xref: /petsc/src/mat/impls/aij/mpi/mpimatmatmult.c (revision 4ae0847b5407bb1f61dd4d8dd55bc243d48f67c9)
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 #undef __FUNCT__
13 #define __FUNCT__ "MatMatMult_MPIAIJ_MPIAIJ"
14 PetscErrorCode MatMatMult_MPIAIJ_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill, Mat *C)
15 {
16   PetscErrorCode ierr;
17 
18   PetscFunctionBegin;
19   if (scall == MAT_INITIAL_MATRIX){
20     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
21     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);/* numeric product is computed as well in old version! */
22     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
23   }
24   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
25   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
26   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
27   PetscFunctionReturn(0);
28 }
29 
30 #undef __FUNCT__
31 #define __FUNCT__ "PetscContainerDestroy_Mat_MatMatMultMPI"
32 PetscErrorCode PetscContainerDestroy_Mat_MatMatMultMPI(void *ptr)
33 {
34   PetscErrorCode       ierr;
35   Mat_MatMatMultMPI    *mult=(Mat_MatMatMultMPI*)ptr;
36 
37   PetscFunctionBegin;
38   ierr = ISDestroy(&mult->isrowa);CHKERRQ(ierr);
39   ierr = ISDestroy(&mult->isrowb);CHKERRQ(ierr);
40   ierr = ISDestroy(&mult->iscolb);CHKERRQ(ierr);
41   ierr = MatDestroy(&mult->C_seq);CHKERRQ(ierr);
42   ierr = MatDestroy(&mult->A_loc);CHKERRQ(ierr);
43   ierr = MatDestroy(&mult->B_seq);CHKERRQ(ierr);
44   ierr = PetscFree(mult);CHKERRQ(ierr);
45   PetscFunctionReturn(0);
46 }
47 
48 #undef __FUNCT__
49 #define __FUNCT__ "MatDestroy_MPIAIJ_MatMatMult_new"
50 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult_new(Mat A)
51 {
52   PetscErrorCode ierr;
53   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
54   Mat_PtAPMPI    *ptap=a->ptap;
55 
56   PetscFunctionBegin;
57   ierr = PetscFree2(ptap->startsj,ptap->startsj_r);CHKERRQ(ierr);
58   ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
59   ierr = MatDestroy(&ptap->B_loc);CHKERRQ(ierr);
60   ierr = MatDestroy(&ptap->B_oth);CHKERRQ(ierr);
61   ierr = PetscFree(ptap->abi);CHKERRQ(ierr);
62   ierr = PetscFree(ptap->abj);CHKERRQ(ierr);
63   ierr = PetscFree(ptap->apa);CHKERRQ(ierr);
64   ierr = ptap->destroy(A);CHKERRQ(ierr);
65   ierr = PetscFree(ptap);CHKERRQ(ierr);
66   PetscFunctionReturn(0);
67 }
68 
69 #undef __FUNCT__
70 #define __FUNCT__ "MatDestroy_MPIAIJ_MatMatMult"
71 PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
72 {
73   PetscErrorCode     ierr;
74   PetscContainer     container;
75   Mat_MatMatMultMPI  *mult=PETSC_NULL;
76 
77   PetscFunctionBegin;
78   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
79   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
80   ierr = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
81   A->ops->destroy   = mult->destroy;
82   A->ops->duplicate = mult->duplicate;
83   if (A->ops->destroy) {
84     ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
85   }
86   ierr = PetscObjectCompose((PetscObject)A,"Mat_MatMatMultMPI",0);CHKERRQ(ierr);
87   PetscFunctionReturn(0);
88 }
89 
90 #undef __FUNCT__
91 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatMatMult"
92 PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult(Mat A, MatDuplicateOption op, Mat *M)
93 {
94   PetscErrorCode     ierr;
95   Mat_MatMatMultMPI  *mult;
96   PetscContainer     container;
97 
98   PetscFunctionBegin;
99   ierr = PetscObjectQuery((PetscObject)A,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
100   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
101   ierr  = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
102   /* Note: the container is not duplicated, because it requires deep copying of
103      several large data sets (see PetscContainerDestroy_Mat_MatMatMultMPI()).
104      These data sets are only used for repeated calling of MatMatMultNumeric().
105      *M is unlikely being used in this way. Thus we create *M with pure mpiaij format */
106   ierr = (*mult->duplicate)(A,op,M);CHKERRQ(ierr);
107   (*M)->ops->destroy   = mult->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's container! */
108   (*M)->ops->duplicate = mult->duplicate; /* = MatDuplicate_MPIAIJ */
109   PetscFunctionReturn(0);
110 }
111 
112 #undef __FUNCT__
113 #define __FUNCT__ "MatDuplicate_MPIAIJ_MatMatMult_new"
114 PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult_new(Mat A, MatDuplicateOption op, Mat *M)
115 {
116   PetscErrorCode     ierr;
117   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
118   Mat_PtAPMPI        *ptap=a->ptap;
119 
120   PetscFunctionBegin;
121   ierr = (*ptap->duplicate)(A,op,M);CHKERRQ(ierr);
122   (*M)->ops->destroy   = ptap->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's special structure! */
123   (*M)->ops->duplicate = ptap->duplicate; /* = MatDuplicate_MPIAIJ */
124   PetscFunctionReturn(0);
125 }
126 
127 #undef __FUNCT__
128 #define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIAIJ_new"
129 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_new(Mat A,Mat P,Mat C)
130 {
131   PetscErrorCode     ierr;
132   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
133   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
134   Mat_SeqAIJ         *cd=(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
135   PetscInt           *adi=ad->i,*adj,*aoi=ao->i,*aoj;
136   PetscScalar        *ada,*aoa,*cda=cd->a,*coa=co->a;
137   Mat_SeqAIJ         *p_loc,*p_oth;
138   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
139   PetscScalar        *pa_loc,*pa_oth,*pa,*apa,valtmp,*ca;
140   PetscInt           cm=C->rmap->n,anz,pnz;
141   Mat_PtAPMPI        *ptap=c->ptap;
142   PetscInt           *api,*apj,*apJ,cnz,i,j,k,row;
143   PetscInt           rstart=C->rmap->rstart,cstart=C->cmap->rstart;
144   PetscInt           cdnz,conz,k0,k1;
145 
146   PetscFunctionBegin;
147   /* 1) get P_oth = ptap->B_oth  and P_loc = ptap->B_loc */
148   /*-----------------------------------------------------*/
149   if (ptap->reuse == MAT_INITIAL_MATRIX){
150     ptap->reuse = MAT_REUSE_MATRIX;
151   } else { /* update numerical values of P_oth and P_loc */
152     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj,&ptap->startsj_r,&ptap->bufa,&ptap->B_oth);CHKERRQ(ierr);
153     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->B_loc);CHKERRQ(ierr);
154   }
155 
156   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
157   /*----------------------------------------------------------*/
158   /* get data from symbolic products */
159   p_loc = (Mat_SeqAIJ*)(ptap->B_loc)->data;
160   p_oth = (Mat_SeqAIJ*)(ptap->B_oth)->data;
161   pi_loc=p_loc->i; pj_loc=p_loc->j; pa_loc=p_loc->a;
162   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
163 
164   /* get apa for storing dense row A[i,:]*P */
165   apa = ptap->apa;
166 
167   for (i=0; i<cm; i++) {
168     /* diagonal portion of A */
169     anz = adi[i+1] - adi[i];
170     adj = ad->j + adi[i];
171     ada = ad->a + adi[i];
172     for (j=0; j<anz; j++) {
173       row = adj[j];
174       pnz = pi_loc[row+1] - pi_loc[row];
175       pj  = pj_loc + pi_loc[row];
176       pa  = pa_loc + pi_loc[row];
177 
178       /* perform dense axpy */
179       valtmp = ada[j];
180       for (k=0; k<pnz; k++){
181         apa[pj[k]] += valtmp*pa[k];
182       }
183       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
184     }
185 
186     /* off-diagonal portion of A */
187     anz = aoi[i+1] - aoi[i];
188     aoj = ao->j + aoi[i];
189     aoa = ao->a + aoi[i];
190     for (j=0; j<anz; j++) {
191       row = aoj[j];
192       pnz = pi_oth[row+1] - pi_oth[row];
193       pj  = pj_oth + pi_oth[row];
194       pa  = pa_oth + pi_oth[row];
195 
196       /* perform dense axpy */
197       valtmp = aoa[j];
198       for (k=0; k<pnz; k++){
199         apa[pj[k]] += valtmp*pa[k];
200       }
201       ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
202     }
203 
204     /* set values in C */
205     row = rstart + i;
206     api = ptap->abi;
207     apj = ptap->abj;
208     apJ = apj + api[i];
209     cnz = api[i+1] - api[i];
210     cdnz = cd->i[i+1] - cd->i[i];
211     conz = co->i[i+1] - co->i[i];
212 
213     /* 1st off-diagoanl part of C */
214     ca = coa + co->i[i];
215     k  = 0;
216     for (k0=0; k0<conz; k0++){
217       if (apJ[k] >= cstart) break;
218       ca[k0]      = apa[apJ[k]];
219       apa[apJ[k]] = 0.0;
220       k++;
221     }
222 
223     /* diagonal part of C */
224     ca = cda + cd->i[i];
225     for (k1=0; k1<cdnz; k1++){
226       ca[k1]      = apa[apJ[k]];
227       apa[apJ[k]] = 0.0;
228       k++;
229     }
230 
231     /* 2nd off-diagoanl part of C */
232     ca = coa + co->i[i];
233     for (; k0<conz; k0++){
234       ca[k0]      = apa[apJ[k]];
235       apa[apJ[k]] = 0.0;
236       k++;
237     }
238   }
239   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
240   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
241   PetscFunctionReturn(0);
242 }
243 
244 #undef __FUNCT__
245 #define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIAIJ_new"
246 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_new(Mat A,Mat P,PetscReal fill,Mat *C)
247 {
248   PetscErrorCode       ierr;
249   MPI_Comm             comm=((PetscObject)A)->comm;
250   PetscMPIInt          size,rank;
251   Mat                  B_mpi;
252   Mat_PtAPMPI          *ptap;
253   PetscFreeSpaceList   free_space=PETSC_NULL,current_space=PETSC_NULL;
254   Mat_MPIAIJ           *a=(Mat_MPIAIJ*)A->data,*c;
255   Mat_SeqAIJ           *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
256   Mat_SeqAIJ           *p_loc,*p_oth;
257   PetscInt             *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
258   PetscInt             *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
259   PetscInt             nlnk,*lnk,i,pnz,row;
260   PetscInt             am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
261   PetscBT              lnkbt;
262   PetscInt             nzi;
263   PetscInt             *api,*apj,*Jptr,apnz,nspacedouble=0,j;
264   PetscScalar          *apa;
265 
266   PetscFunctionBegin;
267   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
268   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
269 
270   /* create struct Mat_PtAPMPI and attached it to C later */
271   ierr = PetscNew(Mat_PtAPMPI,&ptap);CHKERRQ(ierr);
272   ptap->abnz_max = 0;
273   ptap->reuse    = MAT_INITIAL_MATRIX;
274 
275   /* malloc apa to store dense row A[i,:]*P */
276   ierr = PetscMalloc((P->cmap->N)*sizeof(PetscScalar),&apa);CHKERRQ(ierr);
277   ierr = PetscMemzero(apa,P->cmap->N*sizeof(PetscScalar));CHKERRQ(ierr);
278   ptap->apa = apa;
279 
280 
281   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
282   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj,&ptap->startsj_r,&ptap->bufa,&ptap->B_oth);CHKERRQ(ierr);
283   /* get P_loc by taking all local rows of P */
284   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->B_loc);CHKERRQ(ierr);
285 
286   p_loc = (Mat_SeqAIJ*)(ptap->B_loc)->data;
287   p_oth = (Mat_SeqAIJ*)(ptap->B_oth)->data;
288   pi_loc = p_loc->i; pj_loc = p_loc->j;
289   pi_oth = p_oth->i; pj_oth = p_oth->j;
290 
291   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
292   /*-------------------------------------------------------------------*/
293   ierr  = PetscMalloc((am+2)*sizeof(PetscInt),&api);CHKERRQ(ierr);
294   ptap->abi = api;
295   api[0]    = 0;
296 
297   /* create and initialize a linked list */
298   nlnk = pN+1;
299   ierr = PetscLLCreate(pN,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
300 
301   /* Initial FreeSpace size is fill*nnz(A) */
302   ierr = PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am])),&free_space);CHKERRQ(ierr);
303   current_space = free_space;
304 
305   ierr = MatPreallocateInitialize(comm,am,pn,dnz,onz);CHKERRQ(ierr);
306   for (i=0;i<am;i++) {
307     apnz = 0;
308     /* diagonal portion of A */
309     nzi = adi[i+1] - adi[i];
310     for (j=0; j<nzi; j++){
311       row = *adj++;
312       pnz = pi_loc[row+1] - pi_loc[row];
313       Jptr  = pj_loc + pi_loc[row];
314       /* add non-zero cols of P into the sorted linked list lnk */
315       ierr = PetscLLAdd(pnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
316       apnz += nlnk;
317     }
318     /* off-diagonal portion of A */
319     nzi = aoi[i+1] - aoi[i];
320     for (j=0; j<nzi; j++){
321       row = *aoj++;
322       pnz = pi_oth[row+1] - pi_oth[row];
323       Jptr  = pj_oth + pi_oth[row];
324       ierr = PetscLLAdd(pnz,Jptr,pN,nlnk,lnk,lnkbt);CHKERRQ(ierr);
325       apnz += nlnk;
326     }
327 
328     api[i+1] = api[i] + apnz;
329     if (ptap->abnz_max < apnz) ptap->abnz_max = apnz;
330 
331     /* if free space is not available, double the total space in the list */
332     if (current_space->local_remaining<apnz) {
333       ierr = PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);CHKERRQ(ierr);
334       nspacedouble++;
335     }
336 
337     /* Copy data into free space, then initialize lnk */
338     ierr = PetscLLClean(pN,pN,apnz,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
339     ierr = MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);CHKERRQ(ierr);
340     current_space->array           += apnz;
341     current_space->local_used      += apnz;
342     current_space->local_remaining -= apnz;
343   }
344 
345   /* Allocate space for apj, initialize apj, and */
346   /* destroy list of free space and other temporary array(s) */
347   ierr = PetscMalloc((api[am]+1)*sizeof(PetscInt),&ptap->abj);CHKERRQ(ierr);
348   apj = ptap->abj;
349   ierr = PetscFreeSpaceContiguous(&free_space,ptap->abj);CHKERRQ(ierr);
350   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
351 
352   /* create and assemble symbolic parallel matrix B_mpi */
353   /*----------------------------------------------------*/
354   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
355   ierr = MatSetSizes(B_mpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
356   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
357   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
358   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
359   ierr = MatSetBlockSize(B_mpi,1);CHKERRQ(ierr);
360   for (i=0; i<am; i++){
361     row = i + rstart;
362     apnz = api[i+1] - api[i];
363     ierr = MatSetValues(B_mpi,1,&row,apnz,apj,apa,INSERT_VALUES);CHKERRQ(ierr);
364     apj += apnz;
365   }
366   ierr = MatAssemblyBegin(B_mpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
367   ierr = MatAssemblyEnd(B_mpi,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
368 
369   ptap->destroy              = B_mpi->ops->destroy;
370   ptap->duplicate            = B_mpi->ops->duplicate;
371   B_mpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_new;
372   B_mpi->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult_new;
373   B_mpi->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult_new;
374 
375   /* attach the supporting struct to B_mpi for reuse */
376   c = (Mat_MPIAIJ*)B_mpi->data;
377   c->ptap  = ptap;
378 
379   *C = B_mpi;
380   PetscFunctionReturn(0);
381 }
382 
383 #undef __FUNCT__
384 #define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIAIJ"
385 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
386 {
387   PetscErrorCode     ierr;
388   Mat_MatMatMultMPI  *mult;
389   PetscContainer     container;
390   Mat                AB,*seq;
391   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
392   PetscInt           *idx,i,start,ncols,nzA,nzB,*cmap,imark;
393   PetscBool          matmatmult_new=PETSC_FALSE;
394 
395   PetscFunctionBegin;
396   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend){
397     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
398   }
399   ierr = PetscOptionsGetBool(PETSC_NULL,"-matmatmult_new",&matmatmult_new,PETSC_NULL);CHKERRQ(ierr);
400   if (matmatmult_new){
401     ierr = MatMatMultSymbolic_MPIAIJ_MPIAIJ_new(A,B,fill,C);;CHKERRQ(ierr);
402     PetscFunctionReturn(0);
403   }
404 
405   ierr = PetscNew(Mat_MatMatMultMPI,&mult);CHKERRQ(ierr);
406 
407   /* get isrowb: nonzero col of A */
408   start = A->cmap->rstart;
409   cmap  = a->garray;
410   nzA   = a->A->cmap->n;
411   nzB   = a->B->cmap->n;
412   ierr  = PetscMalloc((nzA+nzB)*sizeof(PetscInt), &idx);CHKERRQ(ierr);
413   ncols = 0;
414   for (i=0; i<nzB; i++) {  /* row < local row index */
415     if (cmap[i] < start) idx[ncols++] = cmap[i];
416     else break;
417   }
418   imark = i;
419   for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
420   for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
421   ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&mult->isrowb);CHKERRQ(ierr);
422   ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&mult->iscolb);CHKERRQ(ierr);
423 
424   /*  get isrowa: all local rows of A */
425   ierr = ISCreateStride(PETSC_COMM_SELF,A->rmap->n,A->rmap->rstart,1,&mult->isrowa);CHKERRQ(ierr);
426 
427   /* Below should go to MatMatMultNumeric_MPIAIJ_MPIAIJ() - How to generate C there? */
428   /* create a seq matrix B_seq = submatrix of B by taking rows of B that equal to nonzero col of A */
429   ierr = MatGetSubMatrices(B,1,&mult->isrowb,&mult->iscolb,MAT_INITIAL_MATRIX,&seq);CHKERRQ(ierr);
430   mult->B_seq = *seq;
431   ierr = PetscFree(seq);CHKERRQ(ierr);
432 
433   /*  create a seq matrix A_seq = submatrix of A by taking all local rows of A */
434   ierr = MatGetSubMatrices(A,1,&mult->isrowa,&mult->isrowb,MAT_INITIAL_MATRIX,&seq);CHKERRQ(ierr);
435   mult->A_loc = *seq;
436   ierr = PetscFree(seq);CHKERRQ(ierr);
437 
438   /* compute C_seq = A_seq * B_seq */
439   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(mult->A_loc,mult->B_seq,fill,&mult->C_seq);CHKERRQ(ierr);
440   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ(mult->A_loc,mult->B_seq,mult->C_seq);CHKERRQ(ierr);
441 
442   /* create mpi matrix C by concatinating C_seq */
443   ierr = PetscObjectReference((PetscObject)mult->C_seq);CHKERRQ(ierr); /* prevent C_seq being destroyed by MatMerge() */
444   ierr = MatMergeSymbolic(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,&AB);CHKERRQ(ierr);
445   ierr = MatMergeNumeric(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,AB);CHKERRQ(ierr);
446 
447   /* attach the supporting struct to C for reuse of symbolic C */
448   ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
449   ierr = PetscContainerSetPointer(container,mult);CHKERRQ(ierr);
450   ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_Mat_MatMatMultMPI);CHKERRQ(ierr);
451   ierr = PetscObjectCompose((PetscObject)AB,"Mat_MatMatMultMPI",(PetscObject)container);CHKERRQ(ierr);
452   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
453   mult->destroy      = AB->ops->destroy;
454   mult->duplicate    = AB->ops->duplicate;
455   AB->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
456   AB->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
457   AB->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult;
458   AB->ops->matmult        = MatMatMult_MPIAIJ_MPIAIJ;
459   *C                      = AB;
460   PetscFunctionReturn(0);
461 }
462 
463 /* This routine is called ONLY in the case of reusing previously computed symbolic C */
464 #undef __FUNCT__
465 #define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIAIJ"
466 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat B,Mat C)
467 {
468   PetscErrorCode     ierr;
469   Mat                *seq;
470   Mat_MatMatMultMPI  *mult;
471   PetscContainer     container;
472 
473   PetscFunctionBegin;
474   ierr = PetscObjectQuery((PetscObject)C,"Mat_MatMatMultMPI",(PetscObject *)&container);CHKERRQ(ierr);
475   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
476   ierr  = PetscContainerGetPointer(container,(void **)&mult);CHKERRQ(ierr);
477   seq = &mult->B_seq;
478   ierr = MatGetSubMatrices(B,1,&mult->isrowb,&mult->iscolb,MAT_REUSE_MATRIX,&seq);CHKERRQ(ierr);
479   mult->B_seq = *seq;
480 
481   seq = &mult->A_loc;
482   ierr = MatGetSubMatrices(A,1,&mult->isrowa,&mult->isrowb,MAT_REUSE_MATRIX,&seq);CHKERRQ(ierr);
483   mult->A_loc = *seq;
484 
485   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_SparseAxpy(mult->A_loc,mult->B_seq,mult->C_seq);CHKERRQ(ierr);
486 
487   ierr = PetscObjectReference((PetscObject)mult->C_seq);CHKERRQ(ierr);
488   ierr = MatMerge(((PetscObject)A)->comm,mult->C_seq,B->cmap->n,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
489   PetscFunctionReturn(0);
490 }
491 
492 #undef __FUNCT__
493 #define __FUNCT__ "MatMatMult_MPIAIJ_MPIDense"
494 PetscErrorCode MatMatMult_MPIAIJ_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
495 {
496   PetscErrorCode ierr;
497 
498   PetscFunctionBegin;
499   if (scall == MAT_INITIAL_MATRIX){
500     ierr = MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,fill,C);CHKERRQ(ierr);
501   }
502   ierr = MatMatMultNumeric_MPIAIJ_MPIDense(A,B,*C);CHKERRQ(ierr);
503   PetscFunctionReturn(0);
504 }
505 
506 typedef struct {
507   Mat         workB;
508   PetscScalar *rvalues,*svalues;
509   MPI_Request *rwaits,*swaits;
510 } MPIAIJ_MPIDense;
511 
512 #undef __FUNCT__
513 #define __FUNCT__ "MPIAIJ_MPIDenseDestroy"
514 PetscErrorCode MPIAIJ_MPIDenseDestroy(void *ctx)
515 {
516   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*) ctx;
517   PetscErrorCode  ierr;
518 
519   PetscFunctionBegin;
520   ierr = MatDestroy(&contents->workB);CHKERRQ(ierr);
521   ierr = PetscFree4(contents->rvalues,contents->svalues,contents->rwaits,contents->swaits);CHKERRQ(ierr);
522   ierr = PetscFree(contents);CHKERRQ(ierr);
523   PetscFunctionReturn(0);
524 }
525 
526 #undef __FUNCT__
527 #define __FUNCT__ "MatMatMultSymbolic_MPIAIJ_MPIDense"
528 PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
529 {
530   PetscErrorCode         ierr;
531   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
532   PetscInt               nz = aij->B->cmap->n;
533   PetscContainer         container;
534   MPIAIJ_MPIDense        *contents;
535   VecScatter             ctx = aij->Mvctx;
536   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
537   VecScatter_MPI_General *to   = ( VecScatter_MPI_General*) ctx->todata;
538   PetscInt               m=A->rmap->n,n=B->cmap->n;
539 
540   PetscFunctionBegin;
541   ierr = MatCreate(((PetscObject)B)->comm,C);CHKERRQ(ierr);
542   ierr = MatSetSizes(*C,m,n,A->rmap->N,B->cmap->N);CHKERRQ(ierr);
543   ierr = MatSetType(*C,MATMPIDENSE);CHKERRQ(ierr);
544   ierr = MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
545   ierr = MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
546   (*C)->ops->matmult = MatMatMult_MPIAIJ_MPIDense;
547 
548   ierr = PetscNew(MPIAIJ_MPIDense,&contents);CHKERRQ(ierr);
549   /* Create work matrix used to store off processor rows of B needed for local product */
550   ierr = MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,PETSC_NULL,&contents->workB);CHKERRQ(ierr);
551   /* Create work arrays needed */
552   ierr = PetscMalloc4(B->cmap->N*from->starts[from->n],PetscScalar,&contents->rvalues,
553                       B->cmap->N*to->starts[to->n],PetscScalar,&contents->svalues,
554                       from->n,MPI_Request,&contents->rwaits,
555                       to->n,MPI_Request,&contents->swaits);CHKERRQ(ierr);
556 
557   ierr = PetscContainerCreate(((PetscObject)A)->comm,&container);CHKERRQ(ierr);
558   ierr = PetscContainerSetPointer(container,contents);CHKERRQ(ierr);
559   ierr = PetscContainerSetUserDestroy(container,MPIAIJ_MPIDenseDestroy);CHKERRQ(ierr);
560   ierr = PetscObjectCompose((PetscObject)(*C),"workB",(PetscObject)container);CHKERRQ(ierr);
561   ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
562   PetscFunctionReturn(0);
563 }
564 
565 #undef __FUNCT__
566 #define __FUNCT__ "MatMPIDenseScatter"
567 /*
568     Performs an efficient scatter on the rows of B needed by this process; this is
569     a modification of the VecScatterBegin_() routines.
570 */
571 PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,Mat C,Mat *outworkB)
572 {
573   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)A->data;
574   PetscErrorCode         ierr;
575   PetscScalar            *b,*w,*svalues,*rvalues;
576   VecScatter             ctx = aij->Mvctx;
577   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
578   VecScatter_MPI_General *to   = ( VecScatter_MPI_General*) ctx->todata;
579   PetscInt               i,j,k;
580   PetscInt               *sindices,*sstarts,*rindices,*rstarts;
581   PetscMPIInt            *sprocs,*rprocs,nrecvs;
582   MPI_Request            *swaits,*rwaits;
583   MPI_Comm               comm = ((PetscObject)A)->comm;
584   PetscMPIInt            tag = ((PetscObject)ctx)->tag,ncols = B->cmap->N, nrows = aij->B->cmap->n,imdex,nrowsB = B->rmap->n;
585   MPI_Status             status;
586   MPIAIJ_MPIDense        *contents;
587   PetscContainer         container;
588   Mat                    workB;
589 
590   PetscFunctionBegin;
591   ierr = PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);CHKERRQ(ierr);
592   if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Container does not exit");
593   ierr = PetscContainerGetPointer(container,(void**)&contents);CHKERRQ(ierr);
594 
595   workB = *outworkB = contents->workB;
596   if (nrows != workB->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",nrows,workB->cmap->n);
597   sindices  = to->indices;
598   sstarts   = to->starts;
599   sprocs    = to->procs;
600   swaits    = contents->swaits;
601   svalues   = contents->svalues;
602 
603   rindices  = from->indices;
604   rstarts   = from->starts;
605   rprocs    = from->procs;
606   rwaits    = contents->rwaits;
607   rvalues   = contents->rvalues;
608 
609   ierr = MatGetArray(B,&b);CHKERRQ(ierr);
610   ierr = MatGetArray(workB,&w);CHKERRQ(ierr);
611 
612   for (i=0; i<from->n; i++) {
613     ierr = MPI_Irecv(rvalues+ncols*rstarts[i],ncols*(rstarts[i+1]-rstarts[i]),MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
614   }
615 
616   for (i=0; i<to->n; i++) {
617     /* pack a message at a time */
618     CHKMEMQ;
619     for (j=0; j<sstarts[i+1]-sstarts[i]; j++){
620       for (k=0; k<ncols; k++) {
621         svalues[ncols*(sstarts[i] + j) + k] = b[sindices[sstarts[i]+j] + nrowsB*k];
622       }
623     }
624     CHKMEMQ;
625     ierr = MPI_Isend(svalues+ncols*sstarts[i],ncols*(sstarts[i+1]-sstarts[i]),MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
626   }
627 
628   nrecvs = from->n;
629   while (nrecvs) {
630     ierr = MPI_Waitany(from->n,rwaits,&imdex,&status);CHKERRQ(ierr);
631     nrecvs--;
632     /* unpack a message at a time */
633     CHKMEMQ;
634     for (j=0; j<rstarts[imdex+1]-rstarts[imdex]; j++){
635       for (k=0; k<ncols; k++) {
636         w[rindices[rstarts[imdex]+j] + nrows*k] = rvalues[ncols*(rstarts[imdex] + j) + k];
637       }
638     }
639     CHKMEMQ;
640   }
641   if (to->n) {ierr = MPI_Waitall(to->n,swaits,to->sstatus);CHKERRQ(ierr);}
642 
643   ierr = MatRestoreArray(B,&b);CHKERRQ(ierr);
644   ierr = MatRestoreArray(workB,&w);CHKERRQ(ierr);
645   ierr = MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
646   ierr = MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
647   PetscFunctionReturn(0);
648 }
649 extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);
650 
651 #undef __FUNCT__
652 #define __FUNCT__ "MatMatMultNumeric_MPIAIJ_MPIDense"
653 PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
654 {
655   PetscErrorCode       ierr;
656   Mat_MPIAIJ           *aij = (Mat_MPIAIJ*)A->data;
657   Mat_MPIDense         *bdense = (Mat_MPIDense*)B->data;
658   Mat_MPIDense         *cdense = (Mat_MPIDense*)C->data;
659   Mat                  workB;
660 
661   PetscFunctionBegin;
662 
663   /* diagonal block of A times all local rows of B*/
664   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(aij->A,bdense->A,cdense->A);CHKERRQ(ierr);
665 
666   /* get off processor parts of B needed to complete the product */
667   ierr = MatMPIDenseScatter(A,B,C,&workB);CHKERRQ(ierr);
668 
669   /* off-diagonal block of A times nonlocal rows of B */
670   ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);CHKERRQ(ierr);
671   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
672   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
673   PetscFunctionReturn(0);
674 }
675 
676