xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision f6f667cfabdb84fae686043df9fba3b425683839)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <petscblaslapack.h>
4 
5 static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y);
6 static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y);
7 
8 #undef __FUNCT__
9 #define __FUNCT__ "PCBDDCAdaptiveSelection"
10 PetscErrorCode PCBDDCAdaptiveSelection(PC pc)
11 {
12   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
13   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
14   PetscBLASInt    B_dummyint,B_neigs,B_ierr,B_lwork;
15   PetscBLASInt    *B_iwork,*B_ifail;
16   PetscScalar     *work,lwork;
17   PetscScalar     *St,*S,*eigv;
18   PetscScalar     *Sarray,*Starray;
19   PetscReal       *eigs,thresh;
20   PetscInt        i,nmax,nmin,nv,cum,mss,cum2,cumarray,maxneigs;
21   PetscBool       allocated_S_St;
22 #if defined(PETSC_USE_COMPLEX)
23   PetscReal       *rwork;
24 #endif
25   PetscErrorCode  ierr;
26 
27   PetscFunctionBegin;
28   if (!sub_schurs->use_mumps) {
29     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS");
30   }
31 
32   if (pcbddc->dbg_flag) {
33     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
34     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
35     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check adaptive selection of constraints\n");CHKERRQ(ierr);
36     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
37   }
38 
39   if (pcbddc->dbg_flag) {
40     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d cc %d (%d,%d).\n",PetscGlobalRank,sub_schurs->n_subs,sub_schurs->is_hermitian,sub_schurs->is_posdef);
41   }
42 
43   if (sub_schurs->n_subs && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
44     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Adaptive selection not yet implemented for general matrix pencils (herm %d, posdef %d)\n",sub_schurs->is_hermitian,sub_schurs->is_posdef);
45   }
46 
47   /* max size of subsets */
48   mss = 0;
49   for (i=0;i<sub_schurs->n_subs;i++) {
50     if (PetscBTLookup(sub_schurs->computed_Stilda_subs,i)) {
51       PetscInt subset_size;
52       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
53       mss = PetscMax(mss,subset_size);
54     }
55   }
56 
57   /* min/max and threshold */
58   nmax = pcbddc->adaptive_nmax > 0 ? pcbddc->adaptive_nmax : mss;
59   nmin = pcbddc->adaptive_nmin > 0 ? pcbddc->adaptive_nmin : 0;
60   nmax = PetscMax(nmin,nmax);
61   allocated_S_St = PETSC_FALSE;
62   if (nmin) {
63     allocated_S_St = PETSC_TRUE;
64   }
65 
66   /* allocate lapack workspace */
67   cum = cum2 = 0;
68   maxneigs = 0;
69   for (i=0;i<sub_schurs->n_subs;i++) {
70     if (PetscBTLookup(sub_schurs->computed_Stilda_subs,i)) {
71       PetscInt n,subset_size;
72 
73       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
74       n = PetscMin(subset_size,nmax);
75       cum += subset_size*n;
76       cum2 += n;
77       maxneigs = PetscMax(maxneigs,n);
78     }
79   }
80   if (mss) {
81     if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
82       PetscBLASInt B_itype = 1;
83       PetscBLASInt B_N = mss;
84       PetscReal    zero = 0.0;
85       PetscReal    eps = 0.0; /* dlamch? */
86 
87       B_lwork = -1;
88       S = NULL;
89       St = NULL;
90       eigs = NULL;
91       eigv = NULL;
92       B_iwork = NULL;
93       B_ifail = NULL;
94       thresh = 1.0;
95       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
96 #if defined(PETSC_USE_COMPLEX)
97       PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&zero,&thresh,&B_dummyint,&B_dummyint,&eps,&B_neigs,eigs,eigv,&B_N,&lwork,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
98 #else
99       PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&zero,&thresh,&B_dummyint,&B_dummyint,&eps,&B_neigs,eigs,eigv,&B_N,&lwork,&B_lwork,B_iwork,B_ifail,&B_ierr));
100 #endif
101       if (B_ierr != 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYGVX Lapack routine %d",(int)B_ierr);
102       ierr = PetscFPTrapPop();CHKERRQ(ierr);
103     } else {
104         /* TODO */
105     }
106   } else {
107     lwork = 0;
108   }
109 
110   nv = 0;
111   if (sub_schurs->is_Ej_com && pcbddc->use_vertices) { /* complement of subsets, each entry is a vertex */
112     ierr = ISGetLocalSize(sub_schurs->is_Ej_com,&nv);CHKERRQ(ierr);
113   }
114   ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
115   if (allocated_S_St) {
116     ierr = PetscMalloc2(mss*mss,&S,mss*mss,&St);CHKERRQ(ierr);
117   }
118   ierr = PetscMalloc5(mss*mss,&eigv,mss,&eigs,B_lwork,&work,5*mss,&B_iwork,mss,&B_ifail);CHKERRQ(ierr);
119 #if defined(PETSC_USE_COMPLEX)
120   ierr = PetscMalloc1(7*mss,&rwork);CHKERRQ(ierr);
121 #endif
122   ierr = PetscMalloc4(nv+sub_schurs->n_subs,&pcbddc->adaptive_constraints_n,
123                       nv+cum2+1,&pcbddc->adaptive_constraints_ptrs,
124                       nv+cum,&pcbddc->adaptive_constraints_idxs,
125                       nv+cum,&pcbddc->adaptive_constraints_data);CHKERRQ(ierr);
126   ierr = PetscMemzero(pcbddc->adaptive_constraints_n,(nv+sub_schurs->n_subs)*sizeof(PetscInt));CHKERRQ(ierr);
127 
128   maxneigs = 0;
129   cum = cum2 = cumarray = 0;
130   if (sub_schurs->is_Ej_com && pcbddc->use_vertices) {
131     const PetscInt *idxs;
132 
133     ierr = ISGetIndices(sub_schurs->is_Ej_com,&idxs);CHKERRQ(ierr);
134     for (cum=0;cum<nv;cum++) {
135       pcbddc->adaptive_constraints_n[cum] = 1;
136       pcbddc->adaptive_constraints_idxs[cum] = idxs[cum];
137       pcbddc->adaptive_constraints_ptrs[cum] = cum;
138       pcbddc->adaptive_constraints_data[cum] = 1.0;
139     }
140     cum2 = cum;
141     ierr = ISRestoreIndices(sub_schurs->is_Ej_com,&idxs);CHKERRQ(ierr);
142   }
143 
144   if (mss) { /* multilevel */
145     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);CHKERRQ(ierr);
146     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);CHKERRQ(ierr);
147   }
148 
149   for (i=0;i<sub_schurs->n_subs;i++) {
150     PetscInt j,subset_size;
151 
152     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
153     if (PetscBTLookup(sub_schurs->computed_Stilda_subs,i)) {
154       const PetscInt *idxs;
155       PetscReal      infty = PETSC_MAX_REAL;
156       PetscInt       eigs_start = 0;
157       PetscBLASInt   B_N;
158 
159       ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
160       if (allocated_S_St) { /* S and S_t should be copied since we could need them later */
161         if (sub_schurs->is_hermitian) {
162           PetscInt j;
163           for (j=0;j<subset_size;j++) {
164             ierr = PetscMemcpy(S+j*(subset_size+1),Sarray+cumarray+j*(subset_size+1),(subset_size-j)*sizeof(PetscScalar));CHKERRQ(ierr);
165           }
166           for (j=0;j<subset_size;j++) {
167             ierr = PetscMemcpy(St+j*(subset_size+1),Starray+cumarray+j*(subset_size+1),(subset_size-j)*sizeof(PetscScalar));CHKERRQ(ierr);
168           }
169         } else {
170           ierr = PetscMemcpy(S,Sarray+cumarray,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
171           ierr = PetscMemcpy(St,Starray+cumarray,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
172         }
173       } else {
174         S = Sarray + cumarray;
175         St = Starray + cumarray;
176       }
177 
178       /* Threshold: this is an heuristic for edges */
179       ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
180       thresh = pcbddc->mat_graph->count[idxs[0]]*pcbddc->adaptive_threshold;
181 
182       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
183         PetscBLASInt B_itype = 1;
184         PetscBLASInt B_IL, B_IU;
185         PetscReal    eps = -1.0; /* dlamch? */
186         PetscInt     nmin_s;
187 
188         /* ask for eigenvalues larger than thresh */
189         if (pcbddc->dbg_flag) {
190           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Computing for sub %d/%d %d %d.\n",i,sub_schurs->n_subs,subset_size,pcbddc->mat_graph->count[idxs[0]]);
191         }
192         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
193 #if defined(PETSC_USE_COMPLEX)
194         PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
195 #else
196         PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
197 #endif
198         ierr = PetscFPTrapPop();CHKERRQ(ierr);
199         if (B_ierr) {
200           if (B_ierr < 0 ) {
201             SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
202           } else if (B_ierr <= B_N) {
203             SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: %d eigenvalues failed to converge",(int)B_ierr);
204           } else {
205             SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: leading minor of order %d is not positive definite",(int)B_ierr-B_N-1);
206           }
207         }
208 
209         if (B_neigs > nmax) {
210           if (pcbddc->dbg_flag) {
211             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, more than maximum required %d.\n",B_neigs,nmax);
212           }
213           eigs_start = B_neigs -nmax;
214           B_neigs = nmax;
215         }
216 
217         nmin_s = PetscMin(nmin,B_N);
218         if (B_neigs < nmin_s) {
219           PetscBLASInt B_neigs2;
220 
221           B_IU = B_N - B_neigs;
222           B_IL = B_N - nmin_s + 1;
223           if (pcbddc->dbg_flag) {
224             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, less than minimum required %d. Asking for %d to %d incl (fortran like)\n",B_neigs,nmin,B_IL,B_IU);
225           }
226           if (sub_schurs->is_hermitian) {
227             PetscInt j;
228             for (j=0;j<subset_size;j++) {
229               ierr = PetscMemcpy(S+j*(subset_size+1),Sarray+cumarray+j*(subset_size+1),(subset_size-j)*sizeof(PetscScalar));CHKERRQ(ierr);
230             }
231             for (j=0;j<subset_size;j++) {
232               ierr = PetscMemcpy(St+j*(subset_size+1),Starray+cumarray+j*(subset_size+1),(subset_size-j)*sizeof(PetscScalar));CHKERRQ(ierr);
233             }
234           } else {
235             ierr = PetscMemcpy(S,Sarray+cumarray,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
236             ierr = PetscMemcpy(St,Starray+cumarray,subset_size*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
237           }
238           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
239 #if defined(PETSC_USE_COMPLEX)
240           PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*subset_size,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
241 #else
242           PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*subset_size,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
243 #endif
244           ierr = PetscFPTrapPop();CHKERRQ(ierr);
245           B_neigs += B_neigs2;
246         }
247         if (B_ierr) {
248           if (B_ierr < 0 ) {
249             SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
250           } else if (B_ierr <= B_N) {
251             SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: %d eigenvalues failed to converge",(int)B_ierr);
252           } else {
253             SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: leading minor of order %d is not positive definite",(int)B_ierr-B_N-1);
254           }
255         }
256         if (pcbddc->dbg_flag) {
257           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Got %d eigs\n",B_neigs);
258           for (j=0;j<B_neigs;j++) {
259             if (eigs[j] == 0.0) {
260               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     Inf\n");
261             } else {
262               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",eigs[j+eigs_start]);
263             }
264           }
265         }
266       } else {
267           /* TODO */
268       }
269 
270       maxneigs = PetscMax(B_neigs,maxneigs);
271       pcbddc->adaptive_constraints_n[i+nv] = B_neigs;
272       ierr = PetscMemcpy(pcbddc->adaptive_constraints_data+cum2,eigv+eigs_start*subset_size,B_neigs*subset_size*sizeof(PetscScalar));CHKERRQ(ierr);
273 
274       if (pcbddc->dbg_flag > 1) {
275         PetscInt ii;
276         for (ii=0;ii<B_neigs;ii++) {
277           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector %d/%d (%d)\n",ii,B_neigs,B_N);
278           for (j=0;j<B_N;j++) {
279             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",pcbddc->adaptive_constraints_data[ii*subset_size+j+cum2]);
280           }
281         }
282       }
283       for (j=0;j<B_neigs;j++) {
284 #if 0
285         {
286           PetscBLASInt Blas_N,Blas_one = 1.0;
287           PetscScalar norm;
288           ierr = PetscBLASIntCast(subset_size,&Blas_N);CHKERRQ(ierr);
289           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,pcbddc->adaptive_constraints_data+cum2,&Blas_one,pcbddc->adaptive_constraints_data+cum2,&Blas_one));
290           if (pcbddc->adaptive_constraints_data[cum2] > 0.0) {
291             norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
292           } else {
293             norm = -1.0/PetscSqrtReal(PetscRealPart(norm));
294           }
295           PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,pcbddc->adaptive_constraints_data+cum2,&Blas_one));
296         }
297 #endif
298         ierr = PetscMemcpy(pcbddc->adaptive_constraints_idxs+cum2,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
299         pcbddc->adaptive_constraints_ptrs[cum++] = cum2;
300         cum2 += subset_size;
301       }
302       ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
303     }
304     /* shift for next computation */
305     cumarray += subset_size*subset_size;
306   }
307   if (pcbddc->dbg_flag) {
308     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
309   }
310   pcbddc->adaptive_constraints_ptrs[cum] = cum2;
311 
312   if (mss) {
313     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);CHKERRQ(ierr);
314     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);CHKERRQ(ierr);
315     /* destroy matrices (junk) */
316     ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
317     ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
318   }
319   if (allocated_S_St) {
320     ierr = PetscFree2(S,St);CHKERRQ(ierr);
321   }
322   ierr = PetscFree5(eigv,eigs,work,B_iwork,B_ifail);CHKERRQ(ierr);
323 #if defined(PETSC_USE_COMPLEX)
324   ierr = PetscFree(rwork);CHKERRQ(ierr);
325 #endif
326   if (pcbddc->dbg_flag) {
327     PetscInt maxneigs_r;
328     ierr = MPI_Allreduce(&maxneigs,&maxneigs_r,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
329     ierr = PetscPrintf(PetscObjectComm((PetscObject)pc),"Maximum number of constraints per cc %d\n",maxneigs_r);CHKERRQ(ierr);
330   }
331   PetscFunctionReturn(0);
332 }
333 
334 #undef __FUNCT__
335 #define __FUNCT__ "PCBDDCSetUpSolvers"
336 PetscErrorCode PCBDDCSetUpSolvers(PC pc)
337 {
338   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
339   PetscScalar    *coarse_submat_vals;
340   PetscErrorCode ierr;
341 
342   PetscFunctionBegin;
343   /* Setup local scatters R_to_B and (optionally) R_to_D */
344   /* PCBDDCSetUpLocalWorkVectors should be called first! */
345   ierr = PCBDDCSetUpLocalScatters(pc);CHKERRQ(ierr);
346 
347   /* Setup local neumann solver ksp_R */
348   /* PCBDDCSetUpLocalScatters should be called first! */
349   ierr = PCBDDCSetUpLocalSolvers(pc,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
350 
351   /* Change global null space passed in by the user if change of basis has been requested */
352   if (pcbddc->NullSpace && pcbddc->ChangeOfBasisMatrix) {
353     ierr = PCBDDCNullSpaceAdaptGlobal(pc);CHKERRQ(ierr);
354   }
355 
356   /*
357      Setup local correction and local part of coarse basis.
358      Gives back the dense local part of the coarse matrix in column major ordering
359   */
360   ierr = PCBDDCSetUpCorrection(pc,&coarse_submat_vals);CHKERRQ(ierr);
361 
362   /* Compute total number of coarse nodes and setup coarse solver */
363   ierr = PCBDDCSetUpCoarseSolver(pc,coarse_submat_vals);CHKERRQ(ierr);
364 
365   /* free */
366   ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
367   PetscFunctionReturn(0);
368 }
369 
370 #undef __FUNCT__
371 #define __FUNCT__ "PCBDDCResetCustomization"
372 PetscErrorCode PCBDDCResetCustomization(PC pc)
373 {
374   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
375   PetscErrorCode ierr;
376 
377   PetscFunctionBegin;
378   ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
379   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
380   ierr = MatNullSpaceDestroy(&pcbddc->NullSpace);CHKERRQ(ierr);
381   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
382   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
383   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
384   ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
385   ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
386   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
387   ierr = PCBDDCSetDofsSplitting(pc,0,NULL);CHKERRQ(ierr);
388   ierr = PCBDDCSetDofsSplittingLocal(pc,0,NULL);CHKERRQ(ierr);
389   PetscFunctionReturn(0);
390 }
391 
392 #undef __FUNCT__
393 #define __FUNCT__ "PCBDDCResetTopography"
394 PetscErrorCode PCBDDCResetTopography(PC pc)
395 {
396   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
397   PetscErrorCode ierr;
398 
399   PetscFunctionBegin;
400   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
401   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
402   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
403   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
404   ierr = PCBDDCSubSchursReset(pcbddc->sub_schurs);CHKERRQ(ierr);
405   PetscFunctionReturn(0);
406 }
407 
408 #undef __FUNCT__
409 #define __FUNCT__ "PCBDDCResetSolvers"
410 PetscErrorCode PCBDDCResetSolvers(PC pc)
411 {
412   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
413   PetscScalar    *array;
414   PetscErrorCode ierr;
415 
416   PetscFunctionBegin;
417   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
418   if (pcbddc->coarse_phi_B) {
419     ierr = MatDenseGetArray(pcbddc->coarse_phi_B,&array);CHKERRQ(ierr);
420     ierr = PetscFree(array);CHKERRQ(ierr);
421   }
422   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
423   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
424   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
425   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
426   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
427   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
428   if (pcbddc->local_auxmat2) {
429     ierr = MatDenseGetArray(pcbddc->local_auxmat2,&array);CHKERRQ(ierr);
430     ierr = PetscFree(array);CHKERRQ(ierr);
431   }
432   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
433   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
434   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
435   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
436   ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
437   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
438   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
439   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
440   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
441   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
442   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
443   ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
444   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
445   ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
446   ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
447   ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
448   PetscFunctionReturn(0);
449 }
450 
451 #undef __FUNCT__
452 #define __FUNCT__ "PCBDDCSetUpLocalWorkVectors"
453 PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
454 {
455   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
456   PC_IS          *pcis = (PC_IS*)pc->data;
457   VecType        impVecType;
458   PetscInt       n_constraints,n_R,old_size;
459   PetscErrorCode ierr;
460 
461   PetscFunctionBegin;
462   if (!pcbddc->ConstraintMatrix) {
463     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Constraint matrix has not been created");
464   }
465   /* get sizes */
466   n_constraints = pcbddc->local_primal_size - pcbddc->n_actual_vertices;
467   n_R = pcis->n-pcbddc->n_actual_vertices;
468   ierr = VecGetType(pcis->vec1_N,&impVecType);CHKERRQ(ierr);
469   /* local work vectors (try to avoid unneeded work)*/
470   /* R nodes */
471   old_size = -1;
472   if (pcbddc->vec1_R) {
473     ierr = VecGetSize(pcbddc->vec1_R,&old_size);CHKERRQ(ierr);
474   }
475   if (n_R != old_size) {
476     ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
477     ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
478     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);CHKERRQ(ierr);
479     ierr = VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);CHKERRQ(ierr);
480     ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
481     ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
482   }
483   /* local primal dofs */
484   old_size = -1;
485   if (pcbddc->vec1_P) {
486     ierr = VecGetSize(pcbddc->vec1_P,&old_size);CHKERRQ(ierr);
487   }
488   if (pcbddc->local_primal_size != old_size) {
489     ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
490     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);CHKERRQ(ierr);
491     ierr = VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,pcbddc->local_primal_size);CHKERRQ(ierr);
492     ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
493   }
494   /* local explicit constraints */
495   old_size = -1;
496   if (pcbddc->vec1_C) {
497     ierr = VecGetSize(pcbddc->vec1_C,&old_size);CHKERRQ(ierr);
498   }
499   if (n_constraints && n_constraints != old_size) {
500     ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
501     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);CHKERRQ(ierr);
502     ierr = VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);CHKERRQ(ierr);
503     ierr = VecSetType(pcbddc->vec1_C,impVecType);CHKERRQ(ierr);
504   }
505   PetscFunctionReturn(0);
506 }
507 
508 #undef __FUNCT__
509 #define __FUNCT__ "PCBDDCSetUpCorrection"
510 PetscErrorCode PCBDDCSetUpCorrection(PC pc, PetscScalar **coarse_submat_vals_n)
511 {
512   PetscErrorCode         ierr;
513   /* pointers to pcis and pcbddc */
514   PC_IS*                 pcis = (PC_IS*)pc->data;
515   PC_BDDC*               pcbddc = (PC_BDDC*)pc->data;
516   /* submatrices of local problem */
517   Mat                    A_RV,A_VR,A_VV;
518   /* submatrices of local coarse problem */
519   Mat                    S_VV,S_CV,S_VC,S_CC;
520   /* working matrices */
521   Mat                    C_CR;
522   /* additional working stuff */
523   PC                     pc_R;
524   Mat                    F;
525   PetscBool              isLU,isCHOL,isILU;
526 
527   PetscScalar            *coarse_submat_vals; /* TODO: use a PETSc matrix */
528   PetscScalar            *work;
529   PetscInt               *idx_V_B;
530   PetscInt               n,n_vertices,n_constraints;
531   PetscInt               i,n_R,n_D,n_B;
532   PetscBool              unsymmetric_check;
533   /* matrix type (vector type propagated downstream from vec1_C and local matrix type) */
534   MatType                impMatType;
535   /* some shortcuts to scalars */
536   PetscScalar            one=1.0,m_one=-1.0;
537 
538   PetscFunctionBegin;
539   /* get number of vertices (corners plus constraints with change of basis)
540      pcbddc->n_actual_vertices stores the actual number of vertices, pcbddc->n_vertices the number of corners computed */
541   n_vertices = pcbddc->n_actual_vertices;
542   n_constraints = pcbddc->local_primal_size-n_vertices;
543   /* Set Non-overlapping dimensions */
544   n_B = pcis->n_B; n_D = pcis->n - n_B;
545   n_R = pcis->n-n_vertices;
546 
547   /* Set types for local objects needed by BDDC precondtioner */
548   impMatType = MATSEQDENSE;
549 
550   /* vertices in boundary numbering */
551   ierr = PetscMalloc1(n_vertices,&idx_V_B);CHKERRQ(ierr);
552   ierr = ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,n_vertices,pcbddc->primal_indices_local_idxs,&i,idx_V_B);CHKERRQ(ierr);
553   if (i != n_vertices) {
554     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for BDDC vertices! %d != %d\n",n_vertices,i);
555   }
556 
557   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
558   ierr = PetscMalloc1(pcbddc->local_primal_size*pcbddc->local_primal_size,&coarse_submat_vals);CHKERRQ(ierr);
559   ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_vertices,coarse_submat_vals,&S_VV);CHKERRQ(ierr);
560   ierr = MatSeqDenseSetLDA(S_VV,pcbddc->local_primal_size);CHKERRQ(ierr);
561   ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_vertices,coarse_submat_vals+n_vertices,&S_CV);CHKERRQ(ierr);
562   ierr = MatSeqDenseSetLDA(S_CV,pcbddc->local_primal_size);CHKERRQ(ierr);
563   ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_constraints,coarse_submat_vals+pcbddc->local_primal_size*n_vertices,&S_VC);CHKERRQ(ierr);
564   ierr = MatSeqDenseSetLDA(S_VC,pcbddc->local_primal_size);CHKERRQ(ierr);
565   ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_constraints,coarse_submat_vals+(pcbddc->local_primal_size+1)*n_vertices,&S_CC);CHKERRQ(ierr);
566   ierr = MatSeqDenseSetLDA(S_CC,pcbddc->local_primal_size);CHKERRQ(ierr);
567 
568   unsymmetric_check = PETSC_FALSE;
569   /* allocate workspace */
570   n = 0;
571   if (n_constraints) {
572     n += n_R*n_constraints;
573   }
574   if (n_vertices) {
575     n = PetscMax(2*n_R*n_vertices,n);
576   }
577   if (!pcbddc->issym) {
578     n = PetscMax(2*n_R*pcbddc->local_primal_size,n);
579     unsymmetric_check = PETSC_TRUE;
580   }
581   ierr = PetscMalloc1(n,&work);CHKERRQ(ierr);
582 
583   /* determine if can use MatSolve routines instead of calling KSPSolve on ksp_R */
584   ierr = KSPGetPC(pcbddc->ksp_R,&pc_R);CHKERRQ(ierr);
585   ierr = PetscObjectTypeCompare((PetscObject)pc_R,PCLU,&isLU);CHKERRQ(ierr);
586   ierr = PetscObjectTypeCompare((PetscObject)pc_R,PCILU,&isILU);CHKERRQ(ierr);
587   ierr = PetscObjectTypeCompare((PetscObject)pc_R,PCCHOLESKY,&isCHOL);CHKERRQ(ierr);
588   if (isLU || isILU || isCHOL) {
589     ierr = PCFactorGetMatrix(pc_R,&F);CHKERRQ(ierr);
590   } else {
591     F = NULL;
592   }
593 
594   /* Precompute stuffs needed for preprocessing and application of BDDC*/
595   if (n_constraints) {
596     Mat M1,M2,M3;
597     IS  is_aux;
598     /* see if we can save some allocations */
599     if (pcbddc->local_auxmat2) {
600       PetscInt on_R,on_constraints;
601       ierr = MatGetSize(pcbddc->local_auxmat2,&on_R,&on_constraints);CHKERRQ(ierr);
602       if (on_R != n_R || on_constraints != n_constraints) {
603         PetscScalar *marray;
604 
605         ierr = MatDenseGetArray(pcbddc->local_auxmat2,&marray);CHKERRQ(ierr);
606         ierr = PetscFree(marray);CHKERRQ(ierr);
607         ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
608         ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
609       }
610     }
611     /* auxiliary matrices */
612     if (!pcbddc->local_auxmat2) {
613       PetscScalar *marray;
614 
615       ierr = PetscMalloc1(2*n_R*n_constraints,&marray);CHKERRQ(ierr);
616       ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,marray,&pcbddc->local_auxmat2);CHKERRQ(ierr);
617       marray += n_R*n_constraints;
618       ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_R,marray,&pcbddc->local_auxmat1);CHKERRQ(ierr);
619     }
620 
621     /* Extract constraints on R nodes: C_{CR}  */
622     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);CHKERRQ(ierr);
623     ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
624     ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
625 
626     /* Assemble local_auxmat2 = - A_{RR}^{-1} C^T_{CR} needed by BDDC application */
627     ierr = PetscMemzero(work,n_R*n_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
628     for (i=0;i<n_constraints;i++) {
629       const PetscScalar *row_cmat_values;
630       const PetscInt    *row_cmat_indices;
631       PetscInt          size_of_constraint,j;
632 
633       ierr = MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
634       for (j=0;j<size_of_constraint;j++) {
635         work[row_cmat_indices[j]+i*n_R] = -row_cmat_values[j];
636       }
637       ierr = MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
638     }
639     if (F) {
640       Mat B;
641 
642       ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work,&B);CHKERRQ(ierr);
643       ierr = MatMatSolve(F,B,pcbddc->local_auxmat2);CHKERRQ(ierr);
644       ierr = MatDestroy(&B);CHKERRQ(ierr);
645     } else {
646       PetscScalar *xarray;
647       ierr = MatDenseGetArray(pcbddc->local_auxmat2,&xarray);CHKERRQ(ierr);
648       for (i=0;i<n_constraints;i++) {
649         ierr = VecPlaceArray(pcbddc->vec1_R,work+i*n_R);CHKERRQ(ierr);
650         ierr = VecPlaceArray(pcbddc->vec2_R,xarray+i*n_R);CHKERRQ(ierr);
651         ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
652         ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
653         ierr = VecResetArray(pcbddc->vec2_R);CHKERRQ(ierr);
654       }
655       ierr = MatDenseRestoreArray(pcbddc->local_auxmat2,&xarray);CHKERRQ(ierr);
656     }
657 
658     /* Assemble explicitly S_CC = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1}  */
659     ierr = MatConvert(C_CR,impMatType,MAT_REUSE_MATRIX,&C_CR);CHKERRQ(ierr);
660     ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);CHKERRQ(ierr);
661     ierr = MatDuplicate(M3,MAT_DO_NOT_COPY_VALUES,&M1);CHKERRQ(ierr);
662     ierr = MatDuplicate(M3,MAT_DO_NOT_COPY_VALUES,&M2);CHKERRQ(ierr);
663     ierr = MatLUFactor(M3,NULL,NULL,NULL);CHKERRQ(ierr);
664     ierr = VecSet(pcbddc->vec1_C,m_one);CHKERRQ(ierr);
665     ierr = MatDiagonalSet(M2,pcbddc->vec1_C,INSERT_VALUES);CHKERRQ(ierr);
666     ierr = MatMatSolve(M3,M2,M1);CHKERRQ(ierr);
667     ierr = MatDestroy(&M2);CHKERRQ(ierr);
668     ierr = MatDestroy(&M3);CHKERRQ(ierr);
669     /* Assemble local_auxmat1 = S_CC*C_{CR} needed by BDDC application in KSP and in preproc */
670     ierr = MatMatMult(M1,C_CR,MAT_REUSE_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
671     ierr = MatCopy(M1,S_CC,SAME_NONZERO_PATTERN);CHKERRQ(ierr); /* S_CC can have a different LDA, MatMatSolve doesn't support it */
672     ierr = MatDestroy(&M1);CHKERRQ(ierr);
673   }
674   /* Get submatrices from subdomain matrix */
675   if (n_vertices) {
676     Mat       newmat;
677     IS        is_aux;
678     PetscInt  ibs,mbs;
679     PetscBool issbaij;
680 
681     ierr = ISComplement(pcbddc->is_R_local,0,pcis->n,&is_aux);CHKERRQ(ierr);
682     ierr = MatGetBlockSize(pcbddc->local_mat,&mbs);CHKERRQ(ierr);
683     ierr = ISGetBlockSize(pcbddc->is_R_local,&ibs);CHKERRQ(ierr);
684     if (ibs != mbs) { /* need to convert to SEQAIJ */
685       ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
686       ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
687       ierr = MatGetSubMatrix(newmat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
688       ierr = MatGetSubMatrix(newmat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
689       ierr = MatDestroy(&newmat);CHKERRQ(ierr);
690     } else {
691       /* this is safe */
692       ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
693       ierr = PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
694       if (issbaij) { /* need to convert to BAIJ to get offdiagonal blocks */
695         ierr = MatConvert(pcbddc->local_mat,MATSEQBAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
696         ierr = MatGetSubMatrix(newmat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
697         ierr = MatTranspose(A_VR,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
698         ierr = MatDestroy(&newmat);CHKERRQ(ierr);
699         ierr = MatConvert(A_VV,MATSEQBAIJ,MAT_REUSE_MATRIX,&A_VV);CHKERRQ(ierr);
700       } else {
701         ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
702         ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
703       }
704     }
705     ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
706   }
707 
708   /* Matrix of coarse basis functions (local) */
709   if (pcbddc->coarse_phi_B) {
710     PetscInt on_B,on_primal,on_D=n_D;
711     if (pcbddc->coarse_phi_D) {
712       ierr = MatGetSize(pcbddc->coarse_phi_D,&on_D,NULL);CHKERRQ(ierr);
713     }
714     ierr = MatGetSize(pcbddc->coarse_phi_B,&on_B,&on_primal);CHKERRQ(ierr);
715     if (on_B != n_B || on_primal != pcbddc->local_primal_size || on_D != n_D) {
716       PetscScalar *marray;
717 
718       ierr = MatDenseGetArray(pcbddc->coarse_phi_B,&marray);CHKERRQ(ierr);
719       ierr = PetscFree(marray);CHKERRQ(ierr);
720       ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
721       ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
722       ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
723       ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
724     }
725   }
726 
727   if (!pcbddc->coarse_phi_B) {
728     PetscScalar *marray;
729 
730     n = n_B*pcbddc->local_primal_size;
731     if (pcbddc->switch_static || pcbddc->dbg_flag) {
732       n += n_D*pcbddc->local_primal_size;
733     }
734     if (!pcbddc->issym) {
735       n *= 2;
736     }
737     ierr = PetscCalloc1(n,&marray);CHKERRQ(ierr);
738     ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marray,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
739     n = n_B*pcbddc->local_primal_size;
740     if (pcbddc->switch_static || pcbddc->dbg_flag) {
741       ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
742       n += n_D*pcbddc->local_primal_size;
743     }
744     if (!pcbddc->issym) {
745       ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_psi_B);CHKERRQ(ierr);
746       if (pcbddc->switch_static || pcbddc->dbg_flag) {
747         n = n_B*pcbddc->local_primal_size;
748         ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_psi_D);CHKERRQ(ierr);
749       }
750     } else {
751       ierr = PetscObjectReference((PetscObject)pcbddc->coarse_phi_B);CHKERRQ(ierr);
752       pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
753       if (pcbddc->switch_static || pcbddc->dbg_flag) {
754         ierr = PetscObjectReference((PetscObject)pcbddc->coarse_phi_D);CHKERRQ(ierr);
755         pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
756       }
757     }
758   }
759   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
760   /* vertices */
761   if (n_vertices) {
762 
763     if (n_R) {
764       Mat          A_RRmA_RV,S_VVt; /* S_VVt with LDA=N */
765       PetscBLASInt B_N,B_one = 1;
766       PetscScalar  *x,*y;
767 
768       ierr = PetscMemzero(work,2*n_R*n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
769       ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&A_RRmA_RV);CHKERRQ(ierr);
770       ierr = MatConvert(A_RV,impMatType,MAT_REUSE_MATRIX,&A_RV);CHKERRQ(ierr);
771       if (F) {
772         ierr = MatMatSolve(F,A_RV,A_RRmA_RV);CHKERRQ(ierr);
773       } else {
774         ierr = MatDenseGetArray(A_RV,&y);CHKERRQ(ierr);
775         for (i=0;i<n_vertices;i++) {
776           ierr = VecPlaceArray(pcbddc->vec1_R,y+i*n_R);CHKERRQ(ierr);
777           ierr = VecPlaceArray(pcbddc->vec2_R,work+i*n_R);CHKERRQ(ierr);
778           ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
779           ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
780           ierr = VecResetArray(pcbddc->vec2_R);CHKERRQ(ierr);
781         }
782         ierr = MatDenseRestoreArray(A_RV,&y);CHKERRQ(ierr);
783       }
784       ierr = MatScale(A_RRmA_RV,m_one);CHKERRQ(ierr);
785       /* S_VV and S_CV are the subdomain contribution to coarse matrix. WARNING -> column major ordering */
786       if (n_constraints) {
787         Mat B;
788         ierr = MatMatMult(pcbddc->local_auxmat1,A_RRmA_RV,MAT_REUSE_MATRIX,PETSC_DEFAULT,&S_CV);CHKERRQ(ierr);
789         ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work+n_R*n_vertices,&B);CHKERRQ(ierr);
790         ierr = MatMatMult(pcbddc->local_auxmat2,S_CV,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B);CHKERRQ(ierr);
791         ierr = MatScale(S_CV,m_one);CHKERRQ(ierr);
792         ierr = PetscBLASIntCast(n_R*n_vertices,&B_N);CHKERRQ(ierr);
793         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,work+n_R*n_vertices,&B_one,work,&B_one));
794         ierr = MatDestroy(&B);CHKERRQ(ierr);
795       }
796       ierr = MatConvert(A_VR,impMatType,MAT_REUSE_MATRIX,&A_VR);CHKERRQ(ierr);
797       ierr = MatMatMult(A_VR,A_RRmA_RV,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VVt);CHKERRQ(ierr);
798       ierr = MatConvert(A_VV,impMatType,MAT_REUSE_MATRIX,&A_VV);CHKERRQ(ierr);
799       ierr = PetscBLASIntCast(n_vertices*n_vertices,&B_N);CHKERRQ(ierr);
800       ierr = MatDenseGetArray(A_VV,&x);CHKERRQ(ierr);
801       ierr = MatDenseGetArray(S_VVt,&y);CHKERRQ(ierr);
802       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,x,&B_one,y,&B_one));
803       ierr = MatDenseRestoreArray(A_VV,&x);CHKERRQ(ierr);
804       ierr = MatDenseRestoreArray(S_VVt,&y);CHKERRQ(ierr);
805       ierr = MatCopy(S_VVt,S_VV,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
806       ierr = MatDestroy(&S_VVt);CHKERRQ(ierr);
807       ierr = MatDestroy(&A_RRmA_RV);CHKERRQ(ierr);
808     } else {
809       ierr = MatConvert(A_VV,impMatType,MAT_REUSE_MATRIX,&A_VV);CHKERRQ(ierr);
810       ierr = MatCopy(A_VV,S_VV,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
811     }
812     /* coarse basis functions */
813     for (i=0;i<n_vertices;i++) {
814       PetscScalar *y;
815 
816       ierr = VecPlaceArray(pcbddc->vec1_R,work+n_R*i);CHKERRQ(ierr);
817       ierr = MatDenseGetArray(pcbddc->coarse_phi_B,&y);CHKERRQ(ierr);
818       ierr = VecPlaceArray(pcis->vec1_B,y+n_B*i);CHKERRQ(ierr);
819       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
820       ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
821       y[n_B*i+idx_V_B[i]] = 1.0;
822       ierr = MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);CHKERRQ(ierr);
823       ierr = VecResetArray(pcis->vec1_B);CHKERRQ(ierr);
824 
825       if (pcbddc->switch_static || pcbddc->dbg_flag) {
826         ierr = MatDenseGetArray(pcbddc->coarse_phi_D,&y);CHKERRQ(ierr);
827         ierr = VecPlaceArray(pcis->vec1_D,y+n_D*i);CHKERRQ(ierr);
828         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
829         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
830         ierr = VecResetArray(pcis->vec1_D);CHKERRQ(ierr);
831         ierr = MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);CHKERRQ(ierr);
832       }
833       ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
834     }
835     ierr = MatDestroy(&A_VV);CHKERRQ(ierr);
836     ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
837   }
838 
839   if (n_constraints) {
840     Mat B;
841 
842     ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work,&B);CHKERRQ(ierr);
843     ierr = MatScale(S_CC,m_one);CHKERRQ(ierr);
844     ierr = MatMatMult(pcbddc->local_auxmat2,S_CC,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B);CHKERRQ(ierr);
845     ierr = MatScale(S_CC,m_one);CHKERRQ(ierr);
846     if (n_vertices) {
847       ierr = MatMatMult(A_VR,B,MAT_REUSE_MATRIX,PETSC_DEFAULT,&S_VC);CHKERRQ(ierr);
848     }
849     ierr = MatDestroy(&B);CHKERRQ(ierr);
850     /* coarse basis functions */
851     for (i=0;i<n_constraints;i++) {
852       PetscScalar *y;
853 
854       ierr = VecPlaceArray(pcbddc->vec1_R,work+n_R*i);CHKERRQ(ierr);
855       ierr = MatDenseGetArray(pcbddc->coarse_phi_B,&y);CHKERRQ(ierr);
856       ierr = VecPlaceArray(pcis->vec1_B,y+n_B*(i+n_vertices));CHKERRQ(ierr);
857       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
858       ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
859       ierr = MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);CHKERRQ(ierr);
860       ierr = VecResetArray(pcis->vec1_B);CHKERRQ(ierr);
861 
862       if (pcbddc->switch_static || pcbddc->dbg_flag) {
863         ierr = MatDenseGetArray(pcbddc->coarse_phi_D,&y);CHKERRQ(ierr);
864         ierr = VecPlaceArray(pcis->vec1_D,y+n_D*(i+n_vertices));CHKERRQ(ierr);
865         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
866         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
867         ierr = VecResetArray(pcis->vec1_D);CHKERRQ(ierr);
868         ierr = MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);CHKERRQ(ierr);
869       }
870       ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
871     }
872   }
873 
874   /* compute other basis functions for non-symmetric problems */
875   if (!pcbddc->issym) {
876     Mat B,X;
877 
878     ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,pcbddc->local_primal_size,work,&B);CHKERRQ(ierr);
879 
880     if (n_constraints) {
881       Mat S_CCT,B_C;
882 
883       ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work+n_vertices*n_R,&B_C);CHKERRQ(ierr);
884       ierr = MatTranspose(S_CC,MAT_INITIAL_MATRIX,&S_CCT);CHKERRQ(ierr);
885       ierr = MatTransposeMatMult(C_CR,S_CCT,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B_C);CHKERRQ(ierr);
886       ierr = MatDestroy(&S_CCT);CHKERRQ(ierr);
887       if (n_vertices) {
888         Mat B_V,S_VCT;
889 
890         ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&B_V);CHKERRQ(ierr);
891         ierr = MatTranspose(S_VC,MAT_INITIAL_MATRIX,&S_VCT);CHKERRQ(ierr);
892         ierr = MatTransposeMatMult(C_CR,S_VCT,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B_V);CHKERRQ(ierr);
893         ierr = MatDestroy(&B_V);CHKERRQ(ierr);
894         ierr = MatDestroy(&S_VCT);CHKERRQ(ierr);
895       }
896       ierr = MatDestroy(&B_C);CHKERRQ(ierr);
897     }
898     if (n_vertices && n_R) {
899       Mat          A_VRT;
900       PetscBLASInt B_N,B_one = 1;
901 
902       if (!n_constraints) { /* if there are no constraints, reset work */
903         ierr = PetscMemzero(work,n_R*pcbddc->local_primal_size*sizeof(PetscScalar));CHKERRQ(ierr);
904       }
905       ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work+pcbddc->local_primal_size*n_R,&A_VRT);CHKERRQ(ierr);
906       ierr = MatTranspose(A_VR,MAT_REUSE_MATRIX,&A_VRT);CHKERRQ(ierr);
907       ierr = PetscBLASIntCast(n_vertices*n_R,&B_N);CHKERRQ(ierr);
908       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&m_one,work+pcbddc->local_primal_size*n_R,&B_one,work,&B_one));
909       ierr = MatDestroy(&A_VRT);CHKERRQ(ierr);
910     }
911 
912     ierr = MatCreateSeqDense(PETSC_COMM_SELF,n_R,pcbddc->local_primal_size,work+pcbddc->local_primal_size*n_R,&X);CHKERRQ(ierr);
913     if (F) { /* currently there's no support for MatTransposeMatSolve(F,B,X) */
914       for (i=0;i<pcbddc->local_primal_size;i++) {
915         ierr = VecPlaceArray(pcbddc->vec1_R,work+i*n_R);CHKERRQ(ierr);
916         ierr = VecPlaceArray(pcbddc->vec2_R,work+(i+pcbddc->local_primal_size)*n_R);CHKERRQ(ierr);
917         ierr = MatSolveTranspose(F,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
918         ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
919         ierr = VecResetArray(pcbddc->vec2_R);CHKERRQ(ierr);
920       }
921     } else {
922       for (i=0;i<pcbddc->local_primal_size;i++) {
923         ierr = VecPlaceArray(pcbddc->vec1_R,work+i*n_R);CHKERRQ(ierr);
924         ierr = VecPlaceArray(pcbddc->vec2_R,work+(i+pcbddc->local_primal_size)*n_R);CHKERRQ(ierr);
925         ierr = KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
926         ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
927         ierr = VecResetArray(pcbddc->vec2_R);CHKERRQ(ierr);
928       }
929     }
930     ierr = MatDestroy(&B);CHKERRQ(ierr);
931     /* coarse basis functions */
932     for (i=0;i<pcbddc->local_primal_size;i++) {
933       PetscScalar *y;
934 
935       ierr = VecPlaceArray(pcbddc->vec1_R,work+n_R*(i+pcbddc->local_primal_size));CHKERRQ(ierr);
936       ierr = MatDenseGetArray(pcbddc->coarse_psi_B,&y);CHKERRQ(ierr);
937       ierr = VecPlaceArray(pcis->vec1_B,y+n_B*i);CHKERRQ(ierr);
938       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
939       ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
940       if (i<n_vertices) {
941         y[n_B*i+idx_V_B[i]] = 1.0;
942       }
943       ierr = MatDenseRestoreArray(pcbddc->coarse_psi_B,&y);CHKERRQ(ierr);
944       ierr = VecResetArray(pcis->vec1_B);CHKERRQ(ierr);
945 
946       if (pcbddc->switch_static || pcbddc->dbg_flag) {
947         ierr = MatDenseGetArray(pcbddc->coarse_psi_D,&y);CHKERRQ(ierr);
948         ierr = VecPlaceArray(pcis->vec1_D,y+n_D*i);CHKERRQ(ierr);
949         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
950         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
951         ierr = VecResetArray(pcis->vec1_D);CHKERRQ(ierr);
952         ierr = MatDenseRestoreArray(pcbddc->coarse_psi_D,&y);CHKERRQ(ierr);
953       }
954       ierr = VecResetArray(pcbddc->vec1_R);CHKERRQ(ierr);
955     }
956     ierr = MatDestroy(&X);CHKERRQ(ierr);
957   }
958 
959   ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
960   ierr = MatDestroy(&S_VV);CHKERRQ(ierr);
961   ierr = MatDestroy(&S_CV);CHKERRQ(ierr);
962   ierr = MatDestroy(&S_VC);CHKERRQ(ierr);
963   ierr = MatDestroy(&S_CC);CHKERRQ(ierr);
964   /* Checking coarse_sub_mat and coarse basis functios */
965   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
966   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
967   if (pcbddc->dbg_flag) {
968     Mat         coarse_sub_mat;
969     Mat         AUXMAT,TM1,TM2,TM3,TM4;
970     Mat         coarse_phi_D,coarse_phi_B;
971     Mat         coarse_psi_D,coarse_psi_B;
972     Mat         A_II,A_BB,A_IB,A_BI;
973     Mat         C_B,CPHI;
974     IS          is_dummy;
975     Vec         mones;
976     MatType     checkmattype=MATSEQAIJ;
977     PetscReal   real_value;
978 
979     ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
980     ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
981     ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
982     ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
983     ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
984     ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
985     if (unsymmetric_check) {
986       ierr = MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);CHKERRQ(ierr);
987       ierr = MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);CHKERRQ(ierr);
988     }
989     ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);
990 
991     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
992     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat computation\n");CHKERRQ(ierr);
993     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
994     if (unsymmetric_check) {
995       ierr = MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
996       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
997       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
998       ierr = MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
999       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
1000       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
1001       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
1002       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
1003       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
1004       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
1005       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
1006       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
1007     } else {
1008       ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
1009       ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
1010       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
1011       ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
1012       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
1013       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
1014       ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
1015       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
1016     }
1017     ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
1018     ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
1019     ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
1020     ierr = MatConvert(TM1,MATSEQDENSE,MAT_REUSE_MATRIX,&TM1);CHKERRQ(ierr);
1021     ierr = MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
1022     ierr = MatNorm(TM1,NORM_FROBENIUS,&real_value);CHKERRQ(ierr);
1023     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1024     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d      matrix error % 1.14e\n",PetscGlobalRank,real_value);CHKERRQ(ierr);
1025 
1026     /* check constraints */
1027     ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size,0,1,&is_dummy);CHKERRQ(ierr);
1028     ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);
1029     ierr = MatMatMult(C_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&CPHI);CHKERRQ(ierr);
1030     ierr = MatCreateVecs(CPHI,&mones,NULL);CHKERRQ(ierr);
1031     ierr = VecSet(mones,-1.0);CHKERRQ(ierr);
1032     ierr = MatDiagonalSet(CPHI,mones,ADD_VALUES);CHKERRQ(ierr);
1033     ierr = MatNorm(CPHI,NORM_FROBENIUS,&real_value);CHKERRQ(ierr);
1034     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d constraints error % 1.14e\n",PetscGlobalRank,real_value);CHKERRQ(ierr);
1035     ierr = MatDestroy(&C_B);CHKERRQ(ierr);
1036     ierr = MatDestroy(&CPHI);CHKERRQ(ierr);
1037     ierr = ISDestroy(&is_dummy);CHKERRQ(ierr);
1038     ierr = VecDestroy(&mones);CHKERRQ(ierr);
1039 
1040     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1041     ierr = MatDestroy(&A_II);CHKERRQ(ierr);
1042     ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1043     ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1044     ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1045     ierr = MatDestroy(&TM1);CHKERRQ(ierr);
1046     ierr = MatDestroy(&TM2);CHKERRQ(ierr);
1047     ierr = MatDestroy(&TM3);CHKERRQ(ierr);
1048     ierr = MatDestroy(&TM4);CHKERRQ(ierr);
1049     ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
1050     ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
1051     if (unsymmetric_check) {
1052       ierr = MatDestroy(&coarse_psi_D);CHKERRQ(ierr);
1053       ierr = MatDestroy(&coarse_psi_B);CHKERRQ(ierr);
1054     }
1055     ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
1056   }
1057 
1058   /* free memory */
1059   ierr = PetscFree(work);CHKERRQ(ierr);
1060   if (n_vertices) {
1061     ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
1062   }
1063   if (n_constraints) {
1064     ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
1065   }
1066   /* get back data */
1067   *coarse_submat_vals_n = coarse_submat_vals;
1068   PetscFunctionReturn(0);
1069 }
1070 
1071 #undef __FUNCT__
1072 #define __FUNCT__ "MatGetSubMatrixUnsorted"
1073 PetscErrorCode MatGetSubMatrixUnsorted(Mat A, IS isrow, IS iscol, Mat* B)
1074 {
1075   Mat            *work_mat;
1076   IS             isrow_s,iscol_s;
1077   PetscBool      rsorted,csorted;
1078   PetscInt       rsize,*idxs_perm_r,csize,*idxs_perm_c;
1079   PetscErrorCode ierr;
1080 
1081   PetscFunctionBegin;
1082   ierr = ISSorted(isrow,&rsorted);CHKERRQ(ierr);
1083   ierr = ISSorted(iscol,&csorted);CHKERRQ(ierr);
1084   ierr = ISGetLocalSize(isrow,&rsize);CHKERRQ(ierr);
1085   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
1086 
1087   if (!rsorted) {
1088     const PetscInt *idxs;
1089     PetscInt *idxs_sorted,i;
1090 
1091     ierr = PetscMalloc1(rsize,&idxs_perm_r);CHKERRQ(ierr);
1092     ierr = PetscMalloc1(rsize,&idxs_sorted);CHKERRQ(ierr);
1093     for (i=0;i<rsize;i++) {
1094       idxs_perm_r[i] = i;
1095     }
1096     ierr = ISGetIndices(isrow,&idxs);CHKERRQ(ierr);
1097     ierr = PetscSortIntWithPermutation(rsize,idxs,idxs_perm_r);CHKERRQ(ierr);
1098     for (i=0;i<rsize;i++) {
1099       idxs_sorted[i] = idxs[idxs_perm_r[i]];
1100     }
1101     ierr = ISRestoreIndices(isrow,&idxs);CHKERRQ(ierr);
1102     ierr = ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_sorted,PETSC_OWN_POINTER,&isrow_s);CHKERRQ(ierr);
1103   } else {
1104     ierr = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1105     isrow_s = isrow;
1106   }
1107 
1108   if (!csorted) {
1109     if (isrow == iscol) {
1110       ierr = PetscObjectReference((PetscObject)isrow_s);CHKERRQ(ierr);
1111       iscol_s = isrow_s;
1112     } else {
1113       const PetscInt *idxs;
1114       PetscInt *idxs_sorted,i;
1115 
1116       ierr = PetscMalloc1(csize,&idxs_perm_c);CHKERRQ(ierr);
1117       ierr = PetscMalloc1(csize,&idxs_sorted);CHKERRQ(ierr);
1118       for (i=0;i<csize;i++) {
1119         idxs_perm_c[i] = i;
1120       }
1121       ierr = ISGetIndices(iscol,&idxs);CHKERRQ(ierr);
1122       ierr = PetscSortIntWithPermutation(csize,idxs,idxs_perm_c);CHKERRQ(ierr);
1123       for (i=0;i<csize;i++) {
1124         idxs_sorted[i] = idxs[idxs_perm_c[i]];
1125       }
1126       ierr = ISRestoreIndices(iscol,&idxs);CHKERRQ(ierr);
1127       ierr = ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_sorted,PETSC_OWN_POINTER,&iscol_s);CHKERRQ(ierr);
1128     }
1129   } else {
1130     ierr = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1131     iscol_s = iscol;
1132   }
1133 
1134   ierr = MatGetSubMatrices(A,1,&isrow_s,&iscol_s,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
1135 
1136   if (!rsorted || !csorted) {
1137     Mat      new_mat;
1138     IS       is_perm_r,is_perm_c;
1139 
1140     if (!rsorted) {
1141       PetscInt *idxs_r,i;
1142       ierr = PetscMalloc1(rsize,&idxs_r);CHKERRQ(ierr);
1143       for (i=0;i<rsize;i++) {
1144         idxs_r[idxs_perm_r[i]] = i;
1145       }
1146       ierr = PetscFree(idxs_perm_r);CHKERRQ(ierr);
1147       ierr = ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_r,PETSC_OWN_POINTER,&is_perm_r);CHKERRQ(ierr);
1148     } else {
1149       ierr = ISCreateStride(PETSC_COMM_SELF,rsize,0,1,&is_perm_r);CHKERRQ(ierr);
1150     }
1151     ierr = ISSetPermutation(is_perm_r);CHKERRQ(ierr);
1152 
1153     if (!csorted) {
1154       if (isrow_s == iscol_s) {
1155         ierr = PetscObjectReference((PetscObject)is_perm_r);CHKERRQ(ierr);
1156         is_perm_c = is_perm_r;
1157       } else {
1158         PetscInt *idxs_c,i;
1159         ierr = PetscMalloc1(csize,&idxs_c);CHKERRQ(ierr);
1160         for (i=0;i<csize;i++) {
1161           idxs_c[idxs_perm_c[i]] = i;
1162         }
1163         ierr = PetscFree(idxs_perm_c);CHKERRQ(ierr);
1164         ierr = ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_c,PETSC_OWN_POINTER,&is_perm_c);CHKERRQ(ierr);
1165       }
1166     } else {
1167       ierr = ISCreateStride(PETSC_COMM_SELF,csize,0,1,&is_perm_c);CHKERRQ(ierr);
1168     }
1169     ierr = ISSetPermutation(is_perm_c);CHKERRQ(ierr);
1170 
1171     ierr = MatPermute(work_mat[0],is_perm_r,is_perm_c,&new_mat);CHKERRQ(ierr);
1172     ierr = MatDestroy(&work_mat[0]);CHKERRQ(ierr);
1173     work_mat[0] = new_mat;
1174     ierr = ISDestroy(&is_perm_r);CHKERRQ(ierr);
1175     ierr = ISDestroy(&is_perm_c);CHKERRQ(ierr);
1176   }
1177 
1178   ierr = PetscObjectReference((PetscObject)work_mat[0]);CHKERRQ(ierr);
1179   *B = work_mat[0];
1180   ierr = MatDestroyMatrices(1,&work_mat);CHKERRQ(ierr);
1181   ierr = ISDestroy(&isrow_s);CHKERRQ(ierr);
1182   ierr = ISDestroy(&iscol_s);CHKERRQ(ierr);
1183   PetscFunctionReturn(0);
1184 }
1185 
1186 #undef __FUNCT__
1187 #define __FUNCT__ "PCBDDCComputeLocalMatrix"
1188 PetscErrorCode PCBDDCComputeLocalMatrix(PC pc, Mat ChangeOfBasisMatrix)
1189 {
1190   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
1191   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
1192   Mat            new_mat;
1193   IS             is_local,is_global;
1194   PetscInt       local_size;
1195   PetscBool      isseqaij;
1196   PetscErrorCode ierr;
1197 
1198   PetscFunctionBegin;
1199   ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
1200   ierr = MatGetSize(matis->A,&local_size,NULL);CHKERRQ(ierr);
1201   ierr = ISCreateStride(PetscObjectComm((PetscObject)matis->A),local_size,0,1,&is_local);CHKERRQ(ierr);
1202   ierr = ISLocalToGlobalMappingApplyIS(matis->mapping,is_local,&is_global);CHKERRQ(ierr);
1203   ierr = ISDestroy(&is_local);CHKERRQ(ierr);
1204   ierr = MatGetSubMatrixUnsorted(ChangeOfBasisMatrix,is_global,is_global,&new_mat);CHKERRQ(ierr);
1205   ierr = ISDestroy(&is_global);CHKERRQ(ierr);
1206 
1207   /* check */
1208   if (pcbddc->dbg_flag) {
1209     Vec       x,x_change;
1210     PetscReal error;
1211 
1212     ierr = MatCreateVecs(ChangeOfBasisMatrix,&x,&x_change);CHKERRQ(ierr);
1213     ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
1214     ierr = MatMult(ChangeOfBasisMatrix,x,x_change);CHKERRQ(ierr);
1215     ierr = VecScatterBegin(matis->ctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1216     ierr = VecScatterEnd(matis->ctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1217     ierr = MatMult(new_mat,matis->x,matis->y);CHKERRQ(ierr);
1218     ierr = VecScatterBegin(matis->ctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1219     ierr = VecScatterEnd(matis->ctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1220     ierr = VecAXPY(x,-1.0,x_change);CHKERRQ(ierr);
1221     ierr = VecNorm(x,NORM_INFINITY,&error);CHKERRQ(ierr);
1222     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1223     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change on N: %1.6e\n",error);CHKERRQ(ierr);
1224     ierr = VecDestroy(&x);CHKERRQ(ierr);
1225     ierr = VecDestroy(&x_change);CHKERRQ(ierr);
1226   }
1227 
1228   /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
1229   ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
1230   if (isseqaij) {
1231     ierr = MatPtAP(matis->A,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
1232   } else {
1233     Mat work_mat;
1234     ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
1235     ierr = MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
1236     ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
1237   }
1238   ierr = MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,pcbddc->issym);CHKERRQ(ierr);
1239 #if !defined(PETSC_USE_COMPLEX)
1240   ierr = MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,pcbddc->issym);CHKERRQ(ierr);
1241 #endif
1242   /*
1243   ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
1244   ierr = MatView(new_mat,(PetscViewer)0);CHKERRQ(ierr);
1245   */
1246   ierr = MatDestroy(&new_mat);CHKERRQ(ierr);
1247   PetscFunctionReturn(0);
1248 }
1249 
1250 #undef __FUNCT__
1251 #define __FUNCT__ "PCBDDCSetUpLocalScatters"
1252 PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
1253 {
1254   PC_IS*         pcis = (PC_IS*)(pc->data);
1255   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
1256   IS             is_aux1,is_aux2;
1257   PetscInt       *aux_array1,*aux_array2,*is_indices,*idx_R_local;
1258   PetscInt       n_vertices,i,j,n_R,n_D,n_B;
1259   PetscInt       vbs,bs;
1260   PetscBT        bitmask;
1261   PetscErrorCode ierr;
1262 
1263   PetscFunctionBegin;
1264   /*
1265     No need to setup local scatters if
1266       - primal space is unchanged
1267         AND
1268       - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
1269         AND
1270       - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
1271   */
1272   if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) {
1273     PetscFunctionReturn(0);
1274   }
1275   /* destroy old objects */
1276   ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
1277   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
1278   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
1279   /* Set Non-overlapping dimensions */
1280   n_B = pcis->n_B; n_D = pcis->n - n_B;
1281   n_vertices = pcbddc->n_actual_vertices;
1282   /* create auxiliary bitmask */
1283   ierr = PetscBTCreate(pcis->n,&bitmask);CHKERRQ(ierr);
1284   for (i=0;i<n_vertices;i++) {
1285     ierr = PetscBTSet(bitmask,pcbddc->primal_indices_local_idxs[i]);CHKERRQ(ierr);
1286   }
1287 
1288   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
1289   ierr = PetscMalloc1(pcis->n-n_vertices,&idx_R_local);CHKERRQ(ierr);
1290   for (i=0, n_R=0; i<pcis->n; i++) {
1291     if (!PetscBTLookup(bitmask,i)) {
1292       idx_R_local[n_R] = i;
1293       n_R++;
1294     }
1295   }
1296 
1297   /* Block code */
1298   vbs = 1;
1299   ierr = MatGetBlockSize(pcbddc->local_mat,&bs);CHKERRQ(ierr);
1300   if (bs>1 && !(n_vertices%bs)) {
1301     PetscBool is_blocked = PETSC_TRUE;
1302     PetscInt  *vary;
1303     /* Verify if the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
1304     ierr = PetscMalloc1(pcis->n/bs,&vary);CHKERRQ(ierr);
1305     ierr = PetscMemzero(vary,pcis->n/bs*sizeof(PetscInt));CHKERRQ(ierr);
1306     for (i=0; i<n_vertices; i++) vary[pcbddc->primal_indices_local_idxs[i]/bs]++;
1307     for (i=0; i<n_vertices/bs; i++) {
1308       if (vary[i]!=0 && vary[i]!=bs) {
1309         is_blocked = PETSC_FALSE;
1310         break;
1311       }
1312     }
1313     if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
1314       vbs = bs;
1315       for (i=0;i<n_R/vbs;i++) {
1316         idx_R_local[i] = idx_R_local[vbs*i]/vbs;
1317       }
1318     }
1319     ierr = PetscFree(vary);CHKERRQ(ierr);
1320   }
1321   ierr = ISCreateBlock(PETSC_COMM_SELF,vbs,n_R/vbs,idx_R_local,PETSC_COPY_VALUES,&pcbddc->is_R_local);CHKERRQ(ierr);
1322   ierr = PetscFree(idx_R_local);CHKERRQ(ierr);
1323 
1324   /* print some info if requested */
1325   if (pcbddc->dbg_flag) {
1326     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
1327     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1328     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1329     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
1330     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
1331     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"r_size = %d, v_size = %d, constraints = %d, local_primal_size = %d\n",n_R,n_vertices,pcbddc->local_primal_size-n_vertices,pcbddc->local_primal_size);CHKERRQ(ierr);
1332     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
1333     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1334   }
1335 
1336   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
1337   ierr = ISGetIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
1338   ierr = PetscMalloc1(pcis->n_B-n_vertices,&aux_array1);CHKERRQ(ierr);
1339   ierr = PetscMalloc1(pcis->n_B-n_vertices,&aux_array2);CHKERRQ(ierr);
1340   ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1341   for (i=0; i<n_D; i++) {
1342     ierr = PetscBTSet(bitmask,is_indices[i]);CHKERRQ(ierr);
1343   }
1344   ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1345   for (i=0, j=0; i<n_R; i++) {
1346     if (!PetscBTLookup(bitmask,idx_R_local[i])) {
1347       aux_array1[j++] = i;
1348     }
1349   }
1350   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
1351   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1352   for (i=0, j=0; i<n_B; i++) {
1353     if (!PetscBTLookup(bitmask,is_indices[i])) {
1354       aux_array2[j++] = i;
1355     }
1356   }
1357   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1358   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);CHKERRQ(ierr);
1359   ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
1360   ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
1361   ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
1362 
1363   if (pcbddc->switch_static || pcbddc->dbg_flag) {
1364     ierr = PetscMalloc1(n_D,&aux_array1);CHKERRQ(ierr);
1365     for (i=0, j=0; i<n_R; i++) {
1366       if (PetscBTLookup(bitmask,idx_R_local[i])) {
1367         aux_array1[j++] = i;
1368       }
1369     }
1370     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
1371     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
1372     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
1373   }
1374   ierr = PetscBTDestroy(&bitmask);CHKERRQ(ierr);
1375   ierr = ISRestoreIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
1376   PetscFunctionReturn(0);
1377 }
1378 
1379 
1380 #undef __FUNCT__
1381 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
1382 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, PetscBool dirichlet, PetscBool neumann)
1383 {
1384   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1385   PC_IS          *pcis = (PC_IS*)pc->data;
1386   PC             pc_temp;
1387   Mat            A_RR;
1388   MatReuse       reuse;
1389   PetscScalar    m_one = -1.0;
1390   PetscReal      value;
1391   PetscInt       n_D,n_R,ibs,mbs;
1392   PetscBool      use_exact,use_exact_reduced,issbaij;
1393   PetscErrorCode ierr;
1394   /* prefixes stuff */
1395   char           dir_prefix[256],neu_prefix[256],str_level[16];
1396   size_t         len;
1397 
1398   PetscFunctionBegin;
1399 
1400   /* compute prefixes */
1401   ierr = PetscStrcpy(dir_prefix,"");CHKERRQ(ierr);
1402   ierr = PetscStrcpy(neu_prefix,"");CHKERRQ(ierr);
1403   if (!pcbddc->current_level) {
1404     ierr = PetscStrcpy(dir_prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
1405     ierr = PetscStrcpy(neu_prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
1406     ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
1407     ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
1408   } else {
1409     ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
1410     sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
1411     ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
1412     len -= 15; /* remove "pc_bddc_coarse_" */
1413     if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
1414     if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
1415     ierr = PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
1416     ierr = PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
1417     ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
1418     ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
1419     ierr = PetscStrcat(dir_prefix,str_level);CHKERRQ(ierr);
1420     ierr = PetscStrcat(neu_prefix,str_level);CHKERRQ(ierr);
1421   }
1422 
1423   /* DIRICHLET PROBLEM */
1424   if (dirichlet) {
1425     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
1426     if (pcbddc->issym) {
1427       ierr = MatSetOption(pcis->A_II,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
1428     }
1429     /* Matrix for Dirichlet problem is pcis->A_II */
1430     n_D = pcis->n - pcis->n_B;
1431     if (!pcbddc->ksp_D) { /* create object if not yet build */
1432       ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
1433       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
1434       /* default */
1435       ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
1436       ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);CHKERRQ(ierr);
1437       ierr = PetscObjectTypeCompare((PetscObject)pcis->A_II,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
1438       ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
1439       if (issbaij) {
1440         ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
1441       } else {
1442         ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
1443       }
1444       /* Allow user's customization */
1445       ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
1446       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
1447     }
1448     ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II);CHKERRQ(ierr);
1449     if (sub_schurs->interior_solver) {
1450       ierr = KSPSetPC(pcbddc->ksp_D,sub_schurs->interior_solver);CHKERRQ(ierr);
1451     }
1452     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
1453     if (!n_D) {
1454       ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
1455       ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
1456     }
1457     /* Set Up KSP for Dirichlet problem of BDDC */
1458     ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
1459     /* set ksp_D into pcis data */
1460     ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
1461     ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
1462     pcis->ksp_D = pcbddc->ksp_D;
1463   }
1464 
1465   /* NEUMANN PROBLEM */
1466   A_RR = 0;
1467   if (neumann) {
1468     /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
1469     ierr = ISGetSize(pcbddc->is_R_local,&n_R);CHKERRQ(ierr);
1470     if (pcbddc->ksp_R) { /* already created ksp */
1471       PetscInt nn_R;
1472       ierr = KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);CHKERRQ(ierr);
1473       ierr = PetscObjectReference((PetscObject)A_RR);CHKERRQ(ierr);
1474       ierr = MatGetSize(A_RR,&nn_R,NULL);CHKERRQ(ierr);
1475       if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
1476         ierr = KSPReset(pcbddc->ksp_R);CHKERRQ(ierr);
1477         ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1478         reuse = MAT_INITIAL_MATRIX;
1479       } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
1480         if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
1481           ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1482           reuse = MAT_INITIAL_MATRIX;
1483         } else { /* safe to reuse the matrix */
1484           reuse = MAT_REUSE_MATRIX;
1485         }
1486       }
1487       /* last check */
1488       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
1489         ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1490         reuse = MAT_INITIAL_MATRIX;
1491       }
1492     } else { /* first time, so we need to create the matrix */
1493       reuse = MAT_INITIAL_MATRIX;
1494     }
1495     /* extract A_RR */
1496     ierr = MatGetBlockSize(pcbddc->local_mat,&mbs);CHKERRQ(ierr);
1497     ierr = ISGetBlockSize(pcbddc->is_R_local,&ibs);CHKERRQ(ierr);
1498     if (ibs != mbs) {
1499       Mat newmat;
1500       ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
1501       ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
1502       ierr = MatDestroy(&newmat);CHKERRQ(ierr);
1503     } else {
1504       ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
1505     }
1506     if (pcbddc->issym) {
1507       ierr = MatSetOption(A_RR,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
1508     }
1509     if (!pcbddc->ksp_R) { /* create object if not present */
1510       ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
1511       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
1512       /* default */
1513       ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
1514       ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);CHKERRQ(ierr);
1515       ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
1516       ierr = PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
1517       if (issbaij) {
1518         ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
1519       } else {
1520         ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
1521       }
1522       /* Allow user's customization */
1523       ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
1524       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
1525     }
1526     ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);CHKERRQ(ierr);
1527     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
1528     if (!n_R) {
1529       ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
1530       ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
1531     }
1532     /* Set Up KSP for Neumann problem of BDDC */
1533     ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
1534   }
1535 
1536   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
1537   if (pcbddc->NullSpace || pcbddc->dbg_flag) {
1538     if (pcbddc->dbg_flag) {
1539       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1540       ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1541       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
1542     }
1543     if (dirichlet) { /* Dirichlet */
1544       ierr = VecSetRandom(pcis->vec1_D,NULL);CHKERRQ(ierr);
1545       ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1546       ierr = KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);CHKERRQ(ierr);
1547       ierr = VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);CHKERRQ(ierr);
1548       ierr = VecNorm(pcis->vec1_D,NORM_INFINITY,&value);CHKERRQ(ierr);
1549       /* need to be adapted? */
1550       use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
1551       ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1552       ierr = PCBDDCSetUseExactDirichlet(pc,use_exact_reduced);CHKERRQ(ierr);
1553       /* print info */
1554       if (pcbddc->dbg_flag) {
1555         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve (%s) = % 1.14e \n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_D))->prefix,value);CHKERRQ(ierr);
1556         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1557       }
1558       if (pcbddc->NullSpace && !use_exact_reduced && !pcbddc->switch_static) {
1559         ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcis->is_I_local);CHKERRQ(ierr);
1560       }
1561     }
1562     if (neumann) { /* Neumann */
1563       ierr = VecSetRandom(pcbddc->vec1_R,NULL);CHKERRQ(ierr);
1564       ierr = MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
1565       ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
1566       ierr = VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);CHKERRQ(ierr);
1567       ierr = VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);CHKERRQ(ierr);
1568       /* need to be adapted? */
1569       use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
1570       ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1571       /* print info */
1572       if (pcbddc->dbg_flag) {
1573         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann solve (%s) = % 1.14e\n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_R))->prefix,value);CHKERRQ(ierr);
1574         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1575       }
1576       if (pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
1577         ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcbddc->is_R_local);CHKERRQ(ierr);
1578       }
1579     }
1580   }
1581   /* free Neumann problem's matrix */
1582   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1583   PetscFunctionReturn(0);
1584 }
1585 
1586 #undef __FUNCT__
1587 #define __FUNCT__ "PCBDDCSolveSubstructureCorrection"
1588 static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec rhs, Vec sol, Vec work, PetscBool applytranspose)
1589 {
1590   PetscErrorCode ierr;
1591   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1592 
1593   PetscFunctionBegin;
1594   if (applytranspose) {
1595     if (pcbddc->local_auxmat1) {
1596       ierr = MatMultTranspose(pcbddc->local_auxmat2,rhs,work);CHKERRQ(ierr);
1597       ierr = MatMultTransposeAdd(pcbddc->local_auxmat1,work,rhs,rhs);CHKERRQ(ierr);
1598     }
1599     ierr = KSPSolveTranspose(pcbddc->ksp_R,rhs,sol);CHKERRQ(ierr);
1600   } else {
1601     ierr = KSPSolve(pcbddc->ksp_R,rhs,sol);CHKERRQ(ierr);
1602     if (pcbddc->local_auxmat1) {
1603       ierr = MatMult(pcbddc->local_auxmat1,sol,work);CHKERRQ(ierr);
1604       ierr = MatMultAdd(pcbddc->local_auxmat2,work,sol,sol);CHKERRQ(ierr);
1605     }
1606   }
1607   PetscFunctionReturn(0);
1608 }
1609 
1610 /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
1611 #undef __FUNCT__
1612 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
1613 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
1614 {
1615   PetscErrorCode ierr;
1616   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
1617   PC_IS*            pcis = (PC_IS*)  (pc->data);
1618   const PetscScalar zero = 0.0;
1619 
1620   PetscFunctionBegin;
1621   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
1622   if (applytranspose) {
1623     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1624     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1625   } else {
1626     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1627     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1628   }
1629   /* start communications from local primal nodes to rhs of coarse solver */
1630   ierr = VecSet(pcbddc->coarse_vec,zero);CHKERRQ(ierr);
1631   ierr = PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1632   ierr = PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1633 
1634   /* Coarse solution -> rhs and sol updated inside PCBDDCScattarCoarseDataBegin/End */
1635   /* TODO remove null space when doing multilevel */
1636   if (pcbddc->coarse_ksp) {
1637     Vec rhs,sol;
1638 
1639     ierr = KSPGetRhs(pcbddc->coarse_ksp,&rhs);CHKERRQ(ierr);
1640     ierr = KSPGetSolution(pcbddc->coarse_ksp,&sol);CHKERRQ(ierr);
1641     if (applytranspose) {
1642       ierr = KSPSolveTranspose(pcbddc->coarse_ksp,rhs,sol);CHKERRQ(ierr);
1643     } else {
1644       ierr = KSPSolve(pcbddc->coarse_ksp,rhs,sol);CHKERRQ(ierr);
1645     }
1646   }
1647 
1648   /* Local solution on R nodes */
1649   if (pcis->n) {
1650     ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
1651     ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1652     ierr = VecScatterEnd(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1653     if (pcbddc->switch_static) {
1654       ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1655       ierr = VecScatterEnd(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1656     }
1657     ierr = PCBDDCSolveSubstructureCorrection(pc,pcbddc->vec1_R,pcbddc->vec2_R,pcbddc->vec1_C,applytranspose);CHKERRQ(ierr);
1658     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1659     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1660     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1661     if (pcbddc->switch_static) {
1662       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1663       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1664     }
1665   }
1666 
1667   /* communications from coarse sol to local primal nodes */
1668   ierr = PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1669   ierr = PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1670 
1671   /* Sum contributions from two levels */
1672   if (applytranspose) {
1673     ierr = MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1674     if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1675   } else {
1676     ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1677     if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1678   }
1679   PetscFunctionReturn(0);
1680 }
1681 
1682 #undef __FUNCT__
1683 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
1684 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
1685 {
1686   PetscErrorCode ierr;
1687   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1688   PetscScalar    *array;
1689   Vec            from,to;
1690 
1691   PetscFunctionBegin;
1692   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
1693     from = pcbddc->coarse_vec;
1694     to = pcbddc->vec1_P;
1695     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
1696       Vec tvec;
1697 
1698       ierr = KSPGetRhs(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1699       ierr = VecResetArray(tvec);CHKERRQ(ierr);
1700       ierr = KSPGetSolution(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1701       ierr = VecGetArray(tvec,&array);CHKERRQ(ierr);
1702       ierr = VecPlaceArray(from,array);CHKERRQ(ierr);
1703       ierr = VecRestoreArray(tvec,&array);CHKERRQ(ierr);
1704     }
1705   } else { /* from local to global -> put data in coarse right hand side */
1706     from = pcbddc->vec1_P;
1707     to = pcbddc->coarse_vec;
1708   }
1709   ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
1710   PetscFunctionReturn(0);
1711 }
1712 
1713 #undef __FUNCT__
1714 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
1715 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
1716 {
1717   PetscErrorCode ierr;
1718   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1719   PetscScalar    *array;
1720   Vec            from,to;
1721 
1722   PetscFunctionBegin;
1723   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
1724     from = pcbddc->coarse_vec;
1725     to = pcbddc->vec1_P;
1726   } else { /* from local to global -> put data in coarse right hand side */
1727     from = pcbddc->vec1_P;
1728     to = pcbddc->coarse_vec;
1729   }
1730   ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
1731   if (smode == SCATTER_FORWARD) {
1732     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
1733       Vec tvec;
1734 
1735       ierr = KSPGetRhs(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1736       ierr = VecGetArray(to,&array);CHKERRQ(ierr);
1737       ierr = VecPlaceArray(tvec,array);CHKERRQ(ierr);
1738       ierr = VecRestoreArray(to,&array);CHKERRQ(ierr);
1739     }
1740   } else {
1741     if (pcbddc->coarse_ksp) { /* restore array of pcbddc->coarse_vec */
1742      ierr = VecResetArray(from);CHKERRQ(ierr);
1743     }
1744   }
1745   PetscFunctionReturn(0);
1746 }
1747 
1748 /* uncomment for testing purposes */
1749 /* #define PETSC_MISSING_LAPACK_GESVD 1 */
1750 #undef __FUNCT__
1751 #define __FUNCT__ "PCBDDCConstraintsSetUp"
1752 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
1753 {
1754   PetscErrorCode    ierr;
1755   PC_IS*            pcis = (PC_IS*)(pc->data);
1756   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
1757   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
1758   /* one and zero */
1759   PetscScalar       one=1.0,zero=0.0;
1760   /* space to store constraints and their local indices */
1761   PetscScalar       *temp_quadrature_constraint;
1762   PetscInt          *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B;
1763   /* iterators */
1764   PetscInt          i,j,k,total_counts,temp_start_ptr;
1765   /* BLAS integers */
1766   PetscBLASInt      lwork,lierr;
1767   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
1768   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
1769   /* reuse */
1770   PetscInt          olocal_primal_size;
1771   PetscInt          *oprimal_indices_local_idxs;
1772   /* change of basis */
1773   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
1774   PetscBool         boolforchange,qr_needed;
1775   PetscBT           touched,change_basis,qr_needed_idx;
1776   /* auxiliary stuff */
1777   PetscInt          *nnz,*is_indices,*aux_primal_numbering_B;
1778   PetscInt          ncc,*gidxs=NULL,*permutation=NULL,*temp_indices_to_constraint_work=NULL;
1779   PetscScalar       *temp_quadrature_constraint_work=NULL;
1780   /* some quantities */
1781   PetscInt          n_vertices,total_primal_vertices,valid_constraints;
1782   PetscInt          size_of_constraint,max_size_of_constraint=0,max_constraints,temp_constraints;
1783 
1784   PetscFunctionBegin;
1785   /* Destroy Mat objects computed previously */
1786   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1787   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1788 
1789   /* print some info */
1790   if (pcbddc->dbg_flag) {
1791     IS       vertices;
1792     PetscInt nv,nedges,nfaces;
1793     ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&nfaces,NULL,&nedges,NULL,&vertices);CHKERRQ(ierr);
1794     ierr = ISGetSize(vertices,&nv);CHKERRQ(ierr);
1795     ierr = ISDestroy(&vertices);CHKERRQ(ierr);
1796     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1797     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1798     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%d)\n",PetscGlobalRank,nv,pcbddc->use_vertices);CHKERRQ(ierr);
1799     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%d)\n",PetscGlobalRank,nedges,pcbddc->use_edges);CHKERRQ(ierr);
1800     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%d)\n",PetscGlobalRank,nfaces,pcbddc->use_faces);CHKERRQ(ierr);
1801     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1802   }
1803 
1804   if (!pcbddc->adaptive_selection) {
1805     IS           ISForVertices,*ISForFaces,*ISForEdges,*used_IS;
1806     MatNullSpace nearnullsp;
1807     const Vec    *nearnullvecs;
1808     Vec          *localnearnullsp;
1809     PetscScalar  *array;
1810     PetscInt     n_ISForFaces,n_ISForEdges,nnsp_size;
1811     PetscBool    nnsp_has_cnst;
1812     /* LAPACK working arrays for SVD or POD */
1813     PetscBool    skip_lapack;
1814     PetscScalar  *work;
1815     PetscReal    *singular_vals;
1816 #if defined(PETSC_USE_COMPLEX)
1817     PetscReal    *rwork;
1818 #endif
1819 #if defined(PETSC_MISSING_LAPACK_GESVD)
1820     PetscScalar  *temp_basis,*correlation_mat;
1821 #else
1822     PetscBLASInt dummy_int=1;
1823     PetscScalar  dummy_scalar=1.;
1824 #endif
1825 
1826     /* Get index sets for faces, edges and vertices from graph */
1827     ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);CHKERRQ(ierr);
1828     /* free unneeded index sets */
1829     if (!pcbddc->use_vertices) {
1830       ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1831     }
1832     if (!pcbddc->use_edges) {
1833       for (i=0;i<n_ISForEdges;i++) {
1834         ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1835       }
1836       ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1837       n_ISForEdges = 0;
1838     }
1839     if (!pcbddc->use_faces) {
1840       for (i=0;i<n_ISForFaces;i++) {
1841         ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1842       }
1843       ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1844       n_ISForFaces = 0;
1845     }
1846     /* HACKS (the following two blocks of code) */
1847     if (!ISForVertices && pcbddc->NullSpace && !pcbddc->user_ChangeOfBasisMatrix) {
1848       pcbddc->use_change_of_basis = PETSC_TRUE;
1849       if (!ISForEdges) {
1850         pcbddc->use_change_on_faces = PETSC_TRUE;
1851       }
1852     }
1853     if (pcbddc->NullSpace) {
1854       /* use_change_of_basis should be consistent among processors */
1855       PetscBool tbool[2],gbool[2];
1856       tbool[0] = pcbddc->use_change_of_basis;
1857       tbool[1] = pcbddc->use_change_on_faces;
1858       ierr = MPI_Allreduce(tbool,gbool,2,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1859       pcbddc->use_change_of_basis = gbool[0];
1860       pcbddc->use_change_on_faces = gbool[1];
1861     }
1862 
1863     /* check if near null space is attached to global mat */
1864     ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
1865     if (nearnullsp) {
1866       ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1867       /* remove any stored info */
1868       ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
1869       ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1870       /* store information for BDDC solver reuse */
1871       ierr = PetscObjectReference((PetscObject)nearnullsp);CHKERRQ(ierr);
1872       pcbddc->onearnullspace = nearnullsp;
1873       ierr = PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1874       for (i=0;i<nnsp_size;i++) {
1875         ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);CHKERRQ(ierr);
1876       }
1877     } else { /* if near null space is not provided BDDC uses constants by default */
1878       nnsp_size = 0;
1879       nnsp_has_cnst = PETSC_TRUE;
1880     }
1881     /* get max number of constraints on a single cc */
1882     max_constraints = nnsp_size;
1883     if (nnsp_has_cnst) max_constraints++;
1884 
1885     /*
1886          Evaluate maximum storage size needed by the procedure
1887          - temp_indices will contain start index of each constraint stored as follows
1888          - temp_indices_to_constraint  [temp_indices[i],...,temp_indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
1889          - temp_indices_to_constraint_B[temp_indices[i],...,temp_indices[i+1]-1] will contain the indices (in boundary numbering) on which the constraint acts
1890          - temp_quadrature_constraint  [temp_indices[i],...,temp_indices[i+1]-1] will contain the scalars representing the constraint itself
1891                                                                                                                                                            */
1892     total_counts = n_ISForFaces+n_ISForEdges;
1893     total_counts *= max_constraints;
1894     n_vertices = 0;
1895     if (ISForVertices) {
1896       ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
1897     }
1898     total_counts += n_vertices;
1899     ierr = PetscMalloc1(total_counts+1,&temp_indices);CHKERRQ(ierr);
1900     ierr = PetscBTCreate(total_counts,&change_basis);CHKERRQ(ierr);
1901     total_counts = 0;
1902     max_size_of_constraint = 0;
1903     for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1904       if (i<n_ISForEdges) {
1905         used_IS = &ISForEdges[i];
1906       } else {
1907         used_IS = &ISForFaces[i-n_ISForEdges];
1908       }
1909       ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
1910       total_counts += j;
1911       max_size_of_constraint = PetscMax(j,max_size_of_constraint);
1912     }
1913     total_counts *= max_constraints;
1914     total_counts += n_vertices;
1915     ierr = PetscMalloc3(total_counts,&temp_quadrature_constraint,total_counts,&temp_indices_to_constraint,total_counts,&temp_indices_to_constraint_B);CHKERRQ(ierr);
1916     /* get local part of global near null space vectors */
1917     ierr = PetscMalloc1(nnsp_size,&localnearnullsp);CHKERRQ(ierr);
1918     for (k=0;k<nnsp_size;k++) {
1919       ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
1920       ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1921       ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1922     }
1923 
1924     /* whether or not to skip lapack calls */
1925     skip_lapack = PETSC_TRUE;
1926     if (n_ISForFaces+n_ISForEdges && max_constraints > 1 && !pcbddc->use_nnsp_true) skip_lapack = PETSC_FALSE;
1927 
1928     /* allocate some auxiliary stuff */
1929     if (!skip_lapack || pcbddc->use_qr_single) {
1930       ierr = PetscMalloc4(max_size_of_constraint,&gidxs,max_size_of_constraint,&permutation,max_size_of_constraint,&temp_indices_to_constraint_work,max_size_of_constraint,&temp_quadrature_constraint_work);CHKERRQ(ierr);
1931     } else {
1932       gidxs = NULL;
1933       permutation = NULL;
1934       temp_indices_to_constraint_work = NULL;
1935       temp_quadrature_constraint_work = NULL;
1936     }
1937 
1938     /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
1939     if (!skip_lapack) {
1940       PetscScalar temp_work;
1941 
1942 #if defined(PETSC_MISSING_LAPACK_GESVD)
1943       /* Proper Orthogonal Decomposition (POD) using the snapshot method */
1944       ierr = PetscMalloc1(max_constraints*max_constraints,&correlation_mat);CHKERRQ(ierr);
1945       ierr = PetscMalloc1(max_constraints,&singular_vals);CHKERRQ(ierr);
1946       ierr = PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);CHKERRQ(ierr);
1947 #if defined(PETSC_USE_COMPLEX)
1948       ierr = PetscMalloc1(3*max_constraints,&rwork);CHKERRQ(ierr);
1949 #endif
1950       /* now we evaluate the optimal workspace using query with lwork=-1 */
1951       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1952       ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
1953       lwork = -1;
1954       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1955 #if !defined(PETSC_USE_COMPLEX)
1956       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
1957 #else
1958       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
1959 #endif
1960       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1961       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
1962 #else /* on missing GESVD */
1963       /* SVD */
1964       PetscInt max_n,min_n;
1965       max_n = max_size_of_constraint;
1966       min_n = max_constraints;
1967       if (max_size_of_constraint < max_constraints) {
1968         min_n = max_size_of_constraint;
1969         max_n = max_constraints;
1970       }
1971       ierr = PetscMalloc1(min_n,&singular_vals);CHKERRQ(ierr);
1972 #if defined(PETSC_USE_COMPLEX)
1973       ierr = PetscMalloc1(5*min_n,&rwork);CHKERRQ(ierr);
1974 #endif
1975       /* now we evaluate the optimal workspace using query with lwork=-1 */
1976       lwork = -1;
1977       ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
1978       ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
1979       ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
1980       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1981 #if !defined(PETSC_USE_COMPLEX)
1982       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&temp_quadrature_constraint[0],&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,&lierr));
1983 #else
1984       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&temp_quadrature_constraint[0],&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,rwork,&lierr));
1985 #endif
1986       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1987       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
1988 #endif /* on missing GESVD */
1989       /* Allocate optimal workspace */
1990       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
1991       ierr = PetscMalloc1(lwork,&work);CHKERRQ(ierr);
1992     }
1993     /* Now we can loop on constraining sets */
1994     total_counts = 0;
1995     temp_indices[0] = 0;
1996     /* vertices */
1997     if (ISForVertices) {
1998       ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1999       if (nnsp_has_cnst) { /* consider all vertices */
2000         ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,n_vertices*sizeof(PetscInt));CHKERRQ(ierr);
2001         for (i=0;i<n_vertices;i++) {
2002           temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
2003           temp_indices[total_counts+1]=temp_indices[total_counts]+1;
2004           total_counts++;
2005         }
2006       } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
2007         PetscBool used_vertex;
2008         for (i=0;i<n_vertices;i++) {
2009           used_vertex = PETSC_FALSE;
2010           k = 0;
2011           while (!used_vertex && k<nnsp_size) {
2012             ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
2013             if (PetscAbsScalar(array[is_indices[i]])>0.0) {
2014               temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
2015               temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
2016               temp_indices[total_counts+1]=temp_indices[total_counts]+1;
2017               total_counts++;
2018               used_vertex = PETSC_TRUE;
2019             }
2020             ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
2021             k++;
2022           }
2023         }
2024       }
2025       ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2026       n_vertices = total_counts;
2027     }
2028 
2029     /* edges and faces */
2030     for (ncc=0;ncc<n_ISForEdges+n_ISForFaces;ncc++) {
2031       if (ncc<n_ISForEdges) {
2032         used_IS = &ISForEdges[ncc];
2033         boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
2034       } else {
2035         used_IS = &ISForFaces[ncc-n_ISForEdges];
2036         boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
2037       }
2038       temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
2039       temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
2040       ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
2041       ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2042       /* change of basis should not be performed on local periodic nodes */
2043       if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
2044       if (nnsp_has_cnst) {
2045         PetscScalar quad_value;
2046         temp_constraints++;
2047         if (!pcbddc->use_nnsp_true) {
2048           quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
2049         } else {
2050           quad_value = 1.0;
2051         }
2052         ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
2053         for (j=0;j<size_of_constraint;j++) {
2054           temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
2055         }
2056         /* sort by global ordering if using lapack subroutines (not needed!) */
2057         if (!skip_lapack || pcbddc->use_qr_single) {
2058           ierr = ISLocalToGlobalMappingApply(matis->mapping,size_of_constraint,temp_indices_to_constraint+temp_indices[total_counts],gidxs);CHKERRQ(ierr);
2059           for (j=0;j<size_of_constraint;j++) {
2060             permutation[j]=j;
2061           }
2062           ierr = PetscSortIntWithPermutation(size_of_constraint,gidxs,permutation);CHKERRQ(ierr);
2063           for (j=0;j<size_of_constraint;j++) {
2064             if (permutation[j]!=j) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This should not happen");
2065           }
2066           for (j=0;j<size_of_constraint;j++) {
2067             temp_indices_to_constraint_work[j] = temp_indices_to_constraint[temp_indices[total_counts]+permutation[j]];
2068             temp_quadrature_constraint_work[j] = temp_quadrature_constraint[temp_indices[total_counts]+permutation[j]];
2069           }
2070           ierr = PetscMemcpy(temp_indices_to_constraint+temp_indices[total_counts],temp_indices_to_constraint_work,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
2071           ierr = PetscMemcpy(temp_quadrature_constraint+temp_indices[total_counts],temp_quadrature_constraint_work,size_of_constraint*sizeof(PetscScalar));CHKERRQ(ierr);
2072         }
2073         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
2074         total_counts++;
2075       }
2076       for (k=0;k<nnsp_size;k++) {
2077         PetscReal real_value;
2078         ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
2079         ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
2080         for (j=0;j<size_of_constraint;j++) {
2081           temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
2082         }
2083         ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
2084         /* check if array is null on the connected component */
2085         ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2086         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_one));
2087         if (real_value > 0.0) { /* keep indices and values */
2088           /* sort by global ordering if using lapack subroutines */
2089           if (!skip_lapack || pcbddc->use_qr_single) {
2090             ierr = ISLocalToGlobalMappingApply(matis->mapping,size_of_constraint,temp_indices_to_constraint+temp_indices[total_counts],gidxs);CHKERRQ(ierr);
2091             for (j=0;j<size_of_constraint;j++) {
2092               permutation[j]=j;
2093             }
2094             ierr = PetscSortIntWithPermutation(size_of_constraint,gidxs,permutation);CHKERRQ(ierr);
2095             for (j=0;j<size_of_constraint;j++) {
2096               temp_indices_to_constraint_work[j] = temp_indices_to_constraint[temp_indices[total_counts]+permutation[j]];
2097               temp_quadrature_constraint_work[j] = temp_quadrature_constraint[temp_indices[total_counts]+permutation[j]];
2098             }
2099             ierr = PetscMemcpy(temp_indices_to_constraint+temp_indices[total_counts],temp_indices_to_constraint_work,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
2100             ierr = PetscMemcpy(temp_quadrature_constraint+temp_indices[total_counts],temp_quadrature_constraint_work,size_of_constraint*sizeof(PetscScalar));CHKERRQ(ierr);
2101           }
2102           temp_constraints++;
2103           temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
2104           total_counts++;
2105         }
2106       }
2107       ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2108       valid_constraints = temp_constraints;
2109       if (!pcbddc->use_nnsp_true && temp_constraints) {
2110         if (temp_constraints == 1) { /* just normalize the constraint */
2111           PetscScalar norm;
2112           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2113           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,temp_quadrature_constraint+temp_indices[temp_start_ptr],&Blas_one,temp_quadrature_constraint+temp_indices[temp_start_ptr],&Blas_one));
2114           norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
2115           PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,temp_quadrature_constraint+temp_indices[temp_start_ptr],&Blas_one));
2116         } else { /* perform SVD */
2117           PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
2118 
2119 #if defined(PETSC_MISSING_LAPACK_GESVD)
2120           /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
2121              POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
2122              -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
2123                 the constraints basis will differ (by a complex factor with absolute value equal to 1)
2124                 from that computed using LAPACKgesvd
2125              -> This is due to a different computation of eigenvectors in LAPACKheev
2126              -> The quality of the POD-computed basis will be the same */
2127           ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
2128           /* Store upper triangular part of correlation matrix */
2129           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2130           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2131           for (j=0;j<temp_constraints;j++) {
2132             for (k=0;k<j+1;k++) {
2133               PetscStackCallBLAS("BLASdot",correlation_mat[j*temp_constraints+k]=BLASdot_(&Blas_N,&temp_quadrature_constraint[temp_indices[temp_start_ptr+k]],&Blas_one,&temp_quadrature_constraint[temp_indices[temp_start_ptr+j]],&Blas_one));
2134             }
2135           }
2136           /* compute eigenvalues and eigenvectors of correlation matrix */
2137           ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
2138           ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
2139 #if !defined(PETSC_USE_COMPLEX)
2140           PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
2141 #else
2142           PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
2143 #endif
2144           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2145           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
2146           /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
2147           j = 0;
2148           while (j < temp_constraints && singular_vals[j] < tol) j++;
2149           total_counts = total_counts-j;
2150           valid_constraints = temp_constraints-j;
2151           /* scale and copy POD basis into used quadrature memory */
2152           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2153           ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
2154           ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
2155           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2156           ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
2157           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
2158           if (j<temp_constraints) {
2159             PetscInt ii;
2160             for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
2161             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2162             PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Blas_M,&Blas_N,&Blas_K,&one,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Blas_LDA,correlation_mat,&Blas_LDB,&zero,temp_basis,&Blas_LDC));
2163             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2164             for (k=0;k<temp_constraints-j;k++) {
2165               for (ii=0;ii<size_of_constraint;ii++) {
2166                 temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[temp_constraints-1-k]*temp_basis[(temp_constraints-1-k)*size_of_constraint+ii];
2167               }
2168             }
2169           }
2170 #else  /* on missing GESVD */
2171           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2172           ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
2173           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2174           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2175 #if !defined(PETSC_USE_COMPLEX)
2176           PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,&lierr));
2177 #else
2178           PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,rwork,&lierr));
2179 #endif
2180           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
2181           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2182           /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
2183           k = temp_constraints;
2184           if (k > size_of_constraint) k = size_of_constraint;
2185           j = 0;
2186           while (j < k && singular_vals[k-j-1] < tol) j++;
2187           valid_constraints = k-j;
2188           total_counts = total_counts-temp_constraints+valid_constraints;
2189 #endif /* on missing GESVD */
2190         }
2191       }
2192       /* setting change_of_basis flag is safe now */
2193       if (boolforchange) {
2194         for (j=0;j<valid_constraints;j++) {
2195           PetscBTSet(change_basis,total_counts-j-1);
2196         }
2197       }
2198     }
2199     /* free workspace */
2200     if (!skip_lapack || pcbddc->use_qr_single) {
2201       ierr = PetscFree4(gidxs,permutation,temp_indices_to_constraint_work,temp_quadrature_constraint_work);CHKERRQ(ierr);
2202     }
2203     if (!skip_lapack) {
2204       ierr = PetscFree(work);CHKERRQ(ierr);
2205 #if defined(PETSC_USE_COMPLEX)
2206       ierr = PetscFree(rwork);CHKERRQ(ierr);
2207 #endif
2208       ierr = PetscFree(singular_vals);CHKERRQ(ierr);
2209 #if defined(PETSC_MISSING_LAPACK_GESVD)
2210       ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
2211       ierr = PetscFree(temp_basis);CHKERRQ(ierr);
2212 #endif
2213     }
2214     for (k=0;k<nnsp_size;k++) {
2215       ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
2216     }
2217     ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
2218     /* free index sets of faces, edges and vertices */
2219     for (i=0;i<n_ISForFaces;i++) {
2220       ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
2221     }
2222     if (n_ISForFaces) {
2223       ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
2224     }
2225     for (i=0;i<n_ISForEdges;i++) {
2226       ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
2227     }
2228     if (n_ISForEdges) {
2229       ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
2230     }
2231     ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
2232   } else {
2233     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
2234     PetscInt        cum = 0;
2235 
2236     total_counts = 0;
2237     n_vertices = 0;
2238     if (sub_schurs->is_Ej_com && pcbddc->use_vertices) {
2239       ierr = ISGetLocalSize(sub_schurs->is_Ej_com,&n_vertices);CHKERRQ(ierr);
2240     }
2241     max_constraints = 0;
2242     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
2243       total_counts += pcbddc->adaptive_constraints_n[i];
2244       max_constraints = PetscMax(max_constraints,pcbddc->adaptive_constraints_n[i]);
2245     }
2246     temp_indices = pcbddc->adaptive_constraints_ptrs;
2247     temp_indices_to_constraint = pcbddc->adaptive_constraints_idxs;
2248     temp_quadrature_constraint = pcbddc->adaptive_constraints_data;
2249 
2250 #if 0
2251     printf("Found %d totals\n",total_counts);
2252     for (i=0;i<total_counts;i++) {
2253       printf("const %d, start %d",i,temp_indices[i]);
2254       printf(" end %d:\n",temp_indices[i+1]);
2255       for (j=temp_indices[i];j<temp_indices[i+1];j++) {
2256         printf("  idxs %d",temp_indices_to_constraint[j]);
2257         printf("  data %1.2e\n",temp_quadrature_constraint[j]);
2258       }
2259     }
2260     for (i=0;i<n_vertices;i++) {
2261       PetscPrintf(PETSC_COMM_SELF,"[%d] vertex %d, n %d\n",PetscGlobalRank,i,pcbddc->adaptive_constraints_n[i]);
2262     }
2263     for (i=0;i<sub_schurs->n_subs;i++) {
2264       PetscPrintf(PETSC_COMM_SELF,"[%d] sub %d, edge %d, n %d\n",PetscGlobalRank,i,(PetscBool)PetscBTLookup(sub_schurs->is_edge,i),pcbddc->adaptive_constraints_n[i+n_vertices]);
2265     }
2266 #endif
2267 
2268     max_size_of_constraint = 0;
2269     for (i=0;i<total_counts;i++) max_size_of_constraint = PetscMax(max_size_of_constraint,temp_indices[i+1]-temp_indices[i]);
2270     ierr = PetscMalloc1(temp_indices[total_counts],&temp_indices_to_constraint_B);CHKERRQ(ierr);
2271     /* Change of basis */
2272     ierr = PetscBTCreate(total_counts,&change_basis);CHKERRQ(ierr);
2273     if (pcbddc->use_change_of_basis) {
2274       cum = n_vertices;
2275       for (i=0;i<sub_schurs->n_subs;i++) {
2276         if (PetscBTLookup(sub_schurs->is_edge,i) || pcbddc->use_change_on_faces) {
2277           for (j=0;j<pcbddc->adaptive_constraints_n[i+n_vertices];j++) {
2278             ierr = PetscBTSet(change_basis,cum+j);CHKERRQ(ierr);
2279           }
2280         }
2281         cum += pcbddc->adaptive_constraints_n[i+n_vertices];
2282       }
2283     }
2284   }
2285 
2286   /* map temp_indices_to_constraint in boundary numbering */
2287   ierr = ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,temp_indices[total_counts],temp_indices_to_constraint,&i,temp_indices_to_constraint_B);CHKERRQ(ierr);
2288   if (i != temp_indices[total_counts]) {
2289     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for constraints indices %d != %d\n",temp_indices[total_counts],i);
2290   }
2291 
2292   /* set quantities in pcbddc data structure and store previous primal size */
2293   /* n_vertices defines the number of subdomain corners in the primal space */
2294   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
2295   olocal_primal_size = pcbddc->local_primal_size;
2296   pcbddc->local_primal_size = total_counts;
2297   pcbddc->n_vertices = n_vertices;
2298   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
2299 
2300   /* Create constraint matrix */
2301   /* The constraint matrix is used to compute the l2g map of primal dofs */
2302   /* so we need to set it up properly either with or without change of basis */
2303   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
2304   ierr = MatSetType(pcbddc->ConstraintMatrix,MATAIJ);CHKERRQ(ierr);
2305   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
2306   /* array to compute a local numbering of constraints : vertices first then constraints */
2307   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_numbering);CHKERRQ(ierr);
2308   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
2309   /* note: it should not be needed since IS for faces and edges are already sorted by global ordering when analyzing the graph but... just in case */
2310   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_minloc);CHKERRQ(ierr);
2311   /* auxiliary stuff for basis change */
2312   ierr = PetscMalloc1(max_size_of_constraint,&global_indices);CHKERRQ(ierr);
2313   ierr = PetscBTCreate(pcis->n_B,&touched);CHKERRQ(ierr);
2314 
2315   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
2316   total_primal_vertices=0;
2317   for (i=0;i<pcbddc->local_primal_size;i++) {
2318     size_of_constraint=temp_indices[i+1]-temp_indices[i];
2319     if (size_of_constraint == 1) {
2320       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]]);CHKERRQ(ierr);
2321       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
2322       aux_primal_minloc[total_primal_vertices]=0;
2323       total_primal_vertices++;
2324     } else if (PetscBTLookup(change_basis,i)) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
2325       PetscInt min_loc,min_index;
2326       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
2327       /* find first untouched local node */
2328       k = 0;
2329       while (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) k++;
2330       min_index = global_indices[k];
2331       min_loc = k;
2332       /* search the minimum among global nodes already untouched on the cc */
2333       for (k=1;k<size_of_constraint;k++) {
2334         /* there can be more than one constraint on a single connected component */
2335         if (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k]) && min_index > global_indices[k]) {
2336           min_index = global_indices[k];
2337           min_loc = k;
2338         }
2339       }
2340       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]+min_loc]);CHKERRQ(ierr);
2341       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
2342       aux_primal_minloc[total_primal_vertices]=min_loc;
2343       total_primal_vertices++;
2344     }
2345   }
2346   /* determine if a QR strategy is needed for change of basis */
2347   qr_needed = PETSC_FALSE;
2348   ierr = PetscBTCreate(pcbddc->local_primal_size,&qr_needed_idx);CHKERRQ(ierr);
2349   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
2350     if (PetscBTLookup(change_basis,i)) {
2351       if (!pcbddc->use_qr_single && !pcbddc->faster_deluxe) {
2352         size_of_constraint = temp_indices[i+1]-temp_indices[i];
2353         j = 0;
2354         for (k=0;k<size_of_constraint;k++) {
2355           if (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) {
2356             j++;
2357           }
2358         }
2359         /* found more than one primal dof on the cc */
2360         if (j > 1) {
2361           PetscBTSet(qr_needed_idx,i);
2362           qr_needed = PETSC_TRUE;
2363         }
2364       } else {
2365         PetscBTSet(qr_needed_idx,i);
2366         qr_needed = PETSC_TRUE;
2367       }
2368     }
2369   }
2370   /* free workspace */
2371   ierr = PetscFree(global_indices);CHKERRQ(ierr);
2372 
2373   /* permute indices in order to have a sorted set of vertices */
2374   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);CHKERRQ(ierr);
2375 
2376   /* nonzero structure of constraint matrix */
2377   ierr = PetscMalloc1(pcbddc->local_primal_size,&nnz);CHKERRQ(ierr);
2378   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
2379   j=total_primal_vertices;
2380   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
2381     if (!PetscBTLookup(change_basis,i)) {
2382       nnz[j]=temp_indices[i+1]-temp_indices[i];
2383       j++;
2384     }
2385   }
2386   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
2387   ierr = PetscFree(nnz);CHKERRQ(ierr);
2388   /* set values in constraint matrix */
2389   for (i=0;i<total_primal_vertices;i++) {
2390     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
2391   }
2392   total_counts = total_primal_vertices;
2393   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
2394     if (!PetscBTLookup(change_basis,i)) {
2395       size_of_constraint=temp_indices[i+1]-temp_indices[i];
2396       ierr = MatSetValues(pcbddc->ConstraintMatrix,1,&total_counts,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],&temp_quadrature_constraint[temp_indices[i]],INSERT_VALUES);CHKERRQ(ierr);
2397       total_counts++;
2398     }
2399   }
2400   /* assembling */
2401   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2402   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2403   /*
2404   ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
2405   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
2406   */
2407   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
2408   if (pcbddc->use_change_of_basis) {
2409     /* dual and primal dofs on a single cc */
2410     PetscInt     dual_dofs,primal_dofs;
2411     /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
2412     PetscInt     primal_counter;
2413     /* working stuff for GEQRF */
2414     PetscScalar  *qr_basis,*qr_tau = NULL,*qr_work,lqr_work_t;
2415     PetscBLASInt lqr_work;
2416     /* working stuff for UNGQR */
2417     PetscScalar  *gqr_work,lgqr_work_t;
2418     PetscBLASInt lgqr_work;
2419     /* working stuff for TRTRS */
2420     PetscScalar  *trs_rhs;
2421     PetscBLASInt Blas_NRHS;
2422     /* pointers for values insertion into change of basis matrix */
2423     PetscInt     *start_rows,*start_cols;
2424     PetscScalar  *start_vals;
2425     /* working stuff for values insertion */
2426     PetscBT      is_primal;
2427     /* matrix sizes */
2428     PetscInt     global_size,local_size;
2429     /* temporary change of basis */
2430     Mat          localChangeOfBasisMatrix;
2431     /* extra space for debugging */
2432     PetscScalar  *dbg_work;
2433 
2434     /* local temporary change of basis acts on local interfaces -> dimension is n_B x n_B */
2435     ierr = MatCreate(PETSC_COMM_SELF,&localChangeOfBasisMatrix);CHKERRQ(ierr);
2436     ierr = MatSetType(localChangeOfBasisMatrix,MATAIJ);CHKERRQ(ierr);
2437     ierr = MatSetSizes(localChangeOfBasisMatrix,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
2438     /* nonzeros for local mat */
2439     ierr = PetscMalloc1(pcis->n,&nnz);CHKERRQ(ierr);
2440     for (i=0;i<pcis->n;i++) nnz[i]=1;
2441     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
2442       if (PetscBTLookup(change_basis,i)) {
2443         size_of_constraint = temp_indices[i+1]-temp_indices[i];
2444         if (PetscBTLookup(qr_needed_idx,i)) {
2445           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint[temp_indices[i]+j]] = size_of_constraint;
2446         } else {
2447           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint[temp_indices[i]+j]] = 2;
2448           /* get local primal index on the cc */
2449           j = 0;
2450           while (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+j])) j++;
2451           nnz[temp_indices_to_constraint[temp_indices[i]+j]] = size_of_constraint;
2452         }
2453       }
2454     }
2455     ierr = MatSeqAIJSetPreallocation(localChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
2456     ierr = PetscFree(nnz);CHKERRQ(ierr);
2457     /* Set initial identity in the matrix */
2458     for (i=0;i<pcis->n;i++) {
2459       ierr = MatSetValue(localChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
2460     }
2461 
2462     if (pcbddc->dbg_flag) {
2463       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
2464       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
2465     }
2466 
2467 
2468     /* Now we loop on the constraints which need a change of basis */
2469     /*
2470        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
2471        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)
2472 
2473        Basic blocks of change of basis matrix T computed by
2474 
2475           - Using the following block transformation if there is only a primal dof on the cc (and -pc_bddc_use_qr_single is not specified)
2476 
2477             | 1        0   ...        0         s_1/S |
2478             | 0        1   ...        0         s_2/S |
2479             |              ...                        |
2480             | 0        ...            1     s_{n-1}/S |
2481             | -s_1/s_n ...    -s_{n-1}/s_n      s_n/S |
2482 
2483             with S = \sum_{i=1}^n s_i^2
2484             NOTE: in the above example, the primal dof is the last one of the edge in LOCAL ordering
2485                   in the current implementation, the primal dof is the first one of the edge in GLOBAL ordering
2486 
2487           - QR decomposition of constraints otherwise
2488     */
2489     if (qr_needed) {
2490       /* space to store Q */
2491       ierr = PetscMalloc1(max_size_of_constraint*max_size_of_constraint,&qr_basis);CHKERRQ(ierr);
2492       /* first we issue queries for optimal work */
2493       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
2494       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
2495       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2496       lqr_work = -1;
2497       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
2498       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
2499       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
2500       ierr = PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);CHKERRQ(ierr);
2501       lgqr_work = -1;
2502       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
2503       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
2504       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
2505       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2506       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
2507       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
2508       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
2509       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
2510       ierr = PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);CHKERRQ(ierr);
2511       /* array to store scaling factors for reflectors */
2512       ierr = PetscMalloc1(max_constraints,&qr_tau);CHKERRQ(ierr);
2513       /* array to store rhs and solution of triangular solver */
2514       ierr = PetscMalloc1(max_constraints*max_constraints,&trs_rhs);CHKERRQ(ierr);
2515       /* allocating workspace for check */
2516       if (pcbddc->dbg_flag) {
2517         ierr = PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&dbg_work);CHKERRQ(ierr);
2518       }
2519     }
2520     /* array to store whether a node is primal or not */
2521     ierr = PetscBTCreate(pcis->n_B,&is_primal);CHKERRQ(ierr);
2522     ierr = PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);CHKERRQ(ierr);
2523     ierr = ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,aux_primal_numbering,&i,aux_primal_numbering_B);CHKERRQ(ierr);
2524     if (i != total_primal_vertices) {
2525       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",total_primal_vertices,i);
2526     }
2527     for (i=0;i<total_primal_vertices;i++) {
2528       ierr = PetscBTSet(is_primal,aux_primal_numbering_B[i]);CHKERRQ(ierr);
2529     }
2530     ierr = PetscFree(aux_primal_numbering_B);CHKERRQ(ierr);
2531 
2532     /* loop on constraints and see whether or not they need a change of basis and compute it */
2533     /* -> using implicit ordering contained in temp_indices data */
2534     total_counts = pcbddc->n_vertices;
2535     primal_counter = total_counts;
2536     while (total_counts<pcbddc->local_primal_size) {
2537       primal_dofs = 1;
2538       if (PetscBTLookup(change_basis,total_counts)) {
2539         /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
2540         while (total_counts+primal_dofs < pcbddc->local_primal_size && temp_indices_to_constraint[temp_indices[total_counts]] == temp_indices_to_constraint[temp_indices[total_counts+primal_dofs]]) {
2541           primal_dofs++;
2542         }
2543         /* get constraint info */
2544         size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
2545         dual_dofs = size_of_constraint-primal_dofs;
2546 
2547         if (pcbddc->dbg_flag) {
2548           ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraints %d to %d (incl) need a change of basis (size %d)\n",total_counts,total_counts+primal_dofs-1,size_of_constraint);CHKERRQ(ierr);
2549         }
2550 
2551         if (PetscBTLookup(qr_needed_idx,total_counts)) { /* QR */
2552 
2553           /* copy quadrature constraints for change of basis check */
2554           if (pcbddc->dbg_flag) {
2555             ierr = PetscMemcpy(dbg_work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2556           }
2557           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
2558           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2559 
2560           /* compute QR decomposition of constraints */
2561           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2562           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2563           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2564           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2565           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
2566           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
2567           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2568 
2569           /* explictly compute R^-T */
2570           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
2571           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
2572           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2573           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
2574           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2575           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2576           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2577           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
2578           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
2579           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2580 
2581           /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
2582           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2583           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2584           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2585           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2586           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2587           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
2588           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
2589           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2590 
2591           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
2592              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
2593              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
2594           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2595           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2596           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2597           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2598           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2599           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
2600           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2601           PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Blas_M,&Blas_N,&Blas_K,&one,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&zero,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_LDC));
2602           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2603           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2604 
2605           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
2606           start_rows = &temp_indices_to_constraint[temp_indices[total_counts]];
2607           /* insert cols for primal dofs */
2608           for (j=0;j<primal_dofs;j++) {
2609             start_vals = &qr_basis[j*size_of_constraint];
2610             start_cols = &temp_indices_to_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
2611             ierr = MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2612           }
2613           /* insert cols for dual dofs */
2614           for (j=0,k=0;j<dual_dofs;k++) {
2615             if (!PetscBTLookup(is_primal,temp_indices_to_constraint_B[temp_indices[total_counts]+k])) {
2616               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
2617               start_cols = &temp_indices_to_constraint[temp_indices[total_counts]+k];
2618               ierr = MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2619               j++;
2620             }
2621           }
2622 
2623           /* check change of basis */
2624           if (pcbddc->dbg_flag) {
2625             PetscInt   ii,jj;
2626             PetscBool valid_qr=PETSC_TRUE;
2627             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
2628             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2629             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
2630             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2631             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
2632             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
2633             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2634             PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&Blas_M,&Blas_N,&Blas_K,&one,dbg_work,&Blas_LDA,qr_basis,&Blas_LDB,&zero,&dbg_work[size_of_constraint*primal_dofs],&Blas_LDC));
2635             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2636             for (jj=0;jj<size_of_constraint;jj++) {
2637               for (ii=0;ii<primal_dofs;ii++) {
2638                 if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
2639                 if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
2640               }
2641             }
2642             if (!valid_qr) {
2643               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");CHKERRQ(ierr);
2644               for (jj=0;jj<size_of_constraint;jj++) {
2645                 for (ii=0;ii<primal_dofs;ii++) {
2646                   if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
2647                     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %d is not orthogonal to constraint %d (%1.14e)!\n",jj,ii,PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
2648                   }
2649                   if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
2650                     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %d is not unitary w.r.t constraint %d (%1.14e)!\n",jj,ii,PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
2651                   }
2652                 }
2653               }
2654             } else {
2655               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");CHKERRQ(ierr);
2656             }
2657           }
2658         } else { /* simple transformation block */
2659           PetscInt    row,col;
2660           PetscScalar val,norm;
2661 
2662           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2663           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,temp_quadrature_constraint+temp_indices[total_counts],&Blas_one,temp_quadrature_constraint+temp_indices[total_counts],&Blas_one));
2664           for (j=0;j<size_of_constraint;j++) {
2665             PetscInt row_B = temp_indices_to_constraint_B[temp_indices[total_counts]+j];
2666             row = temp_indices_to_constraint[temp_indices[total_counts]+j];
2667             if (!PetscBTLookup(is_primal,row_B)) {
2668               col = temp_indices_to_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2669               ierr = MatSetValue(localChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);CHKERRQ(ierr);
2670               ierr = MatSetValue(localChangeOfBasisMatrix,row,col,temp_quadrature_constraint[temp_indices[total_counts]+j]/norm,INSERT_VALUES);CHKERRQ(ierr);
2671             } else {
2672               for (k=0;k<size_of_constraint;k++) {
2673                 col = temp_indices_to_constraint[temp_indices[total_counts]+k];
2674                 if (row != col) {
2675                   val = -temp_quadrature_constraint[temp_indices[total_counts]+k]/temp_quadrature_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2676                 } else {
2677                   val = temp_quadrature_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter]]/norm;
2678                 }
2679                 ierr = MatSetValue(localChangeOfBasisMatrix,row,col,val,INSERT_VALUES);CHKERRQ(ierr);
2680               }
2681             }
2682           }
2683           if (pcbddc->dbg_flag) {
2684             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");CHKERRQ(ierr);
2685           }
2686         }
2687         /* increment primal counter */
2688         primal_counter += primal_dofs;
2689       } else {
2690         if (pcbddc->dbg_flag) {
2691           ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %d does not need a change of basis (size %d)\n",total_counts,temp_indices[total_counts+1]-temp_indices[total_counts]);CHKERRQ(ierr);
2692         }
2693       }
2694       /* increment constraint counter total_counts */
2695       total_counts += primal_dofs;
2696     }
2697 
2698     /* free workspace */
2699     if (qr_needed) {
2700       if (pcbddc->dbg_flag) {
2701         ierr = PetscFree(dbg_work);CHKERRQ(ierr);
2702       }
2703       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
2704       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
2705       ierr = PetscFree(qr_work);CHKERRQ(ierr);
2706       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
2707       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
2708     }
2709     ierr = PetscBTDestroy(&is_primal);CHKERRQ(ierr);
2710     ierr = MatAssemblyBegin(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2711     ierr = MatAssemblyEnd(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2712 
2713     /* assembling of global change of variable */
2714     {
2715       Mat      tmat;
2716       PetscInt bs;
2717 
2718       ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
2719       ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
2720       ierr = MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&tmat);CHKERRQ(ierr);
2721       ierr = MatISSetLocalMat(tmat,localChangeOfBasisMatrix);CHKERRQ(ierr);
2722       ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2723       ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,MATAIJ);CHKERRQ(ierr);
2724       ierr = MatGetBlockSize(pc->pmat,&bs);CHKERRQ(ierr);
2725       ierr = MatSetBlockSize(pcbddc->ChangeOfBasisMatrix,bs);CHKERRQ(ierr);
2726       ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
2727       ierr = MatISSetMPIXAIJPreallocation_Private(tmat,pcbddc->ChangeOfBasisMatrix,PETSC_TRUE);CHKERRQ(ierr);
2728       ierr = MatISGetMPIXAIJ(tmat,MAT_REUSE_MATRIX,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2729       ierr = MatDestroy(&tmat);CHKERRQ(ierr);
2730       ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
2731       ierr = VecSet(pcis->vec1_N,1.0);CHKERRQ(ierr);
2732       ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2733       ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2734       ierr = VecReciprocal(pcis->vec1_global);CHKERRQ(ierr);
2735       ierr = MatDiagonalScale(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,NULL);CHKERRQ(ierr);
2736     }
2737     /* check */
2738     if (pcbddc->dbg_flag) {
2739       PetscReal error;
2740       Vec       x,x_change;
2741 
2742       ierr = VecDuplicate(pcis->vec1_global,&x);CHKERRQ(ierr);
2743       ierr = VecDuplicate(pcis->vec1_global,&x_change);CHKERRQ(ierr);
2744       ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
2745       ierr = VecCopy(x,pcis->vec1_global);CHKERRQ(ierr);
2746       ierr = VecScatterBegin(matis->ctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2747       ierr = VecScatterEnd(matis->ctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2748       ierr = MatMult(localChangeOfBasisMatrix,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
2749       ierr = VecScatterBegin(matis->ctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2750       ierr = VecScatterEnd(matis->ctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2751       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);CHKERRQ(ierr);
2752       ierr = VecAXPY(x,-1.0,x_change);CHKERRQ(ierr);
2753       ierr = VecNorm(x,NORM_INFINITY,&error);CHKERRQ(ierr);
2754       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2755       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change: %1.6e\n",error);CHKERRQ(ierr);
2756       ierr = VecDestroy(&x);CHKERRQ(ierr);
2757       ierr = VecDestroy(&x_change);CHKERRQ(ierr);
2758     }
2759 
2760     /* adapt sub_schurs computed (if any) */
2761     if (pcbddc->use_deluxe_scaling) {
2762       PCBDDCSubSchurs sub_schurs=pcbddc->sub_schurs;
2763       if (sub_schurs->S_Ej_all) {
2764         Mat S_new,tmat;
2765         IS is_all_N;
2766 
2767         ierr = ISLocalToGlobalMappingApplyIS(pcis->BtoNmap,sub_schurs->is_Ej_all,&is_all_N);CHKERRQ(ierr);
2768         ierr = MatGetSubMatrixUnsorted(localChangeOfBasisMatrix,is_all_N,is_all_N,&tmat);CHKERRQ(ierr);
2769         ierr = ISDestroy(&is_all_N);CHKERRQ(ierr);
2770         ierr = MatPtAP(sub_schurs->S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);CHKERRQ(ierr);
2771         ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
2772         ierr = PetscObjectReference((PetscObject)S_new);CHKERRQ(ierr);
2773         sub_schurs->S_Ej_all = S_new;
2774         ierr = MatDestroy(&S_new);CHKERRQ(ierr);
2775         if (sub_schurs->sum_S_Ej_all) {
2776           ierr = MatPtAP(sub_schurs->sum_S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);CHKERRQ(ierr);
2777           ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
2778           ierr = PetscObjectReference((PetscObject)S_new);CHKERRQ(ierr);
2779           sub_schurs->sum_S_Ej_all = S_new;
2780           ierr = MatDestroy(&S_new);CHKERRQ(ierr);
2781         }
2782         ierr = MatDestroy(&tmat);CHKERRQ(ierr);
2783       }
2784     }
2785     ierr = MatDestroy(&localChangeOfBasisMatrix);CHKERRQ(ierr);
2786   } else if (pcbddc->user_ChangeOfBasisMatrix) {
2787     ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2788     pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
2789   }
2790 
2791   /* set up change of basis context */
2792   if (pcbddc->ChangeOfBasisMatrix) {
2793     PCBDDCChange_ctx change_ctx;
2794 
2795     if (!pcbddc->new_global_mat) {
2796       PetscInt global_size,local_size;
2797 
2798       ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
2799       ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
2800       ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->new_global_mat);CHKERRQ(ierr);
2801       ierr = MatSetSizes(pcbddc->new_global_mat,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
2802       ierr = MatSetType(pcbddc->new_global_mat,MATSHELL);CHKERRQ(ierr);
2803       ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT,(void (*)(void))PCBDDCMatMult_Private);CHKERRQ(ierr);
2804       ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCMatMultTranspose_Private);CHKERRQ(ierr);
2805       ierr = PetscNew(&change_ctx);CHKERRQ(ierr);
2806       ierr = MatShellSetContext(pcbddc->new_global_mat,change_ctx);CHKERRQ(ierr);
2807     } else {
2808       ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
2809       ierr = MatDestroy(&change_ctx->global_change);CHKERRQ(ierr);
2810       ierr = VecDestroyVecs(2,&change_ctx->work);CHKERRQ(ierr);
2811     }
2812     if (!pcbddc->user_ChangeOfBasisMatrix) {
2813       ierr = PetscObjectReference((PetscObject)pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2814       change_ctx->global_change = pcbddc->ChangeOfBasisMatrix;
2815     } else {
2816       ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2817       change_ctx->global_change = pcbddc->user_ChangeOfBasisMatrix;
2818     }
2819     ierr = VecDuplicateVecs(pcis->vec1_global,2,&change_ctx->work);CHKERRQ(ierr);
2820     ierr = MatSetUp(pcbddc->new_global_mat);CHKERRQ(ierr);
2821     ierr = MatAssemblyBegin(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2822     ierr = MatAssemblyEnd(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2823   }
2824 
2825   /* get indices in local ordering for vertices and constraints */
2826   if (olocal_primal_size == pcbddc->local_primal_size) { /* if this is true, I need to check if a new primal space has been introduced */
2827     ierr = PetscMalloc1(olocal_primal_size,&oprimal_indices_local_idxs);CHKERRQ(ierr);
2828     ierr = PetscMemcpy(oprimal_indices_local_idxs,pcbddc->primal_indices_local_idxs,olocal_primal_size*sizeof(PetscInt));CHKERRQ(ierr);
2829   }
2830   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2831   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2832   ierr = PetscMalloc1(pcbddc->local_primal_size,&pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2833   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&i,&aux_primal_numbering);CHKERRQ(ierr);
2834   ierr = PetscMemcpy(pcbddc->primal_indices_local_idxs,aux_primal_numbering,i*sizeof(PetscInt));CHKERRQ(ierr);
2835   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2836   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&j,&aux_primal_numbering);CHKERRQ(ierr);
2837   ierr = PetscMemcpy(&pcbddc->primal_indices_local_idxs[i],aux_primal_numbering,j*sizeof(PetscInt));CHKERRQ(ierr);
2838   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2839   /* set quantities in PCBDDC data struct */
2840   pcbddc->n_actual_vertices = i;
2841   /* check if a new primal space has been introduced */
2842   pcbddc->new_primal_space_local = PETSC_TRUE;
2843   if (olocal_primal_size == pcbddc->local_primal_size) {
2844     ierr = PetscMemcmp(pcbddc->primal_indices_local_idxs,oprimal_indices_local_idxs,olocal_primal_size,&pcbddc->new_primal_space_local);CHKERRQ(ierr);
2845     pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
2846     ierr = PetscFree(oprimal_indices_local_idxs);CHKERRQ(ierr);
2847   }
2848   /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
2849   ierr = MPI_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
2850 
2851   /* flush dbg viewer */
2852   if (pcbddc->dbg_flag) {
2853     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2854   }
2855 
2856   /* free workspace */
2857   ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2858   ierr = PetscBTDestroy(&qr_needed_idx);CHKERRQ(ierr);
2859   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
2860   ierr = PetscBTDestroy(&change_basis);CHKERRQ(ierr);
2861   if (!pcbddc->adaptive_selection) {
2862     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2863     ierr = PetscFree3(temp_quadrature_constraint,temp_indices_to_constraint,temp_indices_to_constraint_B);CHKERRQ(ierr);
2864   } else {
2865     ierr = PetscFree4(pcbddc->adaptive_constraints_n,
2866                       pcbddc->adaptive_constraints_ptrs,
2867                       pcbddc->adaptive_constraints_idxs,
2868                       pcbddc->adaptive_constraints_data);CHKERRQ(ierr);
2869     ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
2870   }
2871   PetscFunctionReturn(0);
2872 }
2873 
2874 #undef __FUNCT__
2875 #define __FUNCT__ "PCBDDCAnalyzeInterface"
2876 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
2877 {
2878   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
2879   PC_IS       *pcis = (PC_IS*)pc->data;
2880   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
2881   PetscInt    ierr,i,vertex_size;
2882   PetscViewer viewer=pcbddc->dbg_viewer;
2883 
2884   PetscFunctionBegin;
2885   /* Reset previously computed graph */
2886   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
2887   /* Init local Graph struct */
2888   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
2889 
2890   /* Check validity of the csr graph passed in by the user */
2891   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
2892     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
2893   }
2894 
2895   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
2896   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
2897     PetscInt  *xadj,*adjncy;
2898     PetscInt  nvtxs;
2899     PetscBool flg_row=PETSC_FALSE;
2900 
2901     if (pcbddc->use_local_adj) {
2902 
2903       ierr = MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);CHKERRQ(ierr);
2904       if (flg_row) {
2905         ierr = PCBDDCSetLocalAdjacencyGraph(pc,nvtxs,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
2906         pcbddc->computed_rowadj = PETSC_TRUE;
2907       }
2908       ierr = MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);CHKERRQ(ierr);
2909     } else if (pcbddc->current_level) { /* just compute subdomain's connected components for coarser levels */
2910       IS                     is_dummy;
2911       ISLocalToGlobalMapping l2gmap_dummy;
2912       PetscInt               j,sum;
2913       PetscInt               *cxadj,*cadjncy;
2914       const PetscInt         *idxs;
2915       PCBDDCGraph            graph;
2916       PetscBT                is_on_boundary;
2917 
2918       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n,0,1,&is_dummy);CHKERRQ(ierr);
2919       ierr = ISLocalToGlobalMappingCreateIS(is_dummy,&l2gmap_dummy);CHKERRQ(ierr);
2920       ierr = ISDestroy(&is_dummy);CHKERRQ(ierr);
2921       ierr = PCBDDCGraphCreate(&graph);CHKERRQ(ierr);
2922       ierr = PCBDDCGraphInit(graph,l2gmap_dummy);CHKERRQ(ierr);
2923       ierr = ISLocalToGlobalMappingDestroy(&l2gmap_dummy);CHKERRQ(ierr);
2924       ierr = MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);CHKERRQ(ierr);
2925       if (flg_row) {
2926         graph->xadj = xadj;
2927         graph->adjncy = adjncy;
2928       }
2929       ierr = PCBDDCGraphSetUp(graph,1,NULL,NULL,0,NULL,NULL);CHKERRQ(ierr);
2930       ierr = PCBDDCGraphComputeConnectedComponents(graph);CHKERRQ(ierr);
2931       ierr = MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);CHKERRQ(ierr);
2932 
2933       if (pcbddc->dbg_flag) {
2934         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"[%d] Found %d subdomains\n",PetscGlobalRank,graph->ncc);CHKERRQ(ierr);
2935         for (i=0;i<graph->ncc;i++) {
2936           ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"[%d] %d cc size %d\n",PetscGlobalRank,i,graph->cptr[i+1]-graph->cptr[i]);CHKERRQ(ierr);
2937         }
2938         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2939       }
2940 
2941       ierr = PetscBTCreate(pcis->n,&is_on_boundary);CHKERRQ(ierr);
2942       ierr = ISGetIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
2943       for (i=0;i<pcis->n_B;i++) {
2944         ierr = PetscBTSet(is_on_boundary,idxs[i]);CHKERRQ(ierr);
2945       }
2946       ierr = ISRestoreIndices(pcis->is_B_local,&idxs);CHKERRQ(ierr);
2947 
2948       ierr = PetscCalloc1(pcis->n+1,&cxadj);CHKERRQ(ierr);
2949       sum = 0;
2950       for (i=0;i<graph->ncc;i++) {
2951         PetscInt sizecc = 0;
2952         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
2953           if (PetscBTLookup(is_on_boundary,graph->queue[j])) {
2954             sizecc++;
2955           }
2956         }
2957         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
2958           if (PetscBTLookup(is_on_boundary,graph->queue[j])) {
2959             cxadj[graph->queue[j]] = sizecc;
2960           }
2961         }
2962         sum += sizecc*sizecc;
2963       }
2964       ierr = PetscMalloc1(sum,&cadjncy);CHKERRQ(ierr);
2965       sum = 0;
2966       for (i=0;i<pcis->n;i++) {
2967         PetscInt temp = cxadj[i];
2968         cxadj[i] = sum;
2969         sum += temp;
2970       }
2971       cxadj[pcis->n] = sum;
2972       for (i=0;i<graph->ncc;i++) {
2973         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
2974           if (PetscBTLookup(is_on_boundary,graph->queue[j])) {
2975             PetscInt k,sizecc = 0;
2976             for (k=graph->cptr[i];k<graph->cptr[i+1];k++) {
2977               if (PetscBTLookup(is_on_boundary,graph->queue[k])) {
2978                 cadjncy[cxadj[graph->queue[j]]+sizecc]=graph->queue[k];
2979                 sizecc++;
2980               }
2981             }
2982           }
2983         }
2984       }
2985       if (pcis->n) {
2986         ierr = PCBDDCSetLocalAdjacencyGraph(pc,pcis->n,cxadj,cadjncy,PETSC_OWN_POINTER);CHKERRQ(ierr);
2987       } else {
2988         ierr = PetscFree(cxadj);CHKERRQ(ierr);
2989         ierr = PetscFree(cadjncy);CHKERRQ(ierr);
2990       }
2991       graph->xadj = 0;
2992       graph->adjncy = 0;
2993       ierr = PCBDDCGraphDestroy(&graph);CHKERRQ(ierr);
2994       ierr = PetscBTDestroy(&is_on_boundary);CHKERRQ(ierr);
2995     }
2996   }
2997 
2998   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
2999   vertex_size = 1;
3000   if (pcbddc->user_provided_isfordofs) {
3001     if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
3002       ierr = PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
3003       for (i=0;i<pcbddc->n_ISForDofs;i++) {
3004         ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
3005         ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
3006       }
3007       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
3008       pcbddc->n_ISForDofs = 0;
3009       ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
3010     }
3011     /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
3012     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
3013   } else {
3014     if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
3015       ierr = MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);CHKERRQ(ierr);
3016       ierr = PetscMalloc1(pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
3017       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
3018         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
3019       }
3020     }
3021   }
3022 
3023   /* Setup of Graph */
3024   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
3025     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
3026   }
3027   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
3028     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
3029   }
3030   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices);CHKERRQ(ierr);
3031 
3032   /* Graph's connected components analysis */
3033   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
3034 
3035   /* print some info to stdout */
3036   if (pcbddc->dbg_flag) {
3037     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);CHKERRQ(ierr);
3038   }
3039 
3040   /* mark topography has done */
3041   pcbddc->recompute_topography = PETSC_FALSE;
3042   PetscFunctionReturn(0);
3043 }
3044 
3045 #undef __FUNCT__
3046 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
3047 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt **vertices_idx)
3048 {
3049   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
3050   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
3051   PetscErrorCode ierr;
3052 
3053   PetscFunctionBegin;
3054   n = 0;
3055   vertices = 0;
3056   if (pcbddc->ConstraintMatrix) {
3057     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
3058     for (i=0;i<local_primal_size;i++) {
3059       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
3060       if (size_of_constraint == 1) n++;
3061       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
3062     }
3063     if (vertices_idx) {
3064       ierr = PetscMalloc1(n,&vertices);CHKERRQ(ierr);
3065       n = 0;
3066       for (i=0;i<local_primal_size;i++) {
3067         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
3068         if (size_of_constraint == 1) {
3069           vertices[n++]=row_cmat_indices[0];
3070         }
3071         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
3072       }
3073     }
3074   }
3075   *n_vertices = n;
3076   if (vertices_idx) *vertices_idx = vertices;
3077   PetscFunctionReturn(0);
3078 }
3079 
3080 #undef __FUNCT__
3081 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
3082 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt **constraints_idx)
3083 {
3084   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
3085   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
3086   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
3087   PetscBT        touched;
3088   PetscErrorCode ierr;
3089 
3090     /* This function assumes that the number of local constraints per connected component
3091        is not greater than the number of nodes defined for the connected component
3092        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
3093   PetscFunctionBegin;
3094   n = 0;
3095   constraints_index = 0;
3096   if (pcbddc->ConstraintMatrix) {
3097     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
3098     max_size_of_constraint = 0;
3099     for (i=0;i<local_primal_size;i++) {
3100       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
3101       if (size_of_constraint > 1) {
3102         n++;
3103       }
3104       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
3105       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
3106     }
3107     if (constraints_idx) {
3108       ierr = PetscMalloc1(n,&constraints_index);CHKERRQ(ierr);
3109       ierr = PetscMalloc1(max_size_of_constraint,&row_cmat_global_indices);CHKERRQ(ierr);
3110       ierr = PetscBTCreate(local_size,&touched);CHKERRQ(ierr);
3111       n = 0;
3112       for (i=0;i<local_primal_size;i++) {
3113         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
3114         if (size_of_constraint > 1) {
3115           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
3116           /* find first untouched local node */
3117           j = 0;
3118           while (PetscBTLookup(touched,row_cmat_indices[j])) j++;
3119           min_index = row_cmat_global_indices[j];
3120           min_loc = j;
3121           /* search the minimum among nodes not yet touched on the connected component
3122              since there can be more than one constraint on a single cc */
3123           for (j=1;j<size_of_constraint;j++) {
3124             if (!PetscBTLookup(touched,row_cmat_indices[j]) && min_index > row_cmat_global_indices[j]) {
3125               min_index = row_cmat_global_indices[j];
3126               min_loc = j;
3127             }
3128           }
3129           ierr = PetscBTSet(touched,row_cmat_indices[min_loc]);CHKERRQ(ierr);
3130           constraints_index[n++] = row_cmat_indices[min_loc];
3131         }
3132         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
3133       }
3134       ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
3135       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
3136     }
3137   }
3138   *n_constraints = n;
3139   if (constraints_idx) *constraints_idx = constraints_index;
3140   PetscFunctionReturn(0);
3141 }
3142 
3143 #undef __FUNCT__
3144 #define __FUNCT__ "PCBDDCSubsetNumbering"
3145 PetscErrorCode PCBDDCSubsetNumbering(MPI_Comm comm,ISLocalToGlobalMapping l2gmap, PetscInt n_local_dofs, PetscInt local_dofs[], PetscInt local_dofs_mult[], PetscInt* n_global_subset, PetscInt* global_numbering_subset[])
3146 {
3147   Vec            local_vec,global_vec;
3148   IS             seqis,paris;
3149   VecScatter     scatter_ctx;
3150   PetscScalar    *array;
3151   PetscInt       *temp_global_dofs;
3152   PetscScalar    globalsum;
3153   PetscInt       i,j,s;
3154   PetscInt       nlocals,first_index,old_index,max_local,max_global;
3155   PetscMPIInt    rank_prec_comm,size_prec_comm;
3156   PetscInt       *dof_sizes,*dof_displs;
3157   PetscBool      first_found;
3158   PetscErrorCode ierr;
3159 
3160   PetscFunctionBegin;
3161   /* mpi buffers */
3162   ierr = MPI_Comm_size(comm,&size_prec_comm);CHKERRQ(ierr);
3163   ierr = MPI_Comm_rank(comm,&rank_prec_comm);CHKERRQ(ierr);
3164   j = ( !rank_prec_comm ? size_prec_comm : 0);
3165   ierr = PetscMalloc2(j,&dof_sizes,j,&dof_displs);CHKERRQ(ierr);
3166   /* get maximum size of subset */
3167   ierr = PetscMalloc1(n_local_dofs,&temp_global_dofs);CHKERRQ(ierr);
3168   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
3169   max_local = 0;
3170   for (i=0;i<n_local_dofs;i++) {
3171     if (max_local < temp_global_dofs[i] ) {
3172       max_local = temp_global_dofs[i];
3173     }
3174   }
3175   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
3176   max_global++;
3177   max_local = 0;
3178   for (i=0;i<n_local_dofs;i++) {
3179     if (max_local < local_dofs[i] ) {
3180       max_local = local_dofs[i];
3181     }
3182   }
3183   max_local++;
3184   /* allocate workspace */
3185   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
3186   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
3187   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
3188   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
3189   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
3190   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
3191   /* create scatter */
3192   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
3193   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
3194   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
3195   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
3196   ierr = ISDestroy(&paris);CHKERRQ(ierr);
3197   /* init array */
3198   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
3199   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
3200   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
3201   if (local_dofs_mult) {
3202     for (i=0;i<n_local_dofs;i++) {
3203       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
3204     }
3205   } else {
3206     for (i=0;i<n_local_dofs;i++) {
3207       array[local_dofs[i]]=1.0;
3208     }
3209   }
3210   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
3211   /* scatter into global vec and get total number of global dofs */
3212   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3213   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3214   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
3215   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
3216   /* Fill global_vec with cumulative function for global numbering */
3217   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
3218   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
3219   nlocals = 0;
3220   first_index = -1;
3221   first_found = PETSC_FALSE;
3222   for (i=0;i<s;i++) {
3223     if (!first_found && PetscRealPart(array[i]) > 0.1) {
3224       first_found = PETSC_TRUE;
3225       first_index = i;
3226     }
3227     nlocals += (PetscInt)PetscRealPart(array[i]);
3228   }
3229   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
3230   if (!rank_prec_comm) {
3231     dof_displs[0]=0;
3232     for (i=1;i<size_prec_comm;i++) {
3233       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
3234     }
3235   }
3236   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
3237   if (first_found) {
3238     array[first_index] += (PetscScalar)nlocals;
3239     old_index = first_index;
3240     for (i=first_index+1;i<s;i++) {
3241       if (PetscRealPart(array[i]) > 0.1) {
3242         array[i] += array[old_index];
3243         old_index = i;
3244       }
3245     }
3246   }
3247   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
3248   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
3249   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3250   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3251   /* get global ordering of local dofs */
3252   ierr = VecGetArrayRead(local_vec,(const PetscScalar**)&array);CHKERRQ(ierr);
3253   if (local_dofs_mult) {
3254     for (i=0;i<n_local_dofs;i++) {
3255       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
3256     }
3257   } else {
3258     for (i=0;i<n_local_dofs;i++) {
3259       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
3260     }
3261   }
3262   ierr = VecRestoreArrayRead(local_vec,(const PetscScalar**)&array);CHKERRQ(ierr);
3263   /* free workspace */
3264   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
3265   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
3266   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
3267   ierr = PetscFree2(dof_sizes,dof_displs);CHKERRQ(ierr);
3268   /* return pointer to global ordering of local dofs */
3269   *global_numbering_subset = temp_global_dofs;
3270   PetscFunctionReturn(0);
3271 }
3272 
3273 #undef __FUNCT__
3274 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
3275 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
3276 {
3277   PetscInt       i,j;
3278   PetscScalar    *alphas;
3279   PetscErrorCode ierr;
3280 
3281   PetscFunctionBegin;
3282   /* this implements stabilized Gram-Schmidt */
3283   ierr = PetscMalloc1(n,&alphas);CHKERRQ(ierr);
3284   for (i=0;i<n;i++) {
3285     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
3286     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
3287     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
3288   }
3289   ierr = PetscFree(alphas);CHKERRQ(ierr);
3290   PetscFunctionReturn(0);
3291 }
3292 
3293 #undef __FUNCT__
3294 #define __FUNCT__ "MatISGetSubassemblingPattern"
3295 PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscBool contiguous, IS* is_sends)
3296 {
3297   Mat             subdomain_adj;
3298   IS              new_ranks,ranks_send_to;
3299   MatPartitioning partitioner;
3300   Mat_IS          *matis;
3301   PetscInt        n_neighs,*neighs,*n_shared,**shared;
3302   PetscInt        prank;
3303   PetscMPIInt     size,rank,color;
3304   PetscInt        *xadj,*adjncy,*oldranks;
3305   PetscInt        *adjncy_wgt,*v_wgt,*is_indices,*ranks_send_to_idx;
3306   PetscInt        i,local_size,threshold=0;
3307   PetscErrorCode  ierr;
3308   PetscBool       use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
3309   PetscSubcomm    subcomm;
3310 
3311   PetscFunctionBegin;
3312   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_square",&use_square,NULL);CHKERRQ(ierr);
3313   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);CHKERRQ(ierr);
3314   ierr = PetscOptionsGetInt(NULL,"-matis_partitioning_threshold",&threshold,NULL);CHKERRQ(ierr);
3315 
3316   /* Get info on mapping */
3317   matis = (Mat_IS*)(mat->data);
3318   ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&local_size);CHKERRQ(ierr);
3319   ierr = ISLocalToGlobalMappingGetInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
3320 
3321   /* build local CSR graph of subdomains' connectivity */
3322   ierr = PetscMalloc1(2,&xadj);CHKERRQ(ierr);
3323   xadj[0] = 0;
3324   xadj[1] = PetscMax(n_neighs-1,0);
3325   ierr = PetscMalloc1(xadj[1],&adjncy);CHKERRQ(ierr);
3326   ierr = PetscMalloc1(xadj[1],&adjncy_wgt);CHKERRQ(ierr);
3327 
3328   if (threshold) {
3329     PetscInt xadj_count = 0;
3330     for (i=1;i<n_neighs;i++) {
3331       if (n_shared[i] > threshold) {
3332         adjncy[xadj_count] = neighs[i];
3333         adjncy_wgt[xadj_count] = n_shared[i];
3334         xadj_count++;
3335       }
3336     }
3337     xadj[1] = xadj_count;
3338   } else {
3339     if (xadj[1]) {
3340       ierr = PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));CHKERRQ(ierr);
3341       ierr = PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));CHKERRQ(ierr);
3342     }
3343   }
3344   ierr = ISLocalToGlobalMappingRestoreInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
3345   if (use_square) {
3346     for (i=0;i<xadj[1];i++) {
3347       adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
3348     }
3349   }
3350   ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
3351 
3352   ierr = PetscMalloc1(1,&ranks_send_to_idx);CHKERRQ(ierr);
3353 
3354   /*
3355     Restrict work on active processes only.
3356   */
3357   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);CHKERRQ(ierr);
3358   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr); /* 2 groups, active process and not active processes */
3359   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
3360   ierr = PetscMPIIntCast(!local_size,&color);CHKERRQ(ierr);
3361   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
3362   if (color) {
3363     ierr = PetscFree(xadj);CHKERRQ(ierr);
3364     ierr = PetscFree(adjncy);CHKERRQ(ierr);
3365     ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
3366   } else {
3367     PetscInt coarsening_ratio;
3368     ierr = MPI_Comm_size(PetscSubcommChild(subcomm),&size);CHKERRQ(ierr);
3369     ierr = PetscMalloc1(size,&oldranks);CHKERRQ(ierr);
3370     prank = rank;
3371     ierr = MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,PetscSubcommChild(subcomm));CHKERRQ(ierr);
3372     /*
3373     for (i=0;i<size;i++) {
3374       PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
3375     }
3376     */
3377     for (i=0;i<xadj[1];i++) {
3378       ierr = PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);CHKERRQ(ierr);
3379     }
3380     ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
3381     ierr = MatCreateMPIAdj(PetscSubcommChild(subcomm),1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);CHKERRQ(ierr);
3382     /* ierr = MatView(subdomain_adj,0);CHKERRQ(ierr); */
3383 
3384     /* Partition */
3385     ierr = MatPartitioningCreate(PetscSubcommChild(subcomm),&partitioner);CHKERRQ(ierr);
3386     ierr = MatPartitioningSetAdjacency(partitioner,subdomain_adj);CHKERRQ(ierr);
3387     if (use_vwgt) {
3388       ierr = PetscMalloc1(1,&v_wgt);CHKERRQ(ierr);
3389       v_wgt[0] = local_size;
3390       ierr = MatPartitioningSetVertexWeights(partitioner,v_wgt);CHKERRQ(ierr);
3391     }
3392     n_subdomains = PetscMin((PetscInt)size,n_subdomains);
3393     coarsening_ratio = size/n_subdomains;
3394     ierr = MatPartitioningSetNParts(partitioner,n_subdomains);CHKERRQ(ierr);
3395     ierr = MatPartitioningSetFromOptions(partitioner);CHKERRQ(ierr);
3396     ierr = MatPartitioningApply(partitioner,&new_ranks);CHKERRQ(ierr);
3397     /* ierr = MatPartitioningView(partitioner,0);CHKERRQ(ierr); */
3398 
3399     ierr = ISGetIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
3400     if (contiguous) {
3401       ranks_send_to_idx[0] = oldranks[is_indices[0]]; /* contiguos set of processes */
3402     } else {
3403       ranks_send_to_idx[0] = coarsening_ratio*oldranks[is_indices[0]]; /* scattered set of processes */
3404     }
3405     ierr = ISRestoreIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
3406     /* clean up */
3407     ierr = PetscFree(oldranks);CHKERRQ(ierr);
3408     ierr = ISDestroy(&new_ranks);CHKERRQ(ierr);
3409     ierr = MatDestroy(&subdomain_adj);CHKERRQ(ierr);
3410     ierr = MatPartitioningDestroy(&partitioner);CHKERRQ(ierr);
3411   }
3412   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
3413 
3414   /* assemble parallel IS for sends */
3415   i = 1;
3416   if (color) i=0;
3417   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);CHKERRQ(ierr);
3418 
3419   /* get back IS */
3420   *is_sends = ranks_send_to;
3421   PetscFunctionReturn(0);
3422 }
3423 
3424 typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;
3425 
3426 #undef __FUNCT__
3427 #define __FUNCT__ "MatISSubassemble"
3428 PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
3429 {
3430   Mat                    local_mat;
3431   Mat_IS                 *matis;
3432   IS                     is_sends_internal;
3433   PetscInt               rows,cols,new_local_rows;
3434   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
3435   PetscBool              ismatis,isdense,newisdense,destroy_mat;
3436   ISLocalToGlobalMapping l2gmap;
3437   PetscInt*              l2gmap_indices;
3438   const PetscInt*        is_indices;
3439   MatType                new_local_type;
3440   /* buffers */
3441   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
3442   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
3443   PetscInt               *recv_buffer_idxs_local;
3444   PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
3445   /* MPI */
3446   MPI_Comm               comm,comm_n;
3447   PetscSubcomm           subcomm;
3448   PetscMPIInt            n_sends,n_recvs,commsize;
3449   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
3450   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
3451   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
3452   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
3453   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
3454   PetscErrorCode         ierr;
3455 
3456   PetscFunctionBegin;
3457   /* TODO: add missing checks */
3458   PetscValidLogicalCollectiveInt(mat,n_subdomains,3);
3459   PetscValidLogicalCollectiveBool(mat,restrict_comm,4);
3460   PetscValidLogicalCollectiveEnum(mat,reuse,5);
3461   PetscValidLogicalCollectiveInt(mat,nis,7);
3462   ierr = PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);CHKERRQ(ierr);
3463   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
3464   ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
3465   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);CHKERRQ(ierr);
3466   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
3467   ierr = MatGetSize(local_mat,&rows,&cols);CHKERRQ(ierr);
3468   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
3469   if (reuse == MAT_REUSE_MATRIX && *mat_n) {
3470     PetscInt mrows,mcols,mnrows,mncols;
3471     ierr = PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);CHKERRQ(ierr);
3472     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
3473     ierr = MatGetSize(mat,&mrows,&mcols);CHKERRQ(ierr);
3474     ierr = MatGetSize(*mat_n,&mnrows,&mncols);CHKERRQ(ierr);
3475     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
3476     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
3477   }
3478   ierr = MatGetBlockSize(local_mat,&bs);CHKERRQ(ierr);
3479   PetscValidLogicalCollectiveInt(mat,bs,0);
3480   /* prepare IS for sending if not provided */
3481   if (!is_sends) {
3482     PetscBool pcontig = PETSC_TRUE;
3483     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
3484     ierr = MatISGetSubassemblingPattern(mat,n_subdomains,pcontig,&is_sends_internal);CHKERRQ(ierr);
3485   } else {
3486     ierr = PetscObjectReference((PetscObject)is_sends);CHKERRQ(ierr);
3487     is_sends_internal = is_sends;
3488   }
3489 
3490   /* get pointer of MATIS data */
3491   matis = (Mat_IS*)mat->data;
3492 
3493   /* get comm */
3494   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3495 
3496   /* compute number of sends */
3497   ierr = ISGetLocalSize(is_sends_internal,&i);CHKERRQ(ierr);
3498   ierr = PetscMPIIntCast(i,&n_sends);CHKERRQ(ierr);
3499 
3500   /* compute number of receives */
3501   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
3502   ierr = PetscMalloc1(commsize,&iflags);CHKERRQ(ierr);
3503   ierr = PetscMemzero(iflags,commsize*sizeof(*iflags));CHKERRQ(ierr);
3504   ierr = ISGetIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
3505   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
3506   ierr = PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);CHKERRQ(ierr);
3507   ierr = PetscFree(iflags);CHKERRQ(ierr);
3508 
3509   /* restrict comm if requested */
3510   subcomm = 0;
3511   destroy_mat = PETSC_FALSE;
3512   if (restrict_comm) {
3513     PetscMPIInt color,subcommsize;
3514 
3515     color = 0;
3516     if (!n_recvs) color = 1; /* processes not receiving anything will not partecipate in new comm */
3517     ierr = MPI_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3518     subcommsize = commsize - subcommsize;
3519     /* check if reuse has been requested */
3520     if (reuse == MAT_REUSE_MATRIX) {
3521       if (*mat_n) {
3522         PetscMPIInt subcommsize2;
3523         ierr = MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);CHKERRQ(ierr);
3524         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
3525         comm_n = PetscObjectComm((PetscObject)*mat_n);
3526       } else {
3527         comm_n = PETSC_COMM_SELF;
3528       }
3529     } else { /* MAT_INITIAL_MATRIX */
3530       PetscMPIInt rank;
3531 
3532       ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3533       ierr = PetscSubcommCreate(comm,&subcomm);CHKERRQ(ierr);
3534       ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
3535       ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
3536       comm_n = PetscSubcommChild(subcomm);
3537     }
3538     /* flag to destroy *mat_n if not significative */
3539     if (color) destroy_mat = PETSC_TRUE;
3540   } else {
3541     comm_n = comm;
3542   }
3543 
3544   /* prepare send/receive buffers */
3545   ierr = PetscMalloc1(commsize,&ilengths_idxs);CHKERRQ(ierr);
3546   ierr = PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));CHKERRQ(ierr);
3547   ierr = PetscMalloc1(commsize,&ilengths_vals);CHKERRQ(ierr);
3548   ierr = PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));CHKERRQ(ierr);
3549   if (nis) {
3550     ierr = PetscCalloc1(commsize,&ilengths_idxs_is);CHKERRQ(ierr);
3551   }
3552 
3553   /* Get data from local matrices */
3554   if (!isdense) {
3555     SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Subassembling of AIJ local matrices not yet implemented");
3556     /* TODO: See below some guidelines on how to prepare the local buffers */
3557     /*
3558        send_buffer_vals should contain the raw values of the local matrix
3559        send_buffer_idxs should contain:
3560        - MatType_PRIVATE type
3561        - PetscInt        size_of_l2gmap
3562        - PetscInt        global_row_indices[size_of_l2gmap]
3563        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
3564     */
3565   } else {
3566     ierr = MatDenseGetArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3567     ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&i);CHKERRQ(ierr);
3568     ierr = PetscMalloc1(i+2,&send_buffer_idxs);CHKERRQ(ierr);
3569     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
3570     send_buffer_idxs[1] = i;
3571     ierr = ISLocalToGlobalMappingGetIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
3572     ierr = PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));CHKERRQ(ierr);
3573     ierr = ISLocalToGlobalMappingRestoreIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
3574     ierr = PetscMPIIntCast(i,&len);CHKERRQ(ierr);
3575     for (i=0;i<n_sends;i++) {
3576       ilengths_vals[is_indices[i]] = len*len;
3577       ilengths_idxs[is_indices[i]] = len+2;
3578     }
3579   }
3580   ierr = PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);CHKERRQ(ierr);
3581   /* additional is (if any) */
3582   if (nis) {
3583     PetscMPIInt psum;
3584     PetscInt j;
3585     for (j=0,psum=0;j<nis;j++) {
3586       PetscInt plen;
3587       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
3588       ierr = PetscMPIIntCast(plen,&len);CHKERRQ(ierr);
3589       psum += len+1; /* indices + lenght */
3590     }
3591     ierr = PetscMalloc1(psum,&send_buffer_idxs_is);CHKERRQ(ierr);
3592     for (j=0,psum=0;j<nis;j++) {
3593       PetscInt plen;
3594       const PetscInt *is_array_idxs;
3595       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
3596       send_buffer_idxs_is[psum] = plen;
3597       ierr = ISGetIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
3598       ierr = PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));CHKERRQ(ierr);
3599       ierr = ISRestoreIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
3600       psum += plen+1; /* indices + lenght */
3601     }
3602     for (i=0;i<n_sends;i++) {
3603       ilengths_idxs_is[is_indices[i]] = psum;
3604     }
3605     ierr = PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);CHKERRQ(ierr);
3606   }
3607 
3608   buf_size_idxs = 0;
3609   buf_size_vals = 0;
3610   buf_size_idxs_is = 0;
3611   for (i=0;i<n_recvs;i++) {
3612     buf_size_idxs += (PetscInt)olengths_idxs[i];
3613     buf_size_vals += (PetscInt)olengths_vals[i];
3614     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
3615   }
3616   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);CHKERRQ(ierr);
3617   ierr = PetscMalloc1(buf_size_vals,&recv_buffer_vals);CHKERRQ(ierr);
3618   ierr = PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);CHKERRQ(ierr);
3619 
3620   /* get new tags for clean communications */
3621   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);CHKERRQ(ierr);
3622   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_vals);CHKERRQ(ierr);
3623   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);CHKERRQ(ierr);
3624 
3625   /* allocate for requests */
3626   ierr = PetscMalloc1(n_sends,&send_req_idxs);CHKERRQ(ierr);
3627   ierr = PetscMalloc1(n_sends,&send_req_vals);CHKERRQ(ierr);
3628   ierr = PetscMalloc1(n_sends,&send_req_idxs_is);CHKERRQ(ierr);
3629   ierr = PetscMalloc1(n_recvs,&recv_req_idxs);CHKERRQ(ierr);
3630   ierr = PetscMalloc1(n_recvs,&recv_req_vals);CHKERRQ(ierr);
3631   ierr = PetscMalloc1(n_recvs,&recv_req_idxs_is);CHKERRQ(ierr);
3632 
3633   /* communications */
3634   ptr_idxs = recv_buffer_idxs;
3635   ptr_vals = recv_buffer_vals;
3636   ptr_idxs_is = recv_buffer_idxs_is;
3637   for (i=0;i<n_recvs;i++) {
3638     source_dest = onodes[i];
3639     ierr = MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);CHKERRQ(ierr);
3640     ierr = MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);CHKERRQ(ierr);
3641     ptr_idxs += olengths_idxs[i];
3642     ptr_vals += olengths_vals[i];
3643     if (nis) {
3644       ierr = MPI_Irecv(ptr_idxs_is,olengths_idxs_is[i],MPIU_INT,source_dest,tag_idxs_is,comm,&recv_req_idxs_is[i]);CHKERRQ(ierr);
3645       ptr_idxs_is += olengths_idxs_is[i];
3646     }
3647   }
3648   for (i=0;i<n_sends;i++) {
3649     ierr = PetscMPIIntCast(is_indices[i],&source_dest);CHKERRQ(ierr);
3650     ierr = MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);CHKERRQ(ierr);
3651     ierr = MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);CHKERRQ(ierr);
3652     if (nis) {
3653       ierr = MPI_Isend(send_buffer_idxs_is,ilengths_idxs_is[source_dest],MPIU_INT,source_dest,tag_idxs_is,comm,&send_req_idxs_is[i]);CHKERRQ(ierr);
3654     }
3655   }
3656   ierr = ISRestoreIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
3657   ierr = ISDestroy(&is_sends_internal);CHKERRQ(ierr);
3658 
3659   /* assemble new l2g map */
3660   ierr = MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3661   ptr_idxs = recv_buffer_idxs;
3662   new_local_rows = 0;
3663   for (i=0;i<n_recvs;i++) {
3664     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3665     ptr_idxs += olengths_idxs[i];
3666   }
3667   ierr = PetscMalloc1(new_local_rows,&l2gmap_indices);CHKERRQ(ierr);
3668   ptr_idxs = recv_buffer_idxs;
3669   new_local_rows = 0;
3670   for (i=0;i<n_recvs;i++) {
3671     ierr = PetscMemcpy(&l2gmap_indices[new_local_rows],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));CHKERRQ(ierr);
3672     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3673     ptr_idxs += olengths_idxs[i];
3674   }
3675   ierr = PetscSortRemoveDupsInt(&new_local_rows,l2gmap_indices);CHKERRQ(ierr);
3676   ierr = ISLocalToGlobalMappingCreate(comm_n,1,new_local_rows,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);CHKERRQ(ierr);
3677   ierr = PetscFree(l2gmap_indices);CHKERRQ(ierr);
3678 
3679   /* infer new local matrix type from received local matrices type */
3680   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
3681   /* it also assumes that if the block size is set, than it is the same among all local matrices (see checks at the beginning of the function) */
3682   if (n_recvs) {
3683     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
3684     ptr_idxs = recv_buffer_idxs;
3685     for (i=0;i<n_recvs;i++) {
3686       if ((PetscInt)new_local_type_private != *ptr_idxs) {
3687         new_local_type_private = MATAIJ_PRIVATE;
3688         break;
3689       }
3690       ptr_idxs += olengths_idxs[i];
3691     }
3692     switch (new_local_type_private) {
3693       case MATDENSE_PRIVATE:
3694         if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
3695           new_local_type = MATSEQAIJ;
3696           bs = 1;
3697         } else { /* if I receive only 1 dense matrix */
3698           new_local_type = MATSEQDENSE;
3699           bs = 1;
3700         }
3701         break;
3702       case MATAIJ_PRIVATE:
3703         new_local_type = MATSEQAIJ;
3704         bs = 1;
3705         break;
3706       case MATBAIJ_PRIVATE:
3707         new_local_type = MATSEQBAIJ;
3708         break;
3709       case MATSBAIJ_PRIVATE:
3710         new_local_type = MATSEQSBAIJ;
3711         break;
3712       default:
3713         SETERRQ2(comm,PETSC_ERR_SUP,"Unsupported private type %d in %s",new_local_type_private,__FUNCT__);
3714         break;
3715     }
3716   } else { /* by default, new_local_type is seqdense */
3717     new_local_type = MATSEQDENSE;
3718     bs = 1;
3719   }
3720 
3721   /* create MATIS object if needed */
3722   if (reuse == MAT_INITIAL_MATRIX) {
3723     ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
3724     ierr = MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,mat_n);CHKERRQ(ierr);
3725   } else {
3726     /* it also destroys the local matrices */
3727     ierr = MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);CHKERRQ(ierr);
3728   }
3729   ierr = MatISGetLocalMat(*mat_n,&local_mat);CHKERRQ(ierr);
3730   ierr = MatSetType(local_mat,new_local_type);CHKERRQ(ierr);
3731 
3732   ierr = MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3733 
3734   /* Global to local map of received indices */
3735   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs_local);CHKERRQ(ierr); /* needed for values insertion */
3736   ierr = ISGlobalToLocalMappingApply(l2gmap,IS_GTOLM_MASK,buf_size_idxs,recv_buffer_idxs,&i,recv_buffer_idxs_local);CHKERRQ(ierr);
3737   ierr = ISLocalToGlobalMappingDestroy(&l2gmap);CHKERRQ(ierr);
3738 
3739   /* restore attributes -> type of incoming data and its size */
3740   buf_size_idxs = 0;
3741   for (i=0;i<n_recvs;i++) {
3742     recv_buffer_idxs_local[buf_size_idxs] = recv_buffer_idxs[buf_size_idxs];
3743     recv_buffer_idxs_local[buf_size_idxs+1] = recv_buffer_idxs[buf_size_idxs+1];
3744     buf_size_idxs += (PetscInt)olengths_idxs[i];
3745   }
3746   ierr = PetscFree(recv_buffer_idxs);CHKERRQ(ierr);
3747 
3748   /* set preallocation */
3749   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&newisdense);CHKERRQ(ierr);
3750   if (!newisdense) {
3751     PetscInt *new_local_nnz=0;
3752 
3753     ptr_vals = recv_buffer_vals;
3754     ptr_idxs = recv_buffer_idxs_local;
3755     if (n_recvs) {
3756       ierr = PetscCalloc1(new_local_rows,&new_local_nnz);CHKERRQ(ierr);
3757     }
3758     for (i=0;i<n_recvs;i++) {
3759       PetscInt j;
3760       if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
3761         for (j=0;j<*(ptr_idxs+1);j++) {
3762           new_local_nnz[*(ptr_idxs+2+j)] += *(ptr_idxs+1);
3763         }
3764       } else {
3765         /* TODO */
3766       }
3767       ptr_idxs += olengths_idxs[i];
3768     }
3769     if (new_local_nnz) {
3770       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMin(new_local_nnz[i],new_local_rows);
3771       ierr = MatSeqAIJSetPreallocation(local_mat,0,new_local_nnz);CHKERRQ(ierr);
3772       for (i=0;i<new_local_rows;i++) new_local_nnz[i] /= bs;
3773       ierr = MatSeqBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);CHKERRQ(ierr);
3774       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMax(new_local_nnz[i]-i,0);
3775       ierr = MatSeqSBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);CHKERRQ(ierr);
3776     } else {
3777       ierr = MatSetUp(local_mat);CHKERRQ(ierr);
3778     }
3779     ierr = PetscFree(new_local_nnz);CHKERRQ(ierr);
3780   } else {
3781     ierr = MatSetUp(local_mat);CHKERRQ(ierr);
3782   }
3783 
3784   /* set values */
3785   ptr_vals = recv_buffer_vals;
3786   ptr_idxs = recv_buffer_idxs_local;
3787   for (i=0;i<n_recvs;i++) {
3788     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
3789       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
3790       ierr = MatSetValues(local_mat,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);CHKERRQ(ierr);
3791       ierr = MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3792       ierr = MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3793       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
3794     } else {
3795       /* TODO */
3796     }
3797     ptr_idxs += olengths_idxs[i];
3798     ptr_vals += olengths_vals[i];
3799   }
3800   ierr = MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3801   ierr = MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3802   ierr = MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3803   ierr = MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3804   ierr = PetscFree(recv_buffer_vals);CHKERRQ(ierr);
3805   ierr = PetscFree(recv_buffer_idxs_local);CHKERRQ(ierr);
3806 
3807 #if 0
3808   if (!restrict_comm) { /* check */
3809     Vec       lvec,rvec;
3810     PetscReal infty_error;
3811 
3812     ierr = MatCreateVecs(mat,&rvec,&lvec);CHKERRQ(ierr);
3813     ierr = VecSetRandom(rvec,NULL);CHKERRQ(ierr);
3814     ierr = MatMult(mat,rvec,lvec);CHKERRQ(ierr);
3815     ierr = VecScale(lvec,-1.0);CHKERRQ(ierr);
3816     ierr = MatMultAdd(*mat_n,rvec,lvec,lvec);CHKERRQ(ierr);
3817     ierr = VecNorm(lvec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3818     ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
3819     ierr = VecDestroy(&rvec);CHKERRQ(ierr);
3820     ierr = VecDestroy(&lvec);CHKERRQ(ierr);
3821   }
3822 #endif
3823 
3824   /* assemble new additional is (if any) */
3825   if (nis) {
3826     PetscInt **temp_idxs,*count_is,j,psum;
3827 
3828     ierr = MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3829     ierr = PetscCalloc1(nis,&count_is);CHKERRQ(ierr);
3830     ptr_idxs = recv_buffer_idxs_is;
3831     psum = 0;
3832     for (i=0;i<n_recvs;i++) {
3833       for (j=0;j<nis;j++) {
3834         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3835         count_is[j] += plen; /* increment counting of buffer for j-th IS */
3836         psum += plen;
3837         ptr_idxs += plen+1; /* shift pointer to received data */
3838       }
3839     }
3840     ierr = PetscMalloc1(nis,&temp_idxs);CHKERRQ(ierr);
3841     ierr = PetscMalloc1(psum,&temp_idxs[0]);CHKERRQ(ierr);
3842     for (i=1;i<nis;i++) {
3843       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
3844     }
3845     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3846     ptr_idxs = recv_buffer_idxs_is;
3847     for (i=0;i<n_recvs;i++) {
3848       for (j=0;j<nis;j++) {
3849         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3850         ierr = PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));CHKERRQ(ierr);
3851         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
3852         ptr_idxs += plen+1; /* shift pointer to received data */
3853       }
3854     }
3855     for (i=0;i<nis;i++) {
3856       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3857       ierr = PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);CHKERRQ(ierr);CHKERRQ(ierr);
3858       ierr = ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3859     }
3860     ierr = PetscFree(count_is);CHKERRQ(ierr);
3861     ierr = PetscFree(temp_idxs[0]);CHKERRQ(ierr);
3862     ierr = PetscFree(temp_idxs);CHKERRQ(ierr);
3863   }
3864   /* free workspace */
3865   ierr = PetscFree(recv_buffer_idxs_is);CHKERRQ(ierr);
3866   ierr = MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3867   ierr = PetscFree(send_buffer_idxs);CHKERRQ(ierr);
3868   ierr = MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3869   if (isdense) {
3870     ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
3871     ierr = MatDenseRestoreArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3872   } else {
3873     /* ierr = PetscFree(send_buffer_vals);CHKERRQ(ierr); */
3874   }
3875   if (nis) {
3876     ierr = MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3877     ierr = PetscFree(send_buffer_idxs_is);CHKERRQ(ierr);
3878   }
3879   ierr = PetscFree(recv_req_idxs);CHKERRQ(ierr);
3880   ierr = PetscFree(recv_req_vals);CHKERRQ(ierr);
3881   ierr = PetscFree(recv_req_idxs_is);CHKERRQ(ierr);
3882   ierr = PetscFree(send_req_idxs);CHKERRQ(ierr);
3883   ierr = PetscFree(send_req_vals);CHKERRQ(ierr);
3884   ierr = PetscFree(send_req_idxs_is);CHKERRQ(ierr);
3885   ierr = PetscFree(ilengths_vals);CHKERRQ(ierr);
3886   ierr = PetscFree(ilengths_idxs);CHKERRQ(ierr);
3887   ierr = PetscFree(olengths_vals);CHKERRQ(ierr);
3888   ierr = PetscFree(olengths_idxs);CHKERRQ(ierr);
3889   ierr = PetscFree(onodes);CHKERRQ(ierr);
3890   if (nis) {
3891     ierr = PetscFree(ilengths_idxs_is);CHKERRQ(ierr);
3892     ierr = PetscFree(olengths_idxs_is);CHKERRQ(ierr);
3893     ierr = PetscFree(onodes_is);CHKERRQ(ierr);
3894   }
3895   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
3896   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
3897     ierr = MatDestroy(mat_n);CHKERRQ(ierr);
3898     for (i=0;i<nis;i++) {
3899       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3900     }
3901   }
3902   PetscFunctionReturn(0);
3903 }
3904 
3905 /* temporary hack into ksp private data structure */
3906 #include <petsc/private/kspimpl.h>
3907 
3908 #undef __FUNCT__
3909 #define __FUNCT__ "PCBDDCSetUpCoarseSolver"
3910 PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
3911 {
3912   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
3913   PC_IS                  *pcis = (PC_IS*)pc->data;
3914   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
3915   MatNullSpace           CoarseNullSpace=NULL;
3916   ISLocalToGlobalMapping coarse_islg;
3917   IS                     coarse_is,*isarray;
3918   PetscInt               i,im_active=-1,active_procs=-1;
3919   PetscInt               nis,nisdofs,nisneu;
3920   PC                     pc_temp;
3921   PCType                 coarse_pc_type;
3922   KSPType                coarse_ksp_type;
3923   PetscBool              multilevel_requested,multilevel_allowed;
3924   PetscBool              isredundant,isbddc,isnn,coarse_reuse;
3925   Mat                    t_coarse_mat_is;
3926   PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
3927   PetscMPIInt            all_procs;
3928   PetscBool              csin_ml,csin_ds,csin,csin_type_simple,redist;
3929   PetscBool              compute_vecs = PETSC_FALSE;
3930   PetscScalar            *array;
3931   PetscErrorCode         ierr;
3932 
3933   PetscFunctionBegin;
3934   /* Assign global numbering to coarse dofs */
3935   if (pcbddc->new_primal_space || pcbddc->coarse_size == -1) { /* a new primal space is present or it is the first initialization, so recompute global numbering */
3936     PetscInt ocoarse_size;
3937     compute_vecs = PETSC_TRUE;
3938     ocoarse_size = pcbddc->coarse_size;
3939     ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
3940     ierr = PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);CHKERRQ(ierr);
3941     /* see if we can avoid some work */
3942     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
3943       if (ocoarse_size != pcbddc->coarse_size) { /* ...but with different size, so reset it and set reuse flag to false */
3944         ierr = KSPReset(pcbddc->coarse_ksp);CHKERRQ(ierr);
3945         coarse_reuse = PETSC_FALSE;
3946       } else { /* we can safely reuse already computed coarse matrix */
3947         coarse_reuse = PETSC_TRUE;
3948       }
3949     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
3950       coarse_reuse = PETSC_FALSE;
3951     }
3952     /* reset any subassembling information */
3953     ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3954     ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3955   } else { /* primal space is unchanged, so we can reuse coarse matrix */
3956     coarse_reuse = PETSC_TRUE;
3957   }
3958 
3959   /* count "active" (i.e. with positive local size) and "void" processes */
3960   im_active = !!(pcis->n);
3961   ierr = MPI_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3962   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);CHKERRQ(ierr);
3963   void_procs = all_procs-active_procs;
3964   csin_type_simple = PETSC_TRUE;
3965   redist = PETSC_FALSE;
3966   if (pcbddc->current_level && void_procs) {
3967     csin_ml = PETSC_TRUE;
3968     ncoarse_ml = void_procs;
3969     /* it has no sense to redistribute on a set of processors larger than the number of active processes */
3970     if (pcbddc->redistribute_coarse > 0 && pcbddc->redistribute_coarse < active_procs) {
3971       csin_ds = PETSC_TRUE;
3972       ncoarse_ds = pcbddc->redistribute_coarse;
3973       redist = PETSC_TRUE;
3974     } else {
3975       csin_ds = PETSC_TRUE;
3976       ncoarse_ds = active_procs;
3977       redist = PETSC_TRUE;
3978     }
3979   } else {
3980     csin_ml = PETSC_FALSE;
3981     ncoarse_ml = all_procs;
3982     if (void_procs) {
3983       csin_ds = PETSC_TRUE;
3984       ncoarse_ds = void_procs;
3985       csin_type_simple = PETSC_FALSE;
3986     } else {
3987       if (pcbddc->redistribute_coarse > 0 && pcbddc->redistribute_coarse < all_procs) {
3988         csin_ds = PETSC_TRUE;
3989         ncoarse_ds = pcbddc->redistribute_coarse;
3990         redist = PETSC_TRUE;
3991       } else {
3992         csin_ds = PETSC_FALSE;
3993         ncoarse_ds = all_procs;
3994       }
3995     }
3996   }
3997 
3998   /*
3999     test if we can go multilevel: three conditions must be satisfied:
4000     - we have not exceeded the number of levels requested
4001     - we can actually subassemble the active processes
4002     - we can find a suitable number of MPI processes where we can place the subassembled problem
4003   */
4004   multilevel_allowed = PETSC_FALSE;
4005   multilevel_requested = PETSC_FALSE;
4006   if (pcbddc->current_level < pcbddc->max_levels) {
4007     multilevel_requested = PETSC_TRUE;
4008     if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
4009       multilevel_allowed = PETSC_FALSE;
4010     } else {
4011       multilevel_allowed = PETSC_TRUE;
4012     }
4013   }
4014   /* determine number of process partecipating to coarse solver */
4015   if (multilevel_allowed) {
4016     ncoarse = ncoarse_ml;
4017     csin = csin_ml;
4018     redist = PETSC_FALSE;
4019   } else {
4020     ncoarse = ncoarse_ds;
4021     csin = csin_ds;
4022   }
4023 
4024   /* creates temporary l2gmap and IS for coarse indexes */
4025   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);CHKERRQ(ierr);
4026   ierr = ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);CHKERRQ(ierr);
4027 
4028   /* creates temporary MATIS object for coarse matrix */
4029   ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,NULL,&coarse_submat_dense);CHKERRQ(ierr);
4030   ierr = MatDenseGetArray(coarse_submat_dense,&array);CHKERRQ(ierr);
4031   ierr = PetscMemcpy(array,coarse_submat_vals,sizeof(*coarse_submat_vals)*pcbddc->local_primal_size*pcbddc->local_primal_size);CHKERRQ(ierr);
4032   ierr = MatDenseRestoreArray(coarse_submat_dense,&array);CHKERRQ(ierr);
4033 #if 0
4034   {
4035     PetscViewer viewer;
4036     char filename[256];
4037     sprintf(filename,"local_coarse_mat%d.m",PetscGlobalRank);
4038     ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
4039     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
4040     ierr = MatView(coarse_submat_dense,viewer);CHKERRQ(ierr);
4041     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4042   }
4043 #endif
4044   ierr = MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,&t_coarse_mat_is);CHKERRQ(ierr);
4045   ierr = MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);CHKERRQ(ierr);
4046   ierr = MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4047   ierr = MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4048   ierr = MatDestroy(&coarse_submat_dense);CHKERRQ(ierr);
4049 
4050   /* compute dofs splitting and neumann boundaries for coarse dofs */
4051   if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal) ) { /* protects from unneded computations */
4052     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
4053     const PetscInt         *idxs;
4054     ISLocalToGlobalMapping tmap;
4055 
4056     /* create map between primal indices (in local representative ordering) and local primal numbering */
4057     ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);CHKERRQ(ierr);
4058     /* allocate space for temporary storage */
4059     ierr = PetscMalloc1(pcbddc->local_primal_size,&tidxs);CHKERRQ(ierr);
4060     ierr = PetscMalloc1(pcbddc->local_primal_size,&tidxs2);CHKERRQ(ierr);
4061     /* allocate for IS array */
4062     nisdofs = pcbddc->n_ISForDofsLocal;
4063     nisneu = !!pcbddc->NeumannBoundariesLocal;
4064     nis = nisdofs + nisneu;
4065     ierr = PetscMalloc1(nis,&isarray);CHKERRQ(ierr);
4066     /* dofs splitting */
4067     for (i=0;i<nisdofs;i++) {
4068       /* ierr = ISView(pcbddc->ISForDofsLocal[i],0);CHKERRQ(ierr); */
4069       ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);CHKERRQ(ierr);
4070       ierr = ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
4071       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
4072       ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
4073       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
4074       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->ISForDofsLocal[i]),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
4075       /* ierr = ISView(isarray[i],0);CHKERRQ(ierr); */
4076     }
4077     /* neumann boundaries */
4078     if (pcbddc->NeumannBoundariesLocal) {
4079       /* ierr = ISView(pcbddc->NeumannBoundariesLocal,0);CHKERRQ(ierr); */
4080       ierr = ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);CHKERRQ(ierr);
4081       ierr = ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
4082       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
4083       ierr = ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
4084       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
4085       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->NeumannBoundariesLocal),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);CHKERRQ(ierr);
4086       /* ierr = ISView(isarray[nisdofs],0);CHKERRQ(ierr); */
4087     }
4088     /* free memory */
4089     ierr = PetscFree(tidxs);CHKERRQ(ierr);
4090     ierr = PetscFree(tidxs2);CHKERRQ(ierr);
4091     ierr = ISLocalToGlobalMappingDestroy(&tmap);CHKERRQ(ierr);
4092   } else {
4093     nis = 0;
4094     nisdofs = 0;
4095     nisneu = 0;
4096     isarray = NULL;
4097   }
4098   /* destroy no longer needed map */
4099   ierr = ISLocalToGlobalMappingDestroy(&coarse_islg);CHKERRQ(ierr);
4100 
4101   /* restrict on coarse candidates (if needed) */
4102   coarse_mat_is = NULL;
4103   if (csin) {
4104     if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
4105       if (redist) {
4106         PetscMPIInt rank;
4107         PetscInt    spc,n_spc_p1,dest[1],destsize;
4108 
4109         ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
4110         spc = active_procs/ncoarse;
4111         n_spc_p1 = active_procs%ncoarse;
4112         if (im_active) {
4113           destsize = 1;
4114           if (rank > n_spc_p1*(spc+1)-1) {
4115             dest[0] = n_spc_p1+(rank-(n_spc_p1*(spc+1)))/spc;
4116           } else {
4117             dest[0] = rank/(spc+1);
4118           }
4119         } else {
4120           destsize = 0;
4121         }
4122         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),destsize,dest,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
4123       } else if (csin_type_simple) {
4124         PetscMPIInt rank;
4125         PetscInt    issize,isidx;
4126 
4127         ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
4128         if (im_active) {
4129           issize = 1;
4130           isidx = (PetscInt)rank;
4131         } else {
4132           issize = 0;
4133           isidx = -1;
4134         }
4135         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
4136       } else { /* get a suitable subassembling pattern from MATIS code */
4137         ierr = MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,PETSC_TRUE,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
4138       }
4139 
4140       /* we need to shift on coarse candidates either if we are not redistributing or we are redistributing and we have enough void processes */
4141       if (!redist || ncoarse <= void_procs) {
4142         PetscInt ncoarse_cand,tissize,*nisindices;
4143         PetscInt *coarse_candidates;
4144         const PetscInt* tisindices;
4145 
4146         /* get coarse candidates' ranks in pc communicator */
4147         ierr = PetscMalloc1(all_procs,&coarse_candidates);CHKERRQ(ierr);
4148         ierr = MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
4149         for (i=0,ncoarse_cand=0;i<all_procs;i++) {
4150           if (!coarse_candidates[i]) {
4151             coarse_candidates[ncoarse_cand++]=i;
4152           }
4153         }
4154         if (ncoarse_cand < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",ncoarse_cand,ncoarse);
4155 
4156 
4157         if (pcbddc->dbg_flag) {
4158           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
4159           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");CHKERRQ(ierr);
4160           ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
4161           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");CHKERRQ(ierr);
4162           for (i=0;i<ncoarse_cand;i++) {
4163             ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);CHKERRQ(ierr);
4164           }
4165           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");CHKERRQ(ierr);
4166           ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4167         }
4168         /* shift the pattern on coarse candidates */
4169         ierr = ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);CHKERRQ(ierr);
4170         ierr = ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
4171         ierr = PetscMalloc1(tissize,&nisindices);CHKERRQ(ierr);
4172         for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
4173         ierr = ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
4174         ierr = ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);CHKERRQ(ierr);
4175         ierr = PetscFree(coarse_candidates);CHKERRQ(ierr);
4176       }
4177       if (pcbddc->dbg_flag) {
4178         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
4179         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");CHKERRQ(ierr);
4180         ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
4181         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4182       }
4183     }
4184     /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
4185     ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
4186   } else {
4187     if (pcbddc->dbg_flag) {
4188       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
4189       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");CHKERRQ(ierr);
4190       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4191     }
4192     ierr = PetscObjectReference((PetscObject)t_coarse_mat_is);CHKERRQ(ierr);
4193     coarse_mat_is = t_coarse_mat_is;
4194   }
4195 
4196   /* create local to global scatters for coarse problem */
4197   if (compute_vecs) {
4198     PetscInt lrows;
4199     ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
4200     if (coarse_mat_is) {
4201       ierr = MatGetLocalSize(coarse_mat_is,&lrows,NULL);CHKERRQ(ierr);
4202     } else {
4203       lrows = 0;
4204     }
4205     ierr = VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);CHKERRQ(ierr);
4206     ierr = VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);CHKERRQ(ierr);
4207     ierr = VecSetType(pcbddc->coarse_vec,VECSTANDARD);CHKERRQ(ierr);
4208     ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
4209     ierr = VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
4210   }
4211   ierr = ISDestroy(&coarse_is);CHKERRQ(ierr);
4212   ierr = MatDestroy(&t_coarse_mat_is);CHKERRQ(ierr);
4213 
4214   /* set defaults for coarse KSP and PC */
4215   if (multilevel_allowed) {
4216     coarse_ksp_type = KSPRICHARDSON;
4217     coarse_pc_type = PCBDDC;
4218   } else {
4219     coarse_ksp_type = KSPPREONLY;
4220     coarse_pc_type = PCREDUNDANT;
4221   }
4222 
4223   /* print some info if requested */
4224   if (pcbddc->dbg_flag) {
4225     if (!multilevel_allowed) {
4226       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
4227       if (multilevel_requested) {
4228         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Not enough active processes on level %d (active processes %d, coarsening ratio %d)\n",pcbddc->current_level,active_procs,pcbddc->coarsening_ratio);CHKERRQ(ierr);
4229       } else if (pcbddc->max_levels) {
4230         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);CHKERRQ(ierr);
4231       }
4232       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4233     }
4234   }
4235 
4236   /* create the coarse KSP object only once with defaults */
4237   if (coarse_mat_is) {
4238     MatReuse coarse_mat_reuse;
4239     PetscViewer dbg_viewer = NULL;
4240     if (pcbddc->dbg_flag) {
4241       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
4242       ierr = PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
4243     }
4244     if (!pcbddc->coarse_ksp) {
4245       char prefix[256],str_level[16];
4246       size_t len;
4247       ierr = KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);CHKERRQ(ierr);
4248       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
4249       ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
4250       ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);CHKERRQ(ierr);
4251       ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
4252       ierr = KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);CHKERRQ(ierr);
4253       ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
4254       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
4255       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
4256       /* prefix */
4257       ierr = PetscStrcpy(prefix,"");CHKERRQ(ierr);
4258       ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
4259       if (!pcbddc->current_level) {
4260         ierr = PetscStrcpy(prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
4261         ierr = PetscStrcat(prefix,"pc_bddc_coarse_");CHKERRQ(ierr);
4262       } else {
4263         ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
4264         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
4265         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
4266         ierr = PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
4267         sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
4268         ierr = PetscStrcat(prefix,str_level);CHKERRQ(ierr);
4269       }
4270       ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);CHKERRQ(ierr);
4271       /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
4272       ierr = PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);CHKERRQ(ierr);
4273       ierr = PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);CHKERRQ(ierr);
4274       ierr = PCBDDCSetLevels(pc_temp,pcbddc->max_levels);CHKERRQ(ierr);
4275       /* allow user customization */
4276       ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
4277     }
4278     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
4279     if (nisdofs) {
4280       ierr = PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);CHKERRQ(ierr);
4281       for (i=0;i<nisdofs;i++) {
4282         ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
4283       }
4284     }
4285     if (nisneu) {
4286       ierr = PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);CHKERRQ(ierr);
4287       ierr = ISDestroy(&isarray[nisdofs]);CHKERRQ(ierr);
4288     }
4289 
4290     /* get some info after set from options */
4291     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
4292     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);CHKERRQ(ierr);
4293     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);CHKERRQ(ierr);
4294     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);CHKERRQ(ierr);
4295     if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
4296       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
4297       isbddc = PETSC_FALSE;
4298     }
4299     if (isredundant) {
4300       KSP inner_ksp;
4301       PC inner_pc;
4302       ierr = PCRedundantGetKSP(pc_temp,&inner_ksp);CHKERRQ(ierr);
4303       ierr = KSPGetPC(inner_ksp,&inner_pc);CHKERRQ(ierr);
4304       ierr = PCFactorSetReuseFill(inner_pc,PETSC_TRUE);CHKERRQ(ierr);
4305     }
4306 
4307     /* assemble coarse matrix */
4308     if (coarse_reuse) {
4309       ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
4310       ierr = PetscObjectReference((PetscObject)coarse_mat);CHKERRQ(ierr);
4311       coarse_mat_reuse = MAT_REUSE_MATRIX;
4312     } else {
4313       coarse_mat_reuse = MAT_INITIAL_MATRIX;
4314     }
4315     if (isbddc || isnn) {
4316       if (pcbddc->coarsening_ratio > 1) {
4317         if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
4318           ierr = MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,PETSC_TRUE,&pcbddc->coarse_subassembling);CHKERRQ(ierr);
4319           if (pcbddc->dbg_flag) {
4320             ierr = PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
4321             ierr = PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");CHKERRQ(ierr);
4322             ierr = ISView(pcbddc->coarse_subassembling,dbg_viewer);CHKERRQ(ierr);
4323             ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
4324           }
4325         }
4326         ierr = MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);CHKERRQ(ierr);
4327       } else {
4328         ierr = PetscObjectReference((PetscObject)coarse_mat_is);CHKERRQ(ierr);
4329         coarse_mat = coarse_mat_is;
4330       }
4331     } else {
4332       ierr = MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);CHKERRQ(ierr);
4333     }
4334     ierr = MatDestroy(&coarse_mat_is);CHKERRQ(ierr);
4335 
4336     /* propagate symmetry info to coarse matrix */
4337     ierr = MatSetOption(coarse_mat,MAT_SYMMETRIC,pcbddc->issym);CHKERRQ(ierr);
4338     ierr = MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
4339 
4340     /* set operators */
4341     ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
4342     if (pcbddc->dbg_flag) {
4343       ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
4344     }
4345   } else { /* processes non partecipating to coarse solver (if any) */
4346     coarse_mat = 0;
4347   }
4348   ierr = PetscFree(isarray);CHKERRQ(ierr);
4349 #if 0
4350   {
4351     PetscViewer viewer;
4352     char filename[256];
4353     sprintf(filename,"coarse_mat.m");
4354     ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,&viewer);CHKERRQ(ierr);
4355     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
4356     ierr = MatView(coarse_mat,viewer);CHKERRQ(ierr);
4357     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4358   }
4359 #endif
4360 
4361   /* Compute coarse null space (special handling by BDDC only) */
4362   if (pcbddc->NullSpace) {
4363     ierr = PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);CHKERRQ(ierr);
4364   }
4365 
4366   if (pcbddc->coarse_ksp) {
4367     Vec crhs,csol;
4368     PetscBool ispreonly;
4369     if (CoarseNullSpace) {
4370       if (isbddc) {
4371         ierr = PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);CHKERRQ(ierr);
4372       } else {
4373         ierr = KSPSetNullSpace(pcbddc->coarse_ksp,CoarseNullSpace);CHKERRQ(ierr);
4374       }
4375     }
4376     /* setup coarse ksp */
4377     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
4378     ierr = KSPGetSolution(pcbddc->coarse_ksp,&csol);CHKERRQ(ierr);
4379     ierr = KSPGetRhs(pcbddc->coarse_ksp,&crhs);CHKERRQ(ierr);
4380     /* hack */
4381     if (!csol) {
4382       ierr = MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);CHKERRQ(ierr);
4383     }
4384     if (!crhs) {
4385       ierr = MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));CHKERRQ(ierr);
4386     }
4387     /* Check coarse problem if in debug mode or if solving with an iterative method */
4388     ierr = PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);CHKERRQ(ierr);
4389     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
4390       KSP       check_ksp;
4391       KSPType   check_ksp_type;
4392       PC        check_pc;
4393       Vec       check_vec,coarse_vec;
4394       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
4395       PetscInt  its;
4396       PetscBool compute_eigs;
4397       PetscReal *eigs_r,*eigs_c;
4398       PetscInt  neigs;
4399       const char *prefix;
4400 
4401       /* Create ksp object suitable for estimation of extreme eigenvalues */
4402       ierr = KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);CHKERRQ(ierr);
4403       ierr = KSPSetOperators(check_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
4404       ierr = KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
4405       if (ispreonly) {
4406         check_ksp_type = KSPPREONLY;
4407         compute_eigs = PETSC_FALSE;
4408       } else {
4409         check_ksp_type = KSPGMRES;
4410         compute_eigs = PETSC_TRUE;
4411       }
4412       ierr = KSPSetType(check_ksp,check_ksp_type);CHKERRQ(ierr);
4413       ierr = KSPSetComputeSingularValues(check_ksp,compute_eigs);CHKERRQ(ierr);
4414       ierr = KSPSetComputeEigenvalues(check_ksp,compute_eigs);CHKERRQ(ierr);
4415       ierr = KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);CHKERRQ(ierr);
4416       ierr = KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);CHKERRQ(ierr);
4417       ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
4418       ierr = KSPAppendOptionsPrefix(check_ksp,"check_");CHKERRQ(ierr);
4419       ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
4420       ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
4421       ierr = KSPGetPC(pcbddc->coarse_ksp,&check_pc);CHKERRQ(ierr);
4422       ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
4423       /* create random vec */
4424       ierr = KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);CHKERRQ(ierr);
4425       ierr = VecDuplicate(coarse_vec,&check_vec);CHKERRQ(ierr);
4426       ierr = VecSetRandom(check_vec,NULL);CHKERRQ(ierr);
4427       if (CoarseNullSpace) {
4428         ierr = MatNullSpaceRemove(CoarseNullSpace,check_vec);CHKERRQ(ierr);
4429       }
4430       ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
4431       /* solve coarse problem */
4432       ierr = KSPSolve(check_ksp,coarse_vec,coarse_vec);CHKERRQ(ierr);
4433       if (CoarseNullSpace) {
4434         ierr = MatNullSpaceRemove(CoarseNullSpace,coarse_vec);CHKERRQ(ierr);
4435       }
4436       /* set eigenvalue estimation if preonly has not been requested */
4437       if (compute_eigs) {
4438         ierr = PetscMalloc1(pcbddc->coarse_size+1,&eigs_r);CHKERRQ(ierr);
4439         ierr = PetscMalloc1(pcbddc->coarse_size+1,&eigs_c);CHKERRQ(ierr);
4440         ierr = KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);CHKERRQ(ierr);
4441         lambda_max = eigs_r[neigs-1];
4442         lambda_min = eigs_r[0];
4443         if (pcbddc->use_coarse_estimates) {
4444           if (lambda_max>lambda_min) {
4445             ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
4446             ierr = KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));CHKERRQ(ierr);
4447           }
4448         }
4449       }
4450 
4451       /* check coarse problem residual error */
4452       if (pcbddc->dbg_flag) {
4453         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
4454         ierr = PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
4455         ierr = VecAXPY(check_vec,-1.0,coarse_vec);CHKERRQ(ierr);
4456         ierr = VecNorm(check_vec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
4457         ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
4458         ierr = VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);CHKERRQ(ierr);
4459         ierr = VecDestroy(&check_vec);CHKERRQ(ierr);
4460         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (use estimates %d)\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
4461         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);CHKERRQ(ierr);
4462         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);CHKERRQ(ierr);
4463         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);CHKERRQ(ierr);
4464         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);CHKERRQ(ierr);
4465         if (compute_eigs) {
4466           PetscReal lambda_max_s,lambda_min_s;
4467           ierr = KSPGetType(check_ksp,&check_ksp_type);CHKERRQ(ierr);
4468           ierr = KSPGetIterationNumber(check_ksp,&its);CHKERRQ(ierr);
4469           ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);CHKERRQ(ierr);
4470           ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem eigenvalues (estimated with %d iterations of %s): %1.6e %1.6e (%1.6e %1.6e)\n",its,check_ksp_type,lambda_min,lambda_max,lambda_min_s,lambda_max_s);CHKERRQ(ierr);
4471           for (i=0;i<neigs;i++) {
4472             ierr = PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);CHKERRQ(ierr);
4473           }
4474         }
4475         ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
4476         ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
4477       }
4478       ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
4479       if (compute_eigs) {
4480         ierr = PetscFree(eigs_r);CHKERRQ(ierr);
4481         ierr = PetscFree(eigs_c);CHKERRQ(ierr);
4482       }
4483     }
4484   }
4485   /* print additional info */
4486   if (pcbddc->dbg_flag) {
4487     /* waits until all processes reaches this point */
4488     ierr = PetscBarrier((PetscObject)pc);CHKERRQ(ierr);
4489     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);CHKERRQ(ierr);
4490     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4491   }
4492 
4493   /* free memory */
4494   ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
4495   ierr = MatDestroy(&coarse_mat);CHKERRQ(ierr);
4496   PetscFunctionReturn(0);
4497 }
4498 
4499 #undef __FUNCT__
4500 #define __FUNCT__ "PCBDDCComputePrimalNumbering"
4501 PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
4502 {
4503   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
4504   PC_IS*         pcis = (PC_IS*)pc->data;
4505   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
4506   PetscInt       i,coarse_size=0;
4507   PetscInt       *local_primal_indices=NULL;
4508   PetscErrorCode ierr;
4509 
4510   PetscFunctionBegin;
4511   /* Compute global number of coarse dofs */
4512   if (!pcbddc->primal_indices_local_idxs && pcbddc->local_primal_size) {
4513     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Local primal indices have not been created");
4514   }
4515   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)(pc->pmat)),matis->mapping,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,NULL,&coarse_size,&local_primal_indices);CHKERRQ(ierr);
4516 
4517   /* check numbering */
4518   if (pcbddc->dbg_flag) {
4519     PetscScalar coarsesum,*array;
4520     PetscBool set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;
4521 
4522     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4523     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
4524     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");CHKERRQ(ierr);
4525     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
4526     ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
4527     for (i=0;i<pcbddc->local_primal_size;i++) {
4528       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
4529     }
4530     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
4531     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
4532     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4533     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4534     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4535     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4536     ierr = VecScatterEnd(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4537     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4538     for (i=0;i<pcis->n;i++) {
4539       if (array[i] == 1.0) {
4540         set_error = PETSC_TRUE;
4541         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a single process!\n",PetscGlobalRank,i);CHKERRQ(ierr);
4542       }
4543     }
4544     ierr = MPI_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
4545     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4546     for (i=0;i<pcis->n;i++) {
4547       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
4548     }
4549     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4550     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4551     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4552     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4553     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
4554     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));CHKERRQ(ierr);
4555     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
4556       PetscInt *gidxs;
4557 
4558       ierr = PetscMalloc1(pcbddc->local_primal_size,&gidxs);CHKERRQ(ierr);
4559       ierr = ISLocalToGlobalMappingApply(matis->mapping,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,gidxs);CHKERRQ(ierr);
4560       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");CHKERRQ(ierr);
4561       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4562       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
4563       for (i=0;i<pcbddc->local_primal_size;i++) {
4564         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%d]=%d (%d,%d)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i],gidxs[i]);CHKERRQ(ierr);
4565       }
4566       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4567       ierr = PetscFree(gidxs);CHKERRQ(ierr);
4568     }
4569     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4570     if (set_error_reduced) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
4571   }
4572   /* ierr = PetscPrintf(PetscObjectComm((PetscObject)pc),"Size of coarse problem is %d\n",coarse_size);CHKERRQ(ierr); */
4573   /* get back data */
4574   *coarse_size_n = coarse_size;
4575   *local_primal_indices_n = local_primal_indices;
4576   PetscFunctionReturn(0);
4577 }
4578 
4579 #undef __FUNCT__
4580 #define __FUNCT__ "PCBDDCGlobalToLocal"
4581 PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
4582 {
4583   IS             localis_t;
4584   PetscInt       i,lsize,*idxs,n;
4585   PetscScalar    *vals;
4586   PetscErrorCode ierr;
4587 
4588   PetscFunctionBegin;
4589   /* get indices in local ordering exploiting local to global map */
4590   ierr = ISGetLocalSize(globalis,&lsize);CHKERRQ(ierr);
4591   ierr = PetscMalloc1(lsize,&vals);CHKERRQ(ierr);
4592   for (i=0;i<lsize;i++) vals[i] = 1.0;
4593   ierr = ISGetIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
4594   ierr = VecSet(gwork,0.0);CHKERRQ(ierr);
4595   ierr = VecSet(lwork,0.0);CHKERRQ(ierr);
4596   if (idxs) { /* multilevel guard */
4597     ierr = VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
4598   }
4599   ierr = VecAssemblyBegin(gwork);CHKERRQ(ierr);
4600   ierr = ISRestoreIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
4601   ierr = PetscFree(vals);CHKERRQ(ierr);
4602   ierr = VecAssemblyEnd(gwork);CHKERRQ(ierr);
4603   /* now compute set in local ordering */
4604   ierr = VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4605   ierr = VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4606   ierr = VecGetArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
4607   ierr = VecGetSize(lwork,&n);CHKERRQ(ierr);
4608   for (i=0,lsize=0;i<n;i++) {
4609     if (PetscRealPart(vals[i]) > 0.5) {
4610       lsize++;
4611     }
4612   }
4613   ierr = PetscMalloc1(lsize,&idxs);CHKERRQ(ierr);
4614   for (i=0,lsize=0;i<n;i++) {
4615     if (PetscRealPart(vals[i]) > 0.5) {
4616       idxs[lsize++] = i;
4617     }
4618   }
4619   ierr = VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
4620   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);CHKERRQ(ierr);
4621   *localis = localis_t;
4622   PetscFunctionReturn(0);
4623 }
4624 
4625 /* the next two functions will be called in KSPMatMult if a change of basis has been requested */
4626 #undef __FUNCT__
4627 #define __FUNCT__ "PCBDDCMatMult_Private"
4628 static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y)
4629 {
4630   PCBDDCChange_ctx change_ctx;
4631   PetscErrorCode   ierr;
4632 
4633   PetscFunctionBegin;
4634   ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
4635   ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
4636   ierr = MatMult(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
4637   ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
4638   PetscFunctionReturn(0);
4639 }
4640 
4641 #undef __FUNCT__
4642 #define __FUNCT__ "PCBDDCMatMultTranspose_Private"
4643 static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y)
4644 {
4645   PCBDDCChange_ctx change_ctx;
4646   PetscErrorCode   ierr;
4647 
4648   PetscFunctionBegin;
4649   ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
4650   ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
4651   ierr = MatMultTranspose(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
4652   ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
4653   PetscFunctionReturn(0);
4654 }
4655 
4656 #undef __FUNCT__
4657 #define __FUNCT__ "PCBDDCSetUpSubSchurs"
4658 PetscErrorCode PCBDDCSetUpSubSchurs(PC pc)
4659 {
4660   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
4661   PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
4662   PetscInt            *used_xadj,*used_adjncy;
4663   PetscBool           free_used_adj;
4664   PetscErrorCode      ierr;
4665 
4666   PetscFunctionBegin;
4667   /* decide the adjacency to be used for determining internal problems for local schur on subsets */
4668   free_used_adj = PETSC_FALSE;
4669   if (pcbddc->sub_schurs_layers == -1) {
4670     used_xadj = NULL;
4671     used_adjncy = NULL;
4672   } else {
4673     if (pcbddc->sub_schurs_use_useradj && pcbddc->mat_graph->xadj) {
4674       used_xadj = pcbddc->mat_graph->xadj;
4675       used_adjncy = pcbddc->mat_graph->adjncy;
4676     } else if (pcbddc->computed_rowadj) {
4677       used_xadj = pcbddc->mat_graph->xadj;
4678       used_adjncy = pcbddc->mat_graph->adjncy;
4679     } else {
4680       PetscBool      flg_row=PETSC_FALSE;
4681       const PetscInt *xadj,*adjncy;
4682       PetscInt       nvtxs;
4683 
4684       ierr = MatGetRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
4685       if (flg_row) {
4686         ierr = PetscMalloc2(nvtxs+1,&used_xadj,xadj[nvtxs],&used_adjncy);CHKERRQ(ierr);
4687         ierr = PetscMemcpy(used_xadj,xadj,(nvtxs+1)*sizeof(*xadj));CHKERRQ(ierr);
4688         ierr = PetscMemcpy(used_adjncy,adjncy,(xadj[nvtxs])*sizeof(*adjncy));CHKERRQ(ierr);
4689         free_used_adj = PETSC_TRUE;
4690       } else {
4691         pcbddc->sub_schurs_layers = -1;
4692         used_xadj = NULL;
4693         used_adjncy = NULL;
4694       }
4695       ierr = MatRestoreRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
4696     }
4697   }
4698 
4699   /* set Schur complement solver for interior variables (used only when MUMPS is not present) */
4700   if (!sub_schurs->use_mumps) {
4701     ierr = MatSchurComplementSetKSP(sub_schurs->S,pcbddc->ksp_D);CHKERRQ(ierr);
4702   }
4703 
4704   /* setup sub_schurs data */
4705   ierr = PCBDDCSubSchursSetUp(sub_schurs,used_xadj,used_adjncy,pcbddc->sub_schurs_layers,pcbddc->faster_deluxe,pcbddc->adaptive_selection,pcbddc->use_edges,pcbddc->use_faces);CHKERRQ(ierr);
4706 
4707   /* free adjacency */
4708   if (free_used_adj) {
4709     ierr = PetscFree2(used_xadj,used_adjncy);CHKERRQ(ierr);
4710   }
4711   PetscFunctionReturn(0);
4712 }
4713 
4714 #undef __FUNCT__
4715 #define __FUNCT__ "PCBDDCInitSubSchurs"
4716 PetscErrorCode PCBDDCInitSubSchurs(PC pc)
4717 {
4718   PC_IS               *pcis=(PC_IS*)pc->data;
4719   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
4720   PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
4721   PCBDDCGraph         graph;
4722   Mat                 S_j;
4723   PetscErrorCode      ierr;
4724 
4725   PetscFunctionBegin;
4726   /* attach interface graph for determining subsets */
4727   if (pcbddc->sub_schurs_rebuild) { /* in case rebuild has been requested, it uses a graph generated only by the neighbouring information */
4728     IS verticesIS;
4729 
4730     ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);CHKERRQ(ierr);
4731     ierr = PCBDDCGraphCreate(&graph);CHKERRQ(ierr);
4732     ierr = PCBDDCGraphInit(graph,pcbddc->mat_graph->l2gmap);CHKERRQ(ierr);
4733     ierr = PCBDDCGraphSetUp(graph,0,NULL,pcbddc->DirichletBoundariesLocal,0,NULL,verticesIS);CHKERRQ(ierr);
4734     ierr = PCBDDCGraphComputeConnectedComponents(graph);CHKERRQ(ierr);
4735     ierr = ISDestroy(&verticesIS);CHKERRQ(ierr);
4736 /*
4737     if (pcbddc->dbg_flag) {
4738       ierr = PCBDDCGraphASCIIView(graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);CHKERRQ(ierr);
4739     }
4740 */
4741   } else {
4742     graph = pcbddc->mat_graph;
4743   }
4744 
4745   /* Create Schur complement matrix */
4746   ierr = MatCreateSchurComplement(pcis->A_II,pcis->A_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);CHKERRQ(ierr);
4747 
4748   /* sub_schurs init */
4749   ierr = PCBDDCSubSchursInit(sub_schurs,pcbddc->local_mat,S_j,pcis->is_I_local,pcis->is_B_local,graph,pcis->BtoNmap);CHKERRQ(ierr);
4750   ierr = MatDestroy(&S_j);CHKERRQ(ierr);
4751   /* free graph struct */
4752   if (pcbddc->sub_schurs_rebuild) {
4753     ierr = PCBDDCGraphDestroy(&graph);CHKERRQ(ierr);
4754   }
4755   PetscFunctionReturn(0);
4756 }
4757