap;
2237     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatFreeIntermediateDataStructures","Mat");CHKERRQ(ierr);
2238     ap->freestruct = PETSC_FALSE;
2239     ierr = PetscOptionsBool("-mat_freeintermediatedatastructures","Free intermediate data structures", "MatFreeIntermediateDataStructures",ap->freestruct,&ap->freestruct, NULL);CHKERRQ(ierr);
2240     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2241   }
2242   PetscFunctionReturn(0);
2243 }
2244 
2245 /* ---------------------------------------------------------------- */
2246 /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2247 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2248 {
2249   PetscErrorCode ierr;
2250   Mat_Product    *product = C->product;
2251   Mat            A=product->A,B=product->B;
2252 #if defined(PETSC_HAVE_HYPRE)
2253   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","hypre"};
2254   PetscInt       nalg = 4;
2255 #else
2256   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2257   PetscInt       nalg = 3;
2258 #endif
2259   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2260   PetscBool      flg;
2261   MPI_Comm       comm;
2262 
2263   PetscFunctionBegin;
2264   /* Check matrix local sizes */
2265   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2266   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
2267 
2268   /* Set "nonscalable" as default algorithm */
2269   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2270   if (flg) {
2271     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2272 
2273     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2274     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2275       MatInfo     Ainfo,Binfo;
2276       PetscInt    nz_local;
2277       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2278 
2279       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2280       ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2281       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2282 
2283       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2284       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2285 
2286       if (alg_scalable) {
2287         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2288         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2289         ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);CHKERRQ(ierr);
2290       }
2291     }
2292   }
2293 
2294   /* Get runtime option */
2295   if (product->api_user) {
2296     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
2297     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2298     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2299   } else {
2300     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");CHKERRQ(ierr);
2301     ierr = PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2302     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2303   }
2304   if (flg) {
2305     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2306   }
2307 
2308   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2309   PetscFunctionReturn(0);
2310 }
2311 
2312 /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2313 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2314 {
2315   PetscErrorCode ierr;
2316   Mat_Product    *product = C->product;
2317   Mat            A=product->A,B=product->B;
2318   const char     *algTypes[3] = {"scalable","nonscalable","at*b"};
2319   PetscInt       nalg = 3;
2320   PetscInt       alg = 1; /* set default algorithm  */
2321   PetscBool      flg;
2322   MPI_Comm       comm;
2323 
2324   PetscFunctionBegin;
2325   /* Check matrix local sizes */
2326   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2327   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != B (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);
2328 
2329   /* Set default algorithm */
2330   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2331   if (flg) {
2332     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2333   }
2334 
2335   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2336   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2337     MatInfo     Ainfo,Binfo;
2338     PetscInt    nz_local;
2339     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2340 
2341     ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2342     ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2343     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2344 
2345     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2346     ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2347 
2348     if (alg_scalable) {
2349       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2350       ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2351       ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);CHKERRQ(ierr);
2352     }
2353   }
2354 
2355   /* Get runtime option */
2356   if (product->api_user) {
2357     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");CHKERRQ(ierr);
2358     ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2359     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2360   } else {
2361     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");CHKERRQ(ierr);
2362     ierr = PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2363     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2364   }
2365   if (flg) {
2366     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2367   }
2368 
2369   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2370   PetscFunctionReturn(0);
2371 }
2372 
2373 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2374 {
2375   PetscErrorCode ierr;
2376   Mat_Product    *product = C->product;
2377   Mat            A=product->A,P=product->B;
2378   MPI_Comm       comm;
2379   PetscBool      flg;
2380   PetscInt       alg=1; /* set default algorithm */
2381 #if !defined(PETSC_HAVE_HYPRE)
2382   const char     *algTypes[4] = {"scalable","nonscalable","allatonce","allatonce_merged"};
2383   PetscInt       nalg=4;
2384 #else
2385   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","hypre"};
2386   PetscInt       nalg=5;
2387 #endif
2388   PetscInt       pN=P->cmap->N;
2389 
2390   PetscFunctionBegin;
2391   /* Check matrix local sizes */
2392   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2393   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
2394   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
2395 
2396   /* Set "nonscalable" as default algorithm */
2397   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2398   if (flg) {
2399     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2400 
2401     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2402     if (pN > 100000) {
2403       MatInfo     Ainfo,Pinfo;
2404       PetscInt    nz_local;
2405       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2406 
2407       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2408       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
2409       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2410 
2411       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2412       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2413 
2414       if (alg_scalable) {
2415         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2416         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2417       }
2418     }
2419   }
2420 
2421   /* Get runtime option */
2422   if (product->api_user) {
2423     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
2424     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2425     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2426   } else {
2427     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");CHKERRQ(ierr);
2428     ierr = PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2429     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2430   }
2431   if (flg) {
2432     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2433   }
2434 
2435   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2436   PetscFunctionReturn(0);
2437 }
2438 
2439 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2440 {
2441   Mat_Product *product = C->product;
2442   Mat         A = product->A,R=product->B;
2443 
2444   PetscFunctionBegin;
2445   /* Check matrix local sizes */
2446   if (A->cmap->n != R->cmap->n || A->rmap->n != R->cmap->n) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A local (%D, %D), R local (%D,%D)",A->rmap->n,A->rmap->n,R->rmap->n,R->cmap->n);
2447 
2448   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2449   PetscFunctionReturn(0);
2450 }
2451 
2452 /*
2453  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2454 */
2455 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2456 {
2457   PetscErrorCode ierr;
2458   Mat_Product    *product = C->product;
2459   PetscBool      flg = PETSC_FALSE;
2460   PetscInt       alg = 1; /* default algorithm */
2461   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2462   PetscInt       nalg = 3;
2463 
2464   PetscFunctionBegin;
2465   /* Set default algorithm */
2466   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2467   if (flg) {
2468     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2469   }
2470 
2471   /* Get runtime option */
2472   if (product->api_user) {
2473     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");CHKERRQ(ierr);
2474     ierr = PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2475     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2476   } else {
2477     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");CHKERRQ(ierr);
2478     ierr = PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2479     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2480   }
2481   if (flg) {
2482     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2483   }
2484 
2485   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2486   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2487   PetscFunctionReturn(0);
2488 }
2489 
2490 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2491 {
2492   PetscErrorCode ierr;
2493   Mat_Product    *product = C->product;
2494 
2495   PetscFunctionBegin;
2496   switch (product->type) {
2497   case MATPRODUCT_AB:
2498     ierr = MatProductSetFromOptions_MPIAIJ_AB(C);CHKERRQ(ierr);
2499     break;
2500   case MATPRODUCT_AtB:
2501     ierr = MatProductSetFromOptions_MPIAIJ_AtB(C);CHKERRQ(ierr);
2502     break;
2503   case MATPRODUCT_PtAP:
2504     ierr = MatProductSetFromOptions_MPIAIJ_PtAP(C);CHKERRQ(ierr);
2505     break;
2506   case MATPRODUCT_RARt:
2507     ierr = MatProductSetFromOptions_MPIAIJ_RARt(C);CHKERRQ(ierr);
2508     break;
2509   case MATPRODUCT_ABC:
2510     ierr = MatProductSetFromOptions_MPIAIJ_ABC(C);CHKERRQ(ierr);
2511     break;
2512   default: SETERRQ1(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"MatProduct type %s is not supported for MPIAIJ and MPIAIJ matrices",MatProductTypes[product->type]);
2513   }
2514   PetscFunctionReturn(0);
2515 }
2516