xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 07b1e237e1d2cae94a0f38f9255e13fd97bbfafd)
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       PetscBool ex = PETSC_TRUE;
59 
60       if (ex) {
61         Mat Ainvd;
62 
63         ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
64         ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
65         ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
66       } else {
67         Vec         sol,rhs;
68         PetscScalar *arrayrhs,*arraysol;
69         PetscInt    i,nrhs,n;
70 
71         ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
72         ierr = MatGetSize(Bd,&n,&nrhs);CHKERRQ(ierr);
73         ierr = MatDenseGetArray(Bd,&arrayrhs);CHKERRQ(ierr);
74         ierr = MatDenseGetArray(AinvBd,&arraysol);CHKERRQ(ierr);
75         ierr = KSPGetSolution(ksp,&sol);CHKERRQ(ierr);
76         ierr = KSPGetRhs(ksp,&rhs);CHKERRQ(ierr);
77         for (i=0;i<nrhs;i++) {
78           ierr = VecPlaceArray(rhs,arrayrhs+i*n);CHKERRQ(ierr);
79           ierr = VecPlaceArray(sol,arraysol+i*n);CHKERRQ(ierr);
80           ierr = KSPSolve(ksp,rhs,sol);CHKERRQ(ierr);
81           ierr = VecResetArray(rhs);CHKERRQ(ierr);
82           ierr = VecResetArray(sol);CHKERRQ(ierr);
83         }
84         ierr = MatDenseRestoreArray(Bd,&arrayrhs);CHKERRQ(ierr);
85         ierr = MatDenseRestoreArray(AinvBd,&arrayrhs);CHKERRQ(ierr);
86       }
87     }
88     if (!Bdense & !issym) {
89       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
90     }
91 
92     if (!issym) {
93       if (!Cdense) {
94         ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
95       } else {
96         Cd = C;
97       }
98       ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
99       if (!Cdense) {
100         ierr = MatDestroy(&Cd);CHKERRQ(ierr);
101       }
102     } else {
103       ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
104       if (!Bdense) {
105         ierr = MatDestroy(&Bd);CHKERRQ(ierr);
106       }
107     }
108     ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
109   }
110 
111   if (D) {
112     Mat       Dd;
113     PetscBool Ddense;
114 
115     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
116     if (!Ddense) {
117       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
118     } else {
119       Dd = D;
120     }
121     if (n_I) {
122       ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
123     } else {
124       if (reuse == MAT_INITIAL_MATRIX) {
125         ierr = MatDuplicate(Dd,MAT_COPY_VALUES,S);CHKERRQ(ierr);
126       } else {
127         ierr = MatCopy(Dd,*S,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
128       }
129     }
130     if (!Ddense) {
131       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
132     }
133   } else {
134     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
135   }
136   PetscFunctionReturn(0);
137 }
138 
139 #undef __FUNCT__
140 #define __FUNCT__ "PCBDDCSubSchursSetUp"
141 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)
142 {
143   Mat                    A_II,A_IB,A_BI,A_BB;
144   Mat                    AE_II,*AE_IE,*AE_EI,*AE_EE;
145   Mat                    S_all,global_schur_subsets,work_mat;
146   Mat                    S_Ej_tilda_all,S_Ej_inv_all;
147   ISLocalToGlobalMapping l2gmap_subsets;
148   IS                     is_I,*is_subset_B,temp_is;
149   PetscInt               *nnz,*all_local_idx_G,*all_local_idx_N;
150   PetscInt               i,subset_size,max_subset_size_seq;
151   PetscInt               extra,local_size,global_size;
152   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
153   PetscScalar            *Bwork;
154   PetscErrorCode         ierr;
155 
156   PetscFunctionBegin;
157   /* get Schur complement matrices */
158   if (!sub_schurs->use_mumps) {
159     PetscBool isseqaij;
160 
161     if (compute_Stilda) {
162       SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS");
163     }
164     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&A_IB,&A_BI,&A_BB);CHKERRQ(ierr);
165     ierr = PetscObjectTypeCompare((PetscObject)A_BB,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
166     if (!isseqaij) {
167       ierr = MatConvert(A_BB,MATSEQAIJ,MAT_REUSE_MATRIX,&A_BB);CHKERRQ(ierr);
168       ierr = MatConvert(A_IB,MATSEQAIJ,MAT_REUSE_MATRIX,&A_IB);CHKERRQ(ierr);
169       ierr = MatConvert(A_BI,MATSEQAIJ,MAT_REUSE_MATRIX,&A_BI);CHKERRQ(ierr);
170     }
171     ierr = PetscMalloc4(sub_schurs->n_subs,&is_subset_B,
172                         sub_schurs->n_subs,&AE_IE,
173                         sub_schurs->n_subs,&AE_EI,
174                         sub_schurs->n_subs,&AE_EE);CHKERRQ(ierr);
175   } else {
176     is_subset_B = NULL;
177     AE_IE = NULL;
178     AE_EI = NULL;
179     AE_EE = NULL;
180   }
181 
182   /* determine interior problems */
183   ierr = ISDestroy(&sub_schurs->is_I_layer);CHKERRQ(ierr);
184   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
185   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
186     PetscBT                touched;
187     const PetscInt*        idx_B;
188     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
189 
190     if (xadj == NULL || adjncy == NULL) {
191       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
192     }
193     /* get sizes */
194     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
195     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
196 
197     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
198     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
199     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
200 
201     /* all boundary dofs must be skipped when adding layers */
202     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
203     for (j=0;j<n_B;j++) {
204       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
205     }
206     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
207     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
208 
209     /* add prescribed number of layers of dofs */
210     n_local_dofs = n_B;
211     n_prev_added = n_B;
212     for (layer=0;layer<nlayers;layer++) {
213       PetscInt n_added;
214       if (n_local_dofs == n_I+n_B) break;
215       if (n_local_dofs > n_I+n_B) {
216         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);
217       }
218       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
219       n_prev_added = n_added;
220       n_local_dofs += n_added;
221       if (!n_added) break;
222     }
223     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
224 
225     /* IS for I layer dofs in original numbering */
226     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);
227     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
228     ierr = ISSort(sub_schurs->is_I_layer);CHKERRQ(ierr);
229     /* IS for I layer dofs in I numbering */
230     if (!sub_schurs->use_mumps) {
231       ISLocalToGlobalMapping ItoNmap;
232       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
233       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,sub_schurs->is_I_layer,&is_I);CHKERRQ(ierr);
234       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
235 
236       /* II block */
237       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
238     }
239   } else {
240     PetscInt n_I;
241 
242     /* IS for I dofs in original numbering */
243     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
244     sub_schurs->is_I_layer = sub_schurs->is_I;
245 
246     /* IS for I dofs in I numbering (strided 1) */
247     if (!sub_schurs->use_mumps) {
248       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
249       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
250 
251       /* II block is the same */
252       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
253       AE_II = A_II;
254     }
255   }
256   /* Get info on subset sizes and sum of all subsets sizes */
257   max_subset_size_seq = 0;
258   local_size = 0;
259   for (i=0;i<sub_schurs->n_subs_seq;i++) {
260     PetscInt j = sub_schurs->index_sequential[i];
261     ierr = ISGetLocalSize(sub_schurs->is_subs[j],&subset_size);CHKERRQ(ierr);
262     max_subset_size_seq = PetscMax(subset_size,max_subset_size_seq);
263     local_size += subset_size;
264   }
265 
266   /* Work arrays for local indices */
267   extra = 0;
268   if (sub_schurs->use_mumps) {
269     ierr = ISGetLocalSize(sub_schurs->is_I_layer,&extra);CHKERRQ(ierr);
270   }
271   ierr = PetscMalloc1(local_size+extra,&all_local_idx_N);CHKERRQ(ierr);
272   if (extra) {
273     const PetscInt *idxs;
274     ierr = ISGetIndices(sub_schurs->is_I_layer,&idxs);CHKERRQ(ierr);
275     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
276     ierr = ISRestoreIndices(sub_schurs->is_I_layer,&idxs);CHKERRQ(ierr);
277   }
278   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
279 
280   /* Get local indices in local numbering */
281   local_size = 0;
282   for (i=0;i<sub_schurs->n_subs_seq;i++) {
283     PetscInt j;
284     const    PetscInt *idxs;
285 
286     PetscInt local_problem_index = sub_schurs->index_sequential[i];
287     ierr = ISGetLocalSize(sub_schurs->is_subs[local_problem_index],&subset_size);CHKERRQ(ierr);
288     ierr = ISGetIndices(sub_schurs->is_subs[local_problem_index],&idxs);CHKERRQ(ierr);
289     /* subset indices in local numbering */
290     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
291     ierr = ISRestoreIndices(sub_schurs->is_subs[local_problem_index],&idxs);CHKERRQ(ierr);
292     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
293     local_size += subset_size;
294   }
295 
296   S_all = NULL;
297   sub_schurs->is_hermitian = PETSC_FALSE;
298   sub_schurs->is_posdef = PETSC_FALSE;
299   if (sub_schurs->A) {
300     ierr = MatIsHermitian(sub_schurs->A,0.0,&sub_schurs->is_hermitian);CHKERRQ(ierr);
301     if (sub_schurs->is_hermitian) {
302       PetscScalar val;
303       Vec         vec1,vec2;
304 
305       ierr = MatCreateVecs(sub_schurs->A,&vec1,&vec2);CHKERRQ(ierr);
306       ierr = VecSetRandom(vec1,NULL);
307       ierr = VecCopy(vec1,vec2);CHKERRQ(ierr);
308       ierr = MatMult(sub_schurs->A,vec2,vec1);CHKERRQ(ierr);
309       ierr = VecDot(vec1,vec2,&val);CHKERRQ(ierr);
310       if (PetscRealPart(val) > 0. && PetscImaginaryPart(val) == 0.) sub_schurs->is_posdef = PETSC_TRUE;
311       ierr = VecDestroy(&vec1);CHKERRQ(ierr);
312       ierr = VecDestroy(&vec2);CHKERRQ(ierr);
313     }
314   }
315 
316   if (sub_schurs->n_subs) {
317     if (!sub_schurs->use_mumps) {
318       /* subsets in original and boundary numbering */
319       for (i=0;i<sub_schurs->n_subs;i++) {
320         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B[i]);CHKERRQ(ierr);
321       }
322 
323       /* EE block */
324       for (i=0;i<sub_schurs->n_subs;i++) {
325         ierr = MatGetSubMatrix(A_BB,is_subset_B[i],is_subset_B[i],MAT_INITIAL_MATRIX,&AE_EE[i]);CHKERRQ(ierr);
326       }
327 
328       /* IE block */
329       for (i=0;i<sub_schurs->n_subs;i++) {
330         ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B[i],MAT_INITIAL_MATRIX,&AE_IE[i]);CHKERRQ(ierr);
331       }
332 
333       /* EI block */
334       for (i=0;i<sub_schurs->n_subs;i++) {
335         if (sub_schurs->is_hermitian) {
336           ierr = MatCreateTranspose(AE_IE[i],&AE_EI[i]);CHKERRQ(ierr);
337         } else {
338           ierr = MatGetSubMatrix(A_BI,is_subset_B[i],is_I,MAT_INITIAL_MATRIX,&AE_EI[i]);CHKERRQ(ierr);
339         }
340       }
341 
342       /* setup Schur complements on subset */
343       for (i=0;i<sub_schurs->n_subs;i++) {
344         ierr = MatDestroy(&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
345         ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE[i],AE_EI[i],AE_EE[i],&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
346         ierr = MatDestroy(&AE_EE[i]);CHKERRQ(ierr);
347         ierr = MatDestroy(&AE_IE[i]);CHKERRQ(ierr);
348         ierr = MatDestroy(&AE_EI[i]);CHKERRQ(ierr);
349         if (AE_II == A_II) { /* we can reuse the same ksp */
350           KSP ksp;
351           ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
352           ierr = MatSchurComplementSetKSP(sub_schurs->S_Ej[i],ksp);CHKERRQ(ierr);
353         } else { /* build new ksp object which inherits ksp and pc types from the original one */
354           KSP      origksp,schurksp;
355           PC       origpc,schurpc;
356           KSPType  ksp_type;
357           PCType   pc_type;
358           PetscInt n_internal;
359 
360           ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
361           ierr = MatSchurComplementGetKSP(sub_schurs->S_Ej[i],&schurksp);CHKERRQ(ierr);
362           ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
363           ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
364           ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
365           ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
366           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
367           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
368           ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
369           if (n_internal) { /* UMFPACK gives error with 0 sized problems */
370             MatSolverPackage solver=NULL;
371             ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
372             if (solver) {
373               ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
374             }
375           }
376           ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
377         }
378       }
379       /* free */
380       ierr = ISDestroy(&is_I);CHKERRQ(ierr);
381       ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
382       for (i=0;i<sub_schurs->n_subs;i++) {
383         ierr = ISDestroy(&is_subset_B[i]);CHKERRQ(ierr);
384       }
385       ierr = PetscFree4(is_subset_B,AE_IE,AE_EI,AE_EE);CHKERRQ(ierr);
386 #if defined(PETSC_HAVE_MUMPS)
387     } else {
388       Mat           A,F;
389       IS            is_A_all;
390       PetscInt      *idxs_schur,n_I;
391 
392       /* get working mat */
393       ierr = ISGetLocalSize(sub_schurs->is_I_layer,&n_I);CHKERRQ(ierr);
394       ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size+n_I,all_local_idx_N,PETSC_COPY_VALUES,&is_A_all);CHKERRQ(ierr);
395       ierr = MatGetSubMatrixUnsorted(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
396       ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
397 
398       if (n_I) {
399         if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
400           ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
401         } else {
402           ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
403         }
404 
405         /* subsets ordered last */
406         ierr = PetscMalloc1(local_size,&idxs_schur);CHKERRQ(ierr);
407         for (i=0;i<local_size;i++) {
408           idxs_schur[i] = n_I+i+1;
409         }
410         ierr = MatMumpsSetSchurIndices(F,local_size,idxs_schur);CHKERRQ(ierr);
411         ierr = PetscFree(idxs_schur);CHKERRQ(ierr);
412 
413         /* factorization step */
414         if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
415           ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
416           ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
417         } else {
418           ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
419           ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
420         }
421 
422         /* get explicit Schur Complement computed during numeric factorization */
423         ierr = MatMumpsGetSchurComplement(F,&S_all);CHKERRQ(ierr);
424         ierr = MatDestroy(&F);CHKERRQ(ierr);
425       } else {
426         ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
427       }
428       ierr = MatDestroy(&A);CHKERRQ(ierr);
429 #endif
430     }
431   } else {
432     ierr = PetscFree(nnz);CHKERRQ(ierr);
433     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
434   }
435 
436   if (!sub_schurs->n_subs_seq_g) {
437     PetscFunctionReturn(0);
438   }
439 
440   /* subset indices in local boundary numbering */
441   if (!sub_schurs->is_Ej_all) {
442     PetscInt *all_local_idx_B;
443 
444     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
445     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
446     if (subset_size != local_size) {
447       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %d != %d\n",subset_size,local_size);
448     }
449     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
450   }
451 
452   /* Local matrix of all local Schur on subsets transposed */
453   if (!sub_schurs->S_Ej_all) {
454     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
455     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
456     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
457     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
458   } else {
459     ierr = MatZeroEntries(sub_schurs->S_Ej_all);CHKERRQ(ierr);
460   }
461 
462   S_Ej_tilda_all = 0;
463   S_Ej_inv_all = 0;
464   Bwork = NULL;
465   pivots = NULL;
466   if (sub_schurs->n_subs && deluxe && compute_Stilda && !sub_schurs->is_hermitian) { /* workspace needed only for GETRI */
467     PetscScalar lwork;
468 
469     B_lwork = -1;
470     ierr = PetscBLASIntCast(max_subset_size_seq,&B_N);CHKERRQ(ierr);
471     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
472     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,Bwork,&B_N,pivots,&lwork,&B_lwork,&B_ierr));
473     ierr = PetscFPTrapPop();CHKERRQ(ierr);
474     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
475     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
476     ierr = PetscMalloc2(B_lwork,&Bwork,max_subset_size_seq,&pivots);CHKERRQ(ierr);
477   }
478 
479   ierr = PetscBTMemzero(sub_schurs->n_subs,sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
480   if (!sub_schurs->use_mumps) {
481     if (sub_schurs->n_subs_seq) {
482       PetscScalar *work;
483       PetscInt    *dummy_idx;
484 
485       /* Work arrays */
486       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,max_subset_size_seq*max_subset_size_seq,&work);CHKERRQ(ierr);
487 
488       /* Loop on local problems end compute Schur complements explicitly */
489       local_size = 0;
490       for (i=0;i<sub_schurs->n_subs_seq;i++) {
491         Mat       S_Ej_expl;
492         PetscInt  j,lpi = sub_schurs->index_sequential[i];
493         PetscBool Sdense;
494 
495         ierr = ISGetLocalSize(sub_schurs->is_subs[lpi],&subset_size);CHKERRQ(ierr);
496         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
497         ierr = PCBDDCComputeExplicitSchur(sub_schurs->S_Ej[lpi],sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
498         ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
499         if (Sdense) {
500           for (j=0;j<subset_size;j++) {
501             dummy_idx[j]=local_size+j;
502           }
503           ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
504         } else {
505           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
506         }
507         local_size += subset_size;
508         ierr = MatDestroy(&sub_schurs->S_Ej[lpi]);CHKERRQ(ierr);
509         sub_schurs->S_Ej[lpi] = S_Ej_expl;
510       }
511       ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
512     }
513   } else {
514     PetscInt    *dummy_idx,n_all;
515     PetscScalar *work;
516 
517     if (compute_Stilda) {
518       ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_tilda_all);CHKERRQ(ierr);
519       ierr = MatSetSizes(S_Ej_tilda_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
520       ierr = MatSetType(S_Ej_tilda_all,MATAIJ);CHKERRQ(ierr);
521       ierr = MatSeqAIJSetPreallocation(S_Ej_tilda_all,0,nnz);CHKERRQ(ierr);
522       if (deluxe) {
523         ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_inv_all);CHKERRQ(ierr);
524         ierr = MatSetSizes(S_Ej_inv_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
525         ierr = MatSetType(S_Ej_inv_all,MATAIJ);CHKERRQ(ierr);
526         ierr = MatSeqAIJSetPreallocation(S_Ej_inv_all,0,nnz);CHKERRQ(ierr);
527       }
528     }
529 
530     if (S_all) { /* multilevel */
531       ierr = MatGetSize(S_all,&n_all,NULL);CHKERRQ(ierr);
532     } else {
533       n_all = 0;
534     }
535     local_size = 0;
536 
537     /* Work arrays */
538     if (compute_Stilda) {
539       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,n_all*n_all,&work);CHKERRQ(ierr);
540     } else {
541       ierr = PetscMalloc2(max_subset_size_seq,&dummy_idx,0,&work);CHKERRQ(ierr);
542     }
543 
544     for (i=0;i<sub_schurs->n_subs;i++) {
545       IS  is_E;
546       PetscScalar *vals;
547       PetscInt j;
548 
549       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
550       for (j=0;j<subset_size;j++) {
551         dummy_idx[j]=local_size+j;
552       }
553       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),subset_size,local_size,1,&is_E);CHKERRQ(ierr);
554       if (sub_schurs->S_Ej[i]) {
555         ierr = MatGetSubMatrix(S_all,is_E,is_E,MAT_REUSE_MATRIX,&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
556       } else {
557         ierr = MatGetSubMatrix(S_all,is_E,is_E,MAT_INITIAL_MATRIX,&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
558       }
559       ierr = MatDenseGetArray(sub_schurs->S_Ej[i],&vals);CHKERRQ(ierr);
560       ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,vals,INSERT_VALUES);CHKERRQ(ierr);
561       ierr = MatDenseRestoreArray(sub_schurs->S_Ej[i],&vals);CHKERRQ(ierr);
562 
563       if (compute_Stilda && ((PetscBTLookup(sub_schurs->is_edge,i) && use_edges) || use_faces)) {
564         Mat Stilda;
565 
566         ierr = PetscBTSet(sub_schurs->computed_Stilda_subs,i);CHKERRQ(ierr);
567         if (sub_schurs->n_subs == 1) {
568           ierr = PetscObjectReference((PetscObject)sub_schurs->S_Ej[i]);CHKERRQ(ierr);
569           Stilda = sub_schurs->S_Ej[i];
570         } else {
571           KSP         ksp;
572           PC          pc;
573           Mat         S_EF,S_FE,S_FF,Stilda_impl;
574           IS          is_F;
575           PetscInt    nc,cum;
576           PetscBool   chop=PETSC_FALSE;
577 
578           ierr = ISComplement(is_E,0,n_all,&is_F);CHKERRQ(ierr);
579           nc   = n_all - subset_size;
580           cum  = 0;
581           ierr = MatCreateSeqDense(PETSC_COMM_SELF,nc,nc,work+cum,&S_FF);CHKERRQ(ierr);
582           cum += nc*nc;
583           ierr = MatCreateSeqDense(PETSC_COMM_SELF,nc,subset_size,work+cum,&S_FE);CHKERRQ(ierr);
584           cum += nc*subset_size;
585           ierr = MatGetSubMatrix(S_all,is_F,is_F,MAT_REUSE_MATRIX,&S_FF);CHKERRQ(ierr);
586           ierr = MatGetSubMatrix(S_all,is_F,is_E,MAT_REUSE_MATRIX,&S_FE);CHKERRQ(ierr);
587           if (sub_schurs->is_hermitian) { /* just need a placeholder for S_EF */
588             ierr = MatCreateTranspose(S_FE,&S_EF);CHKERRQ(ierr);
589           } else {
590             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,nc,work+cum,&S_EF);CHKERRQ(ierr);
591             cum += nc*subset_size;
592             ierr = MatGetSubMatrix(S_all,is_E,is_F,MAT_REUSE_MATRIX,&S_EF);CHKERRQ(ierr);
593           }
594           ierr = ISDestroy(&is_F);CHKERRQ(ierr);
595           if (chop) {
596             PetscReal eps=1.e-8;
597             ierr = MatChop(S_FF,eps);CHKERRQ(ierr);
598             ierr = MatConvert(S_FF,MATAIJ,MAT_REUSE_MATRIX,&S_FF);CHKERRQ(ierr);
599           }
600           ierr = MatCreateSchurComplement(S_FF,S_FF,S_FE,S_EF,sub_schurs->S_Ej[i],&Stilda_impl);CHKERRQ(ierr);
601           ierr = MatDestroy(&S_FF);CHKERRQ(ierr);
602           ierr = MatDestroy(&S_FE);CHKERRQ(ierr);
603           ierr = MatDestroy(&S_EF);CHKERRQ(ierr);
604           ierr = MatSchurComplementGetKSP(Stilda_impl,&ksp);CHKERRQ(ierr);
605           ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr);
606           ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
607           if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
608             ierr = PCSetType(pc,PCCHOLESKY);CHKERRQ(ierr);
609           } else {
610             ierr = PCSetType(pc,PCLU);CHKERRQ(ierr);
611           }
612           if (!chop) {
613             ierr = PCFactorSetUseInPlace(pc,PETSC_TRUE);CHKERRQ(ierr);
614           } else {
615             ierr = PCFactorSetMatSolverPackage(pc,MATSOLVERMUMPS);CHKERRQ(ierr);
616           }
617           ierr = KSPSetUp(ksp);CHKERRQ(ierr);
618           ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work+cum,&Stilda);CHKERRQ(ierr);
619           ierr = PCBDDCComputeExplicitSchur(Stilda_impl,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&Stilda);CHKERRQ(ierr);
620           ierr = MatDestroy(&Stilda_impl);CHKERRQ(ierr);
621         }
622 /*
623         PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);
624         ierr = MatView(Stilda,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
625         PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
626 */
627         ierr = MatDenseGetArray(Stilda,&vals);CHKERRQ(ierr);
628         if (deluxe) { /* when using deluxe scaling, we need (S_1^-1+S_2^-1)^-1 */
629           PetscScalar *vals2;
630 
631           ierr = MatDenseGetArray(sub_schurs->S_Ej[i],&vals2);CHKERRQ(ierr);
632           ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
633           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
634           if (invert_Stildas) { /* Stildas can be singular */
635             if (!sub_schurs->is_hermitian) {
636               PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,vals,&B_N,pivots,&B_ierr));
637               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
638               PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,vals,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
639               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
640             } else {
641               PetscInt j,k;
642 
643               PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,vals,&B_N,&B_ierr));
644               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
645               PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,vals,&B_N,&B_ierr));
646               if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
647               for (j=0;j<B_N;j++) {
648                 for (k=j+1;k<B_N;k++) {
649                   vals[k*B_N+j] = vals[j*B_N+k];
650                 }
651               }
652             }
653           }
654           if (!sub_schurs->is_hermitian) {
655             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,vals2,&B_N,pivots,&B_ierr));
656             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
657             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,vals2,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
658             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
659           } else {
660             PetscInt j,k;
661 
662             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,vals2,&B_N,&B_ierr));
663             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
664             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,vals2,&B_N,&B_ierr));
665             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
666             for (j=0;j<B_N;j++) {
667               for (k=j+1;k<B_N;k++) {
668                 vals2[k*B_N+j] = vals2[j*B_N+k];
669               }
670             }
671           }
672           ierr = PetscFPTrapPop();CHKERRQ(ierr);
673           ierr = MatSetValues(S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,vals2,INSERT_VALUES);CHKERRQ(ierr);
674           ierr = MatDenseRestoreArray(sub_schurs->S_Ej[i],&vals2);CHKERRQ(ierr);
675         }
676         ierr = MatSetValues(S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,vals,INSERT_VALUES);CHKERRQ(ierr);
677         ierr = MatDenseRestoreArray(Stilda,&vals);CHKERRQ(ierr);
678         ierr = MatDestroy(&Stilda);CHKERRQ(ierr);
679       }
680       ierr = ISDestroy(&is_E);CHKERRQ(ierr);
681       local_size += subset_size;
682     }
683     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
684   }
685   ierr = PetscFree(nnz);CHKERRQ(ierr);
686   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
687   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
688   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
689   if (S_Ej_tilda_all) {
690     ierr = MatAssemblyBegin(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
691     ierr = MatAssemblyEnd(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
692   }
693   if (S_Ej_inv_all) {
694     ierr = MatAssemblyBegin(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
695     ierr = MatAssemblyEnd(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
696   }
697 
698   /* Global matrix of all assembled Schur on subsets */
699   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);
700   ierr = ISLocalToGlobalMappingCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),1,local_size,all_local_idx_G,PETSC_COPY_VALUES,&l2gmap_subsets);CHKERRQ(ierr);
701   ierr = MatCreateIS(PetscObjectComm((PetscObject)sub_schurs->l2gmap),1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,&work_mat);CHKERRQ(ierr);
702   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
703   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
704   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
705   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
706   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
707   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
708   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
709   /* Get local part of (\sum_j S_Ej) */
710   ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
711   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->l2gmap),local_size,all_local_idx_G,PETSC_OWN_POINTER,&temp_is);CHKERRQ(ierr);
712   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
713   ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
714 
715   if (S_Ej_tilda_all) {
716     ierr = MatISSetLocalMat(work_mat,S_Ej_tilda_all);CHKERRQ(ierr);
717     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
718     ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
719     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
720   }
721   if (S_Ej_inv_all) {
722     PetscInt    cum;
723     PetscScalar *array,*array2;
724     ierr = MatISSetLocalMat(work_mat,S_Ej_inv_all);CHKERRQ(ierr);
725     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
726     ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
727     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
728     /* invert blocks of sum_S_Ej_inv_all */
729     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&array);CHKERRQ(ierr);
730     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array2);CHKERRQ(ierr);
731     cum = 0;
732     for (i=0;i<sub_schurs->n_subs;i++) {
733       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
734       if (PetscBTLookup(sub_schurs->computed_Stilda_subs,i)) {
735         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
736         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
737         if (!sub_schurs->is_hermitian) {
738           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
739           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
740           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
741           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
742         } else {
743           PetscInt j,k;
744 
745           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
746           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
747           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
748           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
749           for (j=0;j<B_N;j++) {
750             for (k=j+1;k<B_N;k++) {
751               array[k*B_N+j+cum] = array[j*B_N+k+cum];
752             }
753           }
754         }
755         if (invert_Stildas) { /* Stildas can be singular */
756           if (!sub_schurs->is_hermitian) {
757             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array2+cum,&B_N,pivots,&B_ierr));
758             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
759             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array2+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
760             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
761           } else {
762             PetscInt j,k;
763 
764             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array2+cum,&B_N,&B_ierr));
765             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
766             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array2+cum,&B_N,&B_ierr));
767             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
768             for (j=0;j<B_N;j++) {
769               for (k=j+1;k<B_N;k++) {
770                 array2[k*B_N+j+cum] = array2[j*B_N+k+cum];
771               }
772             }
773           }
774         }
775         ierr = PetscFPTrapPop();CHKERRQ(ierr);
776       }
777       cum += subset_size*subset_size;
778     }
779     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&array);CHKERRQ(ierr);
780     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array2);CHKERRQ(ierr);
781   }
782 
783   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
784   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
785   ierr = MatDestroy(&S_Ej_tilda_all);CHKERRQ(ierr);
786   ierr = MatDestroy(&S_Ej_inv_all);CHKERRQ(ierr);
787   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
788   ierr = ISDestroy(&temp_is);CHKERRQ(ierr);
789   PetscFunctionReturn(0);
790 }
791 
792 #undef __FUNCT__
793 #define __FUNCT__ "PCBDDCSubSchursInit"
794 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, Mat A, Mat S, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscInt seqthreshold)
795 {
796   IS                  *faces,*edges,*all_cc,vertices;
797   PetscInt            *index_sequential,*index_parallel;
798   PetscInt            *auxlocal_sequential,*auxlocal_parallel;
799   PetscInt            *auxglobal_sequential,*auxglobal_parallel;
800   PetscInt            *auxmapping;
801   PetscInt            i,max_subset_size;
802   PetscInt            n_sequential_problems,n_local_sequential_problems,n_parallel_problems,n_local_parallel_problems;
803   PetscInt            n_faces,n_edges,n_all_cc;
804   PetscBool           is_sorted;
805   PetscErrorCode  ierr;
806 
807   PetscFunctionBegin;
808   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
809   if (!is_sorted) {
810     SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
811   }
812   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
813   if (!is_sorted) {
814     SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
815   }
816 
817   /* reset any previous data */
818   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
819 
820   /* get index sets for faces and edges */
821   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
822   n_all_cc = n_faces+n_edges;
823   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
824   ierr = PetscBTCreate(n_all_cc,&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
825   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
826   for (i=0;i<n_faces;i++) {
827     all_cc[i] = faces[i];
828   }
829   for (i=0;i<n_edges;i++) {
830     all_cc[n_faces+i] = edges[i];
831     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
832   }
833   ierr = PetscFree(faces);CHKERRQ(ierr);
834   ierr = PetscFree(edges);CHKERRQ(ierr);
835 
836   /* map interface's subsets */
837   max_subset_size = 0;
838   for (i=0;i<n_all_cc;i++) {
839     PetscInt subset_size;
840     ierr = ISGetLocalSize(all_cc[i],&subset_size);CHKERRQ(ierr);
841     max_subset_size = PetscMax(max_subset_size,subset_size);
842   }
843   ierr = PetscMalloc1(max_subset_size,&auxmapping);CHKERRQ(ierr);
844   ierr = PetscMalloc2(graph->ncc,&auxlocal_sequential,
845                       graph->ncc,&auxlocal_parallel);CHKERRQ(ierr);
846   ierr = PetscMalloc2(graph->ncc,&index_sequential,
847                       graph->ncc,&index_parallel);CHKERRQ(ierr);
848 
849   /* if threshold is negative uses all sequential problems (possibly using MUMPS) */
850   sub_schurs->use_mumps = PETSC_FALSE;
851   if (seqthreshold < 0) {
852     seqthreshold = max_subset_size;
853 #if defined(PETSC_HAVE_MUMPS)
854     sub_schurs->use_mumps = (PetscBool)(!!A);
855 #endif
856   }
857 
858 
859   /* determine which problem has to be solved in parallel or sequentially */
860   n_local_sequential_problems = 0;
861   n_local_parallel_problems = 0;
862   for (i=0;i<n_all_cc;i++) {
863     PetscInt       subset_size,j,min_loc = 0;
864     const PetscInt *idxs;
865 
866     ierr = ISGetLocalSize(all_cc[i],&subset_size);CHKERRQ(ierr);
867     ierr = ISGetIndices(all_cc[i],&idxs);CHKERRQ(ierr);
868     ierr = ISLocalToGlobalMappingApply(graph->l2gmap,subset_size,idxs,auxmapping);CHKERRQ(ierr);
869     for (j=1;j<subset_size;j++) {
870       if (auxmapping[j]<auxmapping[min_loc]) {
871         min_loc = j;
872       }
873     }
874     if (subset_size > seqthreshold) {
875       index_parallel[n_local_parallel_problems] = i;
876       auxlocal_parallel[n_local_parallel_problems] = idxs[min_loc];
877       n_local_parallel_problems++;
878     } else {
879       index_sequential[n_local_sequential_problems] = i;
880       auxlocal_sequential[n_local_sequential_problems] = idxs[min_loc];
881       n_local_sequential_problems++;
882     }
883     ierr = ISRestoreIndices(all_cc[i],&idxs);CHKERRQ(ierr);
884   }
885 
886   /* Number parallel problems */
887   auxglobal_parallel = 0;
888   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)graph->l2gmap),graph->l2gmap,n_local_parallel_problems,auxlocal_parallel,PETSC_NULL,&n_parallel_problems,&auxglobal_parallel);CHKERRQ(ierr);
889 
890   /* Number sequential problems */
891   auxglobal_sequential = 0;
892   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)graph->l2gmap),graph->l2gmap,n_local_sequential_problems,auxlocal_sequential,PETSC_NULL,&n_sequential_problems,&auxglobal_sequential);CHKERRQ(ierr);
893 
894   /* update info in sub_schurs */
895   if (A) {
896     PetscBool isseqaij;
897 
898     ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
899     if (isseqaij) {
900       ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);
901       sub_schurs->A = A;
902     } else { /* SeqBAIJ matrices does not support symmetry checking, SeqSBAIJ does not support MatPermute */
903       ierr = MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
904     }
905   }
906   ierr = PetscObjectReference((PetscObject)S);CHKERRQ(ierr);
907   sub_schurs->S = S;
908   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
909   sub_schurs->is_I = is_I;
910   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
911   sub_schurs->is_B = is_B;
912   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
913   sub_schurs->l2gmap = graph->l2gmap;
914   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
915   sub_schurs->BtoNmap = BtoNmap;
916   sub_schurs->n_subs_seq = n_local_sequential_problems;
917   sub_schurs->n_subs_par = n_local_parallel_problems;
918   sub_schurs->n_subs_seq_g = n_sequential_problems;
919   sub_schurs->n_subs_par_g = n_parallel_problems;
920   sub_schurs->n_subs = sub_schurs->n_subs_seq + sub_schurs->n_subs_par;
921   sub_schurs->is_subs = all_cc;
922   if (!sub_schurs->use_mumps) { /* for adaptive selection */
923     for (i=0;i<sub_schurs->n_subs;i++) {
924       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
925     }
926   }
927   sub_schurs->is_Ej_com = vertices;
928   sub_schurs->index_sequential = index_sequential;
929   sub_schurs->index_parallel = index_parallel;
930   sub_schurs->auxglobal_sequential = auxglobal_sequential;
931   sub_schurs->auxglobal_parallel = auxglobal_parallel;
932 
933 
934   /* allocate space for schur complements */
935   ierr = PetscCalloc1(sub_schurs->n_subs,&sub_schurs->S_Ej);CHKERRQ(ierr);
936   sub_schurs->S_Ej_all = NULL;
937   sub_schurs->sum_S_Ej_all = NULL;
938   sub_schurs->sum_S_Ej_inv_all = NULL;
939   sub_schurs->sum_S_Ej_tilda_all = NULL;
940   sub_schurs->is_Ej_all = NULL;
941 
942   /* free workspace */
943   ierr = PetscFree(auxmapping);CHKERRQ(ierr);
944   ierr = PetscFree2(auxlocal_sequential,auxlocal_parallel);CHKERRQ(ierr);
945 
946   PetscFunctionReturn(0);
947 }
948 
949 #undef __FUNCT__
950 #define __FUNCT__ "PCBDDCSubSchursCreate"
951 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
952 {
953   PCBDDCSubSchurs schurs_ctx;
954   PetscErrorCode  ierr;
955 
956   PetscFunctionBegin;
957   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
958   schurs_ctx->n_subs = 0;
959   *sub_schurs = schurs_ctx;
960   PetscFunctionReturn(0);
961 }
962 
963 #undef __FUNCT__
964 #define __FUNCT__ "PCBDDCSubSchursDestroy"
965 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs *sub_schurs)
966 {
967   PetscErrorCode ierr;
968 
969   PetscFunctionBegin;
970   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
971   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
972   PetscFunctionReturn(0);
973 }
974 
975 #undef __FUNCT__
976 #define __FUNCT__ "PCBDDCSubSchursReset"
977 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
978 {
979   PetscInt       i;
980   PetscErrorCode ierr;
981 
982   PetscFunctionBegin;
983   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
984   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
985   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
986   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
987   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
988   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
989   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
990   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
991   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
992   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
993   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
994   ierr = ISDestroy(&sub_schurs->is_Ej_com);CHKERRQ(ierr);
995   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
996   ierr = PetscBTDestroy(&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
997   for (i=0;i<sub_schurs->n_subs;i++) {
998     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
999     ierr = MatDestroy(&sub_schurs->S_Ej[i]);CHKERRQ(ierr);
1000   }
1001   ierr = ISDestroy(&sub_schurs->is_I_layer);CHKERRQ(ierr);
1002   if (sub_schurs->n_subs) {
1003     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1004     ierr = PetscFree(sub_schurs->S_Ej);CHKERRQ(ierr);
1005   }
1006   ierr = PetscFree2(sub_schurs->index_sequential,sub_schurs->index_parallel);CHKERRQ(ierr);
1007   ierr = PetscFree(sub_schurs->auxglobal_sequential);CHKERRQ(ierr);
1008   ierr = PetscFree(sub_schurs->auxglobal_parallel);CHKERRQ(ierr);
1009   sub_schurs->n_subs = 0;
1010   PetscFunctionReturn(0);
1011 }
1012 
1013 #undef __FUNCT__
1014 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
1015 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1016 {
1017   PetscInt       i,j,n;
1018   PetscErrorCode ierr;
1019 
1020   PetscFunctionBegin;
1021   n = 0;
1022   for (i=-n_prev;i<0;i++) {
1023     PetscInt start_dof = queue_tip[i];
1024     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1025       PetscInt dof = adjncy[j];
1026       if (!PetscBTLookup(touched,dof)) {
1027         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1028         queue_tip[n] = dof;
1029         n++;
1030       }
1031     }
1032   }
1033   *n_added = n;
1034   PetscFunctionReturn(0);
1035 }
1036