xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 2972d61b0bb859cde3c4726a4aafdfae2a88254b)
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   PetscMPIInt    size;
18   PetscErrorCode ierr;
19 
20   PetscFunctionBegin;
21   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);CHKERRQ(ierr);
22   if (size != 1) {
23     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not for parallel matrices");
24   }
25   ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
26   ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
27   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
28   ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
29   ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
30   ierr = PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);CHKERRQ(ierr);
31   ierr = PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);CHKERRQ(ierr);
32   ierr = PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);CHKERRQ(ierr);
33   if (!Bdense) {
34     ierr = MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
35   } else {
36     Bd = B;
37   }
38 
39   if (isLU || isILU || isCHOL) {
40     Mat fact;
41 
42     ierr = KSPSetUp(ksp);CHKERRQ(ierr);
43     ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
44     ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
45     ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
46   } else {
47     Mat Ainvd;
48 
49     ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
50     ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
51     ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
52   }
53   if (!Bdense & !issym) {
54     ierr = MatDestroy(&Bd);CHKERRQ(ierr);
55   }
56 
57   if (!issym) {
58     if (!Cdense) {
59       ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
60     } else {
61       Cd = C;
62     }
63     ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
64     if (!Cdense) {
65       ierr = MatDestroy(&Cd);CHKERRQ(ierr);
66     }
67   } else {
68     ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
69     if (!Bdense) {
70       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
71     }
72   }
73   ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
74 
75   if (D) {
76     Mat       Dd;
77     PetscBool Ddense;
78 
79     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
80     if (!Ddense) {
81       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
82     } else {
83       Dd = D;
84     }
85     ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
86     if (!Ddense) {
87       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
88     }
89   } else {
90     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
91   }
92   PetscFunctionReturn(0);
93 }
94 
95 #undef __FUNCT__
96 #define __FUNCT__ "PCBDDCSubSchursSetUp"
97 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)
98 {
99   Mat                    A_II,A_IB,A_BI,A_BB;
100   Mat                    AE_II,*AE_IE,*AE_EI,*AE_EE;
101   Mat                    S_all,global_schur_subsets,work_mat;
102   Mat                    S_Ej_tilda_all,S_Ej_inv_all;
103   ISLocalToGlobalMapping l2gmap_subsets;
104   IS                     is_I,*is_subset_B,temp_is;
105   PetscInt               *nnz,*all_local_idx_G,*all_local_idx_B,*all_local_idx_N;
106   PetscInt               i,subset_size,max_subset_size_seq;
107   PetscInt               extra,local_size,global_size;
108   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
109   PetscScalar            *Bwork;
110   PetscErrorCode         ierr;
111 
112   PetscFunctionBegin;
113   /* get Schur complement matrices */
114   if (!sub_schurs->use_mumps) {
115     if (compute_Stilda) {
116       SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS");
117     }
118     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&A_IB,&A_BI,&A_BB);CHKERRQ(ierr);
119     ierr = PetscMalloc4(sub_schurs->n_subs,&is_subset_B,
120                         sub_schurs->n_subs,&AE_IE,
121                         sub_schurs->n_subs,&AE_EI,
122                         sub_schurs->n_subs,&AE_EE);CHKERRQ(ierr);
123   } else {
124     is_subset_B = NULL;
125     AE_IE = NULL;
126     AE_EI = NULL;
127     AE_EE = NULL;
128   }
129 
130   /* determine interior problems */
131   ierr = ISDestroy(&sub_schurs->is_I_layer);CHKERRQ(ierr);
132   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
133   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
134     PetscBT                touched;
135     const PetscInt*        idx_B;
136     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
137 
138     if (xadj == NULL || adjncy == NULL) {
139       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
140     }
141     /* get sizes */
142     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
143     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
144 
145     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
146     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
147     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
148 
149     /* all boundary dofs must be skipped when adding layers */
150     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
151     for (j=0;j<n_B;j++) {
152       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
153     }
154     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
155     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
156 
157     /* add prescribed number of layers of dofs */
158     n_local_dofs = n_B;
159     n_prev_added = n_B;
160     for (layer=0;layer<nlayers;layer++) {
161       PetscInt n_added;
162       if (n_local_dofs == n_I+n_B) break;
163       if (n_local_dofs > n_I+n_B) {
164         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);
165       }
166       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
167       n_prev_added = n_added;
168       n_local_dofs += n_added;
169       if (!n_added) break;
170     }
171     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
172 
173     /* IS for I layer dofs in original numbering */
174     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);
175     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
176     ierr = ISSort(sub_schurs->is_I_layer);CHKERRQ(ierr);
177     /* IS for I layer dofs in I numbering */
178     if (!sub_schurs->use_mumps) {
179       ISLocalToGlobalMapping ItoNmap;
180       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
181       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,sub_schurs->is_I_layer,&is_I);CHKERRQ(ierr);
182       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
183 
184       /* II block */
185       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
186     }
187   } else {
188     PetscInt n_I;
189 
190     /* IS for I dofs in original numbering */
191     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
192     sub_schurs->is_I_layer = sub_schurs->is_I;
193 
194     /* IS for I dofs in I numbering (strided 1) */
195     if (!sub_schurs->use_mumps) {
196       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
197       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
198 
199       /* II block is the same */
200       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
201       AE_II = A_II;
202     }
203   }
204   /* Get info on subset sizes and sum of all subsets sizes */
205   max_subset_size_seq = 0;
206   local_size = 0;
207   for (i=0;i<sub_schurs->n_subs_seq;i++) {
208     PetscInt j = sub_schurs->index_sequential[i];
209     ierr = ISGetLocalSize(sub_schurs->is_subs[j],&subset_size);CHKERRQ(ierr);
210     max_subset_size_seq = PetscMax(subset_size,max_subset_size_seq);
211     local_size += subset_size;
212   }
213 
214   /* Work arrays for local indices */
215   ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
216   extra = 0;
217   if (sub_schurs->use_mumps) {
218     ierr = ISGetLocalSize(sub_schurs->is_I_layer,&extra);CHKERRQ(ierr);
219   }
220   ierr = PetscMalloc1(local_size+extra,&all_local_idx_N);CHKERRQ(ierr);
221   if (extra) {
222     const PetscInt *idxs;
223     ierr = ISGetIndices(sub_schurs->is_I_layer,&idxs);CHKERRQ(ierr);
224     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
225     ierr = ISRestoreIndices(sub_schurs->is_I_layer,&idxs);CHKERRQ(ierr);
226   }
227   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
228 
229   /* Get local indices in local numbering */
230   local_size = 0;
231   for (i=0;i<sub_schurs->n_subs_seq;i++) {
232     PetscInt j;
233     const    PetscInt *idxs;
234 
235     PetscInt local_problem_index = sub_schurs->index_sequential[i];
236     ierr = ISGetLocalSize(sub_schurs->is_subs[local_problem_index],&subset_size);CHKERRQ(ierr);
237     ierr = ISGetIndices(sub_schurs->is_subs[local_problem_index],&idxs);CHKERRQ(ierr);
238     /* subset indices in local numbering */
239     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
240     ierr = ISRestoreIndices(sub_schurs->is_subs[local_problem_index],&idxs);CHKERRQ(ierr);
241     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
242     local_size += subset_size;
243   }
244 
245   S_all = NULL;
246   sub_schurs->is_hermitian = PETSC_FALSE;
247   sub_schurs->is_posdef = PETSC_FALSE;
248   if (sub_schurs->A) {
249     ierr = MatIsHermitian(sub_schurs->A,0.0,&sub_schurs->is_hermitian);CHKERRQ(ierr);
250     if (sub_schurs->is_hermitian) {
251       PetscScalar val;
252       Vec         vec1,vec2;
253 
254       ierr = MatCreateVecs(sub_schurs->A,&vec1,&vec2);CHKERRQ(ierr);
255       ierr = VecSetRandom(vec1,NULL);
256       ierr = VecCopy(vec1,vec2);CHKERRQ(ierr);
257       ierr = MatMult(sub_schurs->A,vec2,vec1);CHKERRQ(ierr);
258       ierr = VecDot(vec1,vec2,&val);CHKERRQ(ierr);
259       if (PetscRealPart(val) > 0. && PetscImaginaryPart(val) == 0.) sub_schurs->is_posdef = PETSC_TRUE;
260       ierr = VecDestroy(&vec1);CHKERRQ(ierr);
261       ierr = VecDestroy(&vec2);CHKERRQ(ierr);
262     }
263   }
264 
265   if (sub_schurs->n_subs) {
266     if (!sub_schurs->use_mumps) {
267       /* subsets in original and boundary numbering */
268       for (i=0;i<sub_schurs->n_subs;i++) {
269         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B[i]);CHKERRQ(ierr);
270       }
271 
272       /* EE block */
273       for (i=0;i<sub_schurs->n_subs;i++) {
274         ierr = MatGetSubMatrix(A_BB,is_subset_B[i],is_subset_B[i],MAT_INITIAL_MATRIX,&AE_EE[i]);CHKERRQ(ierr);
275       }
276 
277       /* IE block */
278       for (i=0;i<sub_schurs->n_subs;i++) {
279         ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B[i],MAT_INITIAL_MATRIX,&AE_IE[i]);CHKERRQ(ierr);
280       }
281 
282       /* EI block */
283       for (i=0;i<sub_schurs->n_subs;i++) {
284         if (sub_schurs->is_hermitian) {
285           ierr = MatCreateTranspose(AE_IE[i],&AE_EI[i]);CHKERRQ(ierr);
286         } else {
287           ierr = MatGetSubMatrix(A_BI,is_subset_B[i],is_I,MAT_INITIAL_MATRIX,&AE_EI[i]);CHKERRQ(ierr);
288         }
289       }
290 
291       /* setup Schur complements on subset */
292       for (i=0;i<sub_schurs->n_subs;i++) {
293         ierr = MatDestroy(&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
294         ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE[i],AE_EI[i],AE_EE[i],&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
295         ierr = MatDestroy(&AE_EE[i]);CHKERRQ(ierr);
296         ierr = MatDestroy(&AE_IE[i]);CHKERRQ(ierr);
297         ierr = MatDestroy(&AE_EI[i]);CHKERRQ(ierr);
298         if (AE_II == A_II) { /* we can reuse the same ksp */
299           KSP ksp;
300           ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
301           ierr = MatSchurComplementSetKSP(sub_schurs->S_Ej[i],ksp);CHKERRQ(ierr);
302         } else { /* build new ksp object which inherits ksp and pc types from the original one */
303           KSP      origksp,schurksp;
304           PC       origpc,schurpc;
305           KSPType  ksp_type;
306           PCType   pc_type;
307           PetscInt n_internal;
308 
309           ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
310           ierr = MatSchurComplementGetKSP(sub_schurs->S_Ej[i],&schurksp);CHKERRQ(ierr);
311           ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
312           ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
313           ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
314           ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
315           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
316           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
317           ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
318           if (n_internal) { /* UMFPACK gives error with 0 sized problems */
319             MatSolverPackage solver=NULL;
320             ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
321             if (solver) {
322               ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
323             }
324           }
325           ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
326         }
327       }
328       /* free */
329       ierr = ISDestroy(&is_I);CHKERRQ(ierr);
330       ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
331       for (i=0;i<sub_schurs->n_subs;i++) {
332         ierr = ISDestroy(&is_subset_B[i]);CHKERRQ(ierr);
333       }
334       ierr = PetscFree4(is_subset_B,AE_IE,AE_EI,AE_EE);CHKERRQ(ierr);
335 #if defined(PETSC_HAVE_MUMPS)
336     } else {
337       Mat           A,F;
338       IS            is_A_all;
339       PetscInt      *idxs_schur,n_I;
340 
341       /* get working mat */
342       ierr = ISGetLocalSize(sub_schurs->is_I_layer,&n_I);CHKERRQ(ierr);
343       ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size+n_I,all_local_idx_N,PETSC_COPY_VALUES,&is_A_all);CHKERRQ(ierr);
344       ierr = MatGetSubMatrixUnsorted(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
345       ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
346 
347       if (n_I) {
348         if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
349           ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
350         } else {
351           ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
352         }
353 
354         /* subsets ordered last */
355         ierr = PetscMalloc1(local_size,&idxs_schur);CHKERRQ(ierr);
356         for (i=0;i<local_size;i++) {
357           idxs_schur[i] = n_I+i+1;
358         }
359         ierr = MatMumpsSetSchurIndices(F,local_size,idxs_schur);CHKERRQ(ierr);
360         ierr = PetscFree(idxs_schur);CHKERRQ(ierr);
361 
362         /* factorization step */
363         if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
364           ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
365           ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
366         } else {
367           ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
368           ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
369         }
370 
371         /* get explicit Schur Complement computed during numeric factorization */
372         ierr = MatMumpsGetSchurComplement(F,&S_all);CHKERRQ(ierr);
373         ierr = MatDestroy(&F);CHKERRQ(ierr);
374       } else {
375         ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
376       }
377       ierr = MatDestroy(&A);CHKERRQ(ierr);
378 #endif
379     }
380   } else {
381     ierr = PetscFree(nnz);CHKERRQ(ierr);
382     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
383   }
384 
385   if (!sub_schurs->n_subs_seq_g) {
386     PetscFunctionReturn(0);
387   }
388 
389   /* subset indices in local boundary numbering */
390   if (!sub_schurs->is_Ej_all) {
391     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
392     if (subset_size != local_size) {
393       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %d != %d\n",subset_size,local_size);
394     }
395     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
396   }
397 
398   /* Local matrix of all local Schur on subsets transposed */
399   if (!sub_schurs->S_Ej_all) {
400     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
401     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
402     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
403     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
404   } else {
405     ierr = MatZeroEntries(sub_schurs->S_Ej_all);CHKERRQ(ierr);
406   }
407 
408   S_Ej_tilda_all = 0;
409   S_Ej_inv_all = 0;
410   Bwork = NULL;
411   pivots = NULL;
412   if (sub_schurs->n_subs && deluxe && compute_Stilda && !sub_schurs->is_hermitian) { /* workspace needed only for GETRI */
413     PetscScalar lwork;
414 
415     B_lwork = -1;
416     ierr = PetscBLASIntCast(max_subset_size_seq,&B_N);CHKERRQ(ierr);
417     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
418     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,Bwork,&B_N,pivots,&lwork,&B_lwork,&B_ierr));
419     ierr = PetscFPTrapPop();CHKERRQ(ierr);
420     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
421     ierr = PetscBLASIntCast((PetscInt)lwork,&B_lwork);CHKERRQ(ierr);
422     ierr = PetscMalloc2(B_lwork,&Bwork,max_subset_size_seq,&pivots);CHKERRQ(ierr);
423   }
424 
425   ierr = PetscBTMemzero(sub_schurs->n_subs,sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
426   if (!sub_schurs->use_mumps) {
427     if (sub_schurs->n_subs_seq) {
428       PetscScalar *work;
429       PetscInt    *dummy_idx;
430 
431       /* Work arrays */
432       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,max_subset_size_seq*max_subset_size_seq,&work);CHKERRQ(ierr);
433 
434       /* Loop on local problems end compute Schur complements explicitly */
435       local_size = 0;
436       for (i=0;i<sub_schurs->n_subs_seq;i++) {
437         Mat       S_Ej_expl;
438         PetscInt  j,lpi = sub_schurs->index_sequential[i];
439         PetscBool Sdense;
440 
441         ierr = ISGetLocalSize(sub_schurs->is_subs[lpi],&subset_size);CHKERRQ(ierr);
442         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
443         ierr = PCBDDCComputeExplicitSchur(sub_schurs->S_Ej[lpi],sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
444         ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
445         if (Sdense) {
446           for (j=0;j<subset_size;j++) {
447             dummy_idx[j]=local_size+j;
448           }
449           ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
450         } else {
451           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
452         }
453         local_size += subset_size;
454         ierr = MatDestroy(&sub_schurs->S_Ej[lpi]);CHKERRQ(ierr);
455         sub_schurs->S_Ej[lpi] = S_Ej_expl;
456       }
457       ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
458     }
459   } else {
460     PetscInt    *dummy_idx,n_all;
461     PetscScalar *work;
462 
463     if (compute_Stilda) {
464       ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_tilda_all);CHKERRQ(ierr);
465       ierr = MatSetSizes(S_Ej_tilda_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
466       ierr = MatSetType(S_Ej_tilda_all,MATAIJ);CHKERRQ(ierr);
467       ierr = MatSeqAIJSetPreallocation(S_Ej_tilda_all,0,nnz);CHKERRQ(ierr);
468       if (deluxe) {
469         ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_inv_all);CHKERRQ(ierr);
470         ierr = MatSetSizes(S_Ej_inv_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
471         ierr = MatSetType(S_Ej_inv_all,MATAIJ);CHKERRQ(ierr);
472         ierr = MatSeqAIJSetPreallocation(S_Ej_inv_all,0,nnz);CHKERRQ(ierr);
473       }
474     }
475 
476     if (S_all) { /* multilevel */
477       ierr = MatGetSize(S_all,&n_all,NULL);CHKERRQ(ierr);
478     } else {
479       n_all = 0;
480     }
481     local_size = 0;
482 
483     /* Work arrays */
484     if (compute_Stilda) {
485       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,n_all*n_all,&work);CHKERRQ(ierr);
486     } else {
487       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,0,&work);CHKERRQ(ierr);
488     }
489 
490     for (i=0;i<sub_schurs->n_subs;i++) {
491       IS  is_E;
492       PetscScalar *vals;
493       PetscInt j;
494 
495       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
496       for (j=0;j<subset_size;j++) {
497         dummy_idx[j]=local_size+j;
498       }
499       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),subset_size,local_size,1,&is_E);CHKERRQ(ierr);
500       if (sub_schurs->S_Ej[i]) {
501         ierr = MatGetSubMatrix(S_all,is_E,is_E,MAT_REUSE_MATRIX,&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
502       } else {
503         ierr = MatGetSubMatrix(S_all,is_E,is_E,MAT_INITIAL_MATRIX,&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
504       }
505       ierr = MatDenseGetArray(sub_schurs->S_Ej[i],&vals);CHKERRQ(ierr);
506       ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,vals,INSERT_VALUES);CHKERRQ(ierr);
507       ierr = MatDenseRestoreArray(sub_schurs->S_Ej[i],&vals);CHKERRQ(ierr);
508 
509       if (compute_Stilda && ((PetscBTLookup(sub_schurs->is_edge,i) && use_edges) || use_faces)) {
510         Mat Stilda;
511 
512         ierr = PetscBTSet(sub_schurs->computed_Stilda_subs,i);CHKERRQ(ierr);
513         if (sub_schurs->n_subs == 1) {
514           ierr = PetscObjectReference((PetscObject)sub_schurs->S_Ej[i]);CHKERRQ(ierr);
515           Stilda = sub_schurs->S_Ej[i];
516         } else {
517           KSP         ksp;
518           PC          pc;
519           Mat         S_EF,S_FE,S_FF,Stilda_impl;
520           IS          is_F;
521           PetscScalar eps=1.e-8;
522           PetscInt    nc,cum;
523           PetscBool   chop=PETSC_FALSE;
524 
525           ierr = ISComplement(is_E,0,n_all,&is_F);CHKERRQ(ierr);
526           nc   = n_all - subset_size;
527           cum  = 0;
528           ierr = MatCreateSeqDense(PETSC_COMM_SELF,nc,nc,work+cum,&S_FF);CHKERRQ(ierr);
529           cum += nc*nc;
530           ierr = MatCreateSeqDense(PETSC_COMM_SELF,nc,subset_size,work+cum,&S_FE);CHKERRQ(ierr);
531           cum += nc*subset_size;
532           ierr = MatGetSubMatrix(S_all,is_F,is_F,MAT_REUSE_MATRIX,&S_FF);CHKERRQ(ierr);
533           ierr = MatGetSubMatrix(S_all,is_F,is_E,MAT_REUSE_MATRIX,&S_FE);CHKERRQ(ierr);
534           if (sub_schurs->is_hermitian) { /* just need a placeholder for S_EF */
535             ierr = MatCreateTranspose(S_FE,&S_EF);CHKERRQ(ierr);
536           } else {
537             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,nc,work+cum,&S_EF);CHKERRQ(ierr);
538             cum += nc*subset_size;
539             ierr = MatGetSubMatrix(S_all,is_E,is_F,MAT_REUSE_MATRIX,&S_EF);CHKERRQ(ierr);
540           }
541           ierr = ISDestroy(&is_F);CHKERRQ(ierr);
542           if (chop) {
543             ierr = MatChop(S_FF,eps);CHKERRQ(ierr);
544             ierr = MatConvert(S_FF,MATAIJ,MAT_REUSE_MATRIX,&S_FF);CHKERRQ(ierr);
545           }
546           ierr = MatCreateSchurComplement(S_FF,S_FF,S_FE,S_EF,sub_schurs->S_Ej[i],&Stilda_impl);CHKERRQ(ierr);
547           ierr = MatDestroy(&S_FF);CHKERRQ(ierr);
548           ierr = MatDestroy(&S_FE);CHKERRQ(ierr);
549           ierr = MatDestroy(&S_EF);CHKERRQ(ierr);
550           ierr = MatSchurComplementGetKSP(Stilda_impl,&ksp);CHKERRQ(ierr);
551           ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
552           ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
553           if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
554             ierr = PCSetType(pc,PCCHOLESKY);CHKERRQ(ierr);
555           } else {
556             ierr = PCSetType(pc,PCLU);CHKERRQ(ierr);
557           }
558           if (!chop) {
559             ierr = PCFactorSetUseInPlace(pc,PETSC_TRUE);CHKERRQ(ierr);
560           } else {
561             ierr = PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS);CHKERRQ(ierr);
562           }
563           ierr = KSPSetUp(ksp);CHKERRQ(ierr);
564           ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work+cum,&Stilda);CHKERRQ(ierr);
565           ierr = PCBDDCComputeExplicitSchur(Stilda_impl,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&Stilda);CHKERRQ(ierr);
566           ierr = MatDestroy(&Stilda_impl);CHKERRQ(ierr);
567         }
568 /*
569         PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);
570         ierr = MatView(Stilda,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
571         PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
572 */
573         ierr = MatDenseGetArray(Stilda,&vals);CHKERRQ(ierr);
574         if (deluxe) { /* when using deluxe scaling, we need (S_1^-1+S_2^-1)^-1 */
575           PetscScalar *vals2;
576 
577           ierr = MatDenseGetArray(sub_schurs->S_Ej[i],&vals2);CHKERRQ(ierr);
578           ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
579           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
580           if (invert_Stildas) { /* Stildas can be singular */
581             if (!sub_schurs->is_hermitian) {
582               PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,vals,&B_N,pivots,&B_ierr));
583               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
584               PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,vals,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
585               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
586             } else {
587               PetscInt j,k;
588 
589               PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,vals,&B_N,&B_ierr));
590               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
591               PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,vals,&B_N,&B_ierr));
592               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
593               for (j=0;j<B_N;j++) {
594                 for (k=j+1;k<B_N;k++) {
595                   vals[k*B_N+j] = vals[j*B_N+k];
596                 }
597               }
598             }
599           }
600           if (!sub_schurs->is_hermitian) {
601             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,vals2,&B_N,pivots,&B_ierr));
602             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
603             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,vals2,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
604             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
605           } else {
606             PetscInt j,k;
607 
608             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,vals2,&B_N,&B_ierr));
609             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
610             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,vals2,&B_N,&B_ierr));
611             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
612             for (j=0;j<B_N;j++) {
613               for (k=j+1;k<B_N;k++) {
614                 vals2[k*B_N+j] = vals2[j*B_N+k];
615               }
616             }
617           }
618           ierr = PetscFPTrapPop();CHKERRQ(ierr);
619           ierr = MatSetValues(S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,vals2,INSERT_VALUES);CHKERRQ(ierr);
620           ierr = MatDenseRestoreArray(sub_schurs->S_Ej[i],&vals2);CHKERRQ(ierr);
621         }
622         ierr = MatSetValues(S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,vals,INSERT_VALUES);CHKERRQ(ierr);
623         ierr = MatDenseRestoreArray(Stilda,&vals);CHKERRQ(ierr);
624         ierr = MatDestroy(&Stilda);CHKERRQ(ierr);
625       }
626       ierr = ISDestroy(&is_E);CHKERRQ(ierr);
627       local_size += subset_size;
628     }
629     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
630   }
631   ierr = PetscFree(nnz);CHKERRQ(ierr);
632   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
633   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
634   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
635   if (S_Ej_tilda_all) {
636     ierr = MatAssemblyBegin(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
637     ierr = MatAssemblyEnd(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
638   }
639   if (S_Ej_inv_all) {
640     ierr = MatAssemblyBegin(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
641     ierr = MatAssemblyEnd(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
642   }
643 
644   /* Global matrix of all assembled Schur on subsets */
645   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);
646   ierr = ISLocalToGlobalMappingCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),1,local_size,all_local_idx_G,PETSC_COPY_VALUES,&l2gmap_subsets);CHKERRQ(ierr);
647   ierr = MatCreateIS(PetscObjectComm((PetscObject)sub_schurs->l2gmap),1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,&work_mat);CHKERRQ(ierr);
648   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
649   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
650   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
651   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
652   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
653   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
654   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
655   /* Get local part of (\sum_j S_Ej) */
656   ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
657   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->l2gmap),local_size,all_local_idx_G,PETSC_OWN_POINTER,&temp_is);CHKERRQ(ierr);
658   if (sub_schurs->sum_S_Ej_all) {
659     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,MAT_REUSE_MATRIX,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
660   } else {
661     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,MAT_INITIAL_MATRIX,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
662   }
663 
664   if (S_Ej_tilda_all) {
665     ierr = MatISSetLocalMat(work_mat,S_Ej_tilda_all);CHKERRQ(ierr);
666     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
667     if (sub_schurs->sum_S_Ej_tilda_all) {
668       ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,MAT_REUSE_MATRIX,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
669     } else {
670       ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,MAT_INITIAL_MATRIX,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
671     }
672   }
673   if (S_Ej_inv_all) {
674     PetscInt    cum;
675     PetscScalar *array,*array2;
676     ierr = MatISSetLocalMat(work_mat,S_Ej_inv_all);CHKERRQ(ierr);
677     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
678     if (sub_schurs->sum_S_Ej_inv_all) {
679       ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,MAT_REUSE_MATRIX,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
680     } else {
681       ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,MAT_INITIAL_MATRIX,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
682     }
683     /* invert blocks of sum_S_Ej_inv_all */
684     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&array);CHKERRQ(ierr);
685     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array2);CHKERRQ(ierr);
686     cum = 0;
687     for (i=0;i<sub_schurs->n_subs;i++) {
688       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
689       if (PetscBTLookup(sub_schurs->computed_Stilda_subs,i)) {
690         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
691         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
692         if (!sub_schurs->is_hermitian) {
693           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
694           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
695           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
696           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
697         } else {
698           PetscInt j,k;
699 
700           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
701           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
702           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
703           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
704           for (j=0;j<B_N;j++) {
705             for (k=j+1;k<B_N;k++) {
706               array[k*B_N+j+cum] = array[j*B_N+k+cum];
707             }
708           }
709         }
710         if (invert_Stildas) { /* Stildas can be singular */
711           if (!sub_schurs->is_hermitian) {
712             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array2+cum,&B_N,pivots,&B_ierr));
713             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
714             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array2+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
715             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
716           } else {
717             PetscInt j,k;
718 
719             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array2+cum,&B_N,&B_ierr));
720             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
721             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array2+cum,&B_N,&B_ierr));
722             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
723             for (j=0;j<B_N;j++) {
724               for (k=j+1;k<B_N;k++) {
725                 array2[k*B_N+j+cum] = array2[j*B_N+k+cum];
726               }
727             }
728           }
729         }
730         ierr = PetscFPTrapPop();CHKERRQ(ierr);
731       }
732       cum += subset_size*subset_size;
733     }
734     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&array);CHKERRQ(ierr);
735     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array2);CHKERRQ(ierr);
736   }
737 
738   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
739   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
740   ierr = MatDestroy(&S_Ej_tilda_all);CHKERRQ(ierr);
741   ierr = MatDestroy(&S_Ej_inv_all);CHKERRQ(ierr);
742   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
743   ierr = ISDestroy(&temp_is);CHKERRQ(ierr);
744   PetscFunctionReturn(0);
745 }
746 
747 #undef __FUNCT__
748 #define __FUNCT__ "PCBDDCSubSchursInit"
749 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, Mat A, Mat S, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscInt seqthreshold)
750 {
751   IS                  *faces,*edges,*all_cc,vertices;
752   PetscInt            *index_sequential,*index_parallel;
753   PetscInt            *auxlocal_sequential,*auxlocal_parallel;
754   PetscInt            *auxglobal_sequential,*auxglobal_parallel;
755   PetscInt            *auxmapping;
756   PetscInt            i,max_subset_size;
757   PetscInt            n_sequential_problems,n_local_sequential_problems,n_parallel_problems,n_local_parallel_problems;
758   PetscInt            n_faces,n_edges,n_all_cc;
759   PetscBool           is_sorted;
760   PetscErrorCode  ierr;
761 
762   PetscFunctionBegin;
763   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
764   if (!is_sorted) {
765     SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
766   }
767   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
768   if (!is_sorted) {
769     SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
770   }
771 
772   /* reset any previous data */
773   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
774 
775   /* get index sets for faces and edges */
776   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
777   n_all_cc = n_faces+n_edges;
778   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
779   ierr = PetscBTCreate(n_all_cc,&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
780   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
781   for (i=0;i<n_faces;i++) {
782     all_cc[i] = faces[i];
783   }
784   for (i=0;i<n_edges;i++) {
785     all_cc[n_faces+i] = edges[i];
786     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
787   }
788   ierr = PetscFree(faces);CHKERRQ(ierr);
789   ierr = PetscFree(edges);CHKERRQ(ierr);
790 
791   /* map interface's subsets */
792   max_subset_size = 0;
793   for (i=0;i<n_all_cc;i++) {
794     PetscInt subset_size;
795     ierr = ISGetLocalSize(all_cc[i],&subset_size);CHKERRQ(ierr);
796     max_subset_size = PetscMax(max_subset_size,subset_size);
797   }
798   ierr = PetscMalloc1(max_subset_size,&auxmapping);CHKERRQ(ierr);
799   ierr = PetscMalloc2(graph->ncc,&auxlocal_sequential,
800                       graph->ncc,&auxlocal_parallel);CHKERRQ(ierr);
801   ierr = PetscMalloc2(graph->ncc,&index_sequential,
802                       graph->ncc,&index_parallel);CHKERRQ(ierr);
803 
804   /* if threshold is negative uses all sequential problems (possibly using MUMPS) */
805   sub_schurs->use_mumps = PETSC_FALSE;
806   if (seqthreshold < 0) {
807     seqthreshold = max_subset_size;
808 #if defined(PETSC_HAVE_MUMPS)
809     sub_schurs->use_mumps = !!A;
810 #endif
811   }
812 
813 
814   /* determine which problem has to be solved in parallel or sequentially */
815   n_local_sequential_problems = 0;
816   n_local_parallel_problems = 0;
817   for (i=0;i<n_all_cc;i++) {
818     PetscInt       subset_size,j,min_loc = 0;
819     const PetscInt *idxs;
820 
821     ierr = ISGetLocalSize(all_cc[i],&subset_size);CHKERRQ(ierr);
822     ierr = ISGetIndices(all_cc[i],&idxs);CHKERRQ(ierr);
823     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,subset_size,idxs,auxmapping);CHKERRQ(ierr);
824     for (j=1;j<subset_size;j++) {
825       if (auxmapping[j]<auxmapping[min_loc]) {
826         min_loc = j;
827       }
828     }
829     if (subset_size > seqthreshold) {
830       index_parallel[n_local_parallel_problems] = i;
831       auxlocal_parallel[n_local_parallel_problems] = idxs[min_loc];
832       n_local_parallel_problems++;
833     } else {
834       index_sequential[n_local_sequential_problems] = i;
835       auxlocal_sequential[n_local_sequential_problems] = idxs[min_loc];
836       n_local_sequential_problems++;
837     }
838     ierr = ISRestoreIndices(all_cc[i],&idxs);CHKERRQ(ierr);
839   }
840 
841   /* Number parallel problems */
842   auxglobal_parallel = 0;
843   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)graph->l2gmap),graph->l2gmap,n_local_parallel_problems,auxlocal_parallel,PETSC_NULL,&n_parallel_problems,&auxglobal_parallel);CHKERRQ(ierr);
844 
845   /* Number sequential problems */
846   auxglobal_sequential = 0;
847   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)graph->l2gmap),graph->l2gmap,n_local_sequential_problems,auxlocal_sequential,PETSC_NULL,&n_sequential_problems,&auxglobal_sequential);CHKERRQ(ierr);
848 
849   /* update info in sub_schurs */
850   if (A) {
851     PetscBool isseqaij;
852 
853     ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
854     if (isseqaij) {
855       ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);
856       sub_schurs->A = A;
857     } else { /* SeqBAIJ matrices does not support symmetry checking, SeqSBAIJ does not support MatPermute */
858       ierr = MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
859     }
860   }
861   ierr = PetscObjectReference((PetscObject)S);CHKERRQ(ierr);
862   sub_schurs->S = S;
863   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
864   sub_schurs->is_I = is_I;
865   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
866   sub_schurs->is_B = is_B;
867   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
868   sub_schurs->l2gmap = graph->l2gmap;
869   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
870   sub_schurs->BtoNmap = BtoNmap;
871   sub_schurs->n_subs_seq = n_local_sequential_problems;
872   sub_schurs->n_subs_par = n_local_parallel_problems;
873   sub_schurs->n_subs_seq_g = n_sequential_problems;
874   sub_schurs->n_subs_par_g = n_parallel_problems;
875   sub_schurs->n_subs = sub_schurs->n_subs_seq + sub_schurs->n_subs_par;
876   sub_schurs->is_subs = all_cc;
877   if (!sub_schurs->use_mumps) { /* for adaptive selection */
878     for (i=0;i<sub_schurs->n_subs;i++) {
879       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
880     }
881   }
882   sub_schurs->is_Ej_com = vertices;
883   sub_schurs->index_sequential = index_sequential;
884   sub_schurs->index_parallel = index_parallel;
885   sub_schurs->auxglobal_sequential = auxglobal_sequential;
886   sub_schurs->auxglobal_parallel = auxglobal_parallel;
887 
888 
889   /* allocate space for schur complements */
890   ierr = PetscCalloc1(sub_schurs->n_subs,&sub_schurs->S_Ej);CHKERRQ(ierr);
891   sub_schurs->S_Ej_all = NULL;
892   sub_schurs->sum_S_Ej_all = NULL;
893   sub_schurs->sum_S_Ej_inv_all = NULL;
894   sub_schurs->sum_S_Ej_tilda_all = NULL;
895   sub_schurs->is_Ej_all = NULL;
896 
897   /* free workspace */
898   ierr = PetscFree(auxmapping);CHKERRQ(ierr);
899   ierr = PetscFree2(auxlocal_sequential,auxlocal_parallel);CHKERRQ(ierr);
900 
901   PetscFunctionReturn(0);
902 }
903 
904 #undef __FUNCT__
905 #define __FUNCT__ "PCBDDCSubSchursCreate"
906 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
907 {
908   PCBDDCSubSchurs schurs_ctx;
909   PetscErrorCode  ierr;
910 
911   PetscFunctionBegin;
912   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
913   schurs_ctx->n_subs = 0;
914   *sub_schurs = schurs_ctx;
915   PetscFunctionReturn(0);
916 }
917 
918 #undef __FUNCT__
919 #define __FUNCT__ "PCBDDCSubSchursDestroy"
920 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs *sub_schurs)
921 {
922   PetscErrorCode ierr;
923 
924   PetscFunctionBegin;
925   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
926   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
927   PetscFunctionReturn(0);
928 }
929 
930 #undef __FUNCT__
931 #define __FUNCT__ "PCBDDCSubSchursReset"
932 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
933 {
934   PetscInt       i;
935   PetscErrorCode ierr;
936 
937   PetscFunctionBegin;
938   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
939   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
940   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
941   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
942   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
943   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
944   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
945   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
946   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
947   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
948   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
949   ierr = ISDestroy(&sub_schurs->is_Ej_com);CHKERRQ(ierr);
950   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
951   ierr = PetscBTDestroy(&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
952   for (i=0;i<sub_schurs->n_subs;i++) {
953     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
954     ierr = MatDestroy(&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
955   }
956   ierr = ISDestroy(&sub_schurs->is_I_layer);CHKERRQ(ierr);
957   if (sub_schurs->n_subs) {
958     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
959     ierr = PetscFree(sub_schurs->S_Ej);CHKERRQ(ierr);
960   }
961   ierr = PetscFree2(sub_schurs->index_sequential,sub_schurs->index_parallel);CHKERRQ(ierr);
962   ierr = PetscFree(sub_schurs->auxglobal_sequential);CHKERRQ(ierr);
963   ierr = PetscFree(sub_schurs->auxglobal_parallel);CHKERRQ(ierr);
964   sub_schurs->n_subs = 0;
965   PetscFunctionReturn(0);
966 }
967 
968 #undef __FUNCT__
969 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
970 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
971 {
972   PetscInt       i,j,n;
973   PetscErrorCode ierr;
974 
975   PetscFunctionBegin;
976   n = 0;
977   for (i=-n_prev;i<0;i++) {
978     PetscInt start_dof = queue_tip[i];
979     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
980       PetscInt dof = adjncy[j];
981       if (!PetscBTLookup(touched,dof)) {
982         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
983         queue_tip[n] = dof;
984         n++;
985       }
986     }
987   }
988   *n_added = n;
989   PetscFunctionReturn(0);
990 }
991