xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 4e7385fac521a32d019ba1b91cac4ccec6d80411)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <petscblaslapack.h>
4 
5 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt*,PetscInt,PetscBT,PetscInt*,PetscInt*,PetscInt*);
6 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat,PetscBool,MatReuse,Mat*);
7 
8 #undef __FUNCT__
9 #define __FUNCT__ "PCBDDCComputeExplicitSchur"
10 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
11 {
12   Mat            B, C, D, Bd, Cd, AinvBd;
13   KSP            ksp;
14   PC             pc;
15   PetscBool      isLU, isILU, isCHOL, Bdense, Cdense;
16   PetscReal      fill = 2.0;
17   PetscInt       n_I;
18   PetscMPIInt    size;
19   PetscErrorCode ierr;
20 
21   PetscFunctionBegin;
22   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);CHKERRQ(ierr);
23   if (size != 1) {
24     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not for parallel matrices");
25   }
26   if (reuse == MAT_REUSE_MATRIX) {
27     PetscBool Sdense;
28 
29     ierr = PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense);CHKERRQ(ierr);
30     if (!Sdense) {
31       SETERRQ(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"S should dense");
32     }
33   }
34   ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
35   ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
36   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
37   ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
38   ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
39   ierr = PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);CHKERRQ(ierr);
40   ierr = PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);CHKERRQ(ierr);
41   ierr = PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);CHKERRQ(ierr);
42   ierr = MatGetSize(B,&n_I,NULL);CHKERRQ(ierr);
43   if (n_I) {
44     if (!Bdense) {
45       ierr = MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
46     } else {
47       Bd = B;
48     }
49 
50     if (isLU || isILU || isCHOL) {
51       Mat fact;
52 
53       ierr = KSPSetUp(ksp);CHKERRQ(ierr);
54       ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
55       ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
56       ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
57     } else {
58       Mat Ainvd;
59 
60       ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
61       ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
62       ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
63     }
64     if (!Bdense & !issym) {
65       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
66     }
67 
68     if (!issym) {
69       if (!Cdense) {
70         ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
71       } else {
72         Cd = C;
73       }
74       ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
75       if (!Cdense) {
76         ierr = MatDestroy(&Cd);CHKERRQ(ierr);
77       }
78     } else {
79       ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
80       if (!Bdense) {
81         ierr = MatDestroy(&Bd);CHKERRQ(ierr);
82       }
83     }
84     ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
85   }
86 
87   if (D) {
88     Mat       Dd;
89     PetscBool Ddense;
90 
91     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
92     if (!Ddense) {
93       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
94     } else {
95       Dd = D;
96     }
97     if (n_I) {
98       ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
99     } else {
100       if (reuse == MAT_INITIAL_MATRIX) {
101         ierr = MatDuplicate(Dd,MAT_COPY_VALUES,S);CHKERRQ(ierr);
102       } else {
103         ierr = MatCopy(Dd,*S,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
104       }
105     }
106     if (!Ddense) {
107       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
108     }
109   } else {
110     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
111   }
112   PetscFunctionReturn(0);
113 }
114 
115 #undef __FUNCT__
116 #define __FUNCT__ "PCBDDCSubSchursSetUp"
117 PetscErrorCode PCBDDCSubSchursSetUp(PCBDDCSubSchurs sub_schurs, PetscInt xadj[], PetscInt adjncy[], PetscInt nlayers, PetscBool compute_Stilda, PetscBool deluxe, PetscBool invert_Stildas, PetscBool use_edges, PetscBool use_faces)
118 {
119   Mat                    A_II,A_IB,A_BI,A_BB;
120   Mat                    AE_II,*AE_IE,*AE_EI,*AE_EE;
121   Mat                    S_all,global_schur_subsets,work_mat;
122   Mat                    S_Ej_tilda_all,S_Ej_inv_all;
123   ISLocalToGlobalMapping l2gmap_subsets;
124   IS                     is_I,*is_subset_B,temp_is;
125   PetscInt               *nnz,*all_local_idx_G,*all_local_idx_N;
126   PetscInt               i,subset_size,max_subset_size_seq;
127   PetscInt               extra,local_size,global_size;
128   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
129   PetscScalar            *Bwork;
130   PetscErrorCode         ierr;
131 
132   PetscFunctionBegin;
133   /* get Schur complement matrices */
134   if (!sub_schurs->use_mumps) {
135     PetscBool isseqaij;
136 
137     if (compute_Stilda) {
138       SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS");
139     }
140     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&A_IB,&A_BI,&A_BB);CHKERRQ(ierr);
141     ierr = PetscObjectTypeCompare((PetscObject)A_BB,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
142     if (!isseqaij) {
143       ierr = MatConvert(A_BB,MATSEQAIJ,MAT_REUSE_MATRIX,&A_BB);CHKERRQ(ierr);
144       ierr = MatConvert(A_IB,MATSEQAIJ,MAT_REUSE_MATRIX,&A_IB);CHKERRQ(ierr);
145       ierr = MatConvert(A_BI,MATSEQAIJ,MAT_REUSE_MATRIX,&A_BI);CHKERRQ(ierr);
146     }
147     ierr = PetscMalloc4(sub_schurs->n_subs,&is_subset_B,
148                         sub_schurs->n_subs,&AE_IE,
149                         sub_schurs->n_subs,&AE_EI,
150                         sub_schurs->n_subs,&AE_EE);CHKERRQ(ierr);
151   } else {
152     is_subset_B = NULL;
153     AE_IE = NULL;
154     AE_EI = NULL;
155     AE_EE = NULL;
156   }
157 
158   /* determine interior problems */
159   ierr = ISDestroy(&sub_schurs->is_I_layer);CHKERRQ(ierr);
160   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
161   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
162     PetscBT                touched;
163     const PetscInt*        idx_B;
164     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
165 
166     if (xadj == NULL || adjncy == NULL) {
167       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
168     }
169     /* get sizes */
170     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
171     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
172 
173     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
174     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
175     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
176 
177     /* all boundary dofs must be skipped when adding layers */
178     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
179     for (j=0;j<n_B;j++) {
180       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
181     }
182     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
183     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
184 
185     /* add prescribed number of layers of dofs */
186     n_local_dofs = n_B;
187     n_prev_added = n_B;
188     for (layer=0;layer<nlayers;layer++) {
189       PetscInt n_added;
190       if (n_local_dofs == n_I+n_B) break;
191       if (n_local_dofs > n_I+n_B) {
192         SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error querying layer %d. Out of bound access (%d > %d)",layer,n_local_dofs,n_I+n_B);
193       }
194       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
195       n_prev_added = n_added;
196       n_local_dofs += n_added;
197       if (!n_added) break;
198     }
199     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
200 
201     /* IS for I layer dofs in original numbering */
202     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I),n_local_dofs-n_B,local_numbering+n_B,PETSC_COPY_VALUES,&sub_schurs->is_I_layer);CHKERRQ(ierr);
203     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
204     ierr = ISSort(sub_schurs->is_I_layer);CHKERRQ(ierr);
205     /* IS for I layer dofs in I numbering */
206     if (!sub_schurs->use_mumps) {
207       ISLocalToGlobalMapping ItoNmap;
208       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
209       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,sub_schurs->is_I_layer,&is_I);CHKERRQ(ierr);
210       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
211 
212       /* II block */
213       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
214     }
215   } else {
216     PetscInt n_I;
217 
218     /* IS for I dofs in original numbering */
219     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
220     sub_schurs->is_I_layer = sub_schurs->is_I;
221 
222     /* IS for I dofs in I numbering (strided 1) */
223     if (!sub_schurs->use_mumps) {
224       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
225       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
226 
227       /* II block is the same */
228       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
229       AE_II = A_II;
230     }
231   }
232   /* Get info on subset sizes and sum of all subsets sizes */
233   max_subset_size_seq = 0;
234   local_size = 0;
235   for (i=0;i<sub_schurs->n_subs_seq;i++) {
236     PetscInt j = sub_schurs->index_sequential[i];
237     ierr = ISGetLocalSize(sub_schurs->is_subs[j],&subset_size);CHKERRQ(ierr);
238     max_subset_size_seq = PetscMax(subset_size,max_subset_size_seq);
239     local_size += subset_size;
240   }
241 
242   /* Work arrays for local indices */
243   extra = 0;
244   if (sub_schurs->use_mumps) {
245     ierr = ISGetLocalSize(sub_schurs->is_I_layer,&extra);CHKERRQ(ierr);
246   }
247   ierr = PetscMalloc1(local_size+extra,&all_local_idx_N);CHKERRQ(ierr);
248   if (extra) {
249     const PetscInt *idxs;
250     ierr = ISGetIndices(sub_schurs->is_I_layer,&idxs);CHKERRQ(ierr);
251     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
252     ierr = ISRestoreIndices(sub_schurs->is_I_layer,&idxs);CHKERRQ(ierr);
253   }
254   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
255 
256   /* Get local indices in local numbering */
257   local_size = 0;
258   for (i=0;i<sub_schurs->n_subs_seq;i++) {
259     PetscInt j;
260     const    PetscInt *idxs;
261 
262     PetscInt local_problem_index = sub_schurs->index_sequential[i];
263     ierr = ISGetLocalSize(sub_schurs->is_subs[local_problem_index],&subset_size);CHKERRQ(ierr);
264     ierr = ISGetIndices(sub_schurs->is_subs[local_problem_index],&idxs);CHKERRQ(ierr);
265     /* subset indices in local numbering */
266     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
267     ierr = ISRestoreIndices(sub_schurs->is_subs[local_problem_index],&idxs);CHKERRQ(ierr);
268     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
269     local_size += subset_size;
270   }
271 
272   S_all = NULL;
273   sub_schurs->is_hermitian = PETSC_FALSE;
274   sub_schurs->is_posdef = PETSC_FALSE;
275   if (sub_schurs->A) {
276     ierr = MatIsHermitian(sub_schurs->A,0.0,&sub_schurs->is_hermitian);CHKERRQ(ierr);
277     if (sub_schurs->is_hermitian) {
278       PetscScalar val;
279       Vec         vec1,vec2;
280 
281       ierr = MatCreateVecs(sub_schurs->A,&vec1,&vec2);CHKERRQ(ierr);
282       ierr = VecSetRandom(vec1,NULL);
283       ierr = VecCopy(vec1,vec2);CHKERRQ(ierr);
284       ierr = MatMult(sub_schurs->A,vec2,vec1);CHKERRQ(ierr);
285       ierr = VecDot(vec1,vec2,&val);CHKERRQ(ierr);
286       if (PetscRealPart(val) > 0. && PetscImaginaryPart(val) == 0.) sub_schurs->is_posdef = PETSC_TRUE;
287       ierr = VecDestroy(&vec1);CHKERRQ(ierr);
288       ierr = VecDestroy(&vec2);CHKERRQ(ierr);
289     }
290   }
291 
292   if (sub_schurs->n_subs) {
293     if (!sub_schurs->use_mumps) {
294       /* subsets in original and boundary numbering */
295       for (i=0;i<sub_schurs->n_subs;i++) {
296         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B[i]);CHKERRQ(ierr);
297       }
298 
299       /* EE block */
300       for (i=0;i<sub_schurs->n_subs;i++) {
301         ierr = MatGetSubMatrix(A_BB,is_subset_B[i],is_subset_B[i],MAT_INITIAL_MATRIX,&AE_EE[i]);CHKERRQ(ierr);
302       }
303 
304       /* IE block */
305       for (i=0;i<sub_schurs->n_subs;i++) {
306         ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B[i],MAT_INITIAL_MATRIX,&AE_IE[i]);CHKERRQ(ierr);
307       }
308 
309       /* EI block */
310       for (i=0;i<sub_schurs->n_subs;i++) {
311         if (sub_schurs->is_hermitian) {
312           ierr = MatCreateTranspose(AE_IE[i],&AE_EI[i]);CHKERRQ(ierr);
313         } else {
314           ierr = MatGetSubMatrix(A_BI,is_subset_B[i],is_I,MAT_INITIAL_MATRIX,&AE_EI[i]);CHKERRQ(ierr);
315         }
316       }
317 
318       /* setup Schur complements on subset */
319       for (i=0;i<sub_schurs->n_subs;i++) {
320         ierr = MatDestroy(&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
321         ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE[i],AE_EI[i],AE_EE[i],&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
322         ierr = MatDestroy(&AE_EE[i]);CHKERRQ(ierr);
323         ierr = MatDestroy(&AE_IE[i]);CHKERRQ(ierr);
324         ierr = MatDestroy(&AE_EI[i]);CHKERRQ(ierr);
325         if (AE_II == A_II) { /* we can reuse the same ksp */
326           KSP ksp;
327           ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
328           ierr = MatSchurComplementSetKSP(sub_schurs->S_Ej[i],ksp);CHKERRQ(ierr);
329         } else { /* build new ksp object which inherits ksp and pc types from the original one */
330           KSP      origksp,schurksp;
331           PC       origpc,schurpc;
332           KSPType  ksp_type;
333           PCType   pc_type;
334           PetscInt n_internal;
335 
336           ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
337           ierr = MatSchurComplementGetKSP(sub_schurs->S_Ej[i],&schurksp);CHKERRQ(ierr);
338           ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
339           ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
340           ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
341           ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
342           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
343           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
344           ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
345           if (n_internal) { /* UMFPACK gives error with 0 sized problems */
346             MatSolverPackage solver=NULL;
347             ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
348             if (solver) {
349               ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
350             }
351           }
352           ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
353         }
354       }
355       /* free */
356       ierr = ISDestroy(&is_I);CHKERRQ(ierr);
357       ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
358       for (i=0;i<sub_schurs->n_subs;i++) {
359         ierr = ISDestroy(&is_subset_B[i]);CHKERRQ(ierr);
360       }
361       ierr = PetscFree4(is_subset_B,AE_IE,AE_EI,AE_EE);CHKERRQ(ierr);
362 #if defined(PETSC_HAVE_MUMPS)
363     } else {
364       Mat           A,F;
365       IS            is_A_all;
366       PetscInt      *idxs_schur,n_I;
367 
368       /* get working mat */
369       ierr = ISGetLocalSize(sub_schurs->is_I_layer,&n_I);CHKERRQ(ierr);
370       ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size+n_I,all_local_idx_N,PETSC_COPY_VALUES,&is_A_all);CHKERRQ(ierr);
371       ierr = MatGetSubMatrixUnsorted(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
372       ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
373 
374       if (n_I) {
375         if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
376           ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
377         } else {
378           ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
379         }
380 
381         /* subsets ordered last */
382         ierr = PetscMalloc1(local_size,&idxs_schur);CHKERRQ(ierr);
383         for (i=0;i<local_size;i++) {
384           idxs_schur[i] = n_I+i+1;
385         }
386         ierr = MatMumpsSetSchurIndices(F,local_size,idxs_schur);CHKERRQ(ierr);
387         ierr = PetscFree(idxs_schur);CHKERRQ(ierr);
388 
389         /* factorization step */
390         if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
391           ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
392           ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
393         } else {
394           ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
395           ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
396         }
397 
398         /* get explicit Schur Complement computed during numeric factorization */
399         ierr = MatMumpsGetSchurComplement(F,&S_all);CHKERRQ(ierr);
400         ierr = MatDestroy(&F);CHKERRQ(ierr);
401       } else {
402         ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
403       }
404       ierr = MatDestroy(&A);CHKERRQ(ierr);
405 #endif
406     }
407   } else {
408     ierr = PetscFree(nnz);CHKERRQ(ierr);
409     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
410   }
411 
412   if (!sub_schurs->n_subs_seq_g) {
413     PetscFunctionReturn(0);
414   }
415 
416   /* subset indices in local boundary numbering */
417   if (!sub_schurs->is_Ej_all) {
418     PetscInt *all_local_idx_B;
419 
420     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
421     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
422     if (subset_size != local_size) {
423       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %d != %d\n",subset_size,local_size);
424     }
425     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
426   }
427 
428   /* Local matrix of all local Schur on subsets transposed */
429   if (!sub_schurs->S_Ej_all) {
430     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
431     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
432     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
433     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
434   } else {
435     ierr = MatZeroEntries(sub_schurs->S_Ej_all);CHKERRQ(ierr);
436   }
437 
438   S_Ej_tilda_all = 0;
439   S_Ej_inv_all = 0;
440   Bwork = NULL;
441   pivots = NULL;
442   if (sub_schurs->n_subs && deluxe && compute_Stilda && !sub_schurs->is_hermitian) { /* workspace needed only for GETRI */
443     PetscScalar lwork;
444 
445     B_lwork = -1;
446     ierr = PetscBLASIntCast(max_subset_size_seq,&B_N);CHKERRQ(ierr);
447     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
448     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,Bwork,&B_N,pivots,&lwork,&B_lwork,&B_ierr));
449     ierr = PetscFPTrapPop();CHKERRQ(ierr);
450     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
451     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
452     ierr = PetscMalloc2(B_lwork,&Bwork,max_subset_size_seq,&pivots);CHKERRQ(ierr);
453   }
454 
455   ierr = PetscBTMemzero(sub_schurs->n_subs,sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
456   if (!sub_schurs->use_mumps) {
457     if (sub_schurs->n_subs_seq) {
458       PetscScalar *work;
459       PetscInt    *dummy_idx;
460 
461       /* Work arrays */
462       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,max_subset_size_seq*max_subset_size_seq,&work);CHKERRQ(ierr);
463 
464       /* Loop on local problems end compute Schur complements explicitly */
465       local_size = 0;
466       for (i=0;i<sub_schurs->n_subs_seq;i++) {
467         Mat       S_Ej_expl;
468         PetscInt  j,lpi = sub_schurs->index_sequential[i];
469         PetscBool Sdense;
470 
471         ierr = ISGetLocalSize(sub_schurs->is_subs[lpi],&subset_size);CHKERRQ(ierr);
472         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
473         ierr = PCBDDCComputeExplicitSchur(sub_schurs->S_Ej[lpi],sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
474         ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
475         if (Sdense) {
476           for (j=0;j<subset_size;j++) {
477             dummy_idx[j]=local_size+j;
478           }
479           ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
480         } else {
481           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
482         }
483         local_size += subset_size;
484         ierr = MatDestroy(&sub_schurs->S_Ej[lpi]);CHKERRQ(ierr);
485         sub_schurs->S_Ej[lpi] = S_Ej_expl;
486       }
487       ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
488     }
489   } else {
490     PetscInt    *dummy_idx,n_all;
491     PetscScalar *work;
492 
493     if (compute_Stilda) {
494       ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_tilda_all);CHKERRQ(ierr);
495       ierr = MatSetSizes(S_Ej_tilda_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
496       ierr = MatSetType(S_Ej_tilda_all,MATAIJ);CHKERRQ(ierr);
497       ierr = MatSeqAIJSetPreallocation(S_Ej_tilda_all,0,nnz);CHKERRQ(ierr);
498       if (deluxe) {
499         ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_inv_all);CHKERRQ(ierr);
500         ierr = MatSetSizes(S_Ej_inv_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
501         ierr = MatSetType(S_Ej_inv_all,MATAIJ);CHKERRQ(ierr);
502         ierr = MatSeqAIJSetPreallocation(S_Ej_inv_all,0,nnz);CHKERRQ(ierr);
503       }
504     }
505 
506     if (S_all) { /* multilevel */
507       ierr = MatGetSize(S_all,&n_all,NULL);CHKERRQ(ierr);
508     } else {
509       n_all = 0;
510     }
511     local_size = 0;
512 
513     /* Work arrays */
514     if (compute_Stilda) {
515       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,n_all*n_all,&work);CHKERRQ(ierr);
516     } else {
517       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,0,&work);CHKERRQ(ierr);
518     }
519 
520     for (i=0;i<sub_schurs->n_subs;i++) {
521       IS  is_E;
522       PetscScalar *vals;
523       PetscInt j;
524 
525       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
526       for (j=0;j<subset_size;j++) {
527         dummy_idx[j]=local_size+j;
528       }
529       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),subset_size,local_size,1,&is_E);CHKERRQ(ierr);
530       if (sub_schurs->S_Ej[i]) {
531         ierr = MatGetSubMatrix(S_all,is_E,is_E,MAT_REUSE_MATRIX,&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
532       } else {
533         ierr = MatGetSubMatrix(S_all,is_E,is_E,MAT_INITIAL_MATRIX,&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
534       }
535       ierr = MatDenseGetArray(sub_schurs->S_Ej[i],&vals);CHKERRQ(ierr);
536       ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,vals,INSERT_VALUES);CHKERRQ(ierr);
537       ierr = MatDenseRestoreArray(sub_schurs->S_Ej[i],&vals);CHKERRQ(ierr);
538 
539       if (compute_Stilda && ((PetscBTLookup(sub_schurs->is_edge,i) && use_edges) || use_faces)) {
540         Mat Stilda;
541 
542         ierr = PetscBTSet(sub_schurs->computed_Stilda_subs,i);CHKERRQ(ierr);
543         if (sub_schurs->n_subs == 1) {
544           ierr = PetscObjectReference((PetscObject)sub_schurs->S_Ej[i]);CHKERRQ(ierr);
545           Stilda = sub_schurs->S_Ej[i];
546         } else {
547           KSP         ksp;
548           PC          pc;
549           Mat         S_EF,S_FE,S_FF,Stilda_impl;
550           IS          is_F;
551           PetscInt    nc,cum;
552           PetscBool   chop=PETSC_FALSE;
553 
554           ierr = ISComplement(is_E,0,n_all,&is_F);CHKERRQ(ierr);
555           nc   = n_all - subset_size;
556           cum  = 0;
557           ierr = MatCreateSeqDense(PETSC_COMM_SELF,nc,nc,work+cum,&S_FF);CHKERRQ(ierr);
558           cum += nc*nc;
559           ierr = MatCreateSeqDense(PETSC_COMM_SELF,nc,subset_size,work+cum,&S_FE);CHKERRQ(ierr);
560           cum += nc*subset_size;
561           ierr = MatGetSubMatrix(S_all,is_F,is_F,MAT_REUSE_MATRIX,&S_FF);CHKERRQ(ierr);
562           ierr = MatGetSubMatrix(S_all,is_F,is_E,MAT_REUSE_MATRIX,&S_FE);CHKERRQ(ierr);
563           if (sub_schurs->is_hermitian) { /* just need a placeholder for S_EF */
564             ierr = MatCreateTranspose(S_FE,&S_EF);CHKERRQ(ierr);
565           } else {
566             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,nc,work+cum,&S_EF);CHKERRQ(ierr);
567             cum += nc*subset_size;
568             ierr = MatGetSubMatrix(S_all,is_E,is_F,MAT_REUSE_MATRIX,&S_EF);CHKERRQ(ierr);
569           }
570           ierr = ISDestroy(&is_F);CHKERRQ(ierr);
571           if (chop) {
572             PetscReal eps=1.e-8;
573             ierr = MatChop(S_FF,eps);CHKERRQ(ierr);
574             ierr = MatConvert(S_FF,MATAIJ,MAT_REUSE_MATRIX,&S_FF);CHKERRQ(ierr);
575           }
576           ierr = MatCreateSchurComplement(S_FF,S_FF,S_FE,S_EF,sub_schurs->S_Ej[i],&Stilda_impl);CHKERRQ(ierr);
577           ierr = MatDestroy(&S_FF);CHKERRQ(ierr);
578           ierr = MatDestroy(&S_FE);CHKERRQ(ierr);
579           ierr = MatDestroy(&S_EF);CHKERRQ(ierr);
580           ierr = MatSchurComplementGetKSP(Stilda_impl,&ksp);CHKERRQ(ierr);
581           ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
582           ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
583           if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
584             ierr = PCSetType(pc,PCCHOLESKY);CHKERRQ(ierr);
585           } else {
586             ierr = PCSetType(pc,PCLU);CHKERRQ(ierr);
587           }
588           if (!chop) {
589             ierr = PCFactorSetUseInPlace(pc,PETSC_TRUE);CHKERRQ(ierr);
590           } else {
591             ierr = PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS);CHKERRQ(ierr);
592           }
593           ierr = KSPSetUp(ksp);CHKERRQ(ierr);
594           ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work+cum,&Stilda);CHKERRQ(ierr);
595           ierr = PCBDDCComputeExplicitSchur(Stilda_impl,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&Stilda);CHKERRQ(ierr);
596           ierr = MatDestroy(&Stilda_impl);CHKERRQ(ierr);
597         }
598 /*
599         PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);
600         ierr = MatView(Stilda,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
601         PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
602 */
603         ierr = MatDenseGetArray(Stilda,&vals);CHKERRQ(ierr);
604         if (deluxe) { /* when using deluxe scaling, we need (S_1^-1+S_2^-1)^-1 */
605           PetscScalar *vals2;
606 
607           ierr = MatDenseGetArray(sub_schurs->S_Ej[i],&vals2);CHKERRQ(ierr);
608           ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
609           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
610           if (invert_Stildas) { /* Stildas can be singular */
611             if (!sub_schurs->is_hermitian) {
612               PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,vals,&B_N,pivots,&B_ierr));
613               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
614               PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,vals,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
615               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
616             } else {
617               PetscInt j,k;
618 
619               PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,vals,&B_N,&B_ierr));
620               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
621               PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,vals,&B_N,&B_ierr));
622               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
623               for (j=0;j<B_N;j++) {
624                 for (k=j+1;k<B_N;k++) {
625                   vals[k*B_N+j] = vals[j*B_N+k];
626                 }
627               }
628             }
629           }
630           if (!sub_schurs->is_hermitian) {
631             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,vals2,&B_N,pivots,&B_ierr));
632             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
633             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,vals2,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
634             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
635           } else {
636             PetscInt j,k;
637 
638             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,vals2,&B_N,&B_ierr));
639             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
640             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,vals2,&B_N,&B_ierr));
641             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
642             for (j=0;j<B_N;j++) {
643               for (k=j+1;k<B_N;k++) {
644                 vals2[k*B_N+j] = vals2[j*B_N+k];
645               }
646             }
647           }
648           ierr = PetscFPTrapPop();CHKERRQ(ierr);
649           ierr = MatSetValues(S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,vals2,INSERT_VALUES);CHKERRQ(ierr);
650           ierr = MatDenseRestoreArray(sub_schurs->S_Ej[i],&vals2);CHKERRQ(ierr);
651         }
652         ierr = MatSetValues(S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,vals,INSERT_VALUES);CHKERRQ(ierr);
653         ierr = MatDenseRestoreArray(Stilda,&vals);CHKERRQ(ierr);
654         ierr = MatDestroy(&Stilda);CHKERRQ(ierr);
655       }
656       ierr = ISDestroy(&is_E);CHKERRQ(ierr);
657       local_size += subset_size;
658     }
659     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
660   }
661   ierr = PetscFree(nnz);CHKERRQ(ierr);
662   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
663   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
664   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
665   if (S_Ej_tilda_all) {
666     ierr = MatAssemblyBegin(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
667     ierr = MatAssemblyEnd(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
668   }
669   if (S_Ej_inv_all) {
670     ierr = MatAssemblyBegin(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
671     ierr = MatAssemblyEnd(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
672   }
673 
674   /* Global matrix of all assembled Schur on subsets */
675   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)sub_schurs->l2gmap),sub_schurs->l2gmap,local_size,all_local_idx_N+extra,PETSC_NULL,&global_size,&all_local_idx_G);CHKERRQ(ierr);
676   ierr = ISLocalToGlobalMappingCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),1,local_size,all_local_idx_G,PETSC_COPY_VALUES,&l2gmap_subsets);CHKERRQ(ierr);
677   ierr = MatCreateIS(PetscObjectComm((PetscObject)sub_schurs->l2gmap),1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,&work_mat);CHKERRQ(ierr);
678   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
679   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
680   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
681   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
682   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
683   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
684   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
685   /* Get local part of (\sum_j S_Ej) */
686   ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
687   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->l2gmap),local_size,all_local_idx_G,PETSC_OWN_POINTER,&temp_is);CHKERRQ(ierr);
688   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
689   ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
690 
691   if (S_Ej_tilda_all) {
692     ierr = MatISSetLocalMat(work_mat,S_Ej_tilda_all);CHKERRQ(ierr);
693     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
694     ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
695     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
696   }
697   if (S_Ej_inv_all) {
698     PetscInt    cum;
699     PetscScalar *array,*array2;
700     ierr = MatISSetLocalMat(work_mat,S_Ej_inv_all);CHKERRQ(ierr);
701     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
702     ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
703     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
704     /* invert blocks of sum_S_Ej_inv_all */
705     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&array);CHKERRQ(ierr);
706     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array2);CHKERRQ(ierr);
707     cum = 0;
708     for (i=0;i<sub_schurs->n_subs;i++) {
709       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
710       if (PetscBTLookup(sub_schurs->computed_Stilda_subs,i)) {
711         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
712         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
713         if (!sub_schurs->is_hermitian) {
714           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
715           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
716           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
717           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
718         } else {
719           PetscInt j,k;
720 
721           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
722           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
723           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
724           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
725           for (j=0;j<B_N;j++) {
726             for (k=j+1;k<B_N;k++) {
727               array[k*B_N+j+cum] = array[j*B_N+k+cum];
728             }
729           }
730         }
731         if (invert_Stildas) { /* Stildas can be singular */
732           if (!sub_schurs->is_hermitian) {
733             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array2+cum,&B_N,pivots,&B_ierr));
734             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
735             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array2+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
736             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
737           } else {
738             PetscInt j,k;
739 
740             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array2+cum,&B_N,&B_ierr));
741             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
742             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array2+cum,&B_N,&B_ierr));
743             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
744             for (j=0;j<B_N;j++) {
745               for (k=j+1;k<B_N;k++) {
746                 array2[k*B_N+j+cum] = array2[j*B_N+k+cum];
747               }
748             }
749           }
750         }
751         ierr = PetscFPTrapPop();CHKERRQ(ierr);
752       }
753       cum += subset_size*subset_size;
754     }
755     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&array);CHKERRQ(ierr);
756     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array2);CHKERRQ(ierr);
757   }
758 
759   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
760   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
761   ierr = MatDestroy(&S_Ej_tilda_all);CHKERRQ(ierr);
762   ierr = MatDestroy(&S_Ej_inv_all);CHKERRQ(ierr);
763   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
764   ierr = ISDestroy(&temp_is);CHKERRQ(ierr);
765   PetscFunctionReturn(0);
766 }
767 
768 #undef __FUNCT__
769 #define __FUNCT__ "PCBDDCSubSchursInit"
770 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, Mat A, Mat S, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscInt seqthreshold)
771 {
772   IS                  *faces,*edges,*all_cc,vertices;
773   PetscInt            *index_sequential,*index_parallel;
774   PetscInt            *auxlocal_sequential,*auxlocal_parallel;
775   PetscInt            *auxglobal_sequential,*auxglobal_parallel;
776   PetscInt            *auxmapping;
777   PetscInt            i,max_subset_size;
778   PetscInt            n_sequential_problems,n_local_sequential_problems,n_parallel_problems,n_local_parallel_problems;
779   PetscInt            n_faces,n_edges,n_all_cc;
780   PetscBool           is_sorted;
781   PetscErrorCode  ierr;
782 
783   PetscFunctionBegin;
784   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
785   if (!is_sorted) {
786     SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
787   }
788   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
789   if (!is_sorted) {
790     SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
791   }
792 
793   /* reset any previous data */
794   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
795 
796   /* get index sets for faces and edges */
797   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
798   n_all_cc = n_faces+n_edges;
799   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
800   ierr = PetscBTCreate(n_all_cc,&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
801   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
802   for (i=0;i<n_faces;i++) {
803     all_cc[i] = faces[i];
804   }
805   for (i=0;i<n_edges;i++) {
806     all_cc[n_faces+i] = edges[i];
807     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
808   }
809   ierr = PetscFree(faces);CHKERRQ(ierr);
810   ierr = PetscFree(edges);CHKERRQ(ierr);
811 
812   /* map interface's subsets */
813   max_subset_size = 0;
814   for (i=0;i<n_all_cc;i++) {
815     PetscInt subset_size;
816     ierr = ISGetLocalSize(all_cc[i],&subset_size);CHKERRQ(ierr);
817     max_subset_size = PetscMax(max_subset_size,subset_size);
818   }
819   ierr = PetscMalloc1(max_subset_size,&auxmapping);CHKERRQ(ierr);
820   ierr = PetscMalloc2(graph->ncc,&auxlocal_sequential,
821                       graph->ncc,&auxlocal_parallel);CHKERRQ(ierr);
822   ierr = PetscMalloc2(graph->ncc,&index_sequential,
823                       graph->ncc,&index_parallel);CHKERRQ(ierr);
824 
825   /* if threshold is negative uses all sequential problems (possibly using MUMPS) */
826   sub_schurs->use_mumps = PETSC_FALSE;
827   if (seqthreshold < 0) {
828     seqthreshold = max_subset_size;
829 #if defined(PETSC_HAVE_MUMPS)
830     sub_schurs->use_mumps = (PetscBool)(!!A);
831 #endif
832   }
833 
834 
835   /* determine which problem has to be solved in parallel or sequentially */
836   n_local_sequential_problems = 0;
837   n_local_parallel_problems = 0;
838   for (i=0;i<n_all_cc;i++) {
839     PetscInt       subset_size,j,min_loc = 0;
840     const PetscInt *idxs;
841 
842     ierr = ISGetLocalSize(all_cc[i],&subset_size);CHKERRQ(ierr);
843     ierr = ISGetIndices(all_cc[i],&idxs);CHKERRQ(ierr);
844     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,subset_size,idxs,auxmapping);CHKERRQ(ierr);
845     for (j=1;j<subset_size;j++) {
846       if (auxmapping[j]<auxmapping[min_loc]) {
847         min_loc = j;
848       }
849     }
850     if (subset_size > seqthreshold) {
851       index_parallel[n_local_parallel_problems] = i;
852       auxlocal_parallel[n_local_parallel_problems] = idxs[min_loc];
853       n_local_parallel_problems++;
854     } else {
855       index_sequential[n_local_sequential_problems] = i;
856       auxlocal_sequential[n_local_sequential_problems] = idxs[min_loc];
857       n_local_sequential_problems++;
858     }
859     ierr = ISRestoreIndices(all_cc[i],&idxs);CHKERRQ(ierr);
860   }
861 
862   /* Number parallel problems */
863   auxglobal_parallel = 0;
864   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)graph->l2gmap),graph->l2gmap,n_local_parallel_problems,auxlocal_parallel,PETSC_NULL,&n_parallel_problems,&auxglobal_parallel);CHKERRQ(ierr);
865 
866   /* Number sequential problems */
867   auxglobal_sequential = 0;
868   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)graph->l2gmap),graph->l2gmap,n_local_sequential_problems,auxlocal_sequential,PETSC_NULL,&n_sequential_problems,&auxglobal_sequential);CHKERRQ(ierr);
869 
870   /* update info in sub_schurs */
871   if (A) {
872     PetscBool isseqaij;
873 
874     ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
875     if (isseqaij) {
876       ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);
877       sub_schurs->A = A;
878     } else { /* SeqBAIJ matrices does not support symmetry checking, SeqSBAIJ does not support MatPermute */
879       ierr = MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
880     }
881   }
882   ierr = PetscObjectReference((PetscObject)S);CHKERRQ(ierr);
883   sub_schurs->S = S;
884   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
885   sub_schurs->is_I = is_I;
886   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
887   sub_schurs->is_B = is_B;
888   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
889   sub_schurs->l2gmap = graph->l2gmap;
890   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
891   sub_schurs->BtoNmap = BtoNmap;
892   sub_schurs->n_subs_seq = n_local_sequential_problems;
893   sub_schurs->n_subs_par = n_local_parallel_problems;
894   sub_schurs->n_subs_seq_g = n_sequential_problems;
895   sub_schurs->n_subs_par_g = n_parallel_problems;
896   sub_schurs->n_subs = sub_schurs->n_subs_seq + sub_schurs->n_subs_par;
897   sub_schurs->is_subs = all_cc;
898   if (!sub_schurs->use_mumps) { /* for adaptive selection */
899     for (i=0;i<sub_schurs->n_subs;i++) {
900       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
901     }
902   }
903   sub_schurs->is_Ej_com = vertices;
904   sub_schurs->index_sequential = index_sequential;
905   sub_schurs->index_parallel = index_parallel;
906   sub_schurs->auxglobal_sequential = auxglobal_sequential;
907   sub_schurs->auxglobal_parallel = auxglobal_parallel;
908 
909 
910   /* allocate space for schur complements */
911   ierr = PetscCalloc1(sub_schurs->n_subs,&sub_schurs->S_Ej);CHKERRQ(ierr);
912   sub_schurs->S_Ej_all = NULL;
913   sub_schurs->sum_S_Ej_all = NULL;
914   sub_schurs->sum_S_Ej_inv_all = NULL;
915   sub_schurs->sum_S_Ej_tilda_all = NULL;
916   sub_schurs->is_Ej_all = NULL;
917 
918   /* free workspace */
919   ierr = PetscFree(auxmapping);CHKERRQ(ierr);
920   ierr = PetscFree2(auxlocal_sequential,auxlocal_parallel);CHKERRQ(ierr);
921 
922   PetscFunctionReturn(0);
923 }
924 
925 #undef __FUNCT__
926 #define __FUNCT__ "PCBDDCSubSchursCreate"
927 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
928 {
929   PCBDDCSubSchurs schurs_ctx;
930   PetscErrorCode  ierr;
931 
932   PetscFunctionBegin;
933   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
934   schurs_ctx->n_subs = 0;
935   *sub_schurs = schurs_ctx;
936   PetscFunctionReturn(0);
937 }
938 
939 #undef __FUNCT__
940 #define __FUNCT__ "PCBDDCSubSchursDestroy"
941 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs *sub_schurs)
942 {
943   PetscErrorCode ierr;
944 
945   PetscFunctionBegin;
946   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
947   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
948   PetscFunctionReturn(0);
949 }
950 
951 #undef __FUNCT__
952 #define __FUNCT__ "PCBDDCSubSchursReset"
953 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
954 {
955   PetscInt       i;
956   PetscErrorCode ierr;
957 
958   PetscFunctionBegin;
959   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
960   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
961   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
962   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
963   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
964   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
965   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
966   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
967   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
968   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
969   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
970   ierr = ISDestroy(&sub_schurs->is_Ej_com);CHKERRQ(ierr);
971   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
972   ierr = PetscBTDestroy(&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
973   for (i=0;i<sub_schurs->n_subs;i++) {
974     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
975     ierr = MatDestroy(&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
976   }
977   ierr = ISDestroy(&sub_schurs->is_I_layer);CHKERRQ(ierr);
978   if (sub_schurs->n_subs) {
979     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
980     ierr = PetscFree(sub_schurs->S_Ej);CHKERRQ(ierr);
981   }
982   ierr = PetscFree2(sub_schurs->index_sequential,sub_schurs->index_parallel);CHKERRQ(ierr);
983   ierr = PetscFree(sub_schurs->auxglobal_sequential);CHKERRQ(ierr);
984   ierr = PetscFree(sub_schurs->auxglobal_parallel);CHKERRQ(ierr);
985   sub_schurs->n_subs = 0;
986   PetscFunctionReturn(0);
987 }
988 
989 #undef __FUNCT__
990 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
991 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
992 {
993   PetscInt       i,j,n;
994   PetscErrorCode ierr;
995 
996   PetscFunctionBegin;
997   n = 0;
998   for (i=-n_prev;i<0;i++) {
999     PetscInt start_dof = queue_tip[i];
1000     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1001       PetscInt dof = adjncy[j];
1002       if (!PetscBTLookup(touched,dof)) {
1003         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1004         queue_tip[n] = dof;
1005         n++;
1006       }
1007     }
1008   }
1009   *n_added = n;
1010   PetscFunctionReturn(0);
1011 }
1012