xref: /petsc/src/mat/impls/aij/mpi/mpiptap.c (revision b41ce5d507ea9a58bfa83cf403107a702e77a67d)
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_PtAPMPI       *ptap=a->ptap;
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 MatDestroy_MPIAIJ_PtAP(Mat A)
40 {
41   PetscErrorCode ierr;
42   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
43   Mat_PtAPMPI    *ptap=a->ptap;
44 
45   PetscFunctionBegin;
46   if (ptap) {
47     Mat_Merge_SeqsToMPI *merge=ptap->merge;
48     ierr = PetscFree2(ptap->startsj_s,ptap->startsj_r);CHKERRQ(ierr);
49     ierr = PetscFree(ptap->bufa);CHKERRQ(ierr);
50     ierr = MatDestroy(&ptap->P_loc);CHKERRQ(ierr);
51     ierr = MatDestroy(&ptap->P_oth);CHKERRQ(ierr);
52     ierr = MatDestroy(&ptap->A_loc);CHKERRQ(ierr); /* used by MatTransposeMatMult() */
53     ierr = MatDestroy(&ptap->Rd);CHKERRQ(ierr);
54     ierr = MatDestroy(&ptap->Ro);CHKERRQ(ierr);
55     if (ptap->AP_loc) { /* used by alg_rap */
56       Mat_SeqAIJ *ap = (Mat_SeqAIJ*)(ptap->AP_loc)->data;
57       ierr = PetscFree(ap->i);CHKERRQ(ierr);
58       ierr = PetscFree2(ap->j,ap->a);CHKERRQ(ierr);
59       ierr = MatDestroy(&ptap->AP_loc);CHKERRQ(ierr);
60     } else { /* used by alg_ptap */
61       ierr = PetscFree(ptap->api);CHKERRQ(ierr);
62       ierr = PetscFree(ptap->apj);CHKERRQ(ierr);
63     }
64     ierr = MatDestroy(&ptap->C_loc);CHKERRQ(ierr);
65     ierr = MatDestroy(&ptap->C_oth);CHKERRQ(ierr);
66     if (ptap->apa) {ierr = PetscFree(ptap->apa);CHKERRQ(ierr);}
67 
68     if (merge) { /* used by alg_ptap */
69       ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
70       ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
71       ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
72       ierr = PetscFree(merge->bi);CHKERRQ(ierr);
73       ierr = PetscFree(merge->bj);CHKERRQ(ierr);
74       ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
75       ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
76       ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
77       ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
78       ierr = PetscFree(merge->coi);CHKERRQ(ierr);
79       ierr = PetscFree(merge->coj);CHKERRQ(ierr);
80       ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
81       ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
82       ierr = PetscFree(ptap->merge);CHKERRQ(ierr);
83     }
84 
85     ierr = ptap->destroy(A);CHKERRQ(ierr);
86     ierr = PetscFree(ptap);CHKERRQ(ierr);
87   }
88   PetscFunctionReturn(0);
89 }
90 
91 PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat A, MatDuplicateOption op, Mat *M)
92 {
93   PetscErrorCode ierr;
94   Mat_MPIAIJ     *a     = (Mat_MPIAIJ*)A->data;
95   Mat_PtAPMPI    *ptap  = a->ptap;
96 
97   PetscFunctionBegin;
98   ierr = (*ptap->duplicate)(A,op,M);CHKERRQ(ierr);
99   (*M)->ops->destroy   = ptap->destroy;
100   (*M)->ops->duplicate = ptap->duplicate;
101   PetscFunctionReturn(0);
102 }
103 
104 PETSC_INTERN PetscErrorCode MatPtAP_MPIAIJ_MPIAIJ(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
105 {
106   PetscErrorCode ierr;
107   PetscBool      rap=PETSC_TRUE; /* do R=P^T locally, then C=R*A*P */
108   MPI_Comm       comm;
109 
110   PetscFunctionBegin;
111   /* check if matrix local sizes are compatible */
112   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
113   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);
114   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);
115 
116   ierr = PetscOptionsGetBool(NULL,NULL,"-matrap",&rap,NULL);CHKERRQ(ierr);
117   if (scall == MAT_INITIAL_MATRIX) {
118     ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
119     if (rap) { /* do R=P^T locally, then C=R*A*P */
120       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ(A,P,fill,C);CHKERRQ(ierr);
121     } else {       /* do P^T*A*P */
122       ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_ptap(A,P,fill,C);CHKERRQ(ierr);
123     }
124     ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
125   }
126   ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
127   ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr);
128   ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
129   PetscFunctionReturn(0);
130 }
131 
132 #if defined(PETSC_HAVE_HYPRE)
133 PETSC_INTERN PetscErrorCode MatPtAPSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat*);
134 #endif
135 
136 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,Mat C)
137 {
138   PetscErrorCode    ierr;
139   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
140   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
141   Mat_SeqAIJ        *ap,*p_loc,*p_oth,*c_seq;
142   Mat_PtAPMPI       *ptap = c->ptap;
143   Mat               AP_loc,C_loc,C_oth;
144   PetscInt          i,rstart,rend,cm,ncols,row,*api,*apj,am = A->rmap->n,apnz;
145   PetscScalar       *apa;
146   const PetscInt    *cols;
147   const PetscScalar *vals;
148 
149   PetscFunctionBegin;
150   ierr = MatZeroEntries(C);CHKERRQ(ierr);
151 
152   /* 1) get R = Pd^T,Ro = Po^T */
153   if (ptap->reuse == MAT_REUSE_MATRIX) {
154     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
155     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
156   }
157 
158   /* 2) get AP_loc */
159   AP_loc = ptap->AP_loc;
160   ap = (Mat_SeqAIJ*)AP_loc->data;
161 
162   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
163   /*-----------------------------------------------------*/
164   if (ptap->reuse == MAT_REUSE_MATRIX) {
165     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
166     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
167     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
168   }
169 
170   /* 2-2) compute numeric A_loc*P - dominating part */
171   /* ---------------------------------------------- */
172   /* get data from symbolic products */
173   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
174   if (ptap->P_oth) p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
175   else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"ptap->P_oth is NULL. Cannot proceed!");
176 
177   api   = ap->i;
178   apj   = ap->j;
179   for (i=0; i<am; i++) {
180     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
181     apnz = api[i+1] - api[i];
182     apa = ap->a + api[i];
183     ierr = PetscMemzero(apa,sizeof(PetscScalar)*apnz);CHKERRQ(ierr);
184     AProw_scalable(i,ad,ao,p_loc,p_oth,api,apj,apa);
185     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
186   }
187 
188   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
189   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
190   ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
191 
192   C_loc = ptap->C_loc;
193   C_oth = ptap->C_oth;
194 
195   /* add C_loc and Co to to C */
196   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
197 
198   /* C_loc -> C */
199   cm    = C_loc->rmap->N;
200   c_seq = (Mat_SeqAIJ*)C_loc->data;
201   cols = c_seq->j;
202   vals = c_seq->a;
203   for (i=0; i<cm; i++) {
204     ncols = c_seq->i[i+1] - c_seq->i[i];
205     row = rstart + i;
206     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
207     cols += ncols; vals += ncols;
208   }
209 
210   /* Co -> C, off-processor part */
211   cm = C_oth->rmap->N;
212   c_seq = (Mat_SeqAIJ*)C_oth->data;
213   cols = c_seq->j;
214   vals = c_seq->a;
215   for (i=0; i<cm; i++) {
216     ncols = c_seq->i[i+1] - c_seq->i[i];
217     row = p->garray[i];
218     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
219     cols += ncols; vals += ncols;
220   }
221   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
222   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
223 
224   ptap->reuse = MAT_REUSE_MATRIX;
225   PetscFunctionReturn(0);
226 }
227 
228 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(Mat A,Mat P,PetscReal fill,Mat *C)
229 {
230   PetscErrorCode      ierr;
231   Mat_PtAPMPI         *ptap;
232   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
233   MPI_Comm            comm;
234   PetscMPIInt         size,rank;
235   Mat                 Cmpi,P_loc,P_oth;
236   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
237   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
238   PetscInt            *lnk,i,k,pnz,row,nsend;
239   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
240   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
241   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
242   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
243   MPI_Request         *swaits,*rwaits;
244   MPI_Status          *sstatus,rstatus;
245   PetscLayout         rowmap;
246   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
247   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
248   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,Crmax,*aj,*ai,*pi;
249   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
250   PetscScalar         *apv;
251   PetscTable          ta;
252 #if defined(PETSC_USE_INFO)
253   PetscReal           apfill;
254 #endif
255 
256   PetscFunctionBegin;
257   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
258   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
259   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
260 
261   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
262 
263   /* create symbolic parallel matrix Cmpi */
264   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
265   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
266 
267   /* create struct Mat_PtAPMPI and attached it to C later */
268   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
269   ptap->reuse = MAT_INITIAL_MATRIX;
270   ptap->algType = 0;
271 
272   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
273   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&P_oth);CHKERRQ(ierr);
274   /* get P_loc by taking all local rows of P */
275   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&P_loc);CHKERRQ(ierr);
276 
277   ptap->P_loc = P_loc;
278   ptap->P_oth = P_oth;
279 
280   /* (0) compute Rd = Pd^T, Ro = Po^T  */
281   /* --------------------------------- */
282   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
283   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
284 
285   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
286   /* ----------------------------------------------------------------- */
287   p_loc  = (Mat_SeqAIJ*)P_loc->data;
288   if (P_oth) p_oth = (Mat_SeqAIJ*)P_oth->data;
289 
290   /* create and initialize a linked list */
291   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
292   MatRowMergeMax_SeqAIJ(p_loc,P_loc->rmap->N,ta);
293   MatRowMergeMax_SeqAIJ(p_oth,P_oth->rmap->N,ta);
294   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
295 
296   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
297 
298   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
299   if (ao) {
300     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
301   } else {
302     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
303   }
304   current_space = free_space;
305   nspacedouble  = 0;
306 
307   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
308   api[0] = 0;
309   for (i=0; i<am; i++) {
310     /* diagonal portion: Ad[i,:]*P */
311     ai = ad->i; pi = p_loc->i;
312     nzi = ai[i+1] - ai[i];
313     aj  = ad->j + ai[i];
314     for (j=0; j<nzi; j++) {
315       row  = aj[j];
316       pnz  = pi[row+1] - pi[row];
317       Jptr = p_loc->j + pi[row];
318       /* add non-zero cols of P into the sorted linked list lnk */
319       ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
320     }
321     /* off-diagonal portion: Ao[i,:]*P */
322     if (ao) {
323       ai = ao->i; pi = p_oth->i;
324       nzi = ai[i+1] - ai[i];
325       aj  = ao->j + ai[i];
326       for (j=0; j<nzi; j++) {
327         row  = aj[j];
328         pnz  = pi[row+1] - pi[row];
329         Jptr = p_oth->j + pi[row];
330         ierr = PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);CHKERRQ(ierr);
331       }
332     }
333     apnz     = lnk[0];
334     api[i+1] = api[i] + apnz;
335 
336     /* if free space is not available, double the total space in the list */
337     if (current_space->local_remaining<apnz) {
338       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
339       nspacedouble++;
340     }
341 
342     /* Copy data into free space, then initialize lnk */
343     ierr = PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);CHKERRQ(ierr);
344 
345     current_space->array           += apnz;
346     current_space->local_used      += apnz;
347     current_space->local_remaining -= apnz;
348   }
349   /* Allocate space for apj and apv, initialize apj, and */
350   /* destroy list of free space and other temporary array(s) */
351   ierr = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
352   ierr = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
353   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
354 
355   /* Create AP_loc for reuse */
356   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
357 
358 #if defined(PETSC_USE_INFO)
359   if (ao) {
360     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
361   } else {
362     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
363   }
364   ptap->AP_loc->info.mallocs           = nspacedouble;
365   ptap->AP_loc->info.fill_ratio_given  = fill;
366   ptap->AP_loc->info.fill_ratio_needed = apfill;
367 
368   if (api[am]) {
369     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);
370     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
371   } else {
372     ierr = PetscInfo(ptap->AP_loc,"Scalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
373   }
374 #endif
375 
376   /* (2-1) compute symbolic Co = Ro*AP_loc  */
377   /* ------------------------------------ */
378   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
379 
380   /* (3) send coj of C_oth to other processors  */
381   /* ------------------------------------------ */
382   /* determine row ownership */
383   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
384   rowmap->n  = pn;
385   rowmap->bs = 1;
386   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
387   owners = rowmap->range;
388 
389   /* determine the number of messages to send, their lengths */
390   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
391   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
392   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
393 
394   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
395   coi   = c_oth->i; coj = c_oth->j;
396   con   = ptap->C_oth->rmap->n;
397   proc  = 0;
398   for (i=0; i<con; i++) {
399     while (prmap[i] >= owners[proc+1]) proc++;
400     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
401     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
402   }
403 
404   len          = 0; /* max length of buf_si[], see (4) */
405   owners_co[0] = 0;
406   nsend        = 0;
407   for (proc=0; proc<size; proc++) {
408     owners_co[proc+1] = owners_co[proc] + len_si[proc];
409     if (len_s[proc]) {
410       nsend++;
411       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
412       len         += len_si[proc];
413     }
414   }
415 
416   /* determine the number and length of messages to receive for coi and coj  */
417   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
418   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
419 
420   /* post the Irecv and Isend of coj */
421   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
422   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
423   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
424   for (proc=0, k=0; proc<size; proc++) {
425     if (!len_s[proc]) continue;
426     i    = owners_co[proc];
427     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
428     k++;
429   }
430 
431   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
432   /* ---------------------------------------- */
433   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
434   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
435 
436   /* receives coj are complete */
437   for (i=0; i<nrecv; i++) {
438     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
439   }
440   ierr = PetscFree(rwaits);CHKERRQ(ierr);
441   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
442 
443   /* add received column indices into ta to update Crmax */
444   for (k=0; k<nrecv; k++) {/* k-th received message */
445     Jptr = buf_rj[k];
446     for (j=0; j<len_r[k]; j++) {
447       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
448     }
449   }
450   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
451   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
452 
453   /* (4) send and recv coi */
454   /*-----------------------*/
455   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
456   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
457   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
458   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
459   for (proc=0,k=0; proc<size; proc++) {
460     if (!len_s[proc]) continue;
461     /* form outgoing message for i-structure:
462          buf_si[0]:                 nrows to be sent
463                [1:nrows]:           row index (global)
464                [nrows+1:2*nrows+1]: i-structure index
465     */
466     /*-------------------------------------------*/
467     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
468     buf_si_i    = buf_si + nrows+1;
469     buf_si[0]   = nrows;
470     buf_si_i[0] = 0;
471     nrows       = 0;
472     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
473       nzi = coi[i+1] - coi[i];
474       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
475       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
476       nrows++;
477     }
478     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
479     k++;
480     buf_si += len_si[proc];
481   }
482   for (i=0; i<nrecv; i++) {
483     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
484   }
485   ierr = PetscFree(rwaits);CHKERRQ(ierr);
486   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
487 
488   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
489   ierr = PetscFree(len_ri);CHKERRQ(ierr);
490   ierr = PetscFree(swaits);CHKERRQ(ierr);
491   ierr = PetscFree(buf_s);CHKERRQ(ierr);
492 
493   /* (5) compute the local portion of Cmpi      */
494   /* ------------------------------------------ */
495   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
496   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
497   current_space = free_space;
498 
499   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
500   for (k=0; k<nrecv; k++) {
501     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
502     nrows       = *buf_ri_k[k];
503     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
504     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
505   }
506 
507   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
508   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
509   for (i=0; i<pn; i++) {
510     /* add C_loc into Cmpi */
511     nzi  = c_loc->i[i+1] - c_loc->i[i];
512     Jptr = c_loc->j + c_loc->i[i];
513     ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
514 
515     /* add received col data into lnk */
516     for (k=0; k<nrecv; k++) { /* k-th received message */
517       if (i == *nextrow[k]) { /* i-th row */
518         nzi  = *(nextci[k]+1) - *nextci[k];
519         Jptr = buf_rj[k] + *nextci[k];
520         ierr = PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);CHKERRQ(ierr);
521         nextrow[k]++; nextci[k]++;
522       }
523     }
524     nzi = lnk[0];
525 
526     /* copy data into free space, then initialize lnk */
527     ierr = PetscLLCondensedClean_Scalable(nzi,current_space->array,lnk);CHKERRQ(ierr);
528     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
529   }
530   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
531   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
532   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
533 
534   /* local sizes and preallocation */
535   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
536   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
537   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
538   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
539 
540   /* members in merge */
541   ierr = PetscFree(id_r);CHKERRQ(ierr);
542   ierr = PetscFree(len_r);CHKERRQ(ierr);
543   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
544   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
545   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
546   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
547   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
548 
549   /* attach the supporting struct to Cmpi for reuse */
550   c = (Mat_MPIAIJ*)Cmpi->data;
551   c->ptap         = ptap;
552   ptap->duplicate = Cmpi->ops->duplicate;
553   ptap->destroy   = Cmpi->ops->destroy;
554   ptap->view      = Cmpi->ops->view;
555 
556   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
557   Cmpi->assembled        = PETSC_FALSE;
558   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
559   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
560   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
561   *C                     = Cmpi;
562   PetscFunctionReturn(0);
563 }
564 
565 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
566 {
567   PetscErrorCode      ierr;
568   Mat_PtAPMPI         *ptap;
569   Mat_MPIAIJ          *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
570   MPI_Comm            comm;
571   PetscMPIInt         size,rank;
572   Mat                 Cmpi;
573   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
574   PetscInt            am=A->rmap->n,pm=P->rmap->n,pN=P->cmap->N,pn=P->cmap->n;
575   PetscInt            *lnk,i,k,pnz,row,nsend;
576   PetscBT             lnkbt;
577   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
578   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
579   PetscInt            len,proc,*dnz,*onz,*owners,nzi,nspacedouble;
580   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
581   MPI_Request         *swaits,*rwaits;
582   MPI_Status          *sstatus,rstatus;
583   PetscLayout         rowmap;
584   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
585   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
586   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,con,j,ap_rmax=0,Crmax,*aj,*ai,*pi;
587   Mat_SeqAIJ          *p_loc,*p_oth=NULL,*ad=(Mat_SeqAIJ*)(a->A)->data,*ao=NULL,*c_loc,*c_oth;
588   PetscScalar         *apv;
589   PetscTable          ta;
590 #if defined(PETSC_HAVE_HYPRE)
591   const char          *algTypes[3] = {"scalable","nonscalable","hypre"};
592   PetscInt            nalg = 3;
593 #else
594   const char          *algTypes[2] = {"scalable","nonscalable"};
595   PetscInt            nalg = 2;
596 #endif
597   PetscInt            alg = 1; /* set default algorithm */
598 #if defined(PETSC_USE_INFO)
599   PetscReal           apfill;
600 #endif
601 #if defined(PTAP_PROFILE)
602   PetscLogDouble      t0,t1,t11,t12,t2,t3,t4;
603 #endif
604   PetscBool           flg;
605 
606   PetscFunctionBegin;
607   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
608 
609   /* pick an algorithm */
610   ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
611   PetscOptionsObject->alreadyprinted = PETSC_FALSE; /* a hack to ensure the option shows in '-help' */
612   ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[1],&alg,&flg);CHKERRQ(ierr);
613   ierr = PetscOptionsEnd();CHKERRQ(ierr);
614 
615   if (!flg && pN > 100000) { /* may switch to scalable algorithm as default */
616     MatInfo     Ainfo,Pinfo;
617     PetscInt    nz_local;
618     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;
619 
620     ierr = MatGetInfo(A,MAT_LOCAL,&Ainfo);CHKERRQ(ierr);
621     ierr = MatGetInfo(P,MAT_LOCAL,&Pinfo);CHKERRQ(ierr);
622     nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);
623 
624     if (pN > fill*nz_local) alg_scalable_loc = PETSC_TRUE;
625     ierr = MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);CHKERRQ(ierr);
626 
627     if (alg_scalable) {
628       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
629     }
630   }
631 
632   if (alg == 0) {
633     ierr = MatPtAPSymbolic_MPIAIJ_MPIAIJ_scalable(A,P,fill,C);CHKERRQ(ierr);
634     (*C)->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_scalable;
635     PetscFunctionReturn(0);
636 
637 #if defined(PETSC_HAVE_HYPRE)
638   } else if (alg == 2) {
639     /* Use boomerAMGBuildCoarseOperator */
640     ierr = MatPtAPSymbolic_AIJ_AIJ_wHYPRE(A,P,fill,C);CHKERRQ(ierr);
641     PetscFunctionReturn(0);
642 #endif
643   }
644 
645 #if defined(PTAP_PROFILE)
646   ierr = PetscTime(&t0);CHKERRQ(ierr);
647 #endif
648 
649   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
650   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
651 
652   if (size > 1) ao = (Mat_SeqAIJ*)(a->B)->data;
653 
654   /* create symbolic parallel matrix Cmpi */
655   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
656   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
657 
658   /* Do dense axpy in MatPtAPNumeric_MPIAIJ_MPIAIJ() */
659   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ;
660 
661   /* create struct Mat_PtAPMPI and attached it to C later */
662   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
663   ptap->reuse = MAT_INITIAL_MATRIX;
664   ptap->algType = alg;
665 
666   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
667   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
668   /* get P_loc by taking all local rows of P */
669   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
670 
671   /* (0) compute Rd = Pd^T, Ro = Po^T  */
672   /* --------------------------------- */
673   ierr = MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);CHKERRQ(ierr);
674   ierr = MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);CHKERRQ(ierr);
675 #if defined(PTAP_PROFILE)
676   ierr = PetscTime(&t11);CHKERRQ(ierr);
677 #endif
678 
679   /* (1) compute symbolic AP = A_loc*P = Ad*P_loc + Ao*P_oth (api,apj) */
680   /* ----------------------------------------------------------------- */
681   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
682   if (ptap->P_oth) p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
683 
684   /* create and initialize a linked list */
685   ierr = PetscTableCreate(pn,pN,&ta);CHKERRQ(ierr); /* for compute AP_loc and Cmpi */
686   MatRowMergeMax_SeqAIJ(p_loc,ptap->P_loc->rmap->N,ta);
687   MatRowMergeMax_SeqAIJ(p_oth,ptap->P_oth->rmap->N,ta);
688   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr); /* Crmax = nnz(sum of Prows) */
689   /* printf("[%d] est %d, Crmax %d; pN %d\n",rank,5*(p_loc->rmax+p_oth->rmax + (PetscInt)(1.e-2*pN)),Crmax,pN); */
690 
691   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
692 
693   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) */
694   if (ao) {
695     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],PetscIntSumTruncate(ao->i[am],p_loc->i[pm]))),&free_space);CHKERRQ(ierr);
696   } else {
697     ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ad->i[am],p_loc->i[pm])),&free_space);CHKERRQ(ierr);
698   }
699   current_space = free_space;
700   nspacedouble  = 0;
701 
702   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
703   api[0] = 0;
704   for (i=0; i<am; i++) {
705     /* diagonal portion: Ad[i,:]*P */
706     ai = ad->i; pi = p_loc->i;
707     nzi = ai[i+1] - ai[i];
708     aj  = ad->j + ai[i];
709     for (j=0; j<nzi; j++) {
710       row  = aj[j];
711       pnz  = pi[row+1] - pi[row];
712       Jptr = p_loc->j + pi[row];
713       /* add non-zero cols of P into the sorted linked list lnk */
714       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
715     }
716     /* off-diagonal portion: Ao[i,:]*P */
717     if (ao) {
718       ai = ao->i; pi = p_oth->i;
719       nzi = ai[i+1] - ai[i];
720       aj  = ao->j + ai[i];
721       for (j=0; j<nzi; j++) {
722         row  = aj[j];
723         pnz  = pi[row+1] - pi[row];
724         Jptr = p_oth->j + pi[row];
725         ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
726       }
727     }
728     apnz     = lnk[0];
729     api[i+1] = api[i] + apnz;
730     if (ap_rmax < apnz) ap_rmax = apnz;
731 
732     /* if free space is not available, double the total space in the list */
733     if (current_space->local_remaining<apnz) {
734       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
735       nspacedouble++;
736     }
737 
738     /* Copy data into free space, then initialize lnk */
739     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
740 
741     current_space->array           += apnz;
742     current_space->local_used      += apnz;
743     current_space->local_remaining -= apnz;
744   }
745   /* Allocate space for apj and apv, initialize apj, and */
746   /* destroy list of free space and other temporary array(s) */
747   ierr   = PetscMalloc2(api[am],&apj,api[am],&apv);CHKERRQ(ierr);
748   ierr   = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
749   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
750 
751   /* Create AP_loc for reuse */
752   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,pN,api,apj,apv,&ptap->AP_loc);CHKERRQ(ierr);
753 
754 #if defined(PETSC_USE_INFO)
755   if (ao) {
756     apfill = (PetscReal)api[am]/(ad->i[am]+ao->i[am]+p_loc->i[pm]+1);
757   } else {
758     apfill = (PetscReal)api[am]/(ad->i[am]+p_loc->i[pm]+1);
759   }
760   ptap->AP_loc->info.mallocs           = nspacedouble;
761   ptap->AP_loc->info.fill_ratio_given  = fill;
762   ptap->AP_loc->info.fill_ratio_needed = apfill;
763 
764   if (api[am]) {
765     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);
766     ierr = PetscInfo1(ptap->AP_loc,"Use MatPtAP(A,B,MatReuse,%g,&C) for best AP_loc performance.;\n",(double)apfill);CHKERRQ(ierr);
767   } else {
768     ierr = PetscInfo(ptap->AP_loc,"Nonscalable algorithm, AP_loc is empty \n");CHKERRQ(ierr);
769   }
770 #endif
771 
772 #if defined(PTAP_PROFILE)
773   ierr = PetscTime(&t12);CHKERRQ(ierr);
774 #endif
775 
776   /* (2-1) compute symbolic Co = Ro*AP_loc  */
777   /* ------------------------------------ */
778   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->AP_loc,fill,&ptap->C_oth);CHKERRQ(ierr);
779 #if defined(PTAP_PROFILE)
780   ierr = PetscTime(&t1);CHKERRQ(ierr);
781 #endif
782 
783   /* (3) send coj of C_oth to other processors  */
784   /* ------------------------------------------ */
785   /* determine row ownership */
786   ierr = PetscLayoutCreate(comm,&rowmap);CHKERRQ(ierr);
787   rowmap->n  = pn;
788   rowmap->bs = 1;
789   ierr   = PetscLayoutSetUp(rowmap);CHKERRQ(ierr);
790   owners = rowmap->range;
791 
792   /* determine the number of messages to send, their lengths */
793   ierr = PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);CHKERRQ(ierr);
794   ierr = PetscMemzero(len_s,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
795   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
796 
797   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
798   coi   = c_oth->i; coj = c_oth->j;
799   con   = ptap->C_oth->rmap->n;
800   proc  = 0;
801   for (i=0; i<con; i++) {
802     while (prmap[i] >= owners[proc+1]) proc++;
803     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
804     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
805   }
806 
807   len          = 0; /* max length of buf_si[], see (4) */
808   owners_co[0] = 0;
809   nsend        = 0;
810   for (proc=0; proc<size; proc++) {
811     owners_co[proc+1] = owners_co[proc] + len_si[proc];
812     if (len_s[proc]) {
813       nsend++;
814       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
815       len         += len_si[proc];
816     }
817   }
818 
819   /* determine the number and length of messages to receive for coi and coj  */
820   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);CHKERRQ(ierr);
821   ierr = PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);CHKERRQ(ierr);
822 
823   /* post the Irecv and Isend of coj */
824   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
825   ierr = PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
826   ierr = PetscMalloc1(nsend+1,&swaits);CHKERRQ(ierr);
827   for (proc=0, k=0; proc<size; proc++) {
828     if (!len_s[proc]) continue;
829     i    = owners_co[proc];
830     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
831     k++;
832   }
833 
834   /* (2-2) compute symbolic C_loc = Rd*AP_loc */
835   /* ---------------------------------------- */
836   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->AP_loc,fill,&ptap->C_loc);CHKERRQ(ierr);
837   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;
838 
839   /* receives coj are complete */
840   for (i=0; i<nrecv; i++) {
841     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
842   }
843   ierr = PetscFree(rwaits);CHKERRQ(ierr);
844   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
845 
846   /* add received column indices into ta to update Crmax */
847   for (k=0; k<nrecv; k++) {/* k-th received message */
848     Jptr = buf_rj[k];
849     for (j=0; j<len_r[k]; j++) {
850       ierr = PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);CHKERRQ(ierr);
851     }
852   }
853   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
854   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
855 
856   /* (4) send and recv coi */
857   /*-----------------------*/
858   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
859   ierr   = PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
860   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
861   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
862   for (proc=0,k=0; proc<size; proc++) {
863     if (!len_s[proc]) continue;
864     /* form outgoing message for i-structure:
865          buf_si[0]:                 nrows to be sent
866                [1:nrows]:           row index (global)
867                [nrows+1:2*nrows+1]: i-structure index
868     */
869     /*-------------------------------------------*/
870     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
871     buf_si_i    = buf_si + nrows+1;
872     buf_si[0]   = nrows;
873     buf_si_i[0] = 0;
874     nrows       = 0;
875     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
876       nzi = coi[i+1] - coi[i];
877       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
878       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
879       nrows++;
880     }
881     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
882     k++;
883     buf_si += len_si[proc];
884   }
885   for (i=0; i<nrecv; i++) {
886     ierr = MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
887   }
888   ierr = PetscFree(rwaits);CHKERRQ(ierr);
889   if (nsend) {ierr = MPI_Waitall(nsend,swaits,sstatus);CHKERRQ(ierr);}
890 
891   ierr = PetscFree4(len_s,len_si,sstatus,owners_co);CHKERRQ(ierr);
892   ierr = PetscFree(len_ri);CHKERRQ(ierr);
893   ierr = PetscFree(swaits);CHKERRQ(ierr);
894   ierr = PetscFree(buf_s);CHKERRQ(ierr);
895 #if defined(PTAP_PROFILE)
896   ierr = PetscTime(&t2);CHKERRQ(ierr);
897 #endif
898   /* (5) compute the local portion of Cmpi      */
899   /* ------------------------------------------ */
900   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of Cmpi */
901   ierr          = PetscFreeSpaceGet(Crmax,&free_space);CHKERRQ(ierr);
902   current_space = free_space;
903 
904   ierr = PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);CHKERRQ(ierr);
905   for (k=0; k<nrecv; k++) {
906     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
907     nrows       = *buf_ri_k[k];
908     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
909     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
910   }
911 
912   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
913   ierr = PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);CHKERRQ(ierr);
914   for (i=0; i<pn; i++) {
915     /* add C_loc into Cmpi */
916     nzi  = c_loc->i[i+1] - c_loc->i[i];
917     Jptr = c_loc->j + c_loc->i[i];
918     ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
919 
920     /* add received col data into lnk */
921     for (k=0; k<nrecv; k++) { /* k-th received message */
922       if (i == *nextrow[k]) { /* i-th row */
923         nzi  = *(nextci[k]+1) - *nextci[k];
924         Jptr = buf_rj[k] + *nextci[k];
925         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
926         nextrow[k]++; nextci[k]++;
927       }
928     }
929     nzi = lnk[0];
930 
931     /* copy data into free space, then initialize lnk */
932     ierr = PetscLLCondensedClean(pN,nzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
933     ierr = MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);CHKERRQ(ierr);
934   }
935   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
936   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
937   ierr = PetscFreeSpaceDestroy(free_space);CHKERRQ(ierr);
938 #if defined(PTAP_PROFILE)
939   ierr = PetscTime(&t3);CHKERRQ(ierr);
940 #endif
941 
942   /* local sizes and preallocation */
943   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
944   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
945   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
946   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
947 
948   /* members in merge */
949   ierr = PetscFree(id_r);CHKERRQ(ierr);
950   ierr = PetscFree(len_r);CHKERRQ(ierr);
951   ierr = PetscFree(buf_ri[0]);CHKERRQ(ierr);
952   ierr = PetscFree(buf_ri);CHKERRQ(ierr);
953   ierr = PetscFree(buf_rj[0]);CHKERRQ(ierr);
954   ierr = PetscFree(buf_rj);CHKERRQ(ierr);
955   ierr = PetscLayoutDestroy(&rowmap);CHKERRQ(ierr);
956 
957   /* attach the supporting struct to Cmpi for reuse */
958   c = (Mat_MPIAIJ*)Cmpi->data;
959   c->ptap         = ptap;
960   ptap->duplicate = Cmpi->ops->duplicate;
961   ptap->destroy   = Cmpi->ops->destroy;
962   ptap->view      = Cmpi->ops->view;
963 
964   if (alg == 1) {
965     ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
966   }
967 
968   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
969   Cmpi->assembled        = PETSC_FALSE;
970   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
971   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
972   Cmpi->ops->view        = MatView_MPIAIJ_PtAP;
973   *C                     = Cmpi;
974 
975 #if defined(PTAP_PROFILE)
976   ierr = PetscTime(&t4);CHKERRQ(ierr);
977   if (rank == 1) {
978     printf("PtAPSym: %g + %g + %g + %g + %g + %g = %g\n",t11-t0,t1-t11,t12-t11,t2-t2,t3-t2,t4-t3,t4-t0);
979   }
980 #endif
981   PetscFunctionReturn(0);
982 }
983 
984 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
985 {
986   PetscErrorCode    ierr;
987   Mat_MPIAIJ        *a=(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
988   Mat_SeqAIJ        *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
989   Mat_SeqAIJ        *ap,*p_loc,*p_oth=NULL,*c_seq;
990   Mat_PtAPMPI       *ptap = c->ptap;
991   Mat               AP_loc,C_loc,C_oth;
992   PetscInt          i,rstart,rend,cm,ncols,row;
993   PetscInt          *api,*apj,am = A->rmap->n,j,col,apnz;
994   PetscScalar       *apa;
995   const PetscInt    *cols;
996   const PetscScalar *vals;
997 #if defined(PTAP_PROFILE)
998   PetscMPIInt       rank;
999   MPI_Comm          comm;
1000   PetscLogDouble    t0,t1,t2,t3,t4,eR,eAP,eCseq,eCmpi;
1001 #endif
1002 
1003   PetscFunctionBegin;
1004   ierr = MatZeroEntries(C);CHKERRQ(ierr);
1005 
1006   /* 1) get R = Pd^T,Ro = Po^T */
1007 #if defined(PTAP_PROFILE)
1008   ierr = PetscTime(&t0);CHKERRQ(ierr);
1009 #endif
1010   if (ptap->reuse == MAT_REUSE_MATRIX) {
1011     ierr = MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);CHKERRQ(ierr);
1012     ierr = MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);CHKERRQ(ierr);
1013   }
1014 #if defined(PTAP_PROFILE)
1015   ierr = PetscTime(&t1);CHKERRQ(ierr);
1016   eR = t1 - t0;
1017 #endif
1018 
1019   /* 2) get AP_loc */
1020   AP_loc = ptap->AP_loc;
1021   ap = (Mat_SeqAIJ*)AP_loc->data;
1022 
1023   /* 2-1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
1024   /*-----------------------------------------------------*/
1025   if (ptap->reuse == MAT_REUSE_MATRIX) {
1026     /* P_oth and P_loc are obtained in MatPtASymbolic() when reuse == MAT_INITIAL_MATRIX */
1027     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1028     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1029   }
1030 
1031   /* 2-2) compute numeric A_loc*P - dominating part */
1032   /* ---------------------------------------------- */
1033   /* get data from symbolic products */
1034   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1035   if (ptap->P_oth) {
1036     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
1037   }
1038   apa   = ptap->apa;
1039   api   = ap->i;
1040   apj   = ap->j;
1041   for (i=0; i<am; i++) {
1042     /* AP[i,:] = A[i,:]*P = Ad*P_loc Ao*P_oth */
1043     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);
1044     apnz = api[i+1] - api[i];
1045     for (j=0; j<apnz; j++) {
1046       col = apj[j+api[i]];
1047       ap->a[j+ap->i[i]] = apa[col];
1048       apa[col] = 0.0;
1049     }
1050     ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
1051   }
1052 #if defined(PTAP_PROFILE)
1053   ierr = PetscTime(&t2);CHKERRQ(ierr);
1054   eAP = t2 - t1;
1055 #endif
1056 
1057   /* 3) C_loc = Rd*AP_loc, C_oth = Ro*AP_loc */
1058   ierr = ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,AP_loc,ptap->C_loc);CHKERRQ(ierr);
1059   ierr = ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,AP_loc,ptap->C_oth);CHKERRQ(ierr);
1060   C_loc = ptap->C_loc;
1061   C_oth = ptap->C_oth;
1062 #if defined(PTAP_PROFILE)
1063   ierr = PetscTime(&t3);CHKERRQ(ierr);
1064   eCseq = t3 - t2;
1065 #endif
1066 
1067   /* add C_loc and Co to to C */
1068   ierr = MatGetOwnershipRange(C,&rstart,&rend);CHKERRQ(ierr);
1069 
1070   /* C_loc -> C */
1071   cm    = C_loc->rmap->N;
1072   c_seq = (Mat_SeqAIJ*)C_loc->data;
1073   cols = c_seq->j;
1074   vals = c_seq->a;
1075   for (i=0; i<cm; i++) {
1076     ncols = c_seq->i[i+1] - c_seq->i[i];
1077     row = rstart + i;
1078     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1079     cols += ncols; vals += ncols;
1080   }
1081 
1082   /* Co -> C, off-processor part */
1083   cm = C_oth->rmap->N;
1084   c_seq = (Mat_SeqAIJ*)C_oth->data;
1085   cols = c_seq->j;
1086   vals = c_seq->a;
1087   for (i=0; i<cm; i++) {
1088     ncols = c_seq->i[i+1] - c_seq->i[i];
1089     row = p->garray[i];
1090     ierr = MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);CHKERRQ(ierr);
1091     cols += ncols; vals += ncols;
1092   }
1093   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1094   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1095 #if defined(PTAP_PROFILE)
1096   ierr = PetscTime(&t4);CHKERRQ(ierr);
1097   eCmpi = t4 - t3;
1098 
1099   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1100   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1101   if (rank==1) {
1102     ierr = PetscPrintf(MPI_COMM_SELF," R %g, AP %g, Cseq %g, Cmpi %g = %g\n", eR,eAP,eCseq,eCmpi,eR+eAP+eCseq+eCmpi);CHKERRQ(ierr);
1103   }
1104 #endif
1105   ptap->reuse = MAT_REUSE_MATRIX;
1106   PetscFunctionReturn(0);
1107 }
1108 
1109 PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIAIJ_ptap(Mat A,Mat P,PetscReal fill,Mat *C)
1110 {
1111   PetscErrorCode      ierr;
1112   Mat                 Cmpi;
1113   Mat_PtAPMPI         *ptap;
1114   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1115   Mat_MPIAIJ          *a        =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c;
1116   Mat_SeqAIJ          *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
1117   Mat_SeqAIJ          *p_loc,*p_oth;
1118   PetscInt            *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pdti,*pdtj,*poti,*potj,*ptJ;
1119   PetscInt            *adi=ad->i,*aj,*aoi=ao->i,nnz;
1120   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1121   PetscInt            am=A->rmap->n,pN=P->cmap->N,pm=P->rmap->n,pn=P->cmap->n;
1122   PetscBT             lnkbt;
1123   MPI_Comm            comm;
1124   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0;
1125   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1126   PetscInt            len,proc,*dnz,*onz,*owners;
1127   PetscInt            nzi,*pti,*ptj;
1128   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1129   MPI_Request         *swaits,*rwaits;
1130   MPI_Status          *sstatus,rstatus;
1131   Mat_Merge_SeqsToMPI *merge;
1132   PetscInt            *api,*apj,*Jptr,apnz,*prmap=p->garray,pon,nspacedouble=0,j,ap_rmax=0;
1133   PetscReal           afill=1.0,afill_tmp;
1134 
1135   PetscFunctionBegin;
1136   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
1137   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1138   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1139 
1140   /* create struct Mat_PtAPMPI and attached it to C later */
1141   ierr        = PetscNew(&ptap);CHKERRQ(ierr);
1142   ierr        = PetscNew(&merge);CHKERRQ(ierr);
1143   ptap->merge = merge;
1144   ptap->reuse = MAT_INITIAL_MATRIX;
1145 
1146   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1147   ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1148 
1149   /* get P_loc by taking all local rows of P */
1150   ierr = MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1151 
1152   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1153   p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
1154   pi_loc = p_loc->i; pj_loc = p_loc->j;
1155   pi_oth = p_oth->i; pj_oth = p_oth->j;
1156 
1157   /* (1) compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth (api,apj) */
1158   /*--------------------------------------------------------------------------*/
1159   ierr   = PetscMalloc1(am+1,&api);CHKERRQ(ierr);
1160   api[0] = 0;
1161 
1162   /* create and initialize a linked list */
1163   ierr = PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);CHKERRQ(ierr);
1164 
1165   /* Initial FreeSpace size is fill*(nnz(A) + nnz(P)) -OOM for ex56, np=8k on Intrepid! */
1166   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);CHKERRQ(ierr);
1167   current_space = free_space;
1168 
1169   for (i=0; i<am; i++) {
1170     /* diagonal portion of A */
1171     nzi = adi[i+1] - adi[i];
1172     aj  = ad->j + adi[i];
1173     for (j=0; j<nzi; j++) {
1174       row  = aj[j];
1175       pnz  = pi_loc[row+1] - pi_loc[row];
1176       Jptr = pj_loc + pi_loc[row];
1177       /* add non-zero cols of P into the sorted linked list lnk */
1178       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1179     }
1180     /* off-diagonal portion of A */
1181     nzi = aoi[i+1] - aoi[i];
1182     aj  = ao->j + aoi[i];
1183     for (j=0; j<nzi; j++) {
1184       row  = aj[j];
1185       pnz  = pi_oth[row+1] - pi_oth[row];
1186       Jptr = pj_oth + pi_oth[row];
1187       ierr = PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1188     }
1189     apnz     = lnk[0];
1190     api[i+1] = api[i] + apnz;
1191     if (ap_rmax < apnz) ap_rmax = apnz;
1192 
1193     /* if free space is not available, double the total space in the list */
1194     if (current_space->local_remaining<apnz) {
1195       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1196       nspacedouble++;
1197     }
1198 
1199     /* Copy data into free space, then initialize lnk */
1200     ierr = PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1201 
1202     current_space->array           += apnz;
1203     current_space->local_used      += apnz;
1204     current_space->local_remaining -= apnz;
1205   }
1206 
1207   /* Allocate space for apj, initialize apj, and */
1208   /* destroy list of free space and other temporary array(s) */
1209   ierr      = PetscMalloc1(api[am]+1,&apj);CHKERRQ(ierr);
1210   ierr      = PetscFreeSpaceContiguous(&free_space,apj);CHKERRQ(ierr);
1211   afill_tmp = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1);
1212   if (afill_tmp > afill) afill = afill_tmp;
1213 
1214   /* (2) determine symbolic Co=(p->B)^T*AP - send to others (coi,coj)*/
1215   /*-----------------------------------------------------------------*/
1216   ierr = MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
1217 
1218   /* then, compute symbolic Co = (p->B)^T*AP */
1219   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1220                          >= (num of nonzero rows of C_seq) - pn */
1221   ierr   = PetscMalloc1(pon+1,&coi);CHKERRQ(ierr);
1222   coi[0] = 0;
1223 
1224   /* set initial free space to be fill*(nnz(p->B) + nnz(AP)) */
1225   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],api[am]));
1226   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1227   current_space = free_space;
1228 
1229   for (i=0; i<pon; i++) {
1230     pnz = poti[i+1] - poti[i];
1231     ptJ = potj + poti[i];
1232     for (j=0; j<pnz; j++) {
1233       row  = ptJ[j]; /* row of AP == col of Pot */
1234       apnz = api[row+1] - api[row];
1235       Jptr = apj + api[row];
1236       /* add non-zero cols of AP into the sorted linked list lnk */
1237       ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1238     }
1239     nnz = lnk[0];
1240 
1241     /* If free space is not available, double the total space in the list */
1242     if (current_space->local_remaining<nnz) {
1243       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1244       nspacedouble++;
1245     }
1246 
1247     /* Copy data into free space, and zero out denserows */
1248     ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1249 
1250     current_space->array           += nnz;
1251     current_space->local_used      += nnz;
1252     current_space->local_remaining -= nnz;
1253 
1254     coi[i+1] = coi[i] + nnz;
1255   }
1256 
1257   ierr      = PetscMalloc1(coi[pon],&coj);CHKERRQ(ierr);
1258   ierr      = PetscFreeSpaceContiguous(&free_space,coj);CHKERRQ(ierr);
1259   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + api[am]+1);
1260   if (afill_tmp > afill) afill = afill_tmp;
1261   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);CHKERRQ(ierr);
1262 
1263   /* (3) send j-array (coj) of Co to other processors */
1264   /*--------------------------------------------------*/
1265   ierr = PetscCalloc1(size,&merge->len_s);CHKERRQ(ierr);
1266   len_s        = merge->len_s;
1267   merge->nsend = 0;
1268 
1269 
1270   /* determine row ownership */
1271   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
1272   merge->rowmap->n  = pn;
1273   merge->rowmap->bs = 1;
1274 
1275   ierr   = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
1276   owners = merge->rowmap->range;
1277 
1278   /* determine the number of messages to send, their lengths */
1279   ierr = PetscMalloc2(size,&len_si,size,&sstatus);CHKERRQ(ierr);
1280   ierr = PetscMemzero(len_si,size*sizeof(PetscMPIInt));CHKERRQ(ierr);
1281   ierr = PetscMalloc1(size+2,&owners_co);CHKERRQ(ierr);
1282 
1283   proc = 0;
1284   for (i=0; i<pon; i++) {
1285     while (prmap[i] >= owners[proc+1]) proc++;
1286     len_si[proc]++;               /* num of rows in Co(=Pt*AP) to be sent to [proc] */
1287     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1288   }
1289 
1290   len          = 0; /* max length of buf_si[], see (4) */
1291   owners_co[0] = 0;
1292   for (proc=0; proc<size; proc++) {
1293     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1294     if (len_s[proc]) {
1295       merge->nsend++;
1296       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1297       len         += len_si[proc];
1298     }
1299   }
1300 
1301   /* determine the number and length of messages to receive for coi and coj  */
1302   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
1303   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
1304 
1305   /* post the Irecv and Isend of coj */
1306   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
1307   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);CHKERRQ(ierr);
1308   ierr = PetscMalloc1(merge->nsend+1,&swaits);CHKERRQ(ierr);
1309   for (proc=0, k=0; proc<size; proc++) {
1310     if (!len_s[proc]) continue;
1311     i    = owners_co[proc];
1312     ierr = MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);CHKERRQ(ierr);
1313     k++;
1314   }
1315 
1316   /* receives and sends of coj are complete */
1317   for (i=0; i<merge->nrecv; i++) {
1318     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1319   }
1320   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1321   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
1322 
1323   /* (4) send and recv coi */
1324   /*-----------------------*/
1325   ierr   = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
1326   ierr   = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);CHKERRQ(ierr);
1327   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
1328   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1329   for (proc=0,k=0; proc<size; proc++) {
1330     if (!len_s[proc]) continue;
1331     /* form outgoing message for i-structure:
1332          buf_si[0]:                 nrows to be sent
1333                [1:nrows]:           row index (global)
1334                [nrows+1:2*nrows+1]: i-structure index
1335     */
1336     /*-------------------------------------------*/
1337     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1338     buf_si_i    = buf_si + nrows+1;
1339     buf_si[0]   = nrows;
1340     buf_si_i[0] = 0;
1341     nrows       = 0;
1342     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1343       nzi = coi[i+1] - coi[i];
1344       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1345       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1346       nrows++;
1347     }
1348     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);CHKERRQ(ierr);
1349     k++;
1350     buf_si += len_si[proc];
1351   }
1352   i = merge->nrecv;
1353   while (i--) {
1354     ierr = MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);CHKERRQ(ierr);
1355   }
1356   ierr = PetscFree(rwaits);CHKERRQ(ierr);
1357   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,swaits,sstatus);CHKERRQ(ierr);}
1358 
1359   ierr = PetscFree2(len_si,sstatus);CHKERRQ(ierr);
1360   ierr = PetscFree(len_ri);CHKERRQ(ierr);
1361   ierr = PetscFree(swaits);CHKERRQ(ierr);
1362   ierr = PetscFree(buf_s);CHKERRQ(ierr);
1363 
1364   /* (5) compute the local portion of C (mpi mat) */
1365   /*----------------------------------------------*/
1366   ierr = MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
1367 
1368   /* allocate pti array and free space for accumulating nonzero column info */
1369   ierr   = PetscMalloc1(pn+1,&pti);CHKERRQ(ierr);
1370   pti[0] = 0;
1371 
1372   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1373   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pi_loc[pm],api[am]));
1374   ierr          = PetscFreeSpaceGet(nnz,&free_space);CHKERRQ(ierr);
1375   current_space = free_space;
1376 
1377   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1378   for (k=0; k<merge->nrecv; k++) {
1379     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1380     nrows       = *buf_ri_k[k];
1381     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1382     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1383   }
1384   ierr = MatPreallocateInitialize(comm,pn,pn,dnz,onz);CHKERRQ(ierr);
1385 
1386   for (i=0; i<pn; i++) {
1387     /* add pdt[i,:]*AP into lnk */
1388     pnz = pdti[i+1] - pdti[i];
1389     ptJ = pdtj + pdti[i];
1390     for (j=0; j<pnz; j++) {
1391       row  = ptJ[j];  /* row of AP == col of Pt */
1392       apnz = api[row+1] - api[row];
1393       Jptr = apj + api[row];
1394       /* add non-zero cols of AP into the sorted linked list lnk */
1395       ierr = PetscLLCondensedAddSorted(apnz,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1396     }
1397 
1398     /* add received col data into lnk */
1399     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1400       if (i == *nextrow[k]) { /* i-th row */
1401         nzi  = *(nextci[k]+1) - *nextci[k];
1402         Jptr = buf_rj[k] + *nextci[k];
1403         ierr = PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);CHKERRQ(ierr);
1404         nextrow[k]++; nextci[k]++;
1405       }
1406     }
1407     nnz = lnk[0];
1408 
1409     /* if free space is not available, make more free space */
1410     if (current_space->local_remaining<nnz) {
1411       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);CHKERRQ(ierr);
1412       nspacedouble++;
1413     }
1414     /* copy data into free space, then initialize lnk */
1415     ierr = PetscLLCondensedClean(pN,nnz,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
1416     ierr = MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);CHKERRQ(ierr);
1417 
1418     current_space->array           += nnz;
1419     current_space->local_used      += nnz;
1420     current_space->local_remaining -= nnz;
1421 
1422     pti[i+1] = pti[i] + nnz;
1423   }
1424   ierr = MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);CHKERRQ(ierr);
1425   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1426 
1427   ierr      = PetscMalloc1(pti[pn]+1,&ptj);CHKERRQ(ierr);
1428   ierr      = PetscFreeSpaceContiguous(&free_space,ptj);CHKERRQ(ierr);
1429   afill_tmp = (PetscReal)pti[pn]/(pi_loc[pm] + api[am]+1);
1430   if (afill_tmp > afill) afill = afill_tmp;
1431   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1432 
1433   /* (6) create symbolic parallel matrix Cmpi */
1434   /*------------------------------------------*/
1435   ierr = MatCreate(comm,&Cmpi);CHKERRQ(ierr);
1436   ierr = MatSetSizes(Cmpi,pn,pn,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
1437   ierr = MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(P->cmap->bs));CHKERRQ(ierr);
1438   ierr = MatSetType(Cmpi,MATMPIAIJ);CHKERRQ(ierr);
1439   ierr = MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);CHKERRQ(ierr);
1440   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
1441 
1442   merge->bi        = pti;      /* Cseq->i */
1443   merge->bj        = ptj;      /* Cseq->j */
1444   merge->coi       = coi;      /* Co->i   */
1445   merge->coj       = coj;      /* Co->j   */
1446   merge->buf_ri    = buf_ri;
1447   merge->buf_rj    = buf_rj;
1448   merge->owners_co = owners_co;
1449   merge->destroy   = Cmpi->ops->destroy;
1450 
1451   /* attach the supporting struct to Cmpi for reuse */
1452   c           = (Mat_MPIAIJ*)Cmpi->data;
1453   c->ptap     = ptap;
1454   ptap->api   = api;
1455   ptap->apj   = apj;
1456   ptap->duplicate = Cmpi->ops->duplicate;
1457   ptap->destroy   = Cmpi->ops->destroy;
1458 
1459   /* Cmpi is not ready for use - assembly will be done by MatPtAPNumeric() */
1460   Cmpi->assembled        = PETSC_FALSE;
1461   Cmpi->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
1462   Cmpi->ops->duplicate   = MatDuplicate_MPIAIJ_MatPtAP;
1463   Cmpi->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIAIJ_ptap;
1464   *C                     = Cmpi;
1465 
1466   /* flag 'scalable' determines which implementations to be used:
1467        0: do dense axpy in MatPtAPNumeric() - fast, but requires storage of a nonscalable dense array apa;
1468        1: do sparse axpy in MatPtAPNumeric() - might slow, uses a sparse array apa */
1469   /* set default scalable */
1470   ptap->scalable = PETSC_FALSE; /* PETSC_TRUE; */
1471 
1472   ierr = PetscOptionsGetBool(((PetscObject)Cmpi)->options,((PetscObject)Cmpi)->prefix,"-matptap_scalable",&ptap->scalable,NULL);CHKERRQ(ierr);
1473   if (!ptap->scalable) {  /* Do dense axpy */
1474     ierr = PetscCalloc1(pN,&ptap->apa);CHKERRQ(ierr);
1475   } else {
1476     ierr = PetscCalloc1(ap_rmax+1,&ptap->apa);CHKERRQ(ierr);
1477   }
1478 
1479 #if defined(PETSC_USE_INFO)
1480   if (pti[pn] != 0) {
1481     ierr = PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);CHKERRQ(ierr);
1482     ierr = PetscInfo1(Cmpi,"Use MatPtAP(A,P,MatReuse,%g,&C) for best performance.\n",(double)afill);CHKERRQ(ierr);
1483   } else {
1484     ierr = PetscInfo(Cmpi,"Empty matrix product\n");CHKERRQ(ierr);
1485   }
1486 #endif
1487   PetscFunctionReturn(0);
1488 }
1489 
1490 PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIAIJ_ptap(Mat A,Mat P,Mat C)
1491 {
1492   PetscErrorCode      ierr;
1493   Mat_MPIAIJ          *a =(Mat_MPIAIJ*)A->data,*p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1494   Mat_SeqAIJ          *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
1495   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1496   Mat_SeqAIJ          *p_loc,*p_oth;
1497   Mat_PtAPMPI         *ptap;
1498   Mat_Merge_SeqsToMPI *merge;
1499   PetscInt            *adi=ad->i,*aoi=ao->i,*adj,*aoj,*apJ,nextp;
1500   PetscInt            *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pJ,*pj;
1501   PetscInt            i,j,k,anz,pnz,apnz,nextap,row,*cj;
1502   MatScalar           *ada,*aoa,*apa,*pa,*ca,*pa_loc,*pa_oth,valtmp;
1503   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1504   MPI_Comm            comm;
1505   PetscMPIInt         size,rank,taga,*len_s;
1506   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1507   PetscInt            **buf_ri,**buf_rj;
1508   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1509   MPI_Request         *s_waits,*r_waits;
1510   MPI_Status          *status;
1511   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1512   PetscInt            *api,*apj,*coi,*coj;
1513   PetscInt            *poJ=po->j,*pdJ=pd->j,pcstart=P->cmap->rstart,pcend=P->cmap->rend;
1514   PetscBool           scalable;
1515 #if defined(PTAP_PROFILE)
1516   PetscLogDouble t0,t1,t2,eP,t3,t4,et2_AP=0.0,ePtAP=0.0,t2_0,t2_1,t2_2;
1517 #endif
1518 
1519   PetscFunctionBegin;
1520   ierr = PetscObjectGetComm((PetscObject)C,&comm);CHKERRQ(ierr);
1521 #if defined(PTAP_PROFILE)
1522   ierr = PetscTime(&t0);CHKERRQ(ierr);
1523 #endif
1524   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1525   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
1526 
1527   ptap = c->ptap;
1528   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_INCOMP,"MatPtAP() has not been called to create matrix C yet, cannot use MAT_REUSE_MATRIX");
1529   merge    = ptap->merge;
1530   apa      = ptap->apa;
1531   scalable = ptap->scalable;
1532 
1533   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
1534   /*-----------------------------------------------------*/
1535   if (ptap->reuse == MAT_INITIAL_MATRIX) {
1536     /* P_oth and P_loc are obtained in MatPtASymbolic(), skip calling MatGetBrowsOfAoCols() and MatMPIAIJGetLocalMat() */
1537     ptap->reuse = MAT_REUSE_MATRIX;
1538   } else { /* update numerical values of P_oth and P_loc */
1539     ierr = MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);CHKERRQ(ierr);
1540     ierr = MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);CHKERRQ(ierr);
1541   }
1542 #if defined(PTAP_PROFILE)
1543   ierr = PetscTime(&t1);CHKERRQ(ierr);
1544   eP = t1-t0;
1545 #endif
1546   /*
1547   printf("[%d] Ad: %d, %d; Ao: %d, %d; P_loc: %d, %d; P_oth %d, %d;\n",rank,
1548          a->A->rmap->N,a->A->cmap->N,a->B->rmap->N,a->B->cmap->N,
1549          ptap->P_loc->rmap->N,ptap->P_loc->cmap->N,
1550          ptap->P_oth->rmap->N,ptap->P_oth->cmap->N);
1551    */
1552 
1553   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
1554   /*--------------------------------------------------------------*/
1555   /* get data from symbolic products */
1556   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1557   p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
1558   pi_loc=p_loc->i; pj_loc=p_loc->j; pa_loc=p_loc->a;
1559   pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
1560 
1561   coi  = merge->coi; coj = merge->coj;
1562   ierr = PetscCalloc1(coi[pon]+1,&coa);CHKERRQ(ierr);
1563 
1564   bi     = merge->bi; bj = merge->bj;
1565   owners = merge->rowmap->range;
1566   ierr   = PetscCalloc1(bi[cm]+1,&ba);CHKERRQ(ierr);  /* ba: Cseq->a */
1567 
1568   api = ptap->api; apj = ptap->apj;
1569 
1570   if (!scalable) { /* Do dense axpy on apa (length of pN, stores A[i,:]*P) - nonscalable, but faster (could take 1/3 scalable time) */
1571     ierr = PetscInfo(C,"Using non-scalable dense axpy\n");CHKERRQ(ierr);
1572 #if defined(PTAP_PROFILE)
1573     ierr = PetscTime(&t1);CHKERRQ(ierr);
1574 #endif
1575     for (i=0; i<am; i++) {
1576 #if defined(PTAP_PROFILE)
1577       ierr = PetscTime(&t2_0);CHKERRQ(ierr);
1578 #endif
1579       /* 2-a) form i-th sparse row of A_loc*P = Ad*P_loc + Ao*P_oth */
1580       /*------------------------------------------------------------*/
1581       apJ = apj + api[i];
1582 
1583       /* diagonal portion of A */
1584       anz = adi[i+1] - adi[i];
1585       adj = ad->j + adi[i];
1586       ada = ad->a + adi[i];
1587       for (j=0; j<anz; j++) {
1588         row = adj[j];
1589         pnz = pi_loc[row+1] - pi_loc[row];
1590         pj  = pj_loc + pi_loc[row];
1591         pa  = pa_loc + pi_loc[row];
1592 
1593         /* perform dense axpy */
1594         valtmp = ada[j];
1595         for (k=0; k<pnz; k++) {
1596           apa[pj[k]] += valtmp*pa[k];
1597         }
1598         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
1599       }
1600 
1601       /* off-diagonal portion of A */
1602       anz = aoi[i+1] - aoi[i];
1603       aoj = ao->j + aoi[i];
1604       aoa = ao->a + aoi[i];
1605       for (j=0; j<anz; j++) {
1606         row = aoj[j];
1607         pnz = pi_oth[row+1] - pi_oth[row];
1608         pj  = pj_oth + pi_oth[row];
1609         pa  = pa_oth + pi_oth[row];
1610 
1611         /* perform dense axpy */
1612         valtmp = aoa[j];
1613         for (k=0; k<pnz; k++) {
1614           apa[pj[k]] += valtmp*pa[k];
1615         }
1616         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
1617       }
1618 #if defined(PTAP_PROFILE)
1619       ierr    = PetscTime(&t2_1);CHKERRQ(ierr);
1620       et2_AP += t2_1 - t2_0;
1621 #endif
1622 
1623       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
1624       /*--------------------------------------------------------------*/
1625       apnz = api[i+1] - api[i];
1626       /* put the value into Co=(p->B)^T*AP (off-diagonal part, send to others) */
1627       pnz = po->i[i+1] - po->i[i];
1628       poJ = po->j + po->i[i];
1629       pA  = po->a + po->i[i];
1630       for (j=0; j<pnz; j++) {
1631         row = poJ[j];
1632         cnz = coi[row+1] - coi[row];
1633         cj  = coj + coi[row];
1634         ca  = coa + coi[row];
1635         /* perform dense axpy */
1636         valtmp = pA[j];
1637         for (k=0; k<cnz; k++) {
1638           ca[k] += valtmp*apa[cj[k]];
1639         }
1640         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1641       }
1642       /* put the value into Cd (diagonal part) */
1643       pnz = pd->i[i+1] - pd->i[i];
1644       pdJ = pd->j + pd->i[i];
1645       pA  = pd->a + pd->i[i];
1646       for (j=0; j<pnz; j++) {
1647         row = pdJ[j];
1648         cnz = bi[row+1] - bi[row];
1649         cj  = bj + bi[row];
1650         ca  = ba + bi[row];
1651         /* perform dense axpy */
1652         valtmp = pA[j];
1653         for (k=0; k<cnz; k++) {
1654           ca[k] += valtmp*apa[cj[k]];
1655         }
1656         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1657       }
1658 
1659       /* zero the current row of A*P */
1660       for (k=0; k<apnz; k++) apa[apJ[k]] = 0.0;
1661 #if defined(PTAP_PROFILE)
1662       ierr      = PetscTime(&t2_2);CHKERRQ(ierr);
1663       ePtAP += t2_2 - t2_1;
1664 #endif
1665     }
1666   } else { /* Do sparse axpy on apa (length of ap_rmax, stores A[i,:]*P) - scalable, but slower */
1667     ierr = PetscInfo(C,"Using scalable sparse axpy\n");CHKERRQ(ierr);
1668     /*-----------------------------------------------------------------------------------------*/
1669     pA=pa_loc;
1670     for (i=0; i<am; i++) {
1671 #if defined(PTAP_PROFILE)
1672       ierr = PetscTime(&t2_0);CHKERRQ(ierr);
1673 #endif
1674       /* form i-th sparse row of A*P */
1675       apnz = api[i+1] - api[i];
1676       apJ  = apj + api[i];
1677       /* diagonal portion of A */
1678       anz = adi[i+1] - adi[i];
1679       adj = ad->j + adi[i];
1680       ada = ad->a + adi[i];
1681       for (j=0; j<anz; j++) {
1682         row    = adj[j];
1683         pnz    = pi_loc[row+1] - pi_loc[row];
1684         pj     = pj_loc + pi_loc[row];
1685         pa     = pa_loc + pi_loc[row];
1686         valtmp = ada[j];
1687         nextp  = 0;
1688         for (k=0; nextp<pnz; k++) {
1689           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
1690             apa[k] += valtmp*pa[nextp++];
1691           }
1692         }
1693         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
1694       }
1695       /* off-diagonal portion of A */
1696       anz = aoi[i+1] - aoi[i];
1697       aoj = ao->j + aoi[i];
1698       aoa = ao->a + aoi[i];
1699       for (j=0; j<anz; j++) {
1700         row    = aoj[j];
1701         pnz    = pi_oth[row+1] - pi_oth[row];
1702         pj     = pj_oth + pi_oth[row];
1703         pa     = pa_oth + pi_oth[row];
1704         valtmp = aoa[j];
1705         nextp  = 0;
1706         for (k=0; nextp<pnz; k++) {
1707           if (apJ[k] == pj[nextp]) { /* col of AP == col of P */
1708             apa[k] += valtmp*pa[nextp++];
1709           }
1710         }
1711         ierr = PetscLogFlops(2.0*pnz);CHKERRQ(ierr);
1712       }
1713 #if defined(PTAP_PROFILE)
1714       ierr    = PetscTime(&t2_1);CHKERRQ(ierr);
1715       et2_AP += t2_1 - t2_0;
1716 #endif
1717 
1718       /* 2-b) Compute Cseq = P_loc[i,:]^T*AP[i,:] using outer product */
1719       /*--------------------------------------------------------------*/
1720       pnz = pi_loc[i+1] - pi_loc[i];
1721       pJ  = pj_loc + pi_loc[i];
1722       for (j=0; j<pnz; j++) {
1723         nextap = 0;
1724         row    = pJ[j]; /* global index */
1725         if (row < pcstart || row >=pcend) { /* put the value into Co */
1726           row = *poJ;
1727           cj  = coj + coi[row];
1728           ca  = coa + coi[row]; poJ++;
1729         } else {                            /* put the value into Cd */
1730           row = *pdJ;
1731           cj  = bj + bi[row];
1732           ca  = ba + bi[row]; pdJ++;
1733         }
1734         valtmp = pA[j];
1735         for (k=0; nextap<apnz; k++) {
1736           if (cj[k]==apJ[nextap]) ca[k] += valtmp*apa[nextap++];
1737         }
1738         ierr = PetscLogFlops(2.0*apnz);CHKERRQ(ierr);
1739       }
1740       pA += pnz;
1741       /* zero the current row info for A*P */
1742       ierr = PetscMemzero(apa,apnz*sizeof(MatScalar));CHKERRQ(ierr);
1743 #if defined(PTAP_PROFILE)
1744       ierr      = PetscTime(&t2_2);CHKERRQ(ierr);
1745       ePtAP += t2_2 - t2_1;
1746 #endif
1747     }
1748   }
1749 #if defined(PTAP_PROFILE)
1750   ierr = PetscTime(&t2);CHKERRQ(ierr);
1751 #endif
1752 
1753   /* 3) send and recv matrix values coa */
1754   /*------------------------------------*/
1755   buf_ri = merge->buf_ri;
1756   buf_rj = merge->buf_rj;
1757   len_s  = merge->len_s;
1758   ierr   = PetscCommGetNewTag(comm,&taga);CHKERRQ(ierr);
1759   ierr   = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
1760 
1761   ierr = PetscMalloc2(merge->nsend+1,&s_waits,size,&status);CHKERRQ(ierr);
1762   for (proc=0,k=0; proc<size; proc++) {
1763     if (!len_s[proc]) continue;
1764     i    = merge->owners_co[proc];
1765     ierr = MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
1766     k++;
1767   }
1768   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
1769   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
1770 
1771   ierr = PetscFree2(s_waits,status);CHKERRQ(ierr);
1772   ierr = PetscFree(r_waits);CHKERRQ(ierr);
1773   ierr = PetscFree(coa);CHKERRQ(ierr);
1774 #if defined(PTAP_PROFILE)
1775   ierr = PetscTime(&t3);CHKERRQ(ierr);
1776 #endif
1777 
1778   /* 4) insert local Cseq and received values into Cmpi */
1779   /*------------------------------------------------------*/
1780   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);CHKERRQ(ierr);
1781   for (k=0; k<merge->nrecv; k++) {
1782     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1783     nrows       = *(buf_ri_k[k]);
1784     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1785     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1786   }
1787 
1788   for (i=0; i<cm; i++) {
1789     row  = owners[rank] + i; /* global row index of C_seq */
1790     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1791     ba_i = ba + bi[i];
1792     bnz  = bi[i+1] - bi[i];
1793     /* add received vals into ba */
1794     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1795       /* i-th row */
1796       if (i == *nextrow[k]) {
1797         cnz    = *(nextci[k]+1) - *nextci[k];
1798         cj     = buf_rj[k] + *(nextci[k]);
1799         ca     = abuf_r[k] + *(nextci[k]);
1800         nextcj = 0;
1801         for (j=0; nextcj<cnz; j++) {
1802           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1803             ba_i[j] += ca[nextcj++];
1804           }
1805         }
1806         nextrow[k]++; nextci[k]++;
1807         ierr = PetscLogFlops(2.0*cnz);CHKERRQ(ierr);
1808       }
1809     }
1810     ierr = MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
1811   }
1812   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1813   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1814 
1815   ierr = PetscFree(ba);CHKERRQ(ierr);
1816   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
1817   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
1818   ierr = PetscFree3(buf_ri_k,nextrow,nextci);CHKERRQ(ierr);
1819 #if defined(PTAP_PROFILE)
1820   ierr = PetscTime(&t4);CHKERRQ(ierr);
1821   if (rank==1) {
1822     ierr = PetscPrintf(MPI_COMM_SELF,"  [%d] PtAPNum %g/P + %g/PtAP( %g/A*P + %g/Pt*AP ) + %g/comm + %g/Cloc = %g\n\n",rank,eP,t2-t1,et2_AP,ePtAP,t3-t2,t4-t3,t4-t0);CHKERRQ(ierr);
1823   }
1824 #endif
1825   PetscFunctionReturn(0);
1826 }
1827