xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision 1db2f0e57964f94f63a3f5cf6bb1e5befdb56f30)
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 /*
12 #define DEBUG_MATMATMULT
13  */
14 /*
15 #define DEBUG_MATTrMatMult
16  */
17 
18 #undef __FUNCT__
19 #define __FUNCT__ "MatMatMult_MPIAIJ_MPIAIJ"
20 PetscErrorCode MatMatMult_MPIAIJ_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill, Mat *C)
21 {
22   PetscErrorCode ierr;
23 
24   PetscFunctionBegin;
25   if (scall == MAT_INITIAL_MATRIX){
26     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
27     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
28     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
29   }
30   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
31   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
32   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
33   PetscFunctionReturn(0);
34 }
35 
36 #undef __FUNCT__
37 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatMultMPI"
38 PetscErrorCode PetscContainerDestroy_Mat_MatMatMultMPI(void *ptr)
39 {
40   PetscErrorCode       ierr;
41   Mat_MatMatMultMPI    *mult=(Mat_MatMatMultMPI*)ptr;
42 
43   PetscFunctionBegin;
44   ierr = ISDestroy(&mult->isrowa);CHKERRQ(ierr);
45   ierr = ISDestroy(&mult->isrowb);CHKERRQ(ierr);
46   ierr = ISDestroy(&mult->iscolb);CHKERRQ(ierr);
47   ierr = MatDestroy(&mult->C_seq);CHKERRQ(ierr);
48   ierr = MatDestroy(&mult->A_loc);CHKERRQ(ierr);
49   ierr = MatDestroy(&mult->B_seq);CHKERRQ(ierr);
50   ierr = PetscFree(mult);CHKERRQ(ierr);
51   PetscFunctionReturn(0);
52 }
53 
54 #undef __FUNCT__
55 #define __FUNCT__ "MatDestroy_MPIAIJ_MatMatMult"
56 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
57 {
58   PetscErrorCode ierr;
59   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
60   Mat_PtAPMPI    *ptap=a->ptap;
61 
62   PetscFunctionBegin;
63   ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr);
64   ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
65   ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
66   ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
67   ierr = PetscFree(ptap->api);CHKERRQ(ierr);
68   ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
69   ierr = PetscFree(ptap->apa);CHKERRQ(ierr);
70   ierr = ptap->destroy(A);CHKERRQ(ierr);
71   ierr = PetscFree(ptap);CHKERRQ(ierr);
72   PetscFunctionReturn(0);
73 }
74 
75 #undef __FUNCT__
76 #define __FUNCT__ "MatDestroy_MPIAIJ_MatMatMult_32"
77 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult_32(Mat A)
78 {
79   PetscErrorCode     ierr;
80   PetscContainer     container;
81   Mat_MatMatMultMPI  *mult=PETSC_NULL;
82 
83   PetscFunctionBegin;
84   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
85   if (!container) SETERRQ(((PetscObject)A)->comm,PETSC_ERR_PLIB,"Container does not exist");
86   ierr = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
87   A->ops->destroy   = mult->destroy;
88   A->ops->duplicate = mult->duplicate;
89   if (A->ops->destroy) {
90     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
91   }
92   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatMultMPI",0);CHKERRQ(ierr);
93   PetscFunctionReturn(0);
94 }
95 
96 #undef __FUNCT__
97 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatMatMult_32"
98 PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult_32(Mat A, MatDuplicateOption op, Mat *M)
99 {
100   PetscErrorCode     ierr;
101   Mat_MatMatMultMPI  *mult;
102   PetscContainer     container;
103 
104   PetscFunctionBegin;
105   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
106   if (!container) SETERRQ(((PetscObject)A)->comm,PETSC_ERR_PLIB,"Container does not exist");
107   ierr  = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
108   /* Note: the container is not duplicated, because it requires deep copying of
109      several large data sets (see PetscContainerDestroy_Mat_MatMatMultMPI()).
110      These data sets are only used for repeated calling of MatMatMultNumeric().
111      *M is unlikely being used in this way. Thus we create *M with pure mpiaij format */
112   ierr = (*mult->duplicate)(A,op,M);CHKERRQ(ierr);
113   (*M)->ops->destroy   = mult->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's container! */
114   (*M)->ops->duplicate = mult->duplicate; /* = MatDuplicate_MPIAIJ */
115   PetscFunctionReturn(0);
116 }
117 
118 #undef __FUNCT__
119 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatMatMult"
120 PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult(Mat A, MatDuplicateOption op, Mat *M)
121 {
122   PetscErrorCode     ierr;
123   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
124   Mat_PtAPMPI        *ptap=a->ptap;
125 
126   PetscFunctionBegin;
127   ierr = (*ptap->duplicate)(A,op,M);CHKERRQ(ierr);
128   (*M)->ops->destroy   = ptap->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's special structure! */
129   (*M)->ops->duplicate = ptap->duplicate; /* = MatDuplicate_MPIAIJ */
130   PetscFunctionReturn(0);
131 }
132 
133 #undef __FUNCT__
134 #define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIAIJ"
135 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
136 {
137   PetscErrorCode     ierr;
138   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
139   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
140   Mat_SeqAIJ         *cd=(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
141   PetscInt           *adi=ad->i,*adj,*aoi=ao->i,*aoj;
142   PetscScalar        *ada,*aoa,*cda=cd->a,*coa=co->a;
143   Mat_SeqAIJ         *p_loc,*p_oth;
144   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
145   PetscScalar        *pa_loc,*pa_oth,*pa,*apa,valtmp,*ca;
146   PetscInt           cm=C->rmap->n,anz,pnz;
147   Mat_PtAPMPI        *ptap=c->ptap;
148   PetscInt           *api,*apj,*apJ,i,j,k,row;
149   PetscInt           cstart=C->cmap->rstart;
150   PetscInt           cdnz,conz,k0,k1;
151 #if defined(DEBUG_MATMATMULT)
152   PetscMPIInt        rank=a->rank;
153 #endif
154 
155   PetscFunctionBegin;
156 #if defined(DEBUG_MATMATMULT)
157   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] call MatMatMultNumeric_MPIAIJ_MPIAIJ()...\n",rank);
158 #endif
159 
160   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
161   /*-----------------------------------------------------*/
162   /* update numerical values of P_oth and P_loc */
163   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
164   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
165 #if defined(DEBUG_MATMATMULT)
166   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] got P_oth and P_loc...\n",rank);
167 #endif
168 
169   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
170   /*----------------------------------------------------------*/
171   /* get data from symbolic products */
172   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
173   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
174   pi_loc=p_loc->i; pj_loc=p_loc->j; pa_loc=p_loc->a;
175   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
176 
177   /* get apa for storing dense row A[i,:]*P */
178   apa = ptap->apa;
179 
180   api = ptap->api;
181   apj = ptap->apj;
182   for (i=0; i<cm; i++) {
183     /* diagonal portion of A */
184     anz = adi[i+1] - adi[i];
185     adj = ad->j + adi[i];
186     ada = ad->a + adi[i];
187     for (j=0; j<anz; j++) {
188       row = adj[j];
189       pnz = pi_loc[row+1] - pi_loc[row];
190       pj  = pj_loc + pi_loc[row];
191       pa  = pa_loc + pi_loc[row];
192 
193       /* perform dense axpy */
194       valtmp = ada[j];
195       for (k=0; k<pnz; k++){
196         apa[pj[k]] += valtmp*pa[k];
197       }
198       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
199     }
200 
201     /* off-diagonal portion of A */
202     anz = aoi[i+1] - aoi[i];
203     aoj = ao->j + aoi[i];
204     aoa = ao->a + aoi[i];
205     for (j=0; j<anz; j++) {
206       row = aoj[j];
207       pnz = pi_oth[row+1] - pi_oth[row];
208       pj  = pj_oth + pi_oth[row];
209       pa  = pa_oth + pi_oth[row];
210 
211       /* perform dense axpy */
212       valtmp = aoa[j];
213       for (k=0; k<pnz; k++){
214         apa[pj[k]] += valtmp*pa[k];
215       }
216       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
217     }
218 
219     /* set values in C */
220     apJ = apj + api[i];
221     cdnz = cd->i[i+1] - cd->i[i];
222     conz = co->i[i+1] - co->i[i];
223 
224     /* 1st off-diagoanl part of C */
225     ca = coa + co->i[i];
226     k  = 0;
227     for (k0=0; k0<conz; k0++){
228       if (apJ[k] >= cstart) break;
229       ca[k0]      = apa[apJ[k]];
230       apa[apJ[k]] = 0.0;
231       k++;
232     }
233 
234     /* diagonal part of C */
235     ca = cda + cd->i[i];
236     for (k1=0; k1<cdnz; k1++){
237       ca[k1]      = apa[apJ[k]];
238       apa[apJ[k]] = 0.0;
239       k++;
240     }
241 
242     /* 2nd off-diagoanl part of C */
243     ca = coa + co->i[i];
244     for (; k0<conz; k0++){
245       ca[k0]      = apa[apJ[k]];
246       apa[apJ[k]] = 0.0;
247       k++;
248     }
249   }
250   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
251   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
252   PetscFunctionReturn(0);
253 }
254 
255 #undef __FUNCT__
256 #define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIAIJ"
257 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
258 {
259   PetscErrorCode       ierr;
260   MPI_Comm             comm=((PetscObject)A)->comm;
261   Mat                  Cmpi;
262   Mat_PtAPMPI          *ptap;
263   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
264   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*c;
265   Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
266   PetscInt             *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
267   PetscInt             *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
268   PetscInt             *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
269   PetscInt             am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
270   PetscBT              lnkbt;
271   PetscScalar          *apa;
272   PetscReal            afill;
273   PetscBool            scalable=PETSC_FALSE;
274   PetscInt             nlnk_max,armax,prmax;
275 #if defined(DEBUG_MATMATMULT)
276   PetscMPIInt          rank=a->rank;
277 #endif
278 
279   PetscFunctionBegin;
280   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend){
281     SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
282   }
283 
284   ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
285 
286     ierr = PetscOptionsBool("-matmatmult_32","Use a scalable but slower C=A*B","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
287     if (scalable){
288       ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable_32(A,P,fill,C);;CHKERRQ(ierr);
289       PetscFunctionReturn(0);
290     }
291     ierr = PetscOptionsBool("-matmatmult_scalable","Use a scalable but slower C=A*B","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
292     if (scalable){
293       ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable(A,P,fill,C);;CHKERRQ(ierr);
294       PetscFunctionReturn(0);
295     }
296   ierr = PetscOptionsEnd();CHKERRQ(ierr);
297 
298 #if defined(DEBUG_MATMATMULT)
299   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] call MatMatMultSymbolic_MPIAIJ_MPIAIJ()...\n",rank);
300 #endif
301 
302   /* create struct Mat_PtAPMPI and attached it to C later */
303   ierr = PetscNew(Mat_PtAPMPI,&ptap);CHKERRQ(ierr);
304 
305   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
306   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
307 #if defined(DEBUG_MATMATMULT)
308   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] P_oth is done...\n",rank);
309 #endif
310   /* get P_loc by taking all local rows of P */
311   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
312 
313   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
314   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
315   pi_loc = p_loc->i; pj_loc = p_loc->j;
316   pi_oth = p_oth->i; pj_oth = p_oth->j;
317 
318 #if defined(DEBUG_MATMATMULT)
319   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] P_loc is done, Annz %D * P_locnnz %D = %D...\n",rank,ad->i[am]+ao->i[am],p_loc->rmax,(ad->i[am]+ao->i[am])*p_loc->rmax);
320 #endif
321 
322   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
323   /*-------------------------------------------------------------------*/
324   ierr  = PetscMalloc((am+2)*sizeof(PetscInt),&api);CHKERRQ(ierr);
325   ptap->api = api;
326   api[0]    = 0;
327 
328   /* create and initialize a linked list */
329   armax = ad->rmax+ao->rmax;
330   prmax = PetscMax(p_loc->rmax,p_oth->rmax);
331   nlnk_max = armax*prmax;
332   if (!nlnk_max || nlnk_max > pN) nlnk_max = pN;
333 #if defined(DEBUG_MATMATMULT)
334   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] pN %d; nlnk_max %d; Armax %d+%d=%d; Prmax Max(%d,%d)=%d\n",rank,pN,nlnk_max,ad->rmax,ao->rmax,armax,p_loc->rmax,p_oth->rmax,prmax);
335 #endif
336   ierr = PetscLLCondensedCreate(nlnk_max,pN,&lnk,&lnkbt);CHKERRQ(ierr);
337 
338   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
339   ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr);
340   current_space = free_space;
341 
342   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
343   for (i=0; i<am; i++) {
344     apnz = 0;
345     /* diagonal portion of A */
346     nzi = adi[i+1] - adi[i];
347     for (j=0; j<nzi; j++){
348       row = *adj++;
349       pnz = pi_loc[row+1] - pi_loc[row];
350       Jptr  = pj_loc + pi_loc[row];
351       /* add non-zero cols of P into the sorted linked list lnk */
352       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
353     }
354     /* off-diagonal portion of A */
355     nzi = aoi[i+1] - aoi[i];
356     for (j=0; j<nzi; j++){
357       row = *aoj++;
358       pnz = pi_oth[row+1] - pi_oth[row];
359       Jptr  = pj_oth + pi_oth[row];
360       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
361     }
362 
363     apnz     = lnk[0];
364     api[i+1] = api[i] + apnz;
365 
366     /* if free space is not available, double the total space in the list */
367     if (current_space->local_remaining<apnz) {
368       ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
369       nspacedouble++;
370     }
371 
372     /* Copy data into free space, then initialize lnk */
373     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
374     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
375     current_space->array           += apnz;
376     current_space->local_used      += apnz;
377     current_space->local_remaining -= apnz;
378   }
379 
380   /* Allocate space for apj, initialize apj, and */
381   /* destroy list of free space and other temporary array(s) */
382   ierr = PetscMalloc((api[am]+1)*sizeof(PetscInt),&ptap->apj);CHKERRQ(ierr);
383   apj  = ptap->apj;
384   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
385   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
386 #if defined(DEBUG_MATMATMULT)
387   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] AP is done...\n",rank);
388 #endif
389 
390   /* malloc apa to store dense row A[i,:]*P */
391   ierr = PetscMalloc(pN*sizeof(PetscScalar),&apa);CHKERRQ(ierr);
392   ierr = PetscMemzero(apa,pN*sizeof(PetscScalar));CHKERRQ(ierr);
393   ptap->apa = apa;
394 #if defined(DEBUG_MATMATMULT)
395   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] Malloc apa pN %D is done...\n",rank,pN);
396 #endif
397 
398   /* create and assemble symbolic parallel matrix Cmpi */
399   /*----------------------------------------------------*/
400   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
401   ierr = MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
402   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
403   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
404   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
405   for (i=0; i<am; i++){
406     row  = i + rstart;
407     apnz = api[i+1] - api[i];
408     ierr = MatSetValues(Cmpi,1,&row,apnz,apj,apa,INSERT_VALUES);CHKERRQ(ierr);
409     apj += apnz;
410   }
411   ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
412   ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
413 
414   ptap->destroy             = Cmpi->ops->destroy;
415   ptap->duplicate           = Cmpi->ops->duplicate;
416   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
417   Cmpi->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
418   Cmpi->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult;
419 
420   /* attach the supporting struct to Cmpi for reuse */
421   c = (Mat_MPIAIJ*)Cmpi->data;
422   c->ptap  = ptap;
423 
424   *C = Cmpi;
425 
426   /* set MatInfo */
427   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]) + 1.e-5;
428   if (afill < 1.0) afill = 1.0;
429   Cmpi->info.mallocs           = nspacedouble;
430   Cmpi->info.fill_ratio_given  = fill;
431   Cmpi->info.fill_ratio_needed = afill;
432 
433 #if defined(PETSC_USE_INFO)
434   if (api[am]) {
435     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
436     ierr = PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
437   } else {
438     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
439   }
440 #endif
441   PetscFunctionReturn(0);
442 }
443 
444 /* implementation used in PETSc-3.2 */
445 /* This routine is called ONLY in the case of reusing previously computed symbolic C */
446 #undef __FUNCT__
447 #define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIAIJ_Scalable_32"
448 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_Scalable_32(Mat A,Mat B,Mat C)
449 {
450   PetscErrorCode     ierr;
451   Mat                *seq;
452   Mat_MatMatMultMPI  *mult;
453   PetscContainer     container;
454 
455   PetscFunctionBegin;
456   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
457   if (!container) SETERRQ(((PetscObject)A)->comm,PETSC_ERR_PLIB,"Container does not exist");
458   ierr  = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
459 
460   if (mult->skipNumeric){ /* first numeric product is done during symbolic product */
461     mult->skipNumeric = PETSC_FALSE;
462     PetscFunctionReturn(0);
463   }
464 #if defined(DEBUG_MATMATMULT)
465   PetscMPIInt rank;
466   MPI_Comm    comm = ((PetscObject)C)->comm;
467   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
468   ierr = MPI_Barrier(comm);CHKERRQ(ierr);
469   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] call MatMatMultNumeric_MPIAIJ_MPIAIJ_Scalable_32()...\n",rank);
470 #endif
471 
472   seq = &mult->B_seq;
473   ierr = MatGetSubMatrices(B,1,&mult->isrowb,&mult->iscolb,MAT_REUSE_MATRIX,&seq);CHKERRQ(ierr);
474   mult->B_seq = *seq;
475 
476   seq = &mult->A_loc;
477   ierr = MatGetSubMatrices(A,1,&mult->isrowa,&mult->isrowb,MAT_REUSE_MATRIX,&seq);CHKERRQ(ierr);
478   mult->A_loc = *seq;
479 
480   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(mult->A_loc,mult->B_seq,mult->C_seq);CHKERRQ(ierr);
481 
482   ierr = PetscObjectReference((PetscObject)mult->C_seq);CHKERRQ(ierr);
483   ierr = MatMerge(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
484   PetscFunctionReturn(0);
485 }
486 
487 /* numeric product is computed as well */
488 #undef __FUNCT__
489 #define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable_32"
490 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable_32(Mat A,Mat B,PetscReal fill,Mat *C)
491 {
492   PetscErrorCode     ierr;
493   Mat_MatMatMultMPI  *mult;
494   PetscContainer     container;
495   Mat                AB,*seq;
496   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
497   PetscInt           *idx,i,start,ncols,nzA,nzB,*cmap,imark;
498 #if defined(DEBUG_MATMATMULT)
499   MPI_Comm             comm = ((PetscObject)A)->comm;
500   PetscMPIInt          rank=a->rank;
501 #endif
502 
503   PetscFunctionBegin;
504 #if defined(DEBUG_MATMATMULT)
505   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] call MatMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable_32()...\n",rank);
506 #endif
507   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend){
508     SETERRQ4(((PetscObject)A)->comm,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);
509   }
510 
511   ierr = PetscNew(Mat_MatMatMultMPI,&mult);CHKERRQ(ierr);
512 
513   /* get isrowb: nonzero col of A */
514   start = A->cmap->rstart;
515   cmap  = a->garray;
516   nzA   = a->A->cmap->n;
517   nzB   = a->B->cmap->n;
518   ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
519   ncols = 0;
520   for (i=0; i<nzB; i++) {  /* row < local row index */
521     if (cmap[i] < start) idx[ncols++] = cmap[i];
522     else break;
523   }
524   imark = i;
525   for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
526   for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
527   ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&mult->isrowb);CHKERRQ(ierr);
528   ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&mult->iscolb);CHKERRQ(ierr);
529 
530   /*  get isrowa: all local rows of A */
531   ierr = ISCreateStride(PETSC_COMM_SELF,A->rmap->n,A->rmap->rstart,1,&mult->isrowa);CHKERRQ(ierr);
532 
533   /* Below should go to MatMatMultNumeric_MPIAIJ_MPIAIJ() - How to generate C there? */
534   /* create a seq matrix B_seq = submatrix of B by taking rows of B that equal to nonzero col of A */
535   ierr = MatGetSubMatrices(B,1,&mult->isrowb,&mult->iscolb,MAT_INITIAL_MATRIX,&seq);CHKERRQ(ierr);
536   mult->B_seq = *seq;
537   ierr = PetscFree(seq);CHKERRQ(ierr);
538 #if defined(DEBUG_MATMATMULT)
539   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] B_seq is done...\n",rank);
540 #endif
541 
542   /*  create a seq matrix A_seq = submatrix of A by taking all local rows of A */
543   ierr = MatGetSubMatrices(A,1,&mult->isrowa,&mult->isrowb,MAT_INITIAL_MATRIX,&seq);CHKERRQ(ierr);
544   mult->A_loc = *seq;
545   ierr = PetscFree(seq);CHKERRQ(ierr);
546 #if defined(DEBUG_MATMATMULT)
547   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] A_loc is done...\n",rank);
548 #endif
549 
550   /* compute C_seq = A_seq * B_seq */
551   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(mult->A_loc,mult->B_seq,fill,&mult->C_seq);CHKERRQ(ierr);
552 #if defined(DEBUG_MATMATMULT)
553   ierr = MPI_Barrier(comm);CHKERRQ(ierr);
554   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] C_seq Symbolic is done...\n",rank);
555 #endif
556   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(mult->A_loc,mult->B_seq,mult->C_seq);CHKERRQ(ierr);
557 #if defined(DEBUG_MATMATMULT)
558   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] C_seq Numeric is done...\n",rank);
559 #endif
560 
561   /* create mpi matrix C by concatenating C_seq */
562   ierr = PetscObjectReference((PetscObject)mult->C_seq);CHKERRQ(ierr); /* prevent C_seq being destroyed by MatMerge() */
563   ierr = MatMergeSymbolic(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,&AB);CHKERRQ(ierr);
564   ierr = MatMergeNumeric(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,AB);CHKERRQ(ierr);
565   ierr = MatDestroy(&mult->C_seq);CHKERRQ(ierr);
566 #if defined(DEBUG_MATMATMULT)
567   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] Merge is done...\n",rank);
568 #endif
569 
570   /* attach the supporting struct to C for reuse of symbolic C */
571   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
572   ierr = PetscContainerSetPointer(container,mult);CHKERRQ(ierr);
573   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatMultMPI);CHKERRQ(ierr);
574   ierr = PetscObjectCompose((PetscObject)AB,"Mat_MatMatMultMPI",(PetscObject)container);CHKERRQ(ierr);
575   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
576   mult->skipNumeric  = PETSC_TRUE; /* a numeric product is done here */
577   mult->destroy      = AB->ops->destroy;
578   mult->duplicate    = AB->ops->duplicate;
579   AB->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_Scalable_32;
580   AB->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult_32;
581   AB->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult_32;
582   AB->ops->matmult        = MatMatMult_MPIAIJ_MPIAIJ;
583   *C                      = AB;
584   PetscFunctionReturn(0);
585 }
586 
587 #undef __FUNCT__
588 #define __FUNCT__ "MatMatMult_MPIAIJ_MPIDense"
589 PetscErrorCode MatMatMult_MPIAIJ_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
590 {
591   PetscErrorCode ierr;
592 
593   PetscFunctionBegin;
594   if (scall == MAT_INITIAL_MATRIX){
595     ierr = MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,fill,C);CHKERRQ(ierr);
596   }
597   ierr = MatMatMultNumeric_MPIAIJ_MPIDense(A,B,*C);CHKERRQ(ierr);
598   PetscFunctionReturn(0);
599 }
600 
601 typedef struct {
602   Mat         workB;
603   PetscScalar *rvalues,*svalues;
604   MPI_Request *rwaits,*swaits;
605 } MPIAIJ_MPIDense;
606 
607 #undef __FUNCT__
608 #define __FUNCT__ "MPIAIJ_MPIDenseDestroy"
609 PetscErrorCode MPIAIJ_MPIDenseDestroy(void *ctx)
610 {
611   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*) ctx;
612   PetscErrorCode  ierr;
613 
614   PetscFunctionBegin;
615   ierr = MatDestroy(&contents->workB);CHKERRQ(ierr);
616   ierr = PetscFree4(contents->rvalues,contents->svalues,contents->rwaits,contents->swaits);CHKERRQ(ierr);
617   ierr = PetscFree(contents);CHKERRQ(ierr);
618   PetscFunctionReturn(0);
619 }
620 
621 #undef __FUNCT__
622 #define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIDense"
623 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
624 {
625   PetscErrorCode         ierr;
626   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
627   PetscInt               nz = aij->B->cmap->n;
628   PetscContainer         container;
629   MPIAIJ_MPIDense        *contents;
630   VecScatter             ctx = aij->Mvctx;
631   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
632   VecScatter_MPI_General *to   = ( VecScatter_MPI_General*) ctx->todata;
633   PetscInt               m=A->rmap->n,n=B->cmap->n;
634 
635   PetscFunctionBegin;
636   ierr = MatCreate(((PetscObject)B)->comm,C);CHKERRQ(ierr);
637   ierr = MatSetSizes(*C,m,n,A->rmap->N,B->cmap->N);CHKERRQ(ierr);
638   ierr = MatSetType(*C,MATMPIDENSE);CHKERRQ(ierr);
639   ierr = MatMPIDenseSetPreallocation(*C,PETSC_NULL);CHKERRQ(ierr);
640   ierr = MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
641   ierr = MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
642   (*C)->ops->matmult = MatMatMult_MPIAIJ_MPIDense;
643 
644   ierr = PetscNew(MPIAIJ_MPIDense,&contents);CHKERRQ(ierr);
645   /* Create work matrix used to store off processor rows of B needed for local product */
646   ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,PETSC_NULL,&contents->workB);CHKERRQ(ierr);
647   /* Create work arrays needed */
648   ierr = PetscMalloc4(B->cmap->N*from->starts[from->n],PetscScalar,&contents->rvalues,
649                       B->cmap->N*to->starts[to->n],PetscScalar,&contents->svalues,
650                       from->n,MPI_Request,&contents->rwaits,
651                       to->n,MPI_Request,&contents->swaits);CHKERRQ(ierr);
652 
653   ierr = PetscContainerCreate(((PetscObject)A)->comm,&container);CHKERRQ(ierr);
654   ierr = PetscContainerSetPointer(container,contents);CHKERRQ(ierr);
655   ierr = PetscContainerSetUserDestroy(container,MPIAIJ_MPIDenseDestroy);CHKERRQ(ierr);
656   ierr = PetscObjectCompose((PetscObject)(*C),"workB",(PetscObject)container);CHKERRQ(ierr);
657   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
658   PetscFunctionReturn(0);
659 }
660 
661 #undef __FUNCT__
662 #define __FUNCT__ "MatMPIDenseScatter"
663 /*
664     Performs an efficient scatter on the rows of B needed by this process; this is
665     a modification of the VecScatterBegin_() routines.
666 */
667 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,Mat C,Mat *outworkB)
668 {
669   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)A->data;
670   PetscErrorCode         ierr;
671   PetscScalar            *b,*w,*svalues,*rvalues;
672   VecScatter             ctx = aij->Mvctx;
673   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
674   VecScatter_MPI_General *to   = ( VecScatter_MPI_General*) ctx->todata;
675   PetscInt               i,j,k;
676   PetscInt               *sindices,*sstarts,*rindices,*rstarts;
677   PetscMPIInt            *sprocs,*rprocs,nrecvs;
678   MPI_Request            *swaits,*rwaits;
679   MPI_Comm               comm = ((PetscObject)A)->comm;
680   PetscMPIInt            tag = ((PetscObject)ctx)->tag,ncols = B->cmap->N, nrows = aij->B->cmap->n,imdex,nrowsB = B->rmap->n;
681   MPI_Status             status;
682   MPIAIJ_MPIDense        *contents;
683   PetscContainer         container;
684   Mat                    workB;
685 
686   PetscFunctionBegin;
687   ierr = PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);CHKERRQ(ierr);
688   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
689   ierr = PetscContainerGetPointer(container,(void**)&contents);CHKERRQ(ierr);
690 
691   workB = *outworkB = contents->workB;
692   if (nrows != workB->rmap->n) SETERRQ2(comm,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",nrows,workB->cmap->n);
693   sindices  = to->indices;
694   sstarts   = to->starts;
695   sprocs    = to->procs;
696   swaits    = contents->swaits;
697   svalues   = contents->svalues;
698 
699   rindices  = from->indices;
700   rstarts   = from->starts;
701   rprocs    = from->procs;
702   rwaits    = contents->rwaits;
703   rvalues   = contents->rvalues;
704 
705   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
706   ierr = MatGetArray(workB,&w);CHKERRQ(ierr);
707 
708   for (i=0; i<from->n; i++) {
709     ierr = MPI_Irecv(rvalues+ncols*rstarts[i],ncols*(rstarts[i+1]-rstarts[i]),MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
710   }
711 
712   for (i=0; i<to->n; i++) {
713     /* pack a message at a time */
714     CHKMEMQ;
715     for (j=0; j<sstarts[i+1]-sstarts[i]; j++){
716       for (k=0; k<ncols; k++) {
717         svalues[ncols*(sstarts[i] + j) + k] = b[sindices[sstarts[i]+j] + nrowsB*k];
718       }
719     }
720     CHKMEMQ;
721     ierr = MPI_Isend(svalues+ncols*sstarts[i],ncols*(sstarts[i+1]-sstarts[i]),MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
722   }
723 
724   nrecvs = from->n;
725   while (nrecvs) {
726     ierr = MPI_Waitany(from->n,rwaits,&imdex,&status);CHKERRQ(ierr);
727     nrecvs--;
728     /* unpack a message at a time */
729     CHKMEMQ;
730     for (j=0; j<rstarts[imdex+1]-rstarts[imdex]; j++){
731       for (k=0; k<ncols; k++) {
732         w[rindices[rstarts[imdex]+j] + nrows*k] = rvalues[ncols*(rstarts[imdex] + j) + k];
733       }
734     }
735     CHKMEMQ;
736   }
737   if (to->n) {ierr = MPI_Waitall(to->n,swaits,to->sstatus);CHKERRQ(ierr);}
738 
739   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
740   ierr = MatRestoreArray(workB,&w);CHKERRQ(ierr);
741   ierr = MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
742   ierr = MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
743   PetscFunctionReturn(0);
744 }
745 extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);
746 
747 #undef __FUNCT__
748 #define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIDense"
749 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
750 {
751   PetscErrorCode       ierr;
752   Mat_MPIAIJ           *aij = (Mat_MPIAIJ*)A->data;
753   Mat_MPIDense         *bdense = (Mat_MPIDense*)B->data;
754   Mat_MPIDense         *cdense = (Mat_MPIDense*)C->data;
755   Mat                  workB;
756 
757   PetscFunctionBegin;
758 
759   /* diagonal block of A times all local rows of B*/
760   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(aij->A,bdense->A,cdense->A);CHKERRQ(ierr);
761 
762   /* get off processor parts of B needed to complete the product */
763   ierr = MatMPIDenseScatter(A,B,C,&workB);CHKERRQ(ierr);
764 
765   /* off-diagonal block of A times nonlocal rows of B */
766   ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);CHKERRQ(ierr);
767   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
768   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
769   PetscFunctionReturn(0);
770 }
771 
772 #undef __FUNCT__
773 #define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIAIJ_Scalable"
774 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_Scalable(Mat A,Mat P,Mat C)
775 {
776   PetscErrorCode     ierr;
777   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
778   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
779   Mat_SeqAIJ         *cd=(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
780   PetscInt           *adi=ad->i,*adj,*aoi=ao->i,*aoj;
781   PetscScalar        *ada,*aoa,*cda=cd->a,*coa=co->a;
782   Mat_SeqAIJ         *p_loc,*p_oth;
783   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
784   PetscScalar        *pa_loc,*pa_oth,*pa,valtmp,*ca;
785   PetscInt           cm=C->rmap->n,anz,pnz;
786   Mat_PtAPMPI        *ptap=c->ptap;
787   PetscScalar        *apa_sparse=ptap->apa;
788   PetscInt           *api,*apj,*apJ,i,j,k,row;
789   PetscInt           cstart=C->cmap->rstart;
790   PetscInt           cdnz,conz,k0,k1,nextp;
791 #if defined(DEBUG_MATMATMULT)
792   PetscMPIInt        rank=a->rank;
793 #endif
794 
795   PetscFunctionBegin;
796 #if defined(DEBUG_MATMATMULT)
797   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] call MatMatMultNumeric_MPIAIJ_MPIAIJ_Scalable()...\n",rank);
798 #endif
799 
800   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
801   /*-----------------------------------------------------*/
802   /* update numerical values of P_oth and P_loc */
803   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
804   ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
805 #if defined(DEBUG_MATMATMULT)
806   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] got P_oth and P_loc...\n",rank);
807 #endif
808 
809   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
810   /*----------------------------------------------------------*/
811   /* get data from symbolic products */
812   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
813   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
814   pi_loc=p_loc->i; pj_loc=p_loc->j; pa_loc=p_loc->a;
815   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
816 
817   api = ptap->api;
818   apj = ptap->apj;
819   for (i=0; i<cm; i++) {
820     apJ = apj + api[i];
821 
822     /* diagonal portion of A */
823     anz = adi[i+1] - adi[i];
824     adj = ad->j + adi[i];
825     ada = ad->a + adi[i];
826     for (j=0; j<anz; j++) {
827       row = adj[j];
828       pnz = pi_loc[row+1] - pi_loc[row];
829       pj  = pj_loc + pi_loc[row];
830       pa  = pa_loc + pi_loc[row];
831       /* perform sparse axpy */
832       valtmp = ada[j];
833       nextp  = 0;
834       for (k=0; nextp<pnz; k++) {
835         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
836           apa_sparse[k] += valtmp*pa[nextp++];
837         }
838       }
839       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
840     }
841 
842     /* off-diagonal portion of A */
843     anz = aoi[i+1] - aoi[i];
844     aoj = ao->j + aoi[i];
845     aoa = ao->a + aoi[i];
846     for (j=0; j<anz; j++) {
847       row = aoj[j];
848       pnz = pi_oth[row+1] - pi_oth[row];
849       pj  = pj_oth + pi_oth[row];
850       pa  = pa_oth + pi_oth[row];
851       /* perform sparse axpy */
852       valtmp = aoa[j];
853       nextp  = 0;
854       for (k=0; nextp<pnz; k++) {
855         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
856           apa_sparse[k] += valtmp*pa[nextp++];
857         }
858       }
859       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
860     }
861 
862     /* set values in C */
863     cdnz = cd->i[i+1] - cd->i[i];
864     conz = co->i[i+1] - co->i[i];
865 
866     /* 1st off-diagoanl part of C */
867     ca = coa + co->i[i];
868     k  = 0;
869     for (k0=0; k0<conz; k0++){
870       if (apJ[k] >= cstart) break;
871       ca[k0]      = apa_sparse[k];
872       apa_sparse[k] = 0.0;
873       k++;
874     }
875 
876     /* diagonal part of C */
877     ca = cda + cd->i[i];
878     for (k1=0; k1<cdnz; k1++){
879       ca[k1]      = apa_sparse[k];
880       apa_sparse[k] = 0.0;
881       k++;
882     }
883 
884     /* 2nd off-diagoanl part of C */
885     ca = coa + co->i[i];
886     for (; k0<conz; k0++){
887       ca[k0]      = apa_sparse[k];
888       apa_sparse[k] = 0.0;
889       k++;
890     }
891   }
892   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
893   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
894   PetscFunctionReturn(0);
895 }
896 
897 /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ(), except using LLCondensed to avoid O(BN) memory requirement */
898 #undef __FUNCT__
899 #define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable"
900 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable(Mat A,Mat P,PetscReal fill,Mat *C)
901 {
902   PetscErrorCode       ierr;
903   MPI_Comm             comm=((PetscObject)A)->comm;
904   Mat                  Cmpi;
905   Mat_PtAPMPI          *ptap;
906   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
907   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*c;
908   Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
909   PetscInt             *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
910   PetscInt             *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
911   PetscInt             i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
912   PetscInt             am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
913   PetscInt             nlnk_max,armax,prmax;
914   PetscReal            afill;
915   PetscScalar          *apa;
916 #if defined(DEBUG_MATMATMULT)
917   PetscMPIInt          rank=a->rank;
918 #endif
919 
920   PetscFunctionBegin;
921 #if defined(DEBUG_MATMATMULT)
922   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
923   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] call MatMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable()...\n",rank);
924 #endif
925 
926   /* create struct Mat_PtAPMPI and attached it to C later */
927   ierr = PetscNew(Mat_PtAPMPI,&ptap);CHKERRQ(ierr);
928 
929   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
930   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
931 #if defined(DEBUG_MATMATMULT)
932   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] P_oth is done...\n",rank);
933 #endif
934   /* get P_loc by taking all local rows of P */
935   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
936 
937   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
938   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
939   pi_loc = p_loc->i; pj_loc = p_loc->j;
940   pi_oth = p_oth->i; pj_oth = p_oth->j;
941 
942 #if defined(DEBUG_MATMATMULT)
943   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] P_loc is done, Annz %D * P_locnnz %D = %D...\n",rank,ad->i[am]+ao->i[am],p_loc->rmax,(ad->i[am]+ao->i[am])*p_loc->rmax);
944 #endif
945 
946   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
947   /*-------------------------------------------------------------------*/
948   ierr  = PetscMalloc((am+2)*sizeof(PetscInt),&api);CHKERRQ(ierr);
949   ptap->api = api;
950   api[0]    = 0;
951 
952   /* create and initialize a linked list */
953   armax = ad->rmax+ao->rmax;
954   prmax = PetscMax(p_loc->rmax,p_oth->rmax);
955   nlnk_max = armax*prmax;
956   if (!nlnk_max || nlnk_max > pN) nlnk_max = pN;
957 #if defined(DEBUG_MATMATMULT)
958   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] pN %d; nlnk_max %d; Armax %d+%d=%d; Prmax Max(%d,%d)=%d\n",rank,pN,nlnk_max,ad->rmax,ao->rmax,armax,p_loc->rmax,p_oth->rmax,prmax);
959 #endif
960   ierr = PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);CHKERRQ(ierr);
961 
962   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
963   ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);CHKERRQ(ierr);
964   current_space = free_space;
965 
966   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
967   for (i=0; i<am; i++) {
968     apnz = 0;
969     /* diagonal portion of A */
970     nzi = adi[i+1] - adi[i];
971     for (j=0; j<nzi; j++){
972       row = *adj++;
973       pnz = pi_loc[row+1] - pi_loc[row];
974       Jptr  = pj_loc + pi_loc[row];
975       /* add non-zero cols of P into the sorted linked list lnk */
976       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
977     }
978     /* off-diagonal portion of A */
979     nzi = aoi[i+1] - aoi[i];
980     for (j=0; j<nzi; j++){
981       row = *aoj++;
982       pnz = pi_oth[row+1] - pi_oth[row];
983       Jptr  = pj_oth + pi_oth[row];
984       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
985     }
986 
987     apnz     = *lnk;
988     api[i+1] = api[i] + apnz;
989     if (apnz > apnz_max) apnz_max = apnz;
990 
991     /* if free space is not available, double the total space in the list */
992     if (current_space->local_remaining<apnz) {
993       ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
994       nspacedouble++;
995     }
996 
997     /* Copy data into free space, then initialize lnk */
998     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
999     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
1000     current_space->array           += apnz;
1001     current_space->local_used      += apnz;
1002     current_space->local_remaining -= apnz;
1003   }
1004 
1005   /* Allocate space for apj, initialize apj, and */
1006   /* destroy list of free space and other temporary array(s) */
1007   ierr = PetscMalloc((api[am]+1)*sizeof(PetscInt),&ptap->apj);CHKERRQ(ierr);
1008   apj  = ptap->apj;
1009   ierr = PetscFreeSpaceContiguous(&free_space,ptap->apj);CHKERRQ(ierr);
1010   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
1011 #if defined(DEBUG_MATMATMULT)
1012   if (!rank) ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] AP is done..., apnz_max %d\n",rank,apnz_max);
1013 #endif
1014 
1015   /* create and assemble symbolic parallel matrix Cmpi */
1016   /*----------------------------------------------------*/
1017   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
1018   ierr = MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1019   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
1020   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
1021   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1022   ierr = MatSetBlockSize(Cmpi,1);CHKERRQ(ierr);
1023 
1024   /* malloc apa for assembly Cmpi */
1025   ierr = PetscMalloc(apnz_max*sizeof(PetscScalar),&apa);CHKERRQ(ierr);
1026   ierr = PetscMemzero(apa,apnz_max*sizeof(PetscScalar));CHKERRQ(ierr);
1027   ptap->apa = apa;
1028   for (i=0; i<am; i++){
1029     row  = i + rstart;
1030     apnz = api[i+1] - api[i];
1031     ierr = MatSetValues(Cmpi,1,&row,apnz,apj,apa,INSERT_VALUES);CHKERRQ(ierr);
1032     apj += apnz;
1033   }
1034   ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1035   ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1036 
1037   ptap->destroy             = Cmpi->ops->destroy;
1038   ptap->duplicate           = Cmpi->ops->duplicate;
1039   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_Scalable;
1040   Cmpi->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
1041   Cmpi->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult;
1042 
1043   /* attach the supporting struct to Cmpi for reuse */
1044   c = (Mat_MPIAIJ*)Cmpi->data;
1045   c->ptap  = ptap;
1046 
1047   *C = Cmpi;
1048 
1049   /* set MatInfo */
1050   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]) + 1.e-5;
1051   if (afill < 1.0) afill = 1.0;
1052   Cmpi->info.mallocs           = nspacedouble;
1053   Cmpi->info.fill_ratio_given  = fill;
1054   Cmpi->info.fill_ratio_needed = afill;
1055 
1056 #if defined(PETSC_USE_INFO)
1057   if (api[am]) {
1058     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
1059     ierr = PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%G,&C) for best performance.;\n",afill);CHKERRQ(ierr);
1060   } else {
1061     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
1062   }
1063 #endif
1064   PetscFunctionReturn(0);
1065 }
1066 
1067 /*-------------------------------------------------------------------------*/
1068 #undef __FUNCT__
1069 #define __FUNCT__ "MatTransposeMatMult_MPIAIJ_MPIAIJ"
1070 PetscErrorCode MatTransposeMatMult_MPIAIJ_MPIAIJ(Mat P,Mat A,MatReuse scall,PetscReal fill,Mat *C)
1071 {
1072   PetscErrorCode ierr;
1073   PetscBool      scalable=PETSC_FALSE;
1074 
1075   PetscFunctionBegin;
1076   if (scall == MAT_INITIAL_MATRIX){
1077     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
1078       ierr = PetscOptionsBool("-mattransposematmult_scalable","Use a scalable but slower C=Pt*A","",scalable,&scalable,PETSC_NULL);CHKERRQ(ierr);
1079       if  (scalable){
1080         ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable(P,A,fill,C);CHKERRQ(ierr);
1081       } else {
1082         ierr = MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(P,A,fill,C);CHKERRQ(ierr);
1083       }
1084     ierr = PetscOptionsEnd();CHKERRQ(ierr);
1085   }
1086   ierr = (*(*C)->ops->mattransposemultnumeric)(P,A,*C);CHKERRQ(ierr);
1087   PetscFunctionReturn(0);
1088 }
1089 
1090 #undef __FUNCT__
1091 #define __FUNCT__ "MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ"
1092 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1093 {
1094   PetscErrorCode       ierr;
1095   Mat_Merge_SeqsToMPI  *merge;
1096   Mat_MPIAIJ           *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1097   Mat_SeqAIJ           *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1098   Mat_PtAPMPI          *ptap;
1099   PetscInt             *adj,*aJ;
1100   PetscInt             i,j,k,anz,pnz,row,*cj;
1101   MatScalar            *ada,*aval,*ca,valtmp;
1102   PetscInt             am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1103   MPI_Comm             comm=((PetscObject)C)->comm;
1104   PetscMPIInt          size,rank,taga,*len_s;
1105   PetscInt             *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1106   PetscInt             **buf_ri,**buf_rj;
1107   PetscInt             cnz=0,*bj_i,*bi,*bj,bnz,nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1108   MPI_Request          *s_waits,*r_waits;
1109   MPI_Status           *status;
1110   MatScalar            **abuf_r,*ba_i,*pA,*coa,*ba;
1111   PetscInt             *ai,*aj,*coi,*coj;
1112   PetscInt             *poJ=po->j,*pdJ=pd->j;
1113   Mat                  A_loc;
1114   Mat_SeqAIJ           *a_loc;
1115 
1116   PetscFunctionBegin;
1117   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1118   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1119 
1120   ptap  = c->ptap;
1121   merge = ptap->merge;
1122 
1123  #if defined(DEBUG_MATTrMatMult)
1124   ierr = PetscSynchronizedPrintf(comm,"[%d] TransposeMatMultNumeric: Crmax %d \n",rank,ptap->rmax);
1125   ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
1126 #endif
1127 
1128   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
1129   /*--------------------------------------------------------------*/
1130   /* get data from symbolic products */
1131   coi = merge->coi; coj = merge->coj;
1132   ierr = PetscMalloc((coi[pon]+1)*sizeof(MatScalar),&coa);CHKERRQ(ierr);
1133   ierr = PetscMemzero(coa,coi[pon]*sizeof(MatScalar));CHKERRQ(ierr);
1134 
1135   bi     = merge->bi; bj = merge->bj;
1136   owners = merge->rowmap->range;
1137   ierr   = PetscMalloc((bi[cm]+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
1138   ierr   = PetscMemzero(ba,bi[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1139 
1140   /* get A_loc by taking all local rows of A */
1141   A_loc = ptap->A_loc;
1142   ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr);
1143   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1144   ai   = a_loc->i;
1145   aj   = a_loc->j;
1146 
1147   ierr = PetscMalloc((A->cmap->N)*sizeof(PetscScalar),&aval);CHKERRQ(ierr); /* non-scalable!!! */
1148   ierr = PetscMemzero(aval,A->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
1149 
1150     for (i=0; i<am; i++) {
1151       /* 2-a) put A[i,:] to dense array aval */
1152       anz = ai[i+1] - ai[i];
1153       adj = aj + ai[i];
1154       ada = a_loc->a + ai[i];
1155       for (j=0; j<anz; j++){
1156         aval[adj[j]] = ada[j];
1157       }
1158 
1159       /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1160       /*--------------------------------------------------------------*/
1161       /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1162       pnz = po->i[i+1] - po->i[i];
1163       poJ = po->j + po->i[i];
1164       pA  = po->a + po->i[i];
1165       for (j=0; j<pnz; j++){
1166         row = poJ[j];
1167         cnz = coi[row+1] - coi[row];
1168         cj  = coj + coi[row];
1169         ca  = coa + coi[row];
1170         /* perform dense axpy */
1171         valtmp = pA[j];
1172         for (k=0; k<cnz; k++) {
1173           ca[k] += valtmp*aval[cj[k]];
1174         }
1175         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1176       }
1177 
1178       /* put the value into Cd (diagonal part) */
1179       pnz = pd->i[i+1] - pd->i[i];
1180       pdJ = pd->j + pd->i[i];
1181       pA  = pd->a + pd->i[i];
1182       for (j=0; j<pnz; j++){
1183         row = pdJ[j];
1184         cnz = bi[row+1] - bi[row];
1185         cj  = bj + bi[row];
1186         ca  = ba + bi[row];
1187         /* perform dense axpy */
1188         valtmp = pA[j];
1189         for (k=0; k<cnz; k++) {
1190           ca[k] += valtmp*aval[cj[k]];
1191         }
1192         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1193       }
1194 
1195       /* zero the current row of Pt*A */
1196       aJ = aj + ai[i];
1197       for (k=0; k<anz; k++) aval[aJ[k]] = 0.0;
1198     }
1199 
1200   /* 3) send and recv matrix values coa */
1201   /*------------------------------------*/
1202   buf_ri = merge->buf_ri;
1203   buf_rj = merge->buf_rj;
1204   len_s  = merge->len_s;
1205   ierr = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1206   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1207 
1208   ierr = PetscMalloc2(merge->nsend+1,MPI_Request,&s_waits,size,MPI_Status,&status);CHKERRQ(ierr);
1209   for (proc=0,k=0; proc<size; proc++){
1210     if (!len_s[proc]) continue;
1211     i = merge->owners_co[proc];
1212     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
1213     k++;
1214   }
1215   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
1216   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
1217 
1218   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1219   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1220   ierr = PetscFree(coa);CHKERRQ(ierr);
1221 
1222   /* 4) insert local Cseq and received values into Cmpi */
1223   /*----------------------------------------------------*/
1224   ierr = PetscMalloc3(merge->nrecv,PetscInt**,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextci);CHKERRQ(ierr);
1225   for (k=0; k<merge->nrecv; k++){
1226     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1227     nrows       = *(buf_ri_k[k]);
1228     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1229     nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
1230   }
1231 
1232   for (i=0; i<cm; i++) {
1233     row = owners[rank] + i; /* global row index of C_seq */
1234     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1235     ba_i = ba + bi[i];
1236     bnz  = bi[i+1] - bi[i];
1237     /* add received vals into ba */
1238     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
1239       /* i-th row */
1240       if (i == *nextrow[k]) {
1241         cnz = *(nextci[k]+1) - *nextci[k];
1242         cj  = buf_rj[k] + *(nextci[k]);
1243         ca  = abuf_r[k] + *(nextci[k]);
1244         nextcj = 0;
1245         for (j=0; nextcj<cnz; j++){
1246           if (bj_i[j] == cj[nextcj]){ /* bcol == ccol */
1247             ba_i[j] += ca[nextcj++];
1248           }
1249         }
1250         nextrow[k]++; nextci[k]++;
1251         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1252       }
1253     }
1254     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1255   }
1256   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1257   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1258 
1259   ierr = PetscFree(ba);CHKERRQ(ierr);
1260   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1261   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1262   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1263   ierr = PetscFree(aval);CHKERRQ(ierr);
1264   PetscFunctionReturn(0);
1265 }
1266 
1267 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1268 #undef __FUNCT__
1269 #define __FUNCT__ "MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ"
1270 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat *C)
1271 {
1272   PetscErrorCode       ierr;
1273   Mat                  Cmpi,A_loc,POt,PDt;
1274   Mat_PtAPMPI          *ptap;
1275   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
1276   Mat_MPIAIJ           *p=(Mat_MPIAIJ*)P->data,*c;
1277   PetscInt             *pdti,*pdtj,*poti,*potj,*ptJ;
1278   PetscInt             nnz;
1279   PetscInt             *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1280   PetscInt             am=A->rmap->n,pn=P->cmap->n;
1281   PetscBT              lnkbt;
1282   MPI_Comm             comm=((PetscObject)A)->comm;
1283   PetscMPIInt          size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1284   PetscInt             **buf_rj,**buf_ri,**buf_ri_k;
1285   PetscInt             len,proc,*dnz,*onz,*owners;
1286   PetscInt             nzi,*bi,*bj;
1287   PetscInt             nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1288   MPI_Request          *swaits,*rwaits;
1289   MPI_Status           *sstatus,rstatus;
1290   Mat_Merge_SeqsToMPI  *merge;
1291   PetscInt             *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1292   PetscReal            afill=1.0,afill_tmp;
1293   PetscInt             rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Crmax;
1294   PetscScalar          *vals;
1295   Mat_SeqAIJ           *a_loc, *pdt,*pot;
1296 
1297   PetscFunctionBegin;
1298   /* check if matrix local sizes are compatible */
1299   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend){
1300     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);
1301   }
1302 
1303   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1304   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1305 #if defined(DEBUG_MATTrMatMult)
1306   ierr = PetscSynchronizedPrintf(comm,"[%d] TransposeMatMultSymbolic P: %d %d, %d %d; A %d %d, %d %d\n",rank,P->rmap->N,P->cmap->N,P->rmap->n,P->cmap->n,A->rmap->N,aN,A->rmap->n,A->cmap->n);
1307   ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
1308 #endif
1309 
1310   /* create struct Mat_PtAPMPI and attached it to C later */
1311   ierr = PetscNew(Mat_PtAPMPI,&ptap);CHKERRQ(ierr);
1312 
1313   /* get A_loc by taking all local rows of A */
1314   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr);
1315   ptap->A_loc = A_loc;
1316   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1317   ai   = a_loc->i;
1318   aj   = a_loc->j;
1319 
1320   /* determine symbolic Co=(p->B)^T*A - send to others */
1321   /*----------------------------------------------------*/
1322   ierr = MatTransposeSymbolic_SeqAIJ(p->A,&PDt);CHKERRQ(ierr);
1323   pdt = (Mat_SeqAIJ*)PDt->data;
1324   pdti = pdt->i; pdtj = pdt->j;
1325 
1326   ierr = MatTransposeSymbolic_SeqAIJ(p->B,&POt);CHKERRQ(ierr);
1327   pot = (Mat_SeqAIJ*)POt->data;
1328   poti = pot->i; potj = pot->j;
1329 
1330   /* then, compute symbolic Co = (p->B)^T*A */
1331   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1332                          >= (num of nonzero rows of C_seq) - pn */
1333   ierr = PetscMalloc((pon+1)*sizeof(PetscInt),&coi);CHKERRQ(ierr);
1334   coi[0] = 0;
1335 
1336   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1337   nnz           = fill*(poti[pon] + ai[am]);
1338   ierr          = PetscFreeSpaceGet(nnz,&free_space);
1339   current_space = free_space;
1340 #if defined(DEBUG_MATTrMatMult)
1341   ierr = PetscSynchronizedPrintf(comm, "[%d] nnz = fill %g *(%d + %d)\n",rank,fill,poti[pon],ai[am]);CHKERRQ(ierr);
1342   ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
1343 #endif
1344   /* create and initialize a linked list */
1345   i = PetscMax(pdt->rmax,pot->rmax);
1346   Crmax = i*a_loc->rmax*size;
1347   if (!Crmax || Crmax > aN) Crmax = aN;
1348 #if defined(DEBUG_MATTrMatMult)
1349   printf("[%d] rmax A_loc %d * max(PD %d, PO %d)=%d, Crmax %d\n",rank,a_loc->rmax,pdt->rmax,pot->rmax,i*a_loc->rmax,Crmax);
1350 #endif
1351   ierr = PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);CHKERRQ(ierr);
1352 
1353   for (i=0; i<pon; i++) {
1354     pnz = poti[i+1] - poti[i];
1355     ptJ = potj + poti[i];
1356     for (j=0; j<pnz; j++){
1357       row  = ptJ[j]; /* row of A_loc == col of Pot */
1358       anz  = ai[row+1] - ai[row];
1359       Jptr = aj + ai[row];
1360       /* add non-zero cols of AP into the sorted linked list lnk */
1361       ierr = PetscLLCondensedAddSorted(anz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1362     }
1363     nnz = lnk[0];
1364 
1365     /* If free space is not available, double the total space in the list */
1366     if (current_space->local_remaining<nnz) {
1367       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
1368       nspacedouble++;
1369     }
1370 
1371     /* Copy data into free space, and zero out denserows */
1372     ierr = PetscLLCondensedClean(aN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1373     current_space->array           += nnz;
1374     current_space->local_used      += nnz;
1375     current_space->local_remaining -= nnz;
1376     coi[i+1] = coi[i] + nnz;
1377   }
1378 
1379   ierr = PetscMalloc((coi[pon]+1)*sizeof(PetscInt),&coj);CHKERRQ(ierr);
1380   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1381   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]);
1382   if (afill_tmp > afill) afill = afill_tmp;
1383 
1384   /* send j-array (coj) of Co to other processors */
1385   /*----------------------------------------------*/
1386   /* determine row ownership */
1387   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
1388   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1389   merge->rowmap->n = pn;
1390   merge->rowmap->bs = 1;
1391   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1392   owners = merge->rowmap->range;
1393 
1394   /* determine the number of messages to send, their lengths */
1395   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
1396   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
1397   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
1398   len_s = merge->len_s;
1399   merge->nsend = 0;
1400 
1401   ierr = PetscMalloc((size+2)*sizeof(PetscInt),&owners_co);CHKERRQ(ierr);
1402   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
1403 
1404   proc = 0;
1405   for (i=0; i<pon; i++){
1406     while (prmap[i] >= owners[proc+1]) proc++;
1407     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1408     len_s[proc] += coi[i+1] - coi[i];
1409   }
1410 
1411   len   = 0;  /* max length of buf_si[] */
1412   owners_co[0] = 0;
1413   for (proc=0; proc<size; proc++){
1414     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1415     if (len_si[proc]){
1416       merge->nsend++;
1417       len_si[proc] = 2*(len_si[proc] + 1);
1418       len += len_si[proc];
1419     }
1420   }
1421 
1422   /* determine the number and length of messages to receive for coi and coj  */
1423   ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1424   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1425 
1426   /* post the Irecv and Isend of coj */
1427   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1428   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1429   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&swaits);CHKERRQ(ierr);
1430   for (proc=0, k=0; proc<size; proc++){
1431     if (!len_s[proc]) continue;
1432     i = owners_co[proc];
1433     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
1434     k++;
1435   }
1436 
1437   /* receives and sends of coj are complete */
1438   ierr = PetscMalloc(size*sizeof(MPI_Status),&sstatus);CHKERRQ(ierr);
1439   for (i=0; i<merge->nrecv; i++){
1440     PetscMPIInt icompleted;
1441     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1442   }
1443   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1444   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
1445 
1446   /* send and recv coi */
1447   /*-------------------*/
1448   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1449   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1450   ierr = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
1451   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1452   for (proc=0,k=0; proc<size; proc++){
1453     if (!len_s[proc]) continue;
1454     /* form outgoing message for i-structure:
1455          buf_si[0]:                 nrows to be sent
1456                [1:nrows]:           row index (global)
1457                [nrows+1:2*nrows+1]: i-structure index
1458     */
1459     /*-------------------------------------------*/
1460     nrows = len_si[proc]/2 - 1;
1461     buf_si_i    = buf_si + nrows+1;
1462     buf_si[0]   = nrows;
1463     buf_si_i[0] = 0;
1464     nrows = 0;
1465     for (i=owners_co[proc]; i<owners_co[proc+1]; i++){
1466       nzi = coi[i+1] - coi[i];
1467       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
1468       buf_si[nrows+1] =prmap[i] -owners[proc]; /* local row index */
1469       nrows++;
1470     }
1471     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
1472     k++;
1473     buf_si += len_si[proc];
1474   }
1475   i = merge->nrecv;
1476   while (i--) {
1477     PetscMPIInt icompleted;
1478     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1479   }
1480   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1481   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
1482   ierr = PetscFree(len_si);CHKERRQ(ierr);
1483   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1484   ierr = PetscFree(swaits);CHKERRQ(ierr);
1485   ierr = PetscFree(sstatus);CHKERRQ(ierr);
1486   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1487 
1488   /* compute the local portion of C (mpi mat) */
1489   /*------------------------------------------*/
1490   /* allocate bi array and free space for accumulating nonzero column info */
1491   ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1492   bi[0] = 0;
1493 
1494   /* set initial free space to be fill*(nnz(P) + nnz(A)) */
1495   nnz           = fill*(pdti[pn] + poti[pon] + ai[am]);
1496   ierr          = PetscFreeSpaceGet(nnz,&free_space);
1497   current_space = free_space;
1498 
1499 #if defined(DEBUG_MATTrMatMult)
1500   ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] nnz=fill %g*(%d + %d + %d)\n",rank,fill,pdti[pn],poti[pon],ai[am]);
1501 #endif
1502 
1503   ierr = PetscMalloc3(merge->nrecv,PetscInt**,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextci);CHKERRQ(ierr);
1504   for (k=0; k<merge->nrecv; k++){
1505     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1506     nrows       = *buf_ri_k[k];
1507     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1508     nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
1509   }
1510 
1511   ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr);
1512   rmax = 0;
1513   for (i=0; i<pn; i++) {
1514     /* add pdt[i,:]*AP into lnk */
1515     pnz = pdti[i+1] - pdti[i];
1516     ptJ = pdtj + pdti[i];
1517     for (j=0; j<pnz; j++){
1518       row  = ptJ[j];  /* row of AP == col of Pt */
1519       anz  = ai[row+1] - ai[row];
1520       Jptr = aj + ai[row];
1521       /* add non-zero cols of AP into the sorted linked list lnk */
1522       ierr = PetscLLCondensedAddSorted(anz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1523     }
1524 
1525     /* add received col data into lnk */
1526     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
1527       if (i == *nextrow[k]) { /* i-th row */
1528         nzi = *(nextci[k]+1) - *nextci[k];
1529         Jptr  = buf_rj[k] + *nextci[k];
1530         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1531         nextrow[k]++; nextci[k]++;
1532       }
1533     }
1534     nnz = lnk[0];
1535 
1536     /* if free space is not available, make more free space */
1537     if (current_space->local_remaining<nnz) {
1538       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
1539       nspacedouble++;
1540     }
1541     /* copy data into free space, then initialize lnk */
1542     ierr = PetscLLCondensedClean(aN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1543     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
1544     current_space->array           += nnz;
1545     current_space->local_used      += nnz;
1546     current_space->local_remaining -= nnz;
1547     bi[i+1] = bi[i] + nnz;
1548     if (nnz > rmax) rmax = nnz;
1549   }
1550   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1551 
1552   ierr = PetscMalloc((bi[pn]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1553   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
1554   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]);
1555   if (afill_tmp > afill) afill = afill_tmp;
1556   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
1557   ierr = MatDestroy(&POt);CHKERRQ(ierr);
1558   ierr = MatDestroy(&PDt);CHKERRQ(ierr);
1559 
1560   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
1561   /*----------------------------------------------------------------------------------*/
1562   ierr = PetscMalloc((rmax+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
1563   ierr = PetscMemzero(vals,rmax*sizeof(PetscScalar));CHKERRQ(ierr);
1564 
1565   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
1566   ierr = MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1567   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
1568   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
1569   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1570   ierr = MatSetBlockSize(Cmpi,1);CHKERRQ(ierr);
1571   for (i=0; i<pn; i++){
1572     row = i + rstart;
1573     nnz = bi[i+1] - bi[i];
1574     Jptr = bj + bi[i];
1575     ierr = MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);CHKERRQ(ierr);
1576   }
1577   ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1578   ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1579   ierr = PetscFree(vals);CHKERRQ(ierr);
1580 
1581   merge->bi            = bi;
1582   merge->bj            = bj;
1583   merge->coi           = coi;
1584   merge->coj           = coj;
1585   merge->buf_ri        = buf_ri;
1586   merge->buf_rj        = buf_rj;
1587   merge->owners_co     = owners_co;
1588   merge->destroy       = Cmpi->ops->destroy;
1589   merge->duplicate     = Cmpi->ops->duplicate;
1590 
1591   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
1592   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
1593 
1594   /* attach the supporting struct to Cmpi for reuse */
1595   c = (Mat_MPIAIJ*)Cmpi->data;
1596   c->ptap        = ptap;
1597   ptap->api      = PETSC_NULL;
1598   ptap->apj      = PETSC_NULL;
1599   ptap->merge    = merge;
1600   ptap->rmax     = rmax;
1601 
1602   *C = Cmpi;
1603 #if defined(PETSC_USE_INFO)
1604   if (bi[pn] != 0) {
1605     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
1606     ierr = PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr);
1607   } else {
1608     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
1609   }
1610 #endif
1611   PetscFunctionReturn(0);
1612 }
1613 
1614 #undef __FUNCT__
1615 #define __FUNCT__ "MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_Scalable"
1616 PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_Scalable(Mat P,Mat A,Mat C)
1617 {
1618   PetscErrorCode       ierr;
1619   Mat_Merge_SeqsToMPI  *merge;
1620   Mat_MPIAIJ           *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1621   Mat_SeqAIJ           *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1622   Mat_PtAPMPI          *ptap;
1623   PetscInt             *adj;
1624   PetscInt             i,j,k,anz,pnz,row,*cj,nexta;
1625   MatScalar            *ada,*ca,valtmp;
1626   PetscInt             am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1627   MPI_Comm             comm=((PetscObject)C)->comm;
1628   PetscMPIInt          size,rank,taga,*len_s;
1629   PetscInt             *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1630   PetscInt             **buf_ri,**buf_rj;
1631   PetscInt             cnz=0,*bj_i,*bi,*bj,bnz,nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1632   MPI_Request          *s_waits,*r_waits;
1633   MPI_Status           *status;
1634   MatScalar            **abuf_r,*ba_i,*pA,*coa,*ba;
1635   PetscInt             *ai,*aj,*coi,*coj;
1636   PetscInt             *poJ=po->j,*pdJ=pd->j;
1637   Mat                  A_loc;
1638   Mat_SeqAIJ           *a_loc;
1639 
1640   PetscFunctionBegin;
1641   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1642   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1643 
1644   ptap  = c->ptap;
1645   merge = ptap->merge;
1646 
1647  #if defined(DEBUG_MATTrMatMult)
1648   ierr = PetscSynchronizedPrintf(comm,"[%d] TransposeMatMultNumeric_Scalable: Crmax %d \n",rank,ptap->rmax);
1649   ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
1650 #endif
1651 
1652   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1653   /*------------------------------------------*/
1654   /* get data from symbolic products */
1655   coi = merge->coi; coj = merge->coj;
1656   ierr = PetscMalloc((coi[pon]+1)*sizeof(MatScalar),&coa);CHKERRQ(ierr);
1657   ierr = PetscMemzero(coa,coi[pon]*sizeof(MatScalar));CHKERRQ(ierr);
1658 
1659   bi     = merge->bi; bj = merge->bj;
1660   owners = merge->rowmap->range;
1661   ierr   = PetscMalloc((bi[cm]+1)*sizeof(MatScalar),&ba);CHKERRQ(ierr);
1662   ierr   = PetscMemzero(ba,bi[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1663 
1664   /* get A_loc by taking all local rows of A */
1665   A_loc = ptap->A_loc;
1666   ierr = MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);CHKERRQ(ierr);
1667   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1668   ai   = a_loc->i;
1669   aj   = a_loc->j;
1670 
1671   for (i=0; i<am; i++) {
1672     /* 2-a) put A[i,:] to dense array aval */
1673     anz = ai[i+1] - ai[i];
1674     adj = aj + ai[i];
1675     ada = a_loc->a + ai[i];
1676 
1677     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1678     /*-------------------------------------------------------------*/
1679     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1680     pnz = po->i[i+1] - po->i[i];
1681     poJ = po->j + po->i[i];
1682     pA  = po->a + po->i[i];
1683     for (j=0; j<pnz; j++){
1684       row = poJ[j];
1685       cnz = coi[row+1] - coi[row];
1686       cj  = coj + coi[row];
1687       ca  = coa + coi[row];
1688       /* perform sparse axpy */
1689       nexta  = 0;
1690       valtmp = pA[j];
1691       for (k=0; nexta<anz; k++) {
1692         if (cj[k] == adj[nexta]){
1693           ca[k] += valtmp*ada[nexta];
1694           nexta++;
1695         }
1696       }
1697       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1698     }
1699 
1700     /* put the value into Cd (diagonal part) */
1701     pnz = pd->i[i+1] - pd->i[i];
1702     pdJ = pd->j + pd->i[i];
1703     pA  = pd->a + pd->i[i];
1704     for (j=0; j<pnz; j++){
1705       row = pdJ[j];
1706       cnz = bi[row+1] - bi[row];
1707       cj  = bj + bi[row];
1708       ca  = ba + bi[row];
1709       /* perform sparse axpy */
1710       nexta  = 0;
1711       valtmp = pA[j];
1712       for (k=0; nexta<anz; k++) {
1713         if (cj[k] == adj[nexta]){
1714           ca[k] += valtmp*ada[nexta];
1715           nexta++;
1716         }
1717       }
1718       ierr = PetscLogFlops(2.0*anz);CHKERRQ(ierr);
1719     }
1720 
1721   }
1722 
1723   /* 3) send and recv matrix values coa */
1724   /*------------------------------------*/
1725   buf_ri = merge->buf_ri;
1726   buf_rj = merge->buf_rj;
1727   len_s  = merge->len_s;
1728   ierr = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1729   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1730 
1731   ierr = PetscMalloc2(merge->nsend+1,MPI_Request,&s_waits,size,MPI_Status,&status);CHKERRQ(ierr);
1732   for (proc=0,k=0; proc<size; proc++){
1733     if (!len_s[proc]) continue;
1734     i = merge->owners_co[proc];
1735     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
1736     k++;
1737   }
1738   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
1739   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
1740 
1741   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1742   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1743   ierr = PetscFree(coa);CHKERRQ(ierr);
1744 
1745   /* 4) insert local Cseq and received values into Cmpi */
1746   /*----------------------------------------------------*/
1747   ierr = PetscMalloc3(merge->nrecv,PetscInt**,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextci);CHKERRQ(ierr);
1748   for (k=0; k<merge->nrecv; k++){
1749     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1750     nrows       = *(buf_ri_k[k]);
1751     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1752     nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
1753   }
1754 
1755   for (i=0; i<cm; i++) {
1756     row = owners[rank] + i; /* global row index of C_seq */
1757     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1758     ba_i = ba + bi[i];
1759     bnz  = bi[i+1] - bi[i];
1760     /* add received vals into ba */
1761     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
1762       /* i-th row */
1763       if (i == *nextrow[k]) {
1764         cnz = *(nextci[k]+1) - *nextci[k];
1765         cj  = buf_rj[k] + *(nextci[k]);
1766         ca  = abuf_r[k] + *(nextci[k]);
1767         nextcj = 0;
1768         for (j=0; nextcj<cnz; j++){
1769           if (bj_i[j] == cj[nextcj]){ /* bcol == ccol */
1770             ba_i[j] += ca[nextcj++];
1771           }
1772         }
1773         nextrow[k]++; nextci[k]++;
1774         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1775       }
1776     }
1777     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1778   }
1779   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1780   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1781 
1782   ierr = PetscFree(ba);CHKERRQ(ierr);
1783   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1784   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1785   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1786   PetscFunctionReturn(0);
1787 }
1788 
1789 /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1790 #undef __FUNCT__
1791 #define __FUNCT__ "MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable"
1792 PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_Scalable(Mat P,Mat A,PetscReal fill,Mat *C)
1793 {
1794   PetscErrorCode       ierr;
1795   Mat                  Cmpi,A_loc,POt,PDt;
1796   Mat_PtAPMPI          *ptap;
1797   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
1798   Mat_MPIAIJ           *p=(Mat_MPIAIJ*)P->data,*c;
1799   PetscInt             *pdti,*pdtj,*poti,*potj,*ptJ;
1800   PetscInt             nnz;
1801   PetscInt             *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1802   PetscInt             am=A->rmap->n,pn=P->cmap->n;
1803   MPI_Comm             comm=((PetscObject)A)->comm;
1804   PetscMPIInt          size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1805   PetscInt             **buf_rj,**buf_ri,**buf_ri_k;
1806   PetscInt             len,proc,*dnz,*onz,*owners;
1807   PetscInt             nzi,*bi,*bj;
1808   PetscInt             nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1809   MPI_Request          *swaits,*rwaits;
1810   MPI_Status           *sstatus,rstatus;
1811   Mat_Merge_SeqsToMPI  *merge;
1812   PetscInt             *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1813   PetscReal            afill=1.0,afill_tmp;
1814   PetscInt             rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Crmax;
1815   PetscScalar          *vals;
1816   Mat_SeqAIJ           *a_loc, *pdt,*pot;
1817 
1818   PetscFunctionBegin;
1819   /* check if matrix local sizes are compatible */
1820   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend){
1821     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);
1822   }
1823 
1824   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1825   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1826 #if defined(DEBUG_MATTrMatMult)
1827   ierr = PetscSynchronizedPrintf(comm,"[%d] TransposeMatMultSymbolic_Scalable P: %d %d, %d %d; A %d %d, %d %d\n",rank,P->rmap->N,P->cmap->N,P->rmap->n,P->cmap->n,A->rmap->N,aN,A->rmap->n,A->cmap->n);
1828   ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
1829 #endif
1830 
1831   /* create struct Mat_PtAPMPI and attached it to C later */
1832   ierr = PetscNew(Mat_PtAPMPI,&ptap);CHKERRQ(ierr);
1833 
1834   /* get A_loc by taking all local rows of A */
1835   ierr = MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);CHKERRQ(ierr);
1836   ptap->A_loc = A_loc;
1837   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1838   ai   = a_loc->i;
1839   aj   = a_loc->j;
1840 
1841   /* determine symbolic Co=(p->B)^T*A - send to others */
1842   /*----------------------------------------------------*/
1843   ierr = MatTransposeSymbolic_SeqAIJ(p->A,&PDt);CHKERRQ(ierr);
1844   pdt = (Mat_SeqAIJ*)PDt->data;
1845   pdti = pdt->i; pdtj = pdt->j;
1846 
1847   ierr = MatTransposeSymbolic_SeqAIJ(p->B,&POt);CHKERRQ(ierr);
1848   pot = (Mat_SeqAIJ*)POt->data;
1849   poti = pot->i; potj = pot->j;
1850 
1851   /* then, compute symbolic Co = (p->B)^T*A */
1852   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1853                          >= (num of nonzero rows of C_seq) - pn */
1854   ierr = PetscMalloc((pon+1)*sizeof(PetscInt),&coi);CHKERRQ(ierr);
1855   coi[0] = 0;
1856 
1857   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1858   nnz           = fill*(poti[pon] + ai[am]);
1859   ierr          = PetscFreeSpaceGet(nnz,&free_space);
1860   current_space = free_space;
1861 #if defined(DEBUG_MATTrMatMult)
1862   ierr = PetscSynchronizedPrintf(comm, "[%d] nnz = fill %g *(%d + %d)\n",rank,fill,poti[pon],ai[am]);CHKERRQ(ierr);
1863   ierr = PetscSynchronizedFlush(comm);CHKERRQ(ierr);
1864 #endif
1865   /* create and initialize a linked list */
1866   i = PetscMax(pdt->rmax,pot->rmax);
1867   Crmax = i*a_loc->rmax*size; /* non-scalable! */
1868   if (!Crmax || Crmax > aN) Crmax = aN;
1869 #if defined(DEBUG_MATTrMatMult)
1870   printf("[%d] rmax A_loc %d * max(PD %d, PO %d)=%d, Crmax %d\n",rank,a_loc->rmax,pdt->rmax,pot->rmax,i*a_loc->rmax,Crmax);
1871 #endif
1872   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
1873 
1874   for (i=0; i<pon; i++) {
1875     nnz = 0;
1876     pnz = poti[i+1] - poti[i];
1877     ptJ = potj + poti[i];
1878     for (j=0; j<pnz; j++){
1879       row  = ptJ[j]; /* row of A_loc == col of Pot */
1880       anz  = ai[row+1] - ai[row];
1881       Jptr = aj + ai[row];
1882       /* add non-zero cols of AP into the sorted linked list lnk */
1883       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
1884     }
1885     nnz = lnk[0];
1886 
1887     /* If free space is not available, double the total space in the list */
1888     if (current_space->local_remaining<nnz) {
1889       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
1890       nspacedouble++;
1891     }
1892 
1893     /* Copy data into free space, and zero out denserows */
1894     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
1895     current_space->array           += nnz;
1896     current_space->local_used      += nnz;
1897     current_space->local_remaining -= nnz;
1898     coi[i+1] = coi[i] + nnz;
1899   }
1900 
1901   ierr = PetscMalloc((coi[pon]+1)*sizeof(PetscInt),&coj);CHKERRQ(ierr);
1902   ierr = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1903   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]);
1904   if (afill_tmp > afill) afill = afill_tmp;
1905 
1906   /* send j-array (coj) of Co to other processors */
1907   /*----------------------------------------------*/
1908   /* determine row ownership */
1909   ierr = PetscNew(Mat_Merge_SeqsToMPI,&merge);CHKERRQ(ierr);
1910   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1911   merge->rowmap->n = pn;
1912   merge->rowmap->bs = 1;
1913   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1914   owners = merge->rowmap->range;
1915 
1916   /* determine the number of messages to send, their lengths */
1917   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&len_si);CHKERRQ(ierr);
1918   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
1919   ierr = PetscMalloc(size*sizeof(PetscMPIInt),&merge->len_s);CHKERRQ(ierr);
1920   len_s = merge->len_s;
1921   merge->nsend = 0;
1922 
1923   ierr = PetscMalloc((size+2)*sizeof(PetscInt),&owners_co);CHKERRQ(ierr);
1924   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
1925 
1926   proc = 0;
1927   for (i=0; i<pon; i++){
1928     while (prmap[i] >= owners[proc+1]) proc++;
1929     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1930     len_s[proc] += coi[i+1] - coi[i];
1931   }
1932 
1933   len   = 0;  /* max length of buf_si[] */
1934   owners_co[0] = 0;
1935   for (proc=0; proc<size; proc++){
1936     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1937     if (len_si[proc]){
1938       merge->nsend++;
1939       len_si[proc] = 2*(len_si[proc] + 1);
1940       len += len_si[proc];
1941     }
1942   }
1943 
1944   /* determine the number and length of messages to receive for coi and coj  */
1945   ierr = PetscGatherNumberOfMessages(comm,PETSC_NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1946   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1947 
1948   /* post the Irecv and Isend of coj */
1949   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1950   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1951   ierr = PetscMalloc((merge->nsend+1)*sizeof(MPI_Request),&swaits);CHKERRQ(ierr);
1952   for (proc=0, k=0; proc<size; proc++){
1953     if (!len_s[proc]) continue;
1954     i = owners_co[proc];
1955     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
1956     k++;
1957   }
1958 
1959   /* receives and sends of coj are complete */
1960   ierr = PetscMalloc(size*sizeof(MPI_Status),&sstatus);CHKERRQ(ierr);
1961   for (i=0; i<merge->nrecv; i++){
1962     PetscMPIInt icompleted;
1963     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1964   }
1965   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1966   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
1967 
1968   /* send and recv coi */
1969   /*-------------------*/
1970   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1971   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1972   ierr = PetscMalloc((len+1)*sizeof(PetscInt),&buf_s);CHKERRQ(ierr);
1973   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1974   for (proc=0,k=0; proc<size; proc++){
1975     if (!len_s[proc]) continue;
1976     /* form outgoing message for i-structure:
1977          buf_si[0]:                 nrows to be sent
1978                [1:nrows]:           row index (global)
1979                [nrows+1:2*nrows+1]: i-structure index
1980     */
1981     /*-------------------------------------------*/
1982     nrows = len_si[proc]/2 - 1;
1983     buf_si_i    = buf_si + nrows+1;
1984     buf_si[0]   = nrows;
1985     buf_si_i[0] = 0;
1986     nrows = 0;
1987     for (i=owners_co[proc]; i<owners_co[proc+1]; i++){
1988       nzi = coi[i+1] - coi[i];
1989       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
1990       buf_si[nrows+1] =prmap[i] -owners[proc]; /* local row index */
1991       nrows++;
1992     }
1993     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
1994     k++;
1995     buf_si += len_si[proc];
1996   }
1997   i = merge->nrecv;
1998   while (i--) {
1999     PetscMPIInt icompleted;
2000     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
2001   }
2002   ierr = PetscFree(rwaits);CHKERRQ(ierr);
2003   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
2004   ierr = PetscFree(len_si);CHKERRQ(ierr);
2005   ierr = PetscFree(len_ri);CHKERRQ(ierr);
2006   ierr = PetscFree(swaits);CHKERRQ(ierr);
2007   ierr = PetscFree(sstatus);CHKERRQ(ierr);
2008   ierr = PetscFree(buf_s);CHKERRQ(ierr);
2009 
2010   /* compute the local portion of C (mpi mat) */
2011   /*------------------------------------------*/
2012   /* allocate bi array and free space for accumulating nonzero column info */
2013   ierr = PetscMalloc((pn+1)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
2014   bi[0] = 0;
2015 
2016   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
2017   nnz           = fill*(pdti[pn] + poti[pon] + ai[am]);
2018   ierr          = PetscFreeSpaceGet(nnz,&free_space);
2019   current_space = free_space;
2020 
2021 #if defined(DEBUG_MATTrMatMult)
2022   ierr = PetscPrintf(PETSC_COMM_SELF,"[%d] nnz=%d + %d + %d\n",rank,pdti[pn],poti[pon],ai[am]);
2023 #endif
2024 
2025   ierr = PetscMalloc3(merge->nrecv,PetscInt**,&buf_ri_k,merge->nrecv,PetscInt*,&nextrow,merge->nrecv,PetscInt*,&nextci);CHKERRQ(ierr);
2026   for (k=0; k<merge->nrecv; k++){
2027     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
2028     nrows       = *buf_ri_k[k];
2029     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
2030     nextci[k]   = buf_ri_k[k] + (nrows + 1);/* poins to the next i-structure of k-th recved i-structure  */
2031   }
2032 
2033   ierr = MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);CHKERRQ(ierr);
2034   rmax = 0;
2035   for (i=0; i<pn; i++) {
2036     /* add pdt[i,:]*AP into lnk */
2037     pnz = pdti[i+1] - pdti[i];
2038     ptJ = pdtj + pdti[i];
2039     for (j=0; j<pnz; j++){
2040       row  = ptJ[j];  /* row of AP == col of Pt */
2041       anz  = ai[row+1] - ai[row];
2042       Jptr = aj + ai[row];
2043       /* add non-zero cols of AP into the sorted linked list lnk */
2044       ierr = PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);CHKERRQ(ierr);
2045     }
2046 
2047     /* add received col data into lnk */
2048     for (k=0; k<merge->nrecv; k++){ /* k-th received message */
2049       if (i == *nextrow[k]) { /* i-th row */
2050         nzi = *(nextci[k]+1) - *nextci[k];
2051         Jptr  = buf_rj[k] + *nextci[k];
2052         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
2053         nextrow[k]++; nextci[k]++;
2054       }
2055     }
2056     nnz = lnk[0];
2057 
2058     /* if free space is not available, make more free space */
2059     if (current_space->local_remaining<nnz) {
2060       ierr = PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
2061       nspacedouble++;
2062     }
2063     /* copy data into free space, then initialize lnk */
2064     ierr = PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);CHKERRQ(ierr);
2065     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
2066     current_space->array           += nnz;
2067     current_space->local_used      += nnz;
2068     current_space->local_remaining -= nnz;
2069     bi[i+1] = bi[i] + nnz;
2070     if (nnz > rmax) rmax = nnz;
2071   }
2072   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
2073 
2074   ierr = PetscMalloc((bi[pn]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
2075   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
2076   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]);
2077   if (afill_tmp > afill) afill = afill_tmp;
2078   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
2079   ierr = MatDestroy(&POt);CHKERRQ(ierr);
2080   ierr = MatDestroy(&PDt);CHKERRQ(ierr);
2081 
2082   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
2083   /*----------------------------------------------------------------------------------*/
2084   ierr = PetscMalloc((rmax+1)*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
2085   ierr = PetscMemzero(vals,rmax*sizeof(PetscScalar));CHKERRQ(ierr);
2086 
2087   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
2088   ierr = MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
2089   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
2090   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
2091   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
2092   ierr = MatSetBlockSize(Cmpi,1);CHKERRQ(ierr);
2093   for (i=0; i<pn; i++){
2094     row = i + rstart;
2095     nnz = bi[i+1] - bi[i];
2096     Jptr = bj + bi[i];
2097     ierr = MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);CHKERRQ(ierr);
2098   }
2099   ierr = MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2100   ierr = MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2101   ierr = PetscFree(vals);CHKERRQ(ierr);
2102 
2103   merge->bi            = bi;
2104   merge->bj            = bj;
2105   merge->coi           = coi;
2106   merge->coj           = coj;
2107   merge->buf_ri        = buf_ri;
2108   merge->buf_rj        = buf_rj;
2109   merge->owners_co     = owners_co;
2110   merge->destroy       = Cmpi->ops->destroy;
2111   merge->duplicate     = Cmpi->ops->duplicate;
2112 
2113   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_Scalable;
2114   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
2115 
2116   /* attach the supporting struct to Cmpi for reuse */
2117   c = (Mat_MPIAIJ*)Cmpi->data;
2118   c->ptap        = ptap;
2119   ptap->api      = PETSC_NULL;
2120   ptap->apj      = PETSC_NULL;
2121   ptap->merge    = merge;
2122   ptap->rmax     = rmax;
2123   ptap->apa      = PETSC_NULL;
2124 
2125   *C = Cmpi;
2126 #if defined(PETSC_USE_INFO)
2127   if (bi[pn] != 0) {
2128     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %G needed %G.\n",nspacedouble,fill,afill);CHKERRQ(ierr);
2129     ierr = PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%G,&C) for best performance.\n",afill);CHKERRQ(ierr);
2130   } else {
2131     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
2132   }
2133 #endif
2134   PetscFunctionReturn(0);
2135 }
2136