xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision 4624976ab46e68e12cd1954f5fe8febf094976b9)
1 
2 /*
3   Defines projective product routines where A is a MPIAIJ matrix
4           C = P^T * A * P
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h>   /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <../src/mat/impls/aij/mpi/mpiaij.h>
10 #include <petscbt.h>
11 #include <petsctime.h>
12 
13 /* #define PTAP_PROFILE */
14 
15 PetscErrorCode MatView_MPIAIJ_PtAP(Mat A,PetscViewer viewer)
16 {
17   PetscErrorCode    ierr;
18   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data;
19   Mat_APMPI         *ptap=a->ap;
20   PetscBool         iascii;
21   PetscViewerFormat format;
22 
23   PetscFunctionBegin;
24   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
25   if (iascii) {
26     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
27     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
28       if (ptap->algType == 0) {
29         ierr = PetscViewerASCIIPrintf(viewer,"using scalable MatPtAP() implementation\n");CHKERRQ(ierr);
30       } else if (ptap->algType == 1) {
31         ierr = PetscViewerASCIIPrintf(viewer,"using nonscalable MatPtAP() implementation\n");CHKERRQ(ierr);
32       }
33     }
34   }
35   ierr = (ptap->view)(A,viewer);CHKERRQ(ierr);
36   PetscFunctionReturn(0);
37 }
38 
39 PetscErrorCode MatFreeIntermediateDataStructures_MPIAIJ_AP(Mat A)
40 {
41   PetscErrorCode      ierr;
42   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data;
43   Mat_APMPI           *ptap=a->ap;
44   Mat_Merge_SeqsToMPI *merge=ptap->merge;
45 
46   PetscFunctionBegin;
47   if (!ptap) PetscFunctionReturn(0);
48 
49   ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr);
50   ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
51   ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
52   ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
53   ierr = MatDestroy(&ptap->A_loc);CHKERRQ(ierr); /* used by MatTransposeMatMult() */
54   ierr = MatDestroy(&ptap->Rd);CHKERRQ(ierr);
55   ierr = MatDestroy(&ptap->Ro);CHKERRQ(ierr);
56   if (ptap->AP_loc) { /* used by alg_rap */
57     Mat_SeqAIJ *ap = (Mat_SeqAIJ*)(ptap->AP_loc)->data;
58     ierr = PetscFree(ap->i);CHKERRQ(ierr);
59     ierr = PetscFree2(ap->j,ap->a);CHKERRQ(ierr);
60     ierr = MatDestroy(&ptap->AP_loc);CHKERRQ(ierr);
61   } else { /* used by alg_ptap */
62     ierr = PetscFree(ptap->api);CHKERRQ(ierr);
63     ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
64   }
65   ierr = MatDestroy(&ptap->C_loc);CHKERRQ(ierr);
66   ierr = MatDestroy(&ptap->C_oth);CHKERRQ(ierr);
67   if (ptap->apa) {ierr = PetscFree(ptap->apa);CHKERRQ(ierr);}
68 
69   if (merge) { /* used by alg_ptap */
70     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
71     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
72     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
73     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
74     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
75     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
76     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
77     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
78     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
79     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
80     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
81     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
82     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
83     ierr = PetscFree(ptap->merge);CHKERRQ(ierr);
84   }
85 
86   A->ops->destroy = ptap->destroy;
87   ierr = PetscFree(a->ap);CHKERRQ(ierr);
88   PetscFunctionReturn(0);
89 }
90 
91 PetscErrorCode MatDestroy_MPIAIJ_PtAP(Mat A)
92 {
93   PetscErrorCode ierr;
94 
95   PetscFunctionBegin;
96   ierr = (*A->ops->freeintermediatedatastructures)(A);CHKERRQ(ierr);
97   ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
98   PetscFunctionReturn(0);
99 }
100 
101 PETSC_INTERN PetscErrorCode MatPtAP_MPIAIJ_MPIAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
102 {
103   PetscErrorCode ierr;
104   PetscBool      flg;
105   MPI_Comm       comm;
106 #if !defined(PETSC_HAVE_HYPRE)
107   const char          *algTypes[2] = {"scalable","nonscalable"};
108   PetscInt            nalg=2;
109 #else
110   const char          *algTypes[3] = {"scalable","nonscalable","hypre"};
111   PetscInt            nalg=3;
112 #endif
113   PetscInt            pN=P->cmap->N,alg=1; /* set default algorithm */
114 
115   PetscFunctionBegin;
116   /* check if matrix local sizes are compatible */
117   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
118   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
119   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
120 
121   if (scall == MAT_INITIAL_MATRIX) {
122     /* pick an algorithm */
123     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
124     PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
125     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
126     ierr = PetscOptionsEnd();CHKERRQ(ierr);
127 
128     if (!flg && pN > 100000) { /* may switch to scalable algorithm as default */
129       MatInfo     Ainfo,Pinfo;
130       PetscInt    nz_local;
131       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
132 
133       ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
134       ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
135       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
136 
137       if (pN > fill*nz_local) alg_scalable_loc = PETSC_TRUE;
138       ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
139 
140       if (alg_scalable) {
141         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
142       }
143     }
144 
145     switch (alg) {
146     case 1:
147       /* do R=P^T locally, then C=R*A*P -- nonscalable */
148       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
149       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);
150       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
151       break;
152 #if defined(PETSC_HAVE_HYPRE)
153     case 2:
154       /* Use boomerAMGBuildCoarseOperator */
155       ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr);
156       PetscFunctionReturn(0);
157       break;
158 #endif
159     default:
160       /* do R=P^T locally, then C=R*A*P */
161       ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
162       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(A,P,fill,C);CHKERRQ(ierr);
163       ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
164       break;
165     }
166   }
167   ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
168   ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr);
169   ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
170   PetscFunctionReturn(0);
171 }
172 
173 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,Mat C)
174 {
175   PetscErrorCode    ierr;
176   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
177   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
178   Mat_SeqAIJ        *ap,*p_loc,*p_oth,*c_seq;
179   Mat_APMPI         *ptap = c->ap;
180   Mat               AP_loc,C_loc,C_oth;
181   PetscInt          i,rstart,rend,cm,ncols,row,*api,*apj,am = A->rmap->n,apnz;
182   PetscScalar       *apa;
183   const PetscInt    *cols;
184   const PetscScalar *vals;
185   PetscBool         freestruct;
186 
187   PetscFunctionBegin;
188   if (!ptap) {
189     MPI_Comm comm;
190     ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
191     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
192   }
193 
194   ierr = MatZeroEntries(C);CHKERRQ(ierr);
195 
196   /* 1) get R = Pd^T,Ro = Po^T */
197   if (ptap->reuse == MAT_REUSE_MATRIX) {
198     ierr = MatTranspose(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
199     ierr = MatTranspose(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
200   }
201 
202   /* 2) get AP_loc */
203   AP_loc = ptap->AP_loc;
204   ap = (Mat_SeqAIJ*)AP_loc->data;
205 
206   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
207   /*-----------------------------------------------------*/
208   if (ptap->reuse == MAT_REUSE_MATRIX) {
209     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
210     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
211     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
212   }
213 
214   /* 2-2) compute numeric A_loc*P - dominating part */
215   /* ---------------------------------------------- */
216   /* get data from symbolic products */
217   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
218   if (ptap->P_oth) p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
219   else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"ptap->P_oth is NULL. Cannot proceed!");
220 
221   api   = ap->i;
222   apj   = ap->j;
223   for (i=0; i<am; i++) {
224     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
225     apnz = api[i+1] - api[i];
226     apa = ap->a + api[i];
227     ierr = PetscMemzero(apa,sizeof(PetscScalar)*apnz);CHKERRQ(ierr);
228     AProw_scalable(i,ad,ao,p_loc,p_oth,api,apj,apa);
229     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
230   }
231 
232   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
233   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
234   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
235 
236   C_loc = ptap->C_loc;
237   C_oth = ptap->C_oth;
238 
239   /* add C_loc and Co to to C */
240   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
241 
242   /* C_loc -> C */
243   cm    = C_loc->rmap->N;
244   c_seq = (Mat_SeqAIJ*)C_loc->data;
245   cols = c_seq->j;
246   vals = c_seq->a;
247 
248   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assembled is PETSC_FALSE and */
249   /* when there are no off-processor parts.  */
250   /* If was_assembled is true, then the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart; in MatSetValues_MPIAIJ_CopyFromCSRFormat */
251   /* is no longer true. Then the more complex function MatSetValues_MPIAIJ() has to be used, where the column index is looked up from */
252   /* a table, and other, more complex stuff has to be done. */
253   if (C->assembled) {
254     C->was_assembled = PETSC_TRUE;
255     C->assembled     = PETSC_FALSE;
256   }
257   if (C->was_assembled) {
258     for (i=0; i<cm; i++) {
259       ncols = c_seq->i[i+1] - c_seq->i[i];
260       row = rstart + i;
261       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
262       cols += ncols; vals += ncols;
263     }
264   } else {
265     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a);CHKERRQ(ierr);
266   }
267 
268   /* Co -> C, off-processor part */
269   cm = C_oth->rmap->N;
270   c_seq = (Mat_SeqAIJ*)C_oth->data;
271   cols = c_seq->j;
272   vals = c_seq->a;
273   for (i=0; i<cm; i++) {
274     ncols = c_seq->i[i+1] - c_seq->i[i];
275     row = p->garray[i];
276     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
277     cols += ncols; vals += ncols;
278   }
279   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
280   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
281 
282   ptap->reuse = MAT_REUSE_MATRIX;
283 
284   ierr = PetscObjectOptionsBegin((PetscObject)C);CHKERRQ(ierr);
285   PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
286   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
287   freestruct = PETSC_FALSE;
288   ierr = PetscOptionsBool("-mat_freeintermediatedatastructures","Free intermediate data structures", "MatFreeIntermediateDataStructures",freestruct, &freestruct, NULL);CHKERRQ(ierr);
289   if (freestruct) {
290     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
291   }
292   ierr = PetscOptionsEnd();CHKERRQ(ierr);
293   PetscFunctionReturn(0);
294 }
295 
296 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,PetscReal fill,Mat *C)
297 {
298   PetscErrorCode      ierr;
299   Mat_APMPI           *ptap;
300   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
301   MPI_Comm            comm;
302   PetscMPIInt         size,rank;
303   Mat                 Cmpi,P_loc,P_oth;
304   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
305   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
306   PetscInt            *lnk,i,k,pnz,row,nsend;
307   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
308   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
309   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
310   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
311   MPI_Request         *swaits,*rwaits;
312   MPI_Status          *sstatus,rstatus;
313   PetscLayout         rowmap;
314   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
315   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
316   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,Crmax,*aj,*ai,*pi;
317   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
318   PetscScalar         *apv;
319   PetscTable          ta;
320   MatType             mtype;
321 #if defined(PETSC_USE_INFO)
322   PetscReal           apfill;
323 #endif
324 
325   PetscFunctionBegin;
326   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
327   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
328   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
329 
330   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
331 
332   /* create symbolic parallel matrix Cmpi */
333   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
334   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
335   ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr);
336 
337   /* create struct Mat_APMPI and attached it to C later */
338   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
339   ptap->reuse = MAT_INITIAL_MATRIX;
340   ptap->algType = 0;
341 
342   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
343   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&P_oth);CHKERRQ(ierr);
344   /* get P_loc by taking all local rows of P */
345   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&P_loc);CHKERRQ(ierr);
346 
347   ptap->P_loc = P_loc;
348   ptap->P_oth = P_oth;
349 
350   /* (0) compute Rd = Pd^T, Ro = Po^T  */
351   /* --------------------------------- */
352   ierr = MatTranspose(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
353   ierr = MatTranspose(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
354 
355   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
356   /* ----------------------------------------------------------------- */
357   p_loc  = (Mat_SeqAIJ*)P_loc->data;
358   if (P_oth) p_oth = (Mat_SeqAIJ*)P_oth->data;
359 
360   /* create and initialize a linked list */
361   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
362   MatRowMergeMax_SeqAIJ(p_loc,P_loc->rmap->N,ta);
363   MatRowMergeMax_SeqAIJ(p_oth,P_oth->rmap->N,ta);
364   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
365 
366   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
367 
368   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
369   if (ao) {
370     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
371   } else {
372     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
373   }
374   current_space = free_space;
375   nspacedouble  = 0;
376 
377   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
378   api[0] = 0;
379   for (i=0; i<am; i++) {
380     /* diagonal portion: Ad[i,:]*P */
381     ai = ad->i; pi = p_loc->i;
382     nzi = ai[i+1] - ai[i];
383     aj  = ad->j + ai[i];
384     for (j=0; j<nzi; j++) {
385       row  = aj[j];
386       pnz  = pi[row+1] - pi[row];
387       Jptr = p_loc->j + pi[row];
388       /* add non-zero cols of P into the sorted linked list lnk */
389       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
390     }
391     /* off-diagonal portion: Ao[i,:]*P */
392     if (ao) {
393       ai = ao->i; pi = p_oth->i;
394       nzi = ai[i+1] - ai[i];
395       aj  = ao->j + ai[i];
396       for (j=0; j<nzi; j++) {
397         row  = aj[j];
398         pnz  = pi[row+1] - pi[row];
399         Jptr = p_oth->j + pi[row];
400         ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
401       }
402     }
403     apnz     = lnk[0];
404     api[i+1] = api[i] + apnz;
405 
406     /* if free space is not available, double the total space in the list */
407     if (current_space->local_remaining<apnz) {
408       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
409       nspacedouble++;
410     }
411 
412     /* Copy data into free space, then initialize lnk */
413     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
414 
415     current_space->array           += apnz;
416     current_space->local_used      += apnz;
417     current_space->local_remaining -= apnz;
418   }
419   /* Allocate space for apj and apv, initialize apj, and */
420   /* destroy list of free space and other temporary array(s) */
421   ierr = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
422   ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
423   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
424 
425   /* Create AP_loc for reuse */
426   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
427 
428 #if defined(PETSC_USE_INFO)
429   if (ao) {
430     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
431   } else {
432     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
433   }
434   ptap->AP_loc->info.mallocs           = nspacedouble;
435   ptap->AP_loc->info.fill_ratio_given  = fill;
436   ptap->AP_loc->info.fill_ratio_needed = apfill;
437 
438   if (api[am]) {
439     ierr = PetscInfo3(ptap->AP_loc,"Scalable algorithm, AP_loc reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)apfill);CHKERRQ(ierr);
440     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
441   } else {
442     ierr = PetscInfo(ptap->AP_loc,"Scalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
443   }
444 #endif
445 
446   /* (2-1) compute symbolic Co = Ro*AP_loc  */
447   /* ------------------------------------ */
448   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
449 
450   /* (3) send coj of C_oth to other processors  */
451   /* ------------------------------------------ */
452   /* determine row ownership */
453   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
454   rowmap->n  = pn;
455   rowmap->bs = 1;
456   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
457   owners = rowmap->range;
458 
459   /* determine the number of messages to send, their lengths */
460   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
461   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
462   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
463 
464   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
465   coi   = c_oth->i; coj = c_oth->j;
466   con   = ptap->C_oth->rmap->n;
467   proc  = 0;
468   for (i=0; i<con; i++) {
469     while (prmap[i] >= owners[proc+1]) proc++;
470     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
471     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
472   }
473 
474   len          = 0; /* max length of buf_si[], see (4) */
475   owners_co[0] = 0;
476   nsend        = 0;
477   for (proc=0; proc<size; proc++) {
478     owners_co[proc+1] = owners_co[proc] + len_si[proc];
479     if (len_s[proc]) {
480       nsend++;
481       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
482       len         += len_si[proc];
483     }
484   }
485 
486   /* determine the number and length of messages to receive for coi and coj  */
487   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
488   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
489 
490   /* post the Irecv and Isend of coj */
491   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
492   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
493   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
494   for (proc=0, k=0; proc<size; proc++) {
495     if (!len_s[proc]) continue;
496     i    = owners_co[proc];
497     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
498     k++;
499   }
500 
501   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
502   /* ---------------------------------------- */
503   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
504   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
505 
506   /* receives coj are complete */
507   for (i=0; i<nrecv; i++) {
508     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
509   }
510   ierr = PetscFree(rwaits);CHKERRQ(ierr);
511   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
512 
513   /* add received column indices into ta to update Crmax */
514   for (k=0; k<nrecv; k++) {/* k-th received message */
515     Jptr = buf_rj[k];
516     for (j=0; j<len_r[k]; j++) {
517       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
518     }
519   }
520   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
521   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
522 
523   /* (4) send and recv coi */
524   /*-----------------------*/
525   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
526   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
527   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
528   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
529   for (proc=0,k=0; proc<size; proc++) {
530     if (!len_s[proc]) continue;
531     /* form outgoing message for i-structure:
532          buf_si[0]:                 nrows to be sent
533                [1:nrows]:           row index (global)
534                [nrows+1:2*nrows+1]: i-structure index
535     */
536     /*-------------------------------------------*/
537     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
538     buf_si_i    = buf_si + nrows+1;
539     buf_si[0]   = nrows;
540     buf_si_i[0] = 0;
541     nrows       = 0;
542     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
543       nzi = coi[i+1] - coi[i];
544       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
545       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
546       nrows++;
547     }
548     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
549     k++;
550     buf_si += len_si[proc];
551   }
552   for (i=0; i<nrecv; i++) {
553     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
554   }
555   ierr = PetscFree(rwaits);CHKERRQ(ierr);
556   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
557 
558   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
559   ierr = PetscFree(len_ri);CHKERRQ(ierr);
560   ierr = PetscFree(swaits);CHKERRQ(ierr);
561   ierr = PetscFree(buf_s);CHKERRQ(ierr);
562 
563   /* (5) compute the local portion of Cmpi      */
564   /* ------------------------------------------ */
565   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
566   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
567   current_space = free_space;
568 
569   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
570   for (k=0; k<nrecv; k++) {
571     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
572     nrows       = *buf_ri_k[k];
573     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
574     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
575   }
576 
577   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
578   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
579   for (i=0; i<pn; i++) {
580     /* add C_loc into Cmpi */
581     nzi  = c_loc->i[i+1] - c_loc->i[i];
582     Jptr = c_loc->j + c_loc->i[i];
583     ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
584 
585     /* add received col data into lnk */
586     for (k=0; k<nrecv; k++) { /* k-th received message */
587       if (i == *nextrow[k]) { /* i-th row */
588         nzi  = *(nextci[k]+1) - *nextci[k];
589         Jptr = buf_rj[k] + *nextci[k];
590         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
591         nextrow[k]++; nextci[k]++;
592       }
593     }
594     nzi = lnk[0];
595 
596     /* copy data into free space, then initialize lnk */
597     ierr = PetscLLCondensedClean_Scalable(nzi,current_space->array,lnk);CHKERRQ(ierr);
598     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
599   }
600   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
601   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
602   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
603 
604   /* local sizes and preallocation */
605   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
606   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
607   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
608   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
609 
610   /* members in merge */
611   ierr = PetscFree(id_r);CHKERRQ(ierr);
612   ierr = PetscFree(len_r);CHKERRQ(ierr);
613   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
614   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
615   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
616   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
617   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
618 
619   /* attach the supporting struct to Cmpi for reuse */
620   c = (Mat_MPIAIJ*)Cmpi->data;
621   c->ap           = ptap;
622   ptap->duplicate = Cmpi->ops->duplicate;
623   ptap->destroy   = Cmpi->ops->destroy;
624   ptap->view      = Cmpi->ops->view;
625 
626   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
627   Cmpi->assembled        = PETSC_FALSE;
628   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable;
629   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
630   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
631   Cmpi->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
632   *C                     = Cmpi;
633   PetscFunctionReturn(0);
634 }
635 
636 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
637 {
638   PetscErrorCode      ierr;
639   Mat_APMPI           *ptap;
640   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
641   MPI_Comm            comm;
642   PetscMPIInt         size,rank;
643   Mat                 Cmpi;
644   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
645   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
646   PetscInt            *lnk,i,k,pnz,row,nsend;
647   PetscBT             lnkbt;
648   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
649   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
650   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
651   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
652   MPI_Request         *swaits,*rwaits;
653   MPI_Status          *sstatus,rstatus;
654   PetscLayout         rowmap;
655   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
656   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
657   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,ap_rmax=0,Crmax,*aj,*ai,*pi;
658   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
659   PetscScalar         *apv;
660   PetscTable          ta;
661   MatType             mtype;
662 #if defined(PETSC_USE_INFO)
663   PetscReal           apfill;
664 #endif
665 
666   PetscFunctionBegin;
667   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
668   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
669   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
670 
671   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
672 
673   /* create symbolic parallel matrix Cmpi */
674   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
675   ierr = MatGetType(A,&mtype);CHKERRQ(ierr);
676   ierr = MatSetType(Cmpi,mtype);CHKERRQ(ierr);
677 
678   /* Do dense axpy in MatPtAPNumeric_MPIAIJ_MPIAIJ() */
679   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ;
680 
681   /* create struct Mat_APMPI and attached it to C later */
682   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
683   ptap->reuse = MAT_INITIAL_MATRIX;
684   ptap->algType = 1;
685 
686   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
687   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
688   /* get P_loc by taking all local rows of P */
689   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
690 
691   /* (0) compute Rd = Pd^T, Ro = Po^T  */
692   /* --------------------------------- */
693   ierr = MatTranspose(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
694   ierr = MatTranspose(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
695 
696   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
697   /* ----------------------------------------------------------------- */
698   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
699   if (ptap->P_oth) p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
700 
701   /* create and initialize a linked list */
702   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
703   MatRowMergeMax_SeqAIJ(p_loc,ptap->P_loc->rmap->N,ta);
704   MatRowMergeMax_SeqAIJ(p_oth,ptap->P_oth->rmap->N,ta);
705   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
706   /* printf("[%d] est %d, Crmax %d; pN %d\n",rank,5*(p_loc->rmax+p_oth->rmax + (PetscInt)(1.e-2*pN)),Crmax,pN); */
707 
708   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
709 
710   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
711   if (ao) {
712     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
713   } else {
714     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
715   }
716   current_space = free_space;
717   nspacedouble  = 0;
718 
719   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
720   api[0] = 0;
721   for (i=0; i<am; i++) {
722     /* diagonal portion: Ad[i,:]*P */
723     ai = ad->i; pi = p_loc->i;
724     nzi = ai[i+1] - ai[i];
725     aj  = ad->j + ai[i];
726     for (j=0; j<nzi; j++) {
727       row  = aj[j];
728       pnz  = pi[row+1] - pi[row];
729       Jptr = p_loc->j + pi[row];
730       /* add non-zero cols of P into the sorted linked list lnk */
731       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
732     }
733     /* off-diagonal portion: Ao[i,:]*P */
734     if (ao) {
735       ai = ao->i; pi = p_oth->i;
736       nzi = ai[i+1] - ai[i];
737       aj  = ao->j + ai[i];
738       for (j=0; j<nzi; j++) {
739         row  = aj[j];
740         pnz  = pi[row+1] - pi[row];
741         Jptr = p_oth->j + pi[row];
742         ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
743       }
744     }
745     apnz     = lnk[0];
746     api[i+1] = api[i] + apnz;
747     if (ap_rmax < apnz) ap_rmax = apnz;
748 
749     /* if free space is not available, double the total space in the list */
750     if (current_space->local_remaining<apnz) {
751       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
752       nspacedouble++;
753     }
754 
755     /* Copy data into free space, then initialize lnk */
756     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
757 
758     current_space->array           += apnz;
759     current_space->local_used      += apnz;
760     current_space->local_remaining -= apnz;
761   }
762   /* Allocate space for apj and apv, initialize apj, and */
763   /* destroy list of free space and other temporary array(s) */
764   ierr   = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
765   ierr   = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
766   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
767 
768   /* Create AP_loc for reuse */
769   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
770 
771 #if defined(PETSC_USE_INFO)
772   if (ao) {
773     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
774   } else {
775     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
776   }
777   ptap->AP_loc->info.mallocs           = nspacedouble;
778   ptap->AP_loc->info.fill_ratio_given  = fill;
779   ptap->AP_loc->info.fill_ratio_needed = apfill;
780 
781   if (api[am]) {
782     ierr = PetscInfo3(ptap->AP_loc,"Nonscalable algorithm, AP_loc reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)apfill);CHKERRQ(ierr);
783     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
784   } else {
785     ierr = PetscInfo(ptap->AP_loc,"Nonscalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
786   }
787 #endif
788 
789   /* (2-1) compute symbolic Co = Ro*AP_loc  */
790   /* ------------------------------------ */
791   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
792 
793   /* (3) send coj of C_oth to other processors  */
794   /* ------------------------------------------ */
795   /* determine row ownership */
796   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
797   rowmap->n  = pn;
798   rowmap->bs = 1;
799   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
800   owners = rowmap->range;
801 
802   /* determine the number of messages to send, their lengths */
803   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
804   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
805   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
806 
807   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
808   coi   = c_oth->i; coj = c_oth->j;
809   con   = ptap->C_oth->rmap->n;
810   proc  = 0;
811   for (i=0; i<con; i++) {
812     while (prmap[i] >= owners[proc+1]) proc++;
813     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
814     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
815   }
816 
817   len          = 0; /* max length of buf_si[], see (4) */
818   owners_co[0] = 0;
819   nsend        = 0;
820   for (proc=0; proc<size; proc++) {
821     owners_co[proc+1] = owners_co[proc] + len_si[proc];
822     if (len_s[proc]) {
823       nsend++;
824       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
825       len         += len_si[proc];
826     }
827   }
828 
829   /* determine the number and length of messages to receive for coi and coj  */
830   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
831   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
832 
833   /* post the Irecv and Isend of coj */
834   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
835   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
836   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
837   for (proc=0, k=0; proc<size; proc++) {
838     if (!len_s[proc]) continue;
839     i    = owners_co[proc];
840     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
841     k++;
842   }
843 
844   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
845   /* ---------------------------------------- */
846   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
847   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
848 
849   /* receives coj are complete */
850   for (i=0; i<nrecv; i++) {
851     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
852   }
853   ierr = PetscFree(rwaits);CHKERRQ(ierr);
854   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
855 
856   /* add received column indices into ta to update Crmax */
857   for (k=0; k<nrecv; k++) {/* k-th received message */
858     Jptr = buf_rj[k];
859     for (j=0; j<len_r[k]; j++) {
860       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
861     }
862   }
863   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
864   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
865 
866   /* (4) send and recv coi */
867   /*-----------------------*/
868   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
869   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
870   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
871   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
872   for (proc=0,k=0; proc<size; proc++) {
873     if (!len_s[proc]) continue;
874     /* form outgoing message for i-structure:
875          buf_si[0]:                 nrows to be sent
876                [1:nrows]:           row index (global)
877                [nrows+1:2*nrows+1]: i-structure index
878     */
879     /*-------------------------------------------*/
880     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
881     buf_si_i    = buf_si + nrows+1;
882     buf_si[0]   = nrows;
883     buf_si_i[0] = 0;
884     nrows       = 0;
885     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
886       nzi = coi[i+1] - coi[i];
887       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
888       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
889       nrows++;
890     }
891     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
892     k++;
893     buf_si += len_si[proc];
894   }
895   for (i=0; i<nrecv; i++) {
896     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
897   }
898   ierr = PetscFree(rwaits);CHKERRQ(ierr);
899   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
900 
901   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
902   ierr = PetscFree(len_ri);CHKERRQ(ierr);
903   ierr = PetscFree(swaits);CHKERRQ(ierr);
904   ierr = PetscFree(buf_s);CHKERRQ(ierr);
905 
906   /* (5) compute the local portion of Cmpi      */
907   /* ------------------------------------------ */
908   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
909   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
910   current_space = free_space;
911 
912   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
913   for (k=0; k<nrecv; k++) {
914     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
915     nrows       = *buf_ri_k[k];
916     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
917     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
918   }
919 
920   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
921   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
922   for (i=0; i<pn; i++) {
923     /* add C_loc into Cmpi */
924     nzi  = c_loc->i[i+1] - c_loc->i[i];
925     Jptr = c_loc->j + c_loc->i[i];
926     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
927 
928     /* add received col data into lnk */
929     for (k=0; k<nrecv; k++) { /* k-th received message */
930       if (i == *nextrow[k]) { /* i-th row */
931         nzi  = *(nextci[k]+1) - *nextci[k];
932         Jptr = buf_rj[k] + *nextci[k];
933         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
934         nextrow[k]++; nextci[k]++;
935       }
936     }
937     nzi = lnk[0];
938 
939     /* copy data into free space, then initialize lnk */
940     ierr = PetscLLCondensedClean(pN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
941     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
942   }
943   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
944   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
945   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
946 
947   /* local sizes and preallocation */
948   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
949   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
950   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
951   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
952 
953   /* members in merge */
954   ierr = PetscFree(id_r);CHKERRQ(ierr);
955   ierr = PetscFree(len_r);CHKERRQ(ierr);
956   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
957   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
958   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
959   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
960   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
961 
962   /* attach the supporting struct to Cmpi for reuse */
963   c = (Mat_MPIAIJ*)Cmpi->data;
964   c->ap           = ptap;
965   ptap->duplicate = Cmpi->ops->duplicate;
966   ptap->destroy   = Cmpi->ops->destroy;
967   ptap->view      = Cmpi->ops->view;
968   ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
969 
970   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
971   Cmpi->assembled        = PETSC_FALSE;
972   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
973   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
974   Cmpi->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
975   *C                     = Cmpi;
976   PetscFunctionReturn(0);
977 }
978 
979 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
980 {
981   PetscErrorCode    ierr;
982   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
983   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
984   Mat_SeqAIJ        *ap,*p_loc,*p_oth=NULL,*c_seq;
985   Mat_APMPI         *ptap = c->ap;
986   Mat               AP_loc,C_loc,C_oth;
987   PetscInt          i,rstart,rend,cm,ncols,row;
988   PetscInt          *api,*apj,am = A->rmap->n,j,col,apnz;
989   PetscScalar       *apa;
990   const PetscInt    *cols;
991   const PetscScalar *vals;
992   PetscBool         freestruct;
993 
994   PetscFunctionBegin;
995   if (!ptap) {
996     MPI_Comm comm;
997     ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
998     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
999   }
1000 
1001   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1002   /* 1) get R = Pd^T,Ro = Po^T */
1003   if (ptap->reuse == MAT_REUSE_MATRIX) {
1004     ierr = MatTranspose(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1005     ierr = MatTranspose(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1006   }
1007 
1008   /* 2) get AP_loc */
1009   AP_loc = ptap->AP_loc;
1010   ap = (Mat_SeqAIJ*)AP_loc->data;
1011 
1012   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
1013   /*-----------------------------------------------------*/
1014   if (ptap->reuse == MAT_REUSE_MATRIX) {
1015     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
1016     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1017     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1018   }
1019 
1020   /* 2-2) compute numeric A_loc*P - dominating part */
1021   /* ---------------------------------------------- */
1022   /* get data from symbolic products */
1023   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1024   if (ptap->P_oth) {
1025     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
1026   }
1027   apa   = ptap->apa;
1028   api   = ap->i;
1029   apj   = ap->j;
1030   for (i=0; i<am; i++) {
1031     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
1032     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
1033     apnz = api[i+1] - api[i];
1034     for (j=0; j<apnz; j++) {
1035       col = apj[j+api[i]];
1036       ap->a[j+ap->i[i]] = apa[col];
1037       apa[col] = 0.0;
1038     }
1039     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
1040   }
1041 
1042   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
1043   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
1044   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
1045   C_loc = ptap->C_loc;
1046   C_oth = ptap->C_oth;
1047 
1048   /* add C_loc and Co to to C */
1049   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1050 
1051   /* C_loc -> C */
1052   cm    = C_loc->rmap->N;
1053   c_seq = (Mat_SeqAIJ*)C_loc->data;
1054   cols = c_seq->j;
1055   vals = c_seq->a;
1056 
1057 
1058   /* The (fast) MatSetValues_MPIAIJ_CopyFromCSRFormat function can only be used when C->was_assembled is PETSC_FALSE and */
1059   /* when there are no off-processor parts.  */
1060   /* If was_assembled is true, then the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart; in MatSetValues_MPIAIJ_CopyFromCSRFormat */
1061   /* is no longer true. Then the more complex function MatSetValues_MPIAIJ() has to be used, where the column index is looked up from */
1062   /* a table, and other, more complex stuff has to be done. */
1063   if (C->assembled) {
1064     C->was_assembled = PETSC_TRUE;
1065     C->assembled     = PETSC_FALSE;
1066   }
1067   if (C->was_assembled) {
1068     for (i=0; i<cm; i++) {
1069       ncols = c_seq->i[i+1] - c_seq->i[i];
1070       row = rstart + i;
1071       ierr = MatSetValues_MPIAIJ(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1072       cols += ncols; vals += ncols;
1073     }
1074   } else {
1075     ierr = MatSetValues_MPIAIJ_CopyFromCSRFormat(C,c_seq->j,c_seq->i,c_seq->a);CHKERRQ(ierr);
1076   }
1077 
1078   /* Co -> C, off-processor part */
1079   cm = C_oth->rmap->N;
1080   c_seq = (Mat_SeqAIJ*)C_oth->data;
1081   cols = c_seq->j;
1082   vals = c_seq->a;
1083   for (i=0; i<cm; i++) {
1084     ncols = c_seq->i[i+1] - c_seq->i[i];
1085     row = p->garray[i];
1086     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1087     cols += ncols; vals += ncols;
1088   }
1089 
1090   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1091   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1092 
1093   ptap->reuse = MAT_REUSE_MATRIX;
1094 
1095   ierr = PetscObjectOptionsBegin((PetscObject)C);CHKERRQ(ierr);
1096   PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
1097   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
1098   freestruct = PETSC_FALSE;
1099   ierr = PetscOptionsBool("-mat_freeintermediatedatastructures","Free intermediate data structures", "MatFreeIntermediateDataStructures",freestruct, &freestruct, NULL);CHKERRQ(ierr);
1100   if (freestruct) {
1101     ierr = MatFreeIntermediateDataStructures(C);CHKERRQ(ierr);
1102   }
1103   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1104   PetscFunctionReturn(0);
1105 }
1106