xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision 6a98f8dc3f2c9149905a87dc2e9d0fedaf64e09a)
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-diagoanl 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-diagoanl 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 = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
563   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
564   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
565   PetscFunctionReturn(0);
566 }
567 
568 extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);
569 /*
570     Performs an efficient scatter on the rows of B needed by this process; this is
571     a modification of the VecScatterBegin_() routines.
572 
573     Input: Bbidx = 0: B = Bb
574                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
575 */
576 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
577 {
578   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
579   PetscErrorCode    ierr;
580   const PetscScalar *b;
581   PetscScalar       *rvalues;
582   VecScatter        ctx = aij->Mvctx;
583   const PetscInt    *sindices,*sstarts,*rstarts;
584   const PetscMPIInt *sprocs,*rprocs;
585   PetscInt          i,nsends,nrecvs,nrecvs2;
586   MPI_Request       *swaits,*rwaits;
587   MPI_Comm          comm;
588   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,imdex,nsends_mpi,nrecvs_mpi;
589   MPI_Status        status;
590   MPIAIJ_MPIDense   *contents;
591   PetscContainer    container;
592   Mat               workB;
593   MPI_Datatype      *stype,*rtype;
594 
595   PetscFunctionBegin;
596   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
597   ierr = PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);CHKERRQ(ierr);
598   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
599   ierr = PetscContainerGetPointer(container,(void**)&contents);CHKERRQ(ierr);
600 
601   ierr = VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);CHKERRQ(ierr);
602   ierr = VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);CHKERRQ(ierr);
603   ierr = PetscMPIIntCast(nsends,&nsends_mpi);CHKERRQ(ierr);
604   ierr = PetscMPIIntCast(nrecvs,&nrecvs_mpi);CHKERRQ(ierr);
605   if (Bbidx == 0) {
606     workB = *outworkB = contents->workB;
607   } else {
608     workB = *outworkB = contents->workB1;
609   }
610   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);
611   swaits  = contents->swaits;
612   rwaits  = contents->rwaits;
613 
614   ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr);
615   ierr = MatDenseGetArray(workB,&rvalues);CHKERRQ(ierr);
616 
617   /* Post recv, use MPI derived data type to save memory */
618   rtype = contents->rtype;
619   for (i=0; i<nrecvs; i++) {
620     ierr = MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
621   }
622 
623   stype = contents->stype;
624   for (i=0; i<nsends; i++) {
625     ierr = MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
626   }
627 
628   nrecvs2 = nrecvs;
629   while (nrecvs2) {
630     ierr = MPI_Waitany(nrecvs_mpi,rwaits,&imdex,&status);CHKERRQ(ierr);
631     nrecvs2--;
632   }
633   if (nsends) {ierr = MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);CHKERRQ(ierr);}
634 
635   ierr = VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);CHKERRQ(ierr);
636   ierr = VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);CHKERRQ(ierr);
637   ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr);
638   ierr = MatDenseRestoreArray(workB,&rvalues);CHKERRQ(ierr);
639   ierr = MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
640   ierr = MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
641   PetscFunctionReturn(0);
642 }
643 
644 /*
645   Compute Cb = A*Bb
646 */
647 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)
648 {
649   PetscErrorCode  ierr;
650   PetscInt        start1;
651   Mat             workB;
652   Mat_MPIAIJ      *aij = (Mat_MPIAIJ*)A->data;
653   Mat_MPIDense    *cbdense = (Mat_MPIDense*)Cb->data;
654 
655   PetscFunctionBegin;
656   /* Place barray to Bb */
657   start1 = start*Bb->rmap->n;
658   ierr = MatDensePlaceArray(Bb,barray+start1);CHKERRQ(ierr);
659 
660   /* get off processor parts of Bb needed to complete Cb=A*Bb */
661   ierr = MatMPIDenseScatter(A,Bb,Bbidx,C,&workB);CHKERRQ(ierr);
662   ierr = MatDenseResetArray(Bb);CHKERRQ(ierr);
663 
664   /* off-diagonal block of A times nonlocal rows of Bb */
665   /* Place carray to Cb */
666   start1 = start*Cb->rmap->n;
667   ierr = MatDensePlaceArray(Cb,carray+start1);CHKERRQ(ierr);
668   ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cbdense->A);CHKERRQ(ierr);
669   ierr = MatDenseResetArray(Cb);CHKERRQ(ierr);
670   PetscFunctionReturn(0);
671 }
672 
673 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
674 {
675   PetscErrorCode  ierr;
676   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
677   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
678   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
679   Mat             workB;
680   MPIAIJ_MPIDense *contents;
681   PetscContainer  container;
682   MPI_Comm        comm;
683   PetscInt        numBb;
684 
685   PetscFunctionBegin;
686   /* diagonal block of A times all local rows of B*/
687   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(aij->A,bdense->A,cdense->A);CHKERRQ(ierr);
688 
689   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
690   ierr = PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);CHKERRQ(ierr);
691   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
692   ierr = PetscContainerGetPointer(container,(void**)&contents);CHKERRQ(ierr);
693   numBb = contents->numBb;
694 
695   if (!numBb) {
696     /* get off processor parts of B needed to complete C=A*B */
697     ierr = MatMPIDenseScatter(A,B,0,C,&workB);CHKERRQ(ierr);
698 
699     /* off-diagonal block of A times nonlocal rows of B */
700     ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);CHKERRQ(ierr);
701 
702   } else {
703     const PetscScalar *barray;
704     PetscScalar       *carray;
705     Mat               Bb=contents->Bb,Cb=contents->Cb;
706     PetscInt          BbN=Bb->cmap->N,start,i;
707 
708     ierr = MatDenseGetArrayRead(B,&barray);CHKERRQ(ierr);
709     ierr = MatDenseGetArray(C,&carray);CHKERRQ(ierr);
710     for (i=0; i<numBb; i++) {
711       start = i*BbN;
712       ierr = MatMatMultNumeric_MPIAIJ_MPIDense_private(A,Bb,0,start,C,barray,carray,Cb);CHKERRQ(ierr);
713     }
714 
715     if (contents->Bb1) {
716       Bb = contents->Bb1; Cb = contents->Cb1;
717       start = i*BbN;
718       ierr = MatMatMultNumeric_MPIAIJ_MPIDense_private(A,Bb,1,start,C,barray,carray,Cb);CHKERRQ(ierr);
719     }
720     ierr = MatDenseRestoreArrayRead(B,&barray);CHKERRQ(ierr);
721     ierr = MatDenseRestoreArray(C,&carray);CHKERRQ(ierr);
722   }
723   PetscFunctionReturn(0);
724 }
725 
726 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
727 {
728   PetscErrorCode ierr;
729   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
730   Mat_SeqAIJ     *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
731   Mat_SeqAIJ     *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
732   PetscInt       *adi = ad->i,*adj,*aoi=ao->i,*aoj;
733   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
734   Mat_SeqAIJ     *p_loc,*p_oth;
735   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
736   PetscScalar    *pa_loc,*pa_oth,*pa,valtmp,*ca;
737   PetscInt       cm    = C->rmap->n,anz,pnz;
738   Mat_APMPI      *ptap = c->ap;
739   PetscScalar    *apa_sparse;
740   PetscInt       *api,*apj,*apJ,i,j,k,row;
741   PetscInt       cstart = C->cmap->rstart;
742   PetscInt       cdnz,conz,k0,k1,nextp;
743   MPI_Comm       comm;
744   PetscMPIInt    size;
745 
746   PetscFunctionBegin;
747   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
748   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
749 
750   if (!ptap->P_oth && size>1) {
751     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
752   }
753   apa_sparse = ptap->apa;
754 
755   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
756   /*-----------------------------------------------------*/
757   /* update numerical values of P_oth and P_loc */
758   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
759   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
760 
761   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
762   /*----------------------------------------------------------*/
763   /* get data from symbolic products */
764   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
765   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
766   if (size >1) {
767     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
768     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
769   } else {
770     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
771   }
772 
773   api = ptap->api;
774   apj = ptap->apj;
775   for (i=0; i<cm; i++) {
776     apJ = apj + api[i];
777 
778     /* diagonal portion of A */
779     anz = adi[i+1] - adi[i];
780     adj = ad->j + adi[i];
781     ada = ad->a + adi[i];
782     for (j=0; j<anz; j++) {
783       row = adj[j];
784       pnz = pi_loc[row+1] - pi_loc[row];
785       pj  = pj_loc + pi_loc[row];
786       pa  = pa_loc + pi_loc[row];
787       /* perform sparse axpy */
788       valtmp = ada[j];
789       nextp  = 0;
790       for (k=0; nextp<pnz; k++) {
791         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
792           apa_sparse[k] += valtmp*pa[nextp++];
793         }
794       }
795       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
796     }
797 
798     /* off-diagonal portion of A */
799     anz = aoi[i+1] - aoi[i];
800     aoj = ao->j + aoi[i];
801     aoa = ao->a + aoi[i];
802     for (j=0; j<anz; j++) {
803       row = aoj[j];
804       pnz = pi_oth[row+1] - pi_oth[row];
805       pj  = pj_oth + pi_oth[row];
806       pa  = pa_oth + pi_oth[row];
807       /* perform sparse axpy */
808       valtmp = aoa[j];
809       nextp  = 0;
810       for (k=0; nextp<pnz; k++) {
811         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
812           apa_sparse[k] += valtmp*pa[nextp++];
813         }
814       }
815       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
816     }
817 
818     /* set values in C */
819     cdnz = cd->i[i+1] - cd->i[i];
820     conz = co->i[i+1] - co->i[i];
821 
822     /* 1st off-diagoanl part of C */
823     ca = coa + co->i[i];
824     k  = 0;
825     for (k0=0; k0<conz; k0++) {
826       if (apJ[k] >= cstart) break;
827       ca[k0]        = apa_sparse[k];
828       apa_sparse[k] = 0.0;
829       k++;
830     }
831 
832     /* diagonal part of C */
833     ca = cda + cd->i[i];
834     for (k1=0; k1<cdnz; k1++) {
835       ca[k1]        = apa_sparse[k];
836       apa_sparse[k] = 0.0;
837       k++;
838     }
839 
840     /* 2nd off-diagoanl part of C */
841     ca = coa + co->i[i];
842     for (; k0<conz; k0++) {
843       ca[k0]        = apa_sparse[k];
844       apa_sparse[k] = 0.0;
845       k++;
846     }
847   }
848   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
849   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
850 
851   if (ptap->freestruct) {
852     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
853   }
854   PetscFunctionReturn(0);
855 }
856 
857 /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
858 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
859 {
860   PetscErrorCode     ierr;
861   MPI_Comm           comm;
862   PetscMPIInt        size;
863   Mat_APMPI          *ptap;
864   PetscFreeSpaceList free_space = NULL,current_space=NULL;
865   Mat_MPIAIJ         *a         = (Mat_MPIAIJ*)A->data,*c;
866   Mat_SeqAIJ         *ad        = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
867   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
868   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
869   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
870   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
871   PetscReal          afill;
872   MatType            mtype;
873 
874   PetscFunctionBegin;
875   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
876   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
877 
878   /* create struct Mat_APMPI and attached it to C later */
879   ierr = PetscNew(&ptap);CHKERRQ(ierr);
880 
881   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
882   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
883 
884   /* get P_loc by taking all local rows of P */
885   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
886 
887   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
888   pi_loc = p_loc->i; pj_loc = p_loc->j;
889   if (size > 1) {
890     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
891     pi_oth = p_oth->i; pj_oth = p_oth->j;
892   } else {
893     p_oth  = NULL;
894     pi_oth = NULL; pj_oth = NULL;
895   }
896 
897   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
898   /*-------------------------------------------------------------------*/
899   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
900   ptap->api = api;
901   api[0]    = 0;
902 
903   ierr = PetscLLCondensedCreate_Scalable(lsize,&lnk);CHKERRQ(ierr);
904 
905   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
906   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
907   current_space = free_space;
908   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
909   for (i=0; i<am; i++) {
910     /* diagonal portion of A */
911     nzi = adi[i+1] - adi[i];
912     for (j=0; j<nzi; j++) {
913       row  = *adj++;
914       pnz  = pi_loc[row+1] - pi_loc[row];
915       Jptr = pj_loc + pi_loc[row];
916       /* Expand list if it is not long enough */
917       if (pnz+apnz_max > lsize) {
918         lsize = pnz+apnz_max;
919         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
920       }
921       /* add non-zero cols of P into the sorted linked list lnk */
922       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
923       apnz     = *lnk; /* The first element in the list is the number of items in the list */
924       api[i+1] = api[i] + apnz;
925       if (apnz > apnz_max) apnz_max = apnz;
926     }
927     /* off-diagonal portion of A */
928     nzi = aoi[i+1] - aoi[i];
929     for (j=0; j<nzi; j++) {
930       row  = *aoj++;
931       pnz  = pi_oth[row+1] - pi_oth[row];
932       Jptr = pj_oth + pi_oth[row];
933       /* Expand list if it is not long enough */
934       if (pnz+apnz_max > lsize) {
935         lsize = pnz + apnz_max;
936         ierr = PetscLLCondensedExpand_Scalable(lsize, &lnk);CHKERRQ(ierr);
937       }
938       /* add non-zero cols of P into the sorted linked list lnk */
939       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
940       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
941       api[i+1] = api[i] + apnz;
942       if (apnz > apnz_max) apnz_max = apnz;
943     }
944     apnz     = *lnk;
945     api[i+1] = api[i] + apnz;
946     if (apnz > apnz_max) apnz_max = apnz;
947 
948     /* if free space is not available, double the total space in the list */
949     if (current_space->local_remaining<apnz) {
950       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
951       nspacedouble++;
952     }
953 
954     /* Copy data into free space, then initialize lnk */
955     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
956     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
957 
958     current_space->array           += apnz;
959     current_space->local_used      += apnz;
960     current_space->local_remaining -= apnz;
961   }
962 
963   /* Allocate space for apj, initialize apj, and */
964   /* destroy list of free space and other temporary array(s) */
965   ierr = PetscMalloc1(api[am]+1,&ptap->apj);CHKERRQ(ierr);
966   apj  = ptap->apj;
967   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
968   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
969 
970   /* create and assemble symbolic parallel matrix C */
971   /*----------------------------------------------------*/
972   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
973   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
974   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
975   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
976   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
977 
978   /* malloc apa for assembly C */
979   ierr = PetscCalloc1(apnz_max,&ptap->apa);CHKERRQ(ierr);
980 
981   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
982   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
983   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
984   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
985 
986   ptap->destroy             = C->ops->destroy;
987   ptap->duplicate           = C->ops->duplicate;
988   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
989   C->ops->productnumeric = MatProductNumeric_AB;
990   C->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
991   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
992 
993   /* attach the supporting struct to C for reuse */
994   c     = (Mat_MPIAIJ*)C->data;
995   c->ap = ptap;
996 
997   /* set MatInfo */
998   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
999   if (afill < 1.0) afill = 1.0;
1000   C->info.mallocs           = nspacedouble;
1001   C->info.fill_ratio_given  = fill;
1002   C->info.fill_ratio_needed = afill;
1003 
1004 #if defined(PETSC_USE_INFO)
1005   if (api[am]) {
1006     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1007     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1008   } else {
1009     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1010   }
1011 #endif
1012   PetscFunctionReturn(0);
1013 }
1014 
1015 /* This function is needed for the seqMPI matrix-matrix multiplication.  */
1016 /* Three input arrays are merged to one output array. The size of the    */
1017 /* output array is also output. Duplicate entries only show up once.     */
1018 static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
1019                                PetscInt  size2, PetscInt *in2,
1020                                PetscInt  size3, PetscInt *in3,
1021                                PetscInt *size4, PetscInt *out)
1022 {
1023   int i = 0, j = 0, k = 0, l = 0;
1024 
1025   /* Traverse all three arrays */
1026   while (i<size1 && j<size2 && k<size3) {
1027     if (in1[i] < in2[j] && in1[i] < in3[k]) {
1028       out[l++] = in1[i++];
1029     }
1030     else if(in2[j] < in1[i] && in2[j] < in3[k]) {
1031       out[l++] = in2[j++];
1032     }
1033     else if(in3[k] < in1[i] && in3[k] < in2[j]) {
1034       out[l++] = in3[k++];
1035     }
1036     else if(in1[i] == in2[j] && in1[i] < in3[k]) {
1037       out[l++] = in1[i];
1038       i++, j++;
1039     }
1040     else if(in1[i] == in3[k] && in1[i] < in2[j]) {
1041       out[l++] = in1[i];
1042       i++, k++;
1043     }
1044     else if(in3[k] == in2[j] && in2[j] < in1[i])  {
1045       out[l++] = in2[j];
1046       k++, j++;
1047     }
1048     else if(in1[i] == in2[j] && in1[i] == in3[k]) {
1049       out[l++] = in1[i];
1050       i++, j++, k++;
1051     }
1052   }
1053 
1054   /* Traverse two remaining arrays */
1055   while (i<size1 && j<size2) {
1056     if (in1[i] < in2[j]) {
1057       out[l++] = in1[i++];
1058     }
1059     else if(in1[i] > in2[j]) {
1060       out[l++] = in2[j++];
1061     }
1062     else {
1063       out[l++] = in1[i];
1064       i++, j++;
1065     }
1066   }
1067 
1068   while (i<size1 && k<size3) {
1069     if (in1[i] < in3[k]) {
1070       out[l++] = in1[i++];
1071     }
1072     else if(in1[i] > in3[k]) {
1073       out[l++] = in3[k++];
1074     }
1075     else {
1076       out[l++] = in1[i];
1077       i++, k++;
1078     }
1079   }
1080 
1081   while (k<size3 && j<size2)  {
1082     if (in3[k] < in2[j]) {
1083       out[l++] = in3[k++];
1084     }
1085     else if(in3[k] > in2[j]) {
1086       out[l++] = in2[j++];
1087     }
1088     else {
1089       out[l++] = in3[k];
1090       k++, j++;
1091     }
1092   }
1093 
1094   /* Traverse one remaining array */
1095   while (i<size1) out[l++] = in1[i++];
1096   while (j<size2) out[l++] = in2[j++];
1097   while (k<size3) out[l++] = in3[k++];
1098 
1099   *size4 = l;
1100 }
1101 
1102 /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1103 /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1104 /* matrix-matrix multiplications.  */
1105 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1106 {
1107   PetscErrorCode     ierr;
1108   MPI_Comm           comm;
1109   PetscMPIInt        size;
1110   Mat_APMPI          *ptap;
1111   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
1112   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data;
1113   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
1114   Mat_MPIAIJ         *p        =(Mat_MPIAIJ*)P->data;
1115   Mat_MPIAIJ         *c;
1116   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
1117   PetscInt           adponz, adpdnz;
1118   PetscInt           *pi_loc,*dnz,*onz;
1119   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
1120   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1121                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1122   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1123   PetscBT            lnkbt;
1124   PetscReal          afill;
1125   PetscMPIInt        rank;
1126   Mat                adpd, aopoth;
1127   MatType            mtype;
1128   const char         *prefix;
1129 
1130   PetscFunctionBegin;
1131   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1132   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1133   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1134   ierr = MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend); CHKERRQ(ierr);
1135 
1136   /* create struct Mat_APMPI and attached it to C later */
1137   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1138 
1139   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1140   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1141 
1142   /* get P_loc by taking all local rows of P */
1143   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1144 
1145 
1146   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1147   pi_loc = p_loc->i;
1148 
1149   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1150   ierr      = PetscMalloc1(am+2,&api);CHKERRQ(ierr);
1151   ierr      = PetscMalloc1(am+2,&adpoi);CHKERRQ(ierr);
1152 
1153   adpoi[0]    = 0;
1154   ptap->api = api;
1155   api[0] = 0;
1156 
1157   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1158   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1159   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
1160 
1161   /* Symbolic calc of A_loc_diag * P_loc_diag */
1162   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1163   ierr = MatProductCreate(a->A,p->A,NULL,&adpd);CHKERRQ(ierr);
1164   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1165   ierr = MatSetOptionsPrefix(adpd,prefix);CHKERRQ(ierr);
1166   ierr = MatAppendOptionsPrefix(adpd,"inner_diag_");CHKERRQ(ierr);
1167 
1168   ierr = MatProductSetType(adpd,MATPRODUCT_AB);CHKERRQ(ierr);
1169   ierr = MatProductSetAlgorithm(adpd,"sorted");CHKERRQ(ierr);
1170   ierr = MatProductSetFill(adpd,fill);CHKERRQ(ierr);
1171   ierr = MatProductSetFromOptions(adpd);CHKERRQ(ierr);
1172   ierr = MatProductSymbolic(adpd);CHKERRQ(ierr);
1173 
1174   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1175   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1176   p_off = (Mat_SeqAIJ*)((p->B)->data);
1177   poff_i = p_off->i; poff_j = p_off->j;
1178 
1179   /* j_temp stores indices of a result row before they are added to the linked list */
1180   ierr = PetscMalloc1(pN+2,&j_temp);CHKERRQ(ierr);
1181 
1182 
1183   /* Symbolic calc of the A_diag * p_loc_off */
1184   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1185   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);CHKERRQ(ierr);
1186   current_space = free_space_diag;
1187 
1188   for (i=0; i<am; i++) {
1189     /* A_diag * P_loc_off */
1190     nzi = adi[i+1] - adi[i];
1191     for (j=0; j<nzi; j++) {
1192       row  = *adj++;
1193       pnz  = poff_i[row+1] - poff_i[row];
1194       Jptr = poff_j + poff_i[row];
1195       for(i1 = 0; i1 < pnz; i1++) {
1196         j_temp[i1] = p->garray[Jptr[i1]];
1197       }
1198       /* add non-zero cols of P into the sorted linked list lnk */
1199       ierr = PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);CHKERRQ(ierr);
1200     }
1201 
1202     adponz     = lnk[0];
1203     adpoi[i+1] = adpoi[i] + adponz;
1204 
1205     /* if free space is not available, double the total space in the list */
1206     if (current_space->local_remaining<adponz) {
1207       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1208       nspacedouble++;
1209     }
1210 
1211     /* Copy data into free space, then initialize lnk */
1212     ierr = PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1213 
1214     current_space->array           += adponz;
1215     current_space->local_used      += adponz;
1216     current_space->local_remaining -= adponz;
1217   }
1218 
1219   /* Symbolic calc of A_off * P_oth */
1220   ierr = MatSetOptionsPrefix(a->B,prefix);CHKERRQ(ierr);
1221   ierr = MatAppendOptionsPrefix(a->B,"inner_offdiag_");CHKERRQ(ierr);
1222   ierr = MatCreate(PETSC_COMM_SELF,&aopoth);CHKERRQ(ierr);
1223   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);CHKERRQ(ierr);
1224   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1225   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;
1226 
1227   /* Allocate space for apj, adpj, aopj, ... */
1228   /* destroy lists of free space and other temporary array(s) */
1229 
1230   ierr = PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);CHKERRQ(ierr);
1231   ierr = PetscMalloc1(adpoi[am]+2, &adpoj);CHKERRQ(ierr);
1232 
1233   /* Copy from linked list to j-array */
1234   ierr = PetscFreeSpaceContiguous(&free_space_diag,adpoj);CHKERRQ(ierr);
1235   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1236 
1237   adpoJ = adpoj;
1238   adpdJ = adpdj;
1239   aopJ = aopothj;
1240   apj  = ptap->apj;
1241   apJ = apj; /* still empty */
1242 
1243   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1244   /* A_diag * P_loc_diag to get A*P */
1245   for (i = 0; i < am; i++) {
1246     aopnz  =  aopothi[i+1] -  aopothi[i];
1247     adponz = adpoi[i+1] - adpoi[i];
1248     adpdnz = adpdi[i+1] - adpdi[i];
1249 
1250     /* Correct indices from A_diag*P_diag */
1251     for(i1 = 0; i1 < adpdnz; i1++) {
1252       adpdJ[i1] += p_colstart;
1253     }
1254     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1255     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1256     ierr = MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz); CHKERRQ(ierr);
1257 
1258     aopJ += aopnz;
1259     adpoJ += adponz;
1260     adpdJ += adpdnz;
1261     apJ += apnz;
1262     api[i+1] = api[i] + apnz;
1263   }
1264 
1265   /* malloc apa to store dense row A[i,:]*P */
1266   ierr = PetscCalloc1(pN+2,&ptap->apa);CHKERRQ(ierr);
1267 
1268   /* create and assemble symbolic parallel matrix C */
1269   ierr = MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1270   ierr = MatSetBlockSizesFromMats(C,A,P);CHKERRQ(ierr);
1271   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1272   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1273   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1274 
1275 
1276   ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);CHKERRQ(ierr);
1277   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1278   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1279   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1280 
1281 
1282   ptap->destroy        = C->ops->destroy;
1283   ptap->duplicate      = C->ops->duplicate;
1284   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1285   C->ops->productnumeric = MatProductNumeric_AB;
1286   C->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
1287 
1288   /* attach the supporting struct to C for reuse */
1289   c       = (Mat_MPIAIJ*)C->data;
1290   c->ap = ptap;
1291 
1292   /* set MatInfo */
1293   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1294   if (afill < 1.0) afill = 1.0;
1295   C->info.mallocs           = nspacedouble;
1296   C->info.fill_ratio_given  = fill;
1297   C->info.fill_ratio_needed = afill;
1298 
1299 #if defined(PETSC_USE_INFO)
1300   if (api[am]) {
1301     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1302     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1303   } else {
1304     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1305   }
1306 #endif
1307 
1308   ierr = MatDestroy(&aopoth);CHKERRQ(ierr);
1309   ierr = MatDestroy(&adpd);CHKERRQ(ierr);
1310   ierr = PetscFree(j_temp);CHKERRQ(ierr);
1311   ierr = PetscFree(adpoj);CHKERRQ(ierr);
1312   ierr = PetscFree(adpoi);CHKERRQ(ierr);
1313   PetscFunctionReturn(0);
1314 }
1315 
1316 /*-------------------------------------------------------------------------*/
1317 /* This routine only works when scall=MAT_REUSE_MATRIX! */
1318 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1319 {
1320   PetscErrorCode ierr;
1321   Mat_MPIAIJ     *c=(Mat_MPIAIJ*)C->data;
1322   Mat_APMPI      *ptap= c->ap;
1323   Mat            Pt;
1324 
1325   PetscFunctionBegin;
1326   if (!ptap->Pt) {
1327     MPI_Comm comm;
1328     ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1329     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
1330   }
1331 
1332   Pt = ptap->Pt;
1333   ierr = MatTranspose(P,MAT_REUSE_MATRIX,&Pt);CHKERRQ(ierr);
1334   ierr = MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);CHKERRQ(ierr);
1335 
1336   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
1337   if (ptap->freestruct) {
1338     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
1339   }
1340   PetscFunctionReturn(0);
1341 }
1342 
1343 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1344 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1345 {
1346   PetscErrorCode      ierr;
1347   Mat_APMPI           *ptap;
1348   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*c;
1349   MPI_Comm            comm;
1350   PetscMPIInt         size,rank;
1351   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1352   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1353   PetscInt            *lnk,i,k,nsend;
1354   PetscBT             lnkbt;
1355   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
1356   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1357   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1358   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1359   MPI_Request         *swaits,*rwaits;
1360   MPI_Status          *sstatus,rstatus;
1361   PetscLayout         rowmap;
1362   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1363   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1364   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1365   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1366   PetscTable          ta;
1367   MatType             mtype;
1368   const char          *prefix;
1369 
1370   PetscFunctionBegin;
1371   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1372   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1373   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1374 
1375   /* create symbolic parallel matrix C */
1376   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
1377   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
1378 
1379   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1380 
1381   /* create struct Mat_APMPI and attached it to C later */
1382   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1383   ptap->reuse = MAT_INITIAL_MATRIX;
1384 
1385   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1386   /* --------------------------------- */
1387   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1388   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1389 
1390   /* (1) compute symbolic A_loc */
1391   /* ---------------------------*/
1392   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1393 
1394   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1395   /* ------------------------------------ */
1396   ierr = MatGetOptionsPrefix(A,&prefix);CHKERRQ(ierr);
1397   ierr = MatSetOptionsPrefix(ptap->Ro,prefix);CHKERRQ(ierr);
1398   ierr = MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");CHKERRQ(ierr);
1399   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_oth);CHKERRQ(ierr);
1400   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);CHKERRQ(ierr);
1401 
1402   /* (3) send coj of C_oth to other processors  */
1403   /* ------------------------------------------ */
1404   /* determine row ownership */
1405   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
1406   rowmap->n  = pn;
1407   rowmap->bs = 1;
1408   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
1409   owners = rowmap->range;
1410 
1411   /* determine the number of messages to send, their lengths */
1412   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
1413   ierr = PetscArrayzero(len_s,size);CHKERRQ(ierr);
1414   ierr = PetscArrayzero(len_si,size);CHKERRQ(ierr);
1415 
1416   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1417   coi   = c_oth->i; coj = c_oth->j;
1418   con   = ptap->C_oth->rmap->n;
1419   proc  = 0;
1420   for (i=0; i<con; i++) {
1421     while (prmap[i] >= owners[proc+1]) proc++;
1422     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1423     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1424   }
1425 
1426   len          = 0; /* max length of buf_si[], see (4) */
1427   owners_co[0] = 0;
1428   nsend        = 0;
1429   for (proc=0; proc<size; proc++) {
1430     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1431     if (len_s[proc]) {
1432       nsend++;
1433       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1434       len         += len_si[proc];
1435     }
1436   }
1437 
1438   /* determine the number and length of messages to receive for coi and coj  */
1439   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
1440   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
1441 
1442   /* post the Irecv and Isend of coj */
1443   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1444   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1445   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
1446   for (proc=0, k=0; proc<size; proc++) {
1447     if (!len_s[proc]) continue;
1448     i    = owners_co[proc];
1449     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
1450     k++;
1451   }
1452 
1453   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1454   /* ---------------------------------------- */
1455   ierr = MatSetOptionsPrefix(ptap->Rd,prefix);CHKERRQ(ierr);
1456   ierr = MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");CHKERRQ(ierr);
1457   ierr = MatCreate(PETSC_COMM_SELF,&ptap->C_loc);CHKERRQ(ierr);
1458   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);CHKERRQ(ierr);
1459   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
1460 
1461   /* receives coj are complete */
1462   for (i=0; i<nrecv; i++) {
1463     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1464   }
1465   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1466   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
1467 
1468   /* add received column indices into ta to update Crmax */
1469   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;
1470 
1471   /* create and initialize a linked list */
1472   ierr = PetscTableCreate(an,aN,&ta);CHKERRQ(ierr); /* for compute Crmax */
1473   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);
1474 
1475   for (k=0; k<nrecv; k++) {/* k-th received message */
1476     Jptr = buf_rj[k];
1477     for (j=0; j<len_r[k]; j++) {
1478       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
1479     }
1480   }
1481   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
1482   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
1483 
1484   /* (4) send and recv coi */
1485   /*-----------------------*/
1486   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1487   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1488   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1489   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1490   for (proc=0,k=0; proc<size; proc++) {
1491     if (!len_s[proc]) continue;
1492     /* form outgoing message for i-structure:
1493          buf_si[0]:                 nrows to be sent
1494                [1:nrows]:           row index (global)
1495                [nrows+1:2*nrows+1]: i-structure index
1496     */
1497     /*-------------------------------------------*/
1498     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1499     buf_si_i    = buf_si + nrows+1;
1500     buf_si[0]   = nrows;
1501     buf_si_i[0] = 0;
1502     nrows       = 0;
1503     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1504       nzi = coi[i+1] - coi[i];
1505       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1506       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1507       nrows++;
1508     }
1509     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
1510     k++;
1511     buf_si += len_si[proc];
1512   }
1513   for (i=0; i<nrecv; i++) {
1514     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1515   }
1516   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1517   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
1518 
1519   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
1520   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1521   ierr = PetscFree(swaits);CHKERRQ(ierr);
1522   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1523 
1524   /* (5) compute the local portion of C      */
1525   /* ------------------------------------------ */
1526   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1527   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
1528   current_space = free_space;
1529 
1530   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
1531   for (k=0; k<nrecv; k++) {
1532     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1533     nrows       = *buf_ri_k[k];
1534     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1535     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1536   }
1537 
1538   ierr = MatPreallocateInitialize(comm,pn,an,dnz,onz);CHKERRQ(ierr);
1539   ierr = PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);CHKERRQ(ierr);
1540   for (i=0; i<pn; i++) {
1541     /* add C_loc into C */
1542     nzi  = c_loc->i[i+1] - c_loc->i[i];
1543     Jptr = c_loc->j + c_loc->i[i];
1544     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1545 
1546     /* add received col data into lnk */
1547     for (k=0; k<nrecv; k++) { /* k-th received message */
1548       if (i == *nextrow[k]) { /* i-th row */
1549         nzi  = *(nextci[k]+1) - *nextci[k];
1550         Jptr = buf_rj[k] + *nextci[k];
1551         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1552         nextrow[k]++; nextci[k]++;
1553       }
1554     }
1555     nzi = lnk[0];
1556 
1557     /* copy data into free space, then initialize lnk */
1558     ierr = PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1559     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
1560   }
1561   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1562   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1563   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
1564 
1565   /* local sizes and preallocation */
1566   ierr = MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1567   if (P->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);CHKERRQ(ierr);}
1568   if (A->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);CHKERRQ(ierr);}
1569   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
1570   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1571 
1572   /* members in merge */
1573   ierr = PetscFree(id_r);CHKERRQ(ierr);
1574   ierr = PetscFree(len_r);CHKERRQ(ierr);
1575   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
1576   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
1577   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
1578   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
1579   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
1580 
1581   /* attach the supporting struct to C for reuse */
1582   c = (Mat_MPIAIJ*)C->data;
1583   c->ap         = ptap;
1584   ptap->destroy = C->ops->destroy;
1585 
1586   /* C is not ready for use - assembly will be done by MatPtAPNumeric() */
1587   C->assembled        = PETSC_FALSE;
1588   C->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
1589   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
1590   PetscFunctionReturn(0);
1591 }
1592 
1593 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1594 {
1595   PetscErrorCode    ierr;
1596   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1597   Mat_SeqAIJ        *c_seq;
1598   Mat_APMPI         *ptap = c->ap;
1599   Mat               A_loc,C_loc,C_oth;
1600   PetscInt          i,rstart,rend,cm,ncols,row;
1601   const PetscInt    *cols;
1602   const PetscScalar *vals;
1603 
1604   PetscFunctionBegin;
1605   if (!ptap->A_loc) {
1606     MPI_Comm comm;
1607     ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1608     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
1609   }
1610 
1611   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1612 
1613   if (ptap->reuse == MAT_REUSE_MATRIX) {
1614     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1615     /* 1) get R = Pd^T, Ro = Po^T */
1616     /*----------------------------*/
1617     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1618     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1619 
1620     /* 2) compute numeric A_loc */
1621     /*--------------------------*/
1622     ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);CHKERRQ(ierr);
1623   }
1624 
1625   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1626   A_loc = ptap->A_loc;
1627   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);CHKERRQ(ierr);
1628   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);CHKERRQ(ierr);
1629   C_loc = ptap->C_loc;
1630   C_oth = ptap->C_oth;
1631 
1632   /* add C_loc and Co to to C */
1633   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1634 
1635   /* C_loc -> C */
1636   cm    = C_loc->rmap->N;
1637   c_seq = (Mat_SeqAIJ*)C_loc->data;
1638   cols = c_seq->j;
1639   vals = c_seq->a;
1640   for (i=0; i<cm; i++) {
1641     ncols = c_seq->i[i+1] - c_seq->i[i];
1642     row = rstart + i;
1643     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1644     cols += ncols; vals += ncols;
1645   }
1646 
1647   /* Co -> C, off-processor part */
1648   cm    = C_oth->rmap->N;
1649   c_seq = (Mat_SeqAIJ*)C_oth->data;
1650   cols  = c_seq->j;
1651   vals  = c_seq->a;
1652   for (i=0; i<cm; i++) {
1653     ncols = c_seq->i[i+1] - c_seq->i[i];
1654     row = p->garray[i];
1655     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1656     cols += ncols; vals += ncols;
1657   }
1658   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1659   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1660 
1661   ptap->reuse = MAT_REUSE_MATRIX;
1662 
1663   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
1664   if (ptap->freestruct) {
1665     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
1666   }
1667   PetscFunctionReturn(0);
1668 }
1669 
1670 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1671 {
1672   PetscErrorCode      ierr;
1673   Mat_Merge_SeqsToMPI *merge;
1674   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1675   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1676   Mat_APMPI           *ptap;
1677   PetscInt            *adj;
1678   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1679   MatScalar           *ada,*ca,valtmp;
1680   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1681   MPI_Comm            comm;
1682   PetscMPIInt         size,rank,taga,*len_s;
1683   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1684   PetscInt            **buf_ri,**buf_rj;
1685   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1686   MPI_Request         *s_waits,*r_waits;
1687   MPI_Status          *status;
1688   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1689   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1690   Mat                 A_loc;
1691   Mat_SeqAIJ          *a_loc;
1692 
1693   PetscFunctionBegin;
1694   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1695   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1696   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1697 
1698   ptap  = c->ap;
1699   if (!ptap->A_loc) SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
1700   merge = ptap->merge;
1701 
1702   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1703   /*------------------------------------------*/
1704   /* get data from symbolic products */
1705   coi    = merge->coi; coj = merge->coj;
1706   ierr   = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
1707   bi     = merge->bi; bj = merge->bj;
1708   owners = merge->rowmap->range;
1709   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);
1710 
1711   /* get A_loc by taking all local rows of A */
1712   A_loc = ptap->A_loc;
1713   ierr  = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr);
1714   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1715   ai    = a_loc->i;
1716   aj    = a_loc->j;
1717 
1718   for (i=0; i<am; i++) {
1719     anz = ai[i+1] - ai[i];
1720     adj = aj + ai[i];
1721     ada = a_loc->a + ai[i];
1722 
1723     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1724     /*-------------------------------------------------------------*/
1725     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1726     pnz = po->i[i+1] - po->i[i];
1727     poJ = po->j + po->i[i];
1728     pA  = po->a + po->i[i];
1729     for (j=0; j<pnz; j++) {
1730       row = poJ[j];
1731       cj  = coj + coi[row];
1732       ca  = coa + coi[row];
1733       /* perform sparse axpy */
1734       nexta  = 0;
1735       valtmp = pA[j];
1736       for (k=0; nexta<anz; k++) {
1737         if (cj[k] == adj[nexta]) {
1738           ca[k] += valtmp*ada[nexta];
1739           nexta++;
1740         }
1741       }
1742       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1743     }
1744 
1745     /* put the value into Cd (diagonal part) */
1746     pnz = pd->i[i+1] - pd->i[i];
1747     pdJ = pd->j + pd->i[i];
1748     pA  = pd->a + pd->i[i];
1749     for (j=0; j<pnz; j++) {
1750       row = pdJ[j];
1751       cj  = bj + bi[row];
1752       ca  = ba + bi[row];
1753       /* perform sparse axpy */
1754       nexta  = 0;
1755       valtmp = pA[j];
1756       for (k=0; nexta<anz; k++) {
1757         if (cj[k] == adj[nexta]) {
1758           ca[k] += valtmp*ada[nexta];
1759           nexta++;
1760         }
1761       }
1762       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1763     }
1764   }
1765 
1766   /* 3) send and recv matrix values coa */
1767   /*------------------------------------*/
1768   buf_ri = merge->buf_ri;
1769   buf_rj = merge->buf_rj;
1770   len_s  = merge->len_s;
1771   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1772   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1773 
1774   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
1775   for (proc=0,k=0; proc<size; proc++) {
1776     if (!len_s[proc]) continue;
1777     i    = merge->owners_co[proc];
1778     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
1779     k++;
1780   }
1781   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
1782   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
1783 
1784   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1785   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1786   ierr = PetscFree(coa);CHKERRQ(ierr);
1787 
1788   /* 4) insert local Cseq and received values into Cmpi */
1789   /*----------------------------------------------------*/
1790   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1791   for (k=0; k<merge->nrecv; k++) {
1792     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1793     nrows       = *(buf_ri_k[k]);
1794     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1795     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1796   }
1797 
1798   for (i=0; i<cm; i++) {
1799     row  = owners[rank] + i; /* global row index of C_seq */
1800     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1801     ba_i = ba + bi[i];
1802     bnz  = bi[i+1] - bi[i];
1803     /* add received vals into ba */
1804     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1805       /* i-th row */
1806       if (i == *nextrow[k]) {
1807         cnz    = *(nextci[k]+1) - *nextci[k];
1808         cj     = buf_rj[k] + *(nextci[k]);
1809         ca     = abuf_r[k] + *(nextci[k]);
1810         nextcj = 0;
1811         for (j=0; nextcj<cnz; j++) {
1812           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1813             ba_i[j] += ca[nextcj++];
1814           }
1815         }
1816         nextrow[k]++; nextci[k]++;
1817         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1818       }
1819     }
1820     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1821   }
1822   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1823   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1824 
1825   ierr = PetscFree(ba);CHKERRQ(ierr);
1826   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1827   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1828   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1829 
1830   if (ptap->freestruct) {
1831     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
1832   }
1833   PetscFunctionReturn(0);
1834 }
1835 
1836 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1837 {
1838   PetscErrorCode      ierr;
1839   Mat                 A_loc,POt,PDt;
1840   Mat_APMPI           *ptap;
1841   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1842   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data,*c;
1843   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1844   PetscInt            nnz;
1845   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1846   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1847   MPI_Comm            comm;
1848   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1849   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1850   PetscInt            len,proc,*dnz,*onz,*owners;
1851   PetscInt            nzi,*bi,*bj;
1852   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1853   MPI_Request         *swaits,*rwaits;
1854   MPI_Status          *sstatus,rstatus;
1855   Mat_Merge_SeqsToMPI *merge;
1856   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1857   PetscReal           afill  =1.0,afill_tmp;
1858   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1859   Mat_SeqAIJ          *a_loc,*pdt,*pot;
1860   PetscTable          ta;
1861   MatType             mtype;
1862 
1863   PetscFunctionBegin;
1864   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1865   /* check if matrix local sizes are compatible */
1866   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);
1867 
1868   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1869   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1870 
1871   /* create struct Mat_APMPI and attached it to C later */
1872   ierr = PetscNew(&ptap);CHKERRQ(ierr);
1873 
1874   /* get A_loc by taking all local rows of A */
1875   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr);
1876 
1877   ptap->A_loc = A_loc;
1878   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1879   ai          = a_loc->i;
1880   aj          = a_loc->j;
1881 
1882   /* determine symbolic Co=(p->B)^T*A - send to others */
1883   /*----------------------------------------------------*/
1884   ierr = MatTransposeSymbolic_SeqAIJ(p->A,&PDt);CHKERRQ(ierr);
1885   pdt  = (Mat_SeqAIJ*)PDt->data;
1886   pdti = pdt->i; pdtj = pdt->j;
1887 
1888   ierr = MatTransposeSymbolic_SeqAIJ(p->B,&POt);CHKERRQ(ierr);
1889   pot  = (Mat_SeqAIJ*)POt->data;
1890   poti = pot->i; potj = pot->j;
1891 
1892   /* then, compute symbolic Co = (p->B)^T*A */
1893   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1894                          >= (num of nonzero rows of C_seq) - pn */
1895   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
1896   coi[0] = 0;
1897 
1898   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1899   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1900   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1901   current_space = free_space;
1902 
1903   /* create and initialize a linked list */
1904   ierr = PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);CHKERRQ(ierr);
1905   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1906   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
1907 
1908   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
1909 
1910   for (i=0; i<pon; i++) {
1911     pnz = poti[i+1] - poti[i];
1912     ptJ = potj + poti[i];
1913     for (j=0; j<pnz; j++) {
1914       row  = ptJ[j]; /* row of A_loc == col of Pot */
1915       anz  = ai[row+1] - ai[row];
1916       Jptr = aj + ai[row];
1917       /* add non-zero cols of AP into the sorted linked list lnk */
1918       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
1919     }
1920     nnz = lnk[0];
1921 
1922     /* If free space is not available, double the total space in the list */
1923     if (current_space->local_remaining<nnz) {
1924       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1925       nspacedouble++;
1926     }
1927 
1928     /* Copy data into free space, and zero out denserows */
1929     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
1930 
1931     current_space->array           += nnz;
1932     current_space->local_used      += nnz;
1933     current_space->local_remaining -= nnz;
1934 
1935     coi[i+1] = coi[i] + nnz;
1936   }
1937 
1938   ierr = PetscMalloc1(coi[pon]+1,&coj);CHKERRQ(ierr);
1939   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1940   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr); /* must destroy to get a new one for C */
1941 
1942   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1943   if (afill_tmp > afill) afill = afill_tmp;
1944 
1945   /* send j-array (coj) of Co to other processors */
1946   /*----------------------------------------------*/
1947   /* determine row ownership */
1948   ierr = PetscNew(&merge);CHKERRQ(ierr);
1949   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1950 
1951   merge->rowmap->n  = pn;
1952   merge->rowmap->bs = 1;
1953 
1954   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1955   owners = merge->rowmap->range;
1956 
1957   /* determine the number of messages to send, their lengths */
1958   ierr = PetscCalloc1(size,&len_si);CHKERRQ(ierr);
1959   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
1960 
1961   len_s        = merge->len_s;
1962   merge->nsend = 0;
1963 
1964   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
1965 
1966   proc = 0;
1967   for (i=0; i<pon; i++) {
1968     while (prmap[i] >= owners[proc+1]) proc++;
1969     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1970     len_s[proc] += coi[i+1] - coi[i];
1971   }
1972 
1973   len          = 0; /* max length of buf_si[] */
1974   owners_co[0] = 0;
1975   for (proc=0; proc<size; proc++) {
1976     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1977     if (len_si[proc]) {
1978       merge->nsend++;
1979       len_si[proc] = 2*(len_si[proc] + 1);
1980       len         += len_si[proc];
1981     }
1982   }
1983 
1984   /* determine the number and length of messages to receive for coi and coj  */
1985   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1986   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1987 
1988   /* post the Irecv and Isend of coj */
1989   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1990   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1991   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
1992   for (proc=0, k=0; proc<size; proc++) {
1993     if (!len_s[proc]) continue;
1994     i    = owners_co[proc];
1995     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
1996     k++;
1997   }
1998 
1999   /* receives and sends of coj are complete */
2000   ierr = PetscMalloc1(size,&sstatus);CHKERRQ(ierr);
2001   for (i=0; i<merge->nrecv; i++) {
2002     PetscMPIInt icompleted;
2003     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
2004   }
2005   ierr = PetscFree(rwaits);CHKERRQ(ierr);
2006   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
2007 
2008   /* add received column indices into table to update Armax */
2009   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
2010   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
2011     Jptr = buf_rj[k];
2012     for (j=0; j<merge->len_r[k]; j++) {
2013       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
2014     }
2015   }
2016   ierr = PetscTableGetCount(ta,&Armax);CHKERRQ(ierr);
2017   /* 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); */
2018 
2019   /* send and recv coi */
2020   /*-------------------*/
2021   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
2022   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
2023   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
2024   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
2025   for (proc=0,k=0; proc<size; proc++) {
2026     if (!len_s[proc]) continue;
2027     /* form outgoing message for i-structure:
2028          buf_si[0]:                 nrows to be sent
2029                [1:nrows]:           row index (global)
2030                [nrows+1:2*nrows+1]: i-structure index
2031     */
2032     /*-------------------------------------------*/
2033     nrows       = len_si[proc]/2 - 1;
2034     buf_si_i    = buf_si + nrows+1;
2035     buf_si[0]   = nrows;
2036     buf_si_i[0] = 0;
2037     nrows       = 0;
2038     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
2039       nzi               = coi[i+1] - coi[i];
2040       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
2041       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
2042       nrows++;
2043     }
2044     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
2045     k++;
2046     buf_si += len_si[proc];
2047   }
2048   i = merge->nrecv;
2049   while (i--) {
2050     PetscMPIInt icompleted;
2051     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
2052   }
2053   ierr = PetscFree(rwaits);CHKERRQ(ierr);
2054   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
2055   ierr = PetscFree(len_si);CHKERRQ(ierr);
2056   ierr = PetscFree(len_ri);CHKERRQ(ierr);
2057   ierr = PetscFree(swaits);CHKERRQ(ierr);
2058   ierr = PetscFree(sstatus);CHKERRQ(ierr);
2059   ierr = PetscFree(buf_s);CHKERRQ(ierr);
2060 
2061   /* compute the local portion of C (mpi mat) */
2062   /*------------------------------------------*/
2063   /* allocate bi array and free space for accumulating nonzero column info */
2064   ierr  = PetscMalloc1(pn+1,&bi);CHKERRQ(ierr);
2065   bi[0] = 0;
2066 
2067   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
2068   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
2069   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
2070   current_space = free_space;
2071 
2072   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
2073   for (k=0; k<merge->nrecv; k++) {
2074     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2075     nrows       = *buf_ri_k[k];
2076     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
2077     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recieved i-structure  */
2078   }
2079 
2080   ierr = PetscLLCondensedCreate_Scalable(Armax,&lnk);CHKERRQ(ierr);
2081   ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr);
2082   rmax = 0;
2083   for (i=0; i<pn; i++) {
2084     /* add pdt[i,:]*AP into lnk */
2085     pnz = pdti[i+1] - pdti[i];
2086     ptJ = pdtj + pdti[i];
2087     for (j=0; j<pnz; j++) {
2088       row  = ptJ[j];  /* row of AP == col of Pt */
2089       anz  = ai[row+1] - ai[row];
2090       Jptr = aj + ai[row];
2091       /* add non-zero cols of AP into the sorted linked list lnk */
2092       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
2093     }
2094 
2095     /* add received col data into lnk */
2096     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
2097       if (i == *nextrow[k]) { /* i-th row */
2098         nzi  = *(nextci[k]+1) - *nextci[k];
2099         Jptr = buf_rj[k] + *nextci[k];
2100         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
2101         nextrow[k]++; nextci[k]++;
2102       }
2103     }
2104     nnz = lnk[0];
2105 
2106     /* if free space is not available, make more free space */
2107     if (current_space->local_remaining<nnz) {
2108       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
2109       nspacedouble++;
2110     }
2111     /* copy data into free space, then initialize lnk */
2112     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
2113     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
2114 
2115     current_space->array           += nnz;
2116     current_space->local_used      += nnz;
2117     current_space->local_remaining -= nnz;
2118 
2119     bi[i+1] = bi[i] + nnz;
2120     if (nnz > rmax) rmax = nnz;
2121   }
2122   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
2123 
2124   ierr      = PetscMalloc1(bi[pn]+1,&bj);CHKERRQ(ierr);
2125   ierr      = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
2126   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2127   if (afill_tmp > afill) afill = afill_tmp;
2128   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
2129   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
2130 
2131   ierr = MatDestroy(&POt);CHKERRQ(ierr);
2132   ierr = MatDestroy(&PDt);CHKERRQ(ierr);
2133 
2134   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2135   /*-------------------------------------------------------------------------------*/
2136   ierr = MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2137   ierr = MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));CHKERRQ(ierr);
2138   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
2139   ierr = MatSetType(C,mtype);CHKERRQ(ierr);
2140   ierr = MatMPIAIJSetPreallocation(C,0,dnz,0,onz);CHKERRQ(ierr);
2141   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
2142   ierr = MatSetBlockSize(C,1);CHKERRQ(ierr);
2143   for (i=0; i<pn; i++) {
2144     row  = i + rstart;
2145     nnz  = bi[i+1] - bi[i];
2146     Jptr = bj + bi[i];
2147     ierr = MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);CHKERRQ(ierr);
2148   }
2149   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2150   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2151   merge->bi        = bi;
2152   merge->bj        = bj;
2153   merge->coi       = coi;
2154   merge->coj       = coj;
2155   merge->buf_ri    = buf_ri;
2156   merge->buf_rj    = buf_rj;
2157   merge->owners_co = owners_co;
2158 
2159   /* attach the supporting struct to C for reuse */
2160   c = (Mat_MPIAIJ*)C->data;
2161 
2162   c->ap       = ptap;
2163   ptap->api   = NULL;
2164   ptap->apj   = NULL;
2165   ptap->merge = merge;
2166   ptap->apa   = NULL;
2167   ptap->destroy   = C->ops->destroy;
2168   ptap->duplicate = C->ops->duplicate;
2169 
2170   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
2171   C->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
2172   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
2173 
2174 #if defined(PETSC_USE_INFO)
2175   if (bi[pn] != 0) {
2176     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
2177     ierr = PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
2178   } else {
2179     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
2180   }
2181 #endif
2182   PetscFunctionReturn(0);
2183 }
2184 
2185 /* ---------------------------------------------------------------- */
2186 static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2187 {
2188   PetscErrorCode ierr;
2189   Mat_Product    *product = C->product;
2190   Mat            A=product->A,B=product->B;
2191   PetscReal      fill=product->fill;
2192   PetscBool      flg;
2193 
2194   PetscFunctionBegin;
2195   /* scalable */
2196   ierr = PetscStrcmp(product->alg,"scalable",&flg);CHKERRQ(ierr);
2197   if (flg) {
2198     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
2199     goto next;
2200   }
2201 
2202   /* nonscalable */
2203   ierr = PetscStrcmp(product->alg,"nonscalable",&flg);CHKERRQ(ierr);
2204   if (flg) {
2205     ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);CHKERRQ(ierr);
2206     goto next;
2207   }
2208 
2209   /* matmatmult */
2210   ierr = PetscStrcmp(product->alg,"at*b",&flg);CHKERRQ(ierr);
2211   if (flg) {
2212     Mat         At;
2213     Mat_APMPI   *ptap;
2214     Mat_MPIAIJ  *c;
2215     ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
2216 
2217     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);CHKERRQ(ierr);
2218     c    = (Mat_MPIAIJ*)C->data;
2219     ptap = c->ap;
2220     if (ptap) {
2221       ptap->Pt = At;
2222       C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
2223     }
2224     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2225     goto next;
2226   }
2227 
2228   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");
2229 
2230 next:
2231   C->ops->productnumeric = MatProductNumeric_AtB;
2232 
2233   {
2234     Mat_MPIAIJ *c  = (Mat_MPIAIJ*)C->data;
2235     Mat_APMPI  *ap = c->ap;
2236     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatFreeIntermediateDataStructures","Mat");CHKERRQ(ierr);
2237     ap->freestruct = PETSC_FALSE;
2238     ierr = PetscOptionsBool("-mat_freeintermediatedatastructures","Free intermediate data structures", "MatFreeIntermediateDataStructures",ap->freestruct,&ap->freestruct, NULL);CHKERRQ(ierr);
2239     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2240   }
2241   PetscFunctionReturn(0);
2242 }
2243 
2244 /* ---------------------------------------------------------------- */
2245 /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2246 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2247 {
2248   PetscErrorCode ierr;
2249   Mat_Product    *product = C->product;
2250   Mat            A=product->A,B=product->B;
2251 #if defined(PETSC_HAVE_HYPRE)
2252   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","hypre"};
2253   PetscInt       nalg = 4;
2254 #else
2255   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2256   PetscInt       nalg = 3;
2257 #endif
2258   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2259   PetscBool      flg;
2260   MPI_Comm       comm;
2261 
2262   PetscFunctionBegin;
2263   /* Check matrix local sizes */
2264   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2265   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);
2266 
2267   /* Set "nonscalable" as default algorithm */
2268   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2269   if (flg) {
2270     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2271 
2272     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2273     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2274       MatInfo     Ainfo,Binfo;
2275       PetscInt    nz_local;
2276       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2277 
2278       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2279       ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2280       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2281 
2282       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2283       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2284 
2285       if (alg_scalable) {
2286         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2287         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2288         ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);CHKERRQ(ierr);
2289       }
2290     }
2291   }
2292 
2293   /* Get runtime option */
2294   if (product->api_user) {
2295     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
2296     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2297     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2298   } else {
2299     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");CHKERRQ(ierr);
2300     ierr = PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2301     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2302   }
2303   if (flg) {
2304     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2305   }
2306 
2307   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2308   PetscFunctionReturn(0);
2309 }
2310 
2311 /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2312 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2313 {
2314   PetscErrorCode ierr;
2315   Mat_Product    *product = C->product;
2316   Mat            A=product->A,B=product->B;
2317   const char     *algTypes[3] = {"scalable","nonscalable","at*b"};
2318   PetscInt       nalg = 3;
2319   PetscInt       alg = 1; /* set default algorithm  */
2320   PetscBool      flg;
2321   MPI_Comm       comm;
2322 
2323   PetscFunctionBegin;
2324   /* Check matrix local sizes */
2325   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2326   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);
2327 
2328   /* Set default algorithm */
2329   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2330   if (flg) {
2331     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2332   }
2333 
2334   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2335   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2336     MatInfo     Ainfo,Binfo;
2337     PetscInt    nz_local;
2338     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2339 
2340     ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2341     ierr = MatGetInfo(B,MAT_LOCAL,&Binfo);CHKERRQ(ierr);
2342     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);
2343 
2344     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2345     ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2346 
2347     if (alg_scalable) {
2348       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2349       ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2350       ierr = PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);CHKERRQ(ierr);
2351     }
2352   }
2353 
2354   /* Get runtime option */
2355   if (product->api_user) {
2356     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");CHKERRQ(ierr);
2357     ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2358     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2359   } else {
2360     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");CHKERRQ(ierr);
2361     ierr = PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2362     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2363   }
2364   if (flg) {
2365     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2366   }
2367 
2368   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2369   PetscFunctionReturn(0);
2370 }
2371 
2372 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2373 {
2374   PetscErrorCode ierr;
2375   Mat_Product    *product = C->product;
2376   Mat            A=product->A,P=product->B;
2377   MPI_Comm       comm;
2378   PetscBool      flg;
2379   PetscInt       alg=1; /* set default algorithm */
2380 #if !defined(PETSC_HAVE_HYPRE)
2381   const char     *algTypes[4] = {"scalable","nonscalable","allatonce","allatonce_merged"};
2382   PetscInt       nalg=4;
2383 #else
2384   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","hypre"};
2385   PetscInt       nalg=5;
2386 #endif
2387   PetscInt       pN=P->cmap->N;
2388 
2389   PetscFunctionBegin;
2390   /* Check matrix local sizes */
2391   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
2392   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);
2393   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);
2394 
2395   /* Set "nonscalable" as default algorithm */
2396   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2397   if (flg) {
2398     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2399 
2400     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2401     if (pN > 100000) {
2402       MatInfo     Ainfo,Pinfo;
2403       PetscInt    nz_local;
2404       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
2405 
2406       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
2407       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
2408       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
2409 
2410       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2411       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
2412 
2413       if (alg_scalable) {
2414         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2415         ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2416       }
2417     }
2418   }
2419 
2420   /* Get runtime option */
2421   if (product->api_user) {
2422     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
2423     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2424     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2425   } else {
2426     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");CHKERRQ(ierr);
2427     ierr = PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2428     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2429   }
2430   if (flg) {
2431     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2432   }
2433 
2434   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2435   PetscFunctionReturn(0);
2436 }
2437 
2438 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2439 {
2440   Mat_Product *product = C->product;
2441   Mat         A = product->A,R=product->B;
2442 
2443   PetscFunctionBegin;
2444   /* Check matrix local sizes */
2445   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);
2446 
2447   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2448   PetscFunctionReturn(0);
2449 }
2450 
2451 /*
2452  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2453 */
2454 static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2455 {
2456   PetscErrorCode ierr;
2457   Mat_Product    *product = C->product;
2458   PetscBool      flg = PETSC_FALSE;
2459   PetscInt       alg = 1; /* default algorithm */
2460   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2461   PetscInt       nalg = 3;
2462 
2463   PetscFunctionBegin;
2464   /* Set default algorithm */
2465   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2466   if (flg) {
2467     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2468   }
2469 
2470   /* Get runtime option */
2471   if (product->api_user) {
2472     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");CHKERRQ(ierr);
2473     ierr = PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2474     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2475   } else {
2476     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");CHKERRQ(ierr);
2477     ierr = PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2478     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2479   }
2480   if (flg) {
2481     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2482   }
2483 
2484   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2485   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2486   PetscFunctionReturn(0);
2487 }
2488 
2489 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2490 {
2491   PetscErrorCode ierr;
2492   Mat_Product    *product = C->product;
2493 
2494   PetscFunctionBegin;
2495   switch (product->type) {
2496   case MATPRODUCT_AB:
2497     ierr = MatProductSetFromOptions_MPIAIJ_AB(C);CHKERRQ(ierr);
2498     break;
2499   case MATPRODUCT_AtB:
2500     ierr = MatProductSetFromOptions_MPIAIJ_AtB(C);CHKERRQ(ierr);
2501     break;
2502   case MATPRODUCT_PtAP:
2503     ierr = MatProductSetFromOptions_MPIAIJ_PtAP(C);CHKERRQ(ierr);
2504     break;
2505   case MATPRODUCT_RARt:
2506     ierr = MatProductSetFromOptions_MPIAIJ_RARt(C);CHKERRQ(ierr);
2507     break;
2508   case MATPRODUCT_ABC:
2509     ierr = MatProductSetFromOptions_MPIAIJ_ABC(C);CHKERRQ(ierr);
2510     break;
2511   default: SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"MatProduct type is not supported");
2512   }
2513   PetscFunctionReturn(0);
2514 }
2515