xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision be83ff473a1423cc2ab5775993c40ed29465416d)
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 static PetscErrorCode PCBDDCMumpsInteriorSolve(PC,Vec,Vec);
8 static PetscErrorCode PCBDDCMumpsCorrectionSolve(PC,Vec,Vec);
9 
10 #undef __FUNCT__
11 #define __FUNCT__ "PCBDDCMumpsCorrectionSolve"
12 static PetscErrorCode PCBDDCMumpsCorrectionSolve(PC pc, Vec rhs, Vec sol)
13 {
14   PCBDDCReuseMumps ctx;
15   PetscInt         ival;
16   PetscErrorCode   ierr;
17 
18   PetscFunctionBegin;
19   ierr = PCShellGetContext(pc,(void **)&ctx);CHKERRQ(ierr);
20 #if defined(PETSC_HAVE_MUMPS)
21   ierr = MatMumpsGetIcntl(ctx->F,26,&ival);CHKERRQ(ierr);
22   ierr = MatMumpsSetIcntl(ctx->F,26,-1);CHKERRQ(ierr);
23 #endif
24   ierr = MatSolve(ctx->F,rhs,sol);CHKERRQ(ierr);
25 #if defined(PETSC_HAVE_MUMPS)
26   ierr = MatMumpsSetIcntl(ctx->F,26,ival);CHKERRQ(ierr);
27 #endif
28   PetscFunctionReturn(0);
29 }
30 
31 #undef __FUNCT__
32 #define __FUNCT__ "PCBDDCReuseMumpsReset"
33 static PetscErrorCode PCBDDCReuseMumpsReset(PCBDDCReuseMumps reuse)
34 {
35   PetscErrorCode ierr;
36 
37   PetscFunctionBegin;
38   ierr = MatDestroy(&reuse->F);CHKERRQ(ierr);
39   ierr = VecDestroy(&reuse->sol);CHKERRQ(ierr);
40   ierr = VecDestroy(&reuse->rhs);CHKERRQ(ierr);
41   ierr = PCDestroy(&reuse->interior_solver);CHKERRQ(ierr);
42   ierr = PCDestroy(&reuse->correction_solver);CHKERRQ(ierr);
43   ierr = VecScatterDestroy(&reuse->correction_scatter_B);CHKERRQ(ierr);
44   ierr = VecDestroy(&reuse->solB);CHKERRQ(ierr);
45   ierr = VecDestroy(&reuse->rhsB);CHKERRQ(ierr);
46   PetscFunctionReturn(0);
47 }
48 
49 #undef __FUNCT__
50 #define __FUNCT__ "PCBDDCMumpsInteriorSolve"
51 static PetscErrorCode PCBDDCMumpsInteriorSolve(PC pc, Vec rhs, Vec sol)
52 {
53   PCBDDCReuseMumps ctx;
54   PetscScalar      *array,*array_mumps;
55   PetscInt         ival;
56   PetscErrorCode   ierr;
57 
58   PetscFunctionBegin;
59   ierr = PCShellGetContext(pc,(void **)&ctx);CHKERRQ(ierr);
60 #if defined(PETSC_HAVE_MUMPS)
61   ierr = MatMumpsGetIcntl(ctx->F,26,&ival);CHKERRQ(ierr);
62   ierr = MatMumpsSetIcntl(ctx->F,26,0);CHKERRQ(ierr);
63 #endif
64   /* copy rhs into factored matrix workspace (can it be avoided?, MatSolve_MUMPS has another copy b->x internally) */
65   ierr = VecGetArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
66   ierr = VecGetArray(ctx->rhs,&array_mumps);CHKERRQ(ierr);
67   ierr = PetscMemcpy(array_mumps,array,ctx->n_I*sizeof(PetscScalar));CHKERRQ(ierr);
68   ierr = VecRestoreArray(ctx->rhs,&array_mumps);CHKERRQ(ierr);
69   ierr = VecRestoreArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
70 
71   ierr = MatSolve(ctx->F,ctx->rhs,ctx->sol);CHKERRQ(ierr);
72 
73   /* get back data to caller worskpace */
74   ierr = VecGetArrayRead(ctx->sol,(const PetscScalar**)&array_mumps);CHKERRQ(ierr);
75   ierr = VecGetArray(sol,&array);CHKERRQ(ierr);
76   ierr = PetscMemcpy(array,array_mumps,ctx->n_I*sizeof(PetscScalar));CHKERRQ(ierr);
77   ierr = VecRestoreArray(sol,&array);CHKERRQ(ierr);
78   ierr = VecRestoreArrayRead(ctx->sol,(const PetscScalar**)&array_mumps);CHKERRQ(ierr);
79 #if defined(PETSC_HAVE_MUMPS)
80   ierr = MatMumpsSetIcntl(ctx->F,26,ival);CHKERRQ(ierr);
81 #endif
82   PetscFunctionReturn(0);
83 }
84 
85 #undef __FUNCT__
86 #define __FUNCT__ "PCBDDCComputeExplicitSchur"
87 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
88 {
89   Mat            B, C, D, Bd, Cd, AinvBd;
90   KSP            ksp;
91   PC             pc;
92   PetscBool      isLU, isILU, isCHOL, Bdense, Cdense;
93   PetscReal      fill = 2.0;
94   PetscInt       n_I;
95   PetscMPIInt    size;
96   PetscErrorCode ierr;
97 
98   PetscFunctionBegin;
99   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);CHKERRQ(ierr);
100   if (size != 1) {
101     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not for parallel matrices");
102   }
103   if (reuse == MAT_REUSE_MATRIX) {
104     PetscBool Sdense;
105 
106     ierr = PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense);CHKERRQ(ierr);
107     if (!Sdense) {
108       SETERRQ(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"S should dense");
109     }
110   }
111   ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
112   ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
113   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
114   ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
115   ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
116   ierr = PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);CHKERRQ(ierr);
117   ierr = PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);CHKERRQ(ierr);
118   ierr = PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);CHKERRQ(ierr);
119   ierr = MatGetSize(B,&n_I,NULL);CHKERRQ(ierr);
120   if (n_I) {
121     if (!Bdense) {
122       ierr = MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
123     } else {
124       Bd = B;
125     }
126 
127     if (isLU || isILU || isCHOL) {
128       Mat fact;
129       ierr = KSPSetUp(ksp);CHKERRQ(ierr);
130       ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
131       ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
132       ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
133     } else {
134       PetscBool ex = PETSC_TRUE;
135 
136       if (ex) {
137         Mat Ainvd;
138 
139         ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
140         ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
141         ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
142       } else {
143         Vec         sol,rhs;
144         PetscScalar *arrayrhs,*arraysol;
145         PetscInt    i,nrhs,n;
146 
147         ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
148         ierr = MatGetSize(Bd,&n,&nrhs);CHKERRQ(ierr);
149         ierr = MatDenseGetArray(Bd,&arrayrhs);CHKERRQ(ierr);
150         ierr = MatDenseGetArray(AinvBd,&arraysol);CHKERRQ(ierr);
151         ierr = KSPGetSolution(ksp,&sol);CHKERRQ(ierr);
152         ierr = KSPGetRhs(ksp,&rhs);CHKERRQ(ierr);
153         for (i=0;i<nrhs;i++) {
154           ierr = VecPlaceArray(rhs,arrayrhs+i*n);CHKERRQ(ierr);
155           ierr = VecPlaceArray(sol,arraysol+i*n);CHKERRQ(ierr);
156           ierr = KSPSolve(ksp,rhs,sol);CHKERRQ(ierr);
157           ierr = VecResetArray(rhs);CHKERRQ(ierr);
158           ierr = VecResetArray(sol);CHKERRQ(ierr);
159         }
160         ierr = MatDenseRestoreArray(Bd,&arrayrhs);CHKERRQ(ierr);
161         ierr = MatDenseRestoreArray(AinvBd,&arrayrhs);CHKERRQ(ierr);
162       }
163     }
164     if (!Bdense & !issym) {
165       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
166     }
167 
168     if (!issym) {
169       if (!Cdense) {
170         ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
171       } else {
172         Cd = C;
173       }
174       ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
175       if (!Cdense) {
176         ierr = MatDestroy(&Cd);CHKERRQ(ierr);
177       }
178     } else {
179       ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
180       if (!Bdense) {
181         ierr = MatDestroy(&Bd);CHKERRQ(ierr);
182       }
183     }
184     ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
185   }
186 
187   if (D) {
188     Mat       Dd;
189     PetscBool Ddense;
190 
191     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
192     if (!Ddense) {
193       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
194     } else {
195       Dd = D;
196     }
197     if (n_I) {
198       ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
199     } else {
200       if (reuse == MAT_INITIAL_MATRIX) {
201         ierr = MatDuplicate(Dd,MAT_COPY_VALUES,S);CHKERRQ(ierr);
202       } else {
203         ierr = MatCopy(Dd,*S,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
204       }
205     }
206     if (!Ddense) {
207       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
208     }
209   } else {
210     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
211   }
212   PetscFunctionReturn(0);
213 }
214 
215 #undef __FUNCT__
216 #define __FUNCT__ "PCBDDCSubSchursSetUp"
217 PetscErrorCode PCBDDCSubSchursSetUp(PCBDDCSubSchurs sub_schurs, Mat Ain, Mat Sin, PetscInt xadj[], PetscInt adjncy[], PetscInt nlayers, PetscBool faster_deluxe, PetscBool compute_Stilda, PetscBool reuse_solvers,PetscBool use_edges, PetscBool use_faces)
218 {
219   Mat                    F,A_II,A_IB,A_BI,A_BB,AE_II;
220   Mat                    S_all;
221   Mat                    global_schur_subsets,work_mat;
222   Mat                    S_Ej_tilda_all,S_Ej_inv_all;
223   ISLocalToGlobalMapping l2gmap_subsets;
224   IS                     is_I,is_I_layer,temp_is;
225   PetscInt               *nnz,*all_local_idx_G,*all_local_idx_N;
226   PetscInt               *auxnum1,*auxnum2,*all_local_idx_G_rep;
227   PetscInt               i,subset_size,max_subset_size;
228   PetscInt               extra,local_size,global_size;
229   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
230   PetscScalar            *Bwork;
231   PetscSubcomm           subcomm;
232   PetscMPIInt            color,rank;
233   MPI_Comm               comm_n;
234   PetscErrorCode         ierr;
235 
236   PetscFunctionBegin;
237   /* update info in sub_schurs */
238   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
239   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
240   if (Ain) {
241     PetscBool isseqaij;
242 
243     ierr = PetscObjectTypeCompare((PetscObject)Ain,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
244     if (isseqaij) {
245       ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
246       sub_schurs->A = Ain;
247     } else { /* SeqBAIJ matrices does not support symmetry checking, SeqSBAIJ does not support MatPermute */
248       ierr = MatConvert(Ain,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
249     }
250   }
251   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
252   sub_schurs->S = Sin;
253   if (sub_schurs->use_mumps) {
254     sub_schurs->use_mumps = (PetscBool)(!!sub_schurs->A);
255   }
256 
257   /* preliminary checks */
258   if (!sub_schurs->use_mumps && compute_Stilda) {
259     SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS");
260   }
261   /* determine if we are dealing with hermitian positive definite problems */
262   sub_schurs->is_hermitian = PETSC_FALSE;
263   sub_schurs->is_posdef = PETSC_FALSE;
264   if (sub_schurs->A) {
265     PetscInt lsize;
266 
267     ierr = MatGetSize(sub_schurs->A,&lsize,NULL);CHKERRQ(ierr);
268     if (lsize) {
269       ierr = MatIsHermitian(sub_schurs->A,0.0,&sub_schurs->is_hermitian);CHKERRQ(ierr);
270       if (sub_schurs->is_hermitian) {
271         PetscScalar val;
272         Vec         vec1,vec2;
273 
274         ierr = MatCreateVecs(sub_schurs->A,&vec1,&vec2);CHKERRQ(ierr);
275         ierr = VecSetRandom(vec1,NULL);
276         ierr = VecCopy(vec1,vec2);CHKERRQ(ierr);
277         ierr = MatMult(sub_schurs->A,vec2,vec1);CHKERRQ(ierr);
278         ierr = VecDot(vec1,vec2,&val);CHKERRQ(ierr);
279         if (PetscRealPart(val) > 0. && PetscImaginaryPart(val) == 0.) sub_schurs->is_posdef = PETSC_TRUE;
280         ierr = VecDestroy(&vec1);CHKERRQ(ierr);
281         ierr = VecDestroy(&vec2);CHKERRQ(ierr);
282       }
283     } else {
284       sub_schurs->is_hermitian = PETSC_TRUE;
285       sub_schurs->is_posdef = PETSC_TRUE;
286     }
287     if (compute_Stilda && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
288       SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"General matrix pencils are not currently supported");
289     }
290   }
291   /* restrict work on active processes */
292   color = 0;
293   if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
294   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
295   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
296   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
297   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
298   ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
299   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
300   if (!sub_schurs->n_subs) {
301     ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
302     PetscFunctionReturn(0);
303   }
304 
305   /* get Schur complement matrices */
306   if (!sub_schurs->use_mumps) {
307     Mat       tA_IB,tA_BI,tA_BB;
308     PetscBool isseqaij;
309     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
310     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
311     if (!isseqaij) {
312       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
313       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
314       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
315     } else {
316       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
317       A_BB = tA_BB;
318       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
319       A_IB = tA_IB;
320       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
321       A_BI = tA_BI;
322     }
323   } else {
324     A_II = NULL;
325     A_IB = NULL;
326     A_BI = NULL;
327     A_BB = NULL;
328   }
329   S_all = NULL;
330   S_Ej_tilda_all = NULL;
331   S_Ej_inv_all = NULL;
332 
333   /* determine interior problems */
334   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
335   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
336     PetscBT                touched;
337     const PetscInt*        idx_B;
338     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
339 
340     if (xadj == NULL || adjncy == NULL) {
341       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
342     }
343     /* get sizes */
344     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
345     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
346 
347     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
348     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
349     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
350 
351     /* all boundary dofs must be skipped when adding layers */
352     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
353     for (j=0;j<n_B;j++) {
354       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
355     }
356     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
357     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
358 
359     /* add prescribed number of layers of dofs */
360     n_local_dofs = n_B;
361     n_prev_added = n_B;
362     for (layer=0;layer<nlayers;layer++) {
363       PetscInt n_added;
364       if (n_local_dofs == n_I+n_B) break;
365       if (n_local_dofs > n_I+n_B) {
366         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);
367       }
368       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
369       n_prev_added = n_added;
370       n_local_dofs += n_added;
371       if (!n_added) break;
372     }
373     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
374 
375     /* IS for I layer dofs in original numbering */
376     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I),n_local_dofs-n_B,local_numbering+n_B,PETSC_COPY_VALUES,&is_I_layer);CHKERRQ(ierr);
377     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
378     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
379     /* IS for I layer dofs in I numbering */
380     if (!sub_schurs->use_mumps) {
381       ISLocalToGlobalMapping ItoNmap;
382       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
383       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
384       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
385 
386       /* II block */
387       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
388     }
389   } else {
390     PetscInt n_I;
391 
392     /* IS for I dofs in original numbering */
393     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
394     is_I_layer = sub_schurs->is_I;
395 
396     /* IS for I dofs in I numbering (strided 1) */
397     if (!sub_schurs->use_mumps) {
398       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
399       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
400 
401       /* II block is the same */
402       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
403       AE_II = A_II;
404     }
405   }
406 
407   /* Get info on subset sizes and sum of all subsets sizes */
408   max_subset_size = 0;
409   local_size = 0;
410   for (i=0;i<sub_schurs->n_subs;i++) {
411     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
412     max_subset_size = PetscMax(subset_size,max_subset_size);
413     local_size += subset_size;
414   }
415 
416   /* Work arrays for local indices */
417   extra = 0;
418   if (sub_schurs->use_mumps) {
419     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
420   }
421   ierr = PetscMalloc1(local_size+extra,&all_local_idx_N);CHKERRQ(ierr);
422   if (extra) {
423     const PetscInt *idxs;
424     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
425     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
426     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
427   }
428   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
429   ierr = PetscMalloc2(sub_schurs->n_subs,&auxnum1,sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
430 
431   /* Get local indices in local numbering */
432   local_size = 0;
433   for (i=0;i<sub_schurs->n_subs;i++) {
434     PetscInt j;
435     const    PetscInt *idxs;
436 
437     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
438     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
439     /* start (smallest in global ordering) and multiplicity */
440     auxnum1[i] = idxs[0];
441     auxnum2[i] = subset_size;
442     /* subset indices in local numbering */
443     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
444     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
445     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
446     local_size += subset_size;
447   }
448 
449   /* allocate extra workspace needed only for GETRI */
450   Bwork = NULL;
451   pivots = NULL;
452   if (sub_schurs->n_subs && !sub_schurs->is_hermitian) {
453     PetscScalar lwork;
454 
455     B_lwork = -1;
456     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
457     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
458     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,Bwork,&B_N,pivots,&lwork,&B_lwork,&B_ierr));
459     ierr = PetscFPTrapPop();CHKERRQ(ierr);
460     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
461     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
462     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
463   }
464 
465   /* prepare parallel matrices for summing up properly schurs on subsets */
466   ierr = PCBDDCSubsetNumbering(comm_n,sub_schurs->l2gmap,sub_schurs->n_subs,auxnum1,auxnum2,&global_size,&all_local_idx_G_rep);CHKERRQ(ierr);
467   ierr = PetscMalloc1(local_size,&all_local_idx_G);CHKERRQ(ierr);
468   local_size = 0;
469   for (i=0;i<sub_schurs->n_subs;i++) {
470     PetscInt j;
471     for (j=0;j<auxnum2[i];j++) all_local_idx_G[local_size++] = all_local_idx_G_rep[i] + j;
472   }
473   ierr = PetscFree(all_local_idx_G_rep);CHKERRQ(ierr);
474   ierr = PetscFree2(auxnum1,auxnum2);CHKERRQ(ierr);
475   ierr = ISLocalToGlobalMappingCreate(comm_n,1,local_size,all_local_idx_G,PETSC_COPY_VALUES,&l2gmap_subsets);CHKERRQ(ierr);
476   ierr = MatCreateIS(comm_n,1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,&work_mat);CHKERRQ(ierr);
477   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
478   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
479   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
480   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
481 
482   /* subset indices in local boundary numbering */
483   if (!sub_schurs->is_Ej_all) {
484     PetscInt *all_local_idx_B;
485 
486     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
487     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
488     if (subset_size != local_size) {
489       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %d != %d\n",subset_size,local_size);
490     }
491     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
492   }
493 
494   /* Local matrix of all local Schur on subsets (transposed) */
495   if (!sub_schurs->S_Ej_all) {
496     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
497     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
498     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
499     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
500   } else {
501     ierr = MatZeroEntries(sub_schurs->S_Ej_all);CHKERRQ(ierr);
502   }
503 
504   /* Compute Schur complements explicitly */
505   F = NULL;
506   ierr = PetscBTMemzero(sub_schurs->n_subs,sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
507   if (!sub_schurs->use_mumps) {
508     Mat         S_Ej_expl;
509     PetscScalar *work;
510     PetscInt    j,*dummy_idx;
511     PetscBool   Sdense;
512 
513     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
514     local_size = 0;
515     for (i=0;i<sub_schurs->n_subs;i++) {
516       IS  is_subset_B;
517       Mat AE_EE,AE_IE,AE_EI,S_Ej;
518 
519       /* subsets in original and boundary numbering */
520       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
521       /* EE block */
522       ierr = MatGetSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
523       /* IE block */
524       ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
525       /* EI block */
526       if (sub_schurs->is_hermitian) {
527         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
528       } else {
529         ierr = MatGetSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
530       }
531       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
532       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
533       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
534       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
535       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
536       if (AE_II == A_II) { /* we can reuse the same ksp */
537         KSP ksp;
538         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
539         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
540       } else { /* build new ksp object which inherits ksp and pc types from the original one */
541         KSP       origksp,schurksp;
542         PC        origpc,schurpc;
543         KSPType   ksp_type;
544         PetscInt  n_internal;
545         PetscBool ispcnone;
546 
547         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
548         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
549         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
550         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
551         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
552         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
553         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
554         if (!ispcnone) {
555           PCType pc_type;
556           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
557           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
558         } else {
559           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
560         }
561         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
562         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
563           MatSolverPackage solver=NULL;
564           ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
565           if (solver) {
566             ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
567           }
568         }
569         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
570       }
571       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
572       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
573       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
574       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
575       if (Sdense) {
576         for (j=0;j<subset_size;j++) {
577           dummy_idx[j]=local_size+j;
578         }
579         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
580       } else {
581         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
582       }
583       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
584       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
585       local_size += subset_size;
586     }
587     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
588     /* free */
589     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
590     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
591     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
592   } else {
593     Mat         A;
594     IS          is_A_all;
595     PetscScalar *work,*S_data;
596     PetscInt    *idxs_schur,n_I,n_I_all,*dummy_idx,size_schur,size_active_schur,cum,cum2;
597     PetscBool   restore_S;
598 
599     /* get working mat */
600     ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
601     if (!sub_schurs->is_dir) {
602       ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size+n_I,all_local_idx_N,PETSC_COPY_VALUES,&is_A_all);CHKERRQ(ierr);
603       size_schur = local_size;
604     } else {
605       IS list[2];
606 
607       ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size+n_I,all_local_idx_N,PETSC_COPY_VALUES,&list[0]);CHKERRQ(ierr);
608       list[1] = sub_schurs->is_dir;
609       ierr = ISConcatenate(PETSC_COMM_SELF,2,list,&is_A_all);CHKERRQ(ierr);
610       ierr = ISDestroy(&list[0]);CHKERRQ(ierr);
611       ierr = ISGetLocalSize(sub_schurs->is_dir,&size_schur);CHKERRQ(ierr);
612       size_schur += local_size;
613     }
614     size_active_schur = local_size;
615     ierr = MatGetSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
616     ierr = MatSetOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
617 
618     if (n_I) {
619       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
620         ierr = MatSetOption(A,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
621         ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
622       } else {
623         ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_hermitian);CHKERRQ(ierr);
624         ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
625       }
626 
627       /* subsets ordered last */
628       ierr = PetscMalloc1(size_schur,&idxs_schur);CHKERRQ(ierr);
629       for (i=0;i<size_schur;i++) {
630         idxs_schur[i] = n_I+i+1;
631       }
632 #if defined(PETSC_HAVE_MUMPS)
633       ierr = MatMumpsSetSchurIndices(F,size_schur,idxs_schur);CHKERRQ(ierr);
634 #endif
635       ierr = PetscFree(idxs_schur);CHKERRQ(ierr);
636 
637       /* factorization step */
638       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
639         ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
640 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
641         ierr = MatMumpsSetIcntl(F,19,2);CHKERRQ(ierr);
642 #endif
643         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
644       } else {
645         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
646 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
647         ierr = MatMumpsSetIcntl(F,19,3);CHKERRQ(ierr);
648 #endif
649         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
650       }
651 
652       /* get explicit Schur Complement computed during numeric factorization */
653 #if defined(PETSC_HAVE_MUMPS)
654       ierr = MatMumpsGetSchurComplement(F,&S_all);CHKERRQ(ierr);
655 #endif
656 
657       /* we can reuse the solvers if we are not using the economic version */
658       ierr = ISGetLocalSize(sub_schurs->is_I,&n_I_all);CHKERRQ(ierr);
659       reuse_solvers = (PetscBool)(reuse_solvers && (n_I == n_I_all));
660       restore_S = PETSC_TRUE;
661     } else { /* we can't use MUMPS when size_schur == size_of_the_problem */
662       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
663       reuse_solvers = PETSC_FALSE;
664       restore_S = PETSC_FALSE;
665     }
666     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
667     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
668 
669     if (reuse_solvers) {
670       Mat              A_II;
671       PCBDDCReuseMumps msolv_ctx;
672 
673       if (sub_schurs->reuse_mumps) {
674         ierr = PCBDDCReuseMumpsReset(sub_schurs->reuse_mumps);CHKERRQ(ierr);
675         ierr = PetscFree(sub_schurs->reuse_mumps);CHKERRQ(ierr);
676       }
677       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
678       ierr = PetscNew(&msolv_ctx);CHKERRQ(ierr);
679       ierr = MatGetSize(A_II,&msolv_ctx->n_I,NULL);CHKERRQ(ierr);
680       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
681       msolv_ctx->F = F;
682       ierr = MatCreateVecs(F,&msolv_ctx->sol,&msolv_ctx->rhs);CHKERRQ(ierr);
683 
684       /* interior solver */
685       ierr = PCCreate(PETSC_COMM_SELF,&msolv_ctx->interior_solver);CHKERRQ(ierr);
686       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
687       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
688       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
689       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCMumpsInteriorSolve);CHKERRQ(ierr);
690 
691       /* correction solver */
692       /* auxiliary scatters are needed and are created in PCBDDCSetUpLocalScatters */
693       ierr = PCCreate(PETSC_COMM_SELF,&msolv_ctx->correction_solver);CHKERRQ(ierr);
694       ierr = PCSetOperators(msolv_ctx->correction_solver,A,A);CHKERRQ(ierr);
695       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
696       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
697       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCMumpsCorrectionSolve);CHKERRQ(ierr);
698       ierr = MatCreateVecs(S_all,&msolv_ctx->solB,&msolv_ctx->rhsB);CHKERRQ(ierr);
699       sub_schurs->reuse_mumps = msolv_ctx;
700     }
701     ierr = MatDestroy(&A);CHKERRQ(ierr);
702 
703     /* Work arrays */
704     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
705     if (compute_Stilda) {
706       ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_tilda_all);CHKERRQ(ierr);
707       ierr = MatSetSizes(S_Ej_tilda_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
708       ierr = MatSetType(S_Ej_tilda_all,MATAIJ);CHKERRQ(ierr);
709       ierr = MatSeqAIJSetPreallocation(S_Ej_tilda_all,0,nnz);CHKERRQ(ierr);
710       ierr = MatCreate(PETSC_COMM_SELF,&S_Ej_inv_all);CHKERRQ(ierr);
711       ierr = MatSetSizes(S_Ej_inv_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
712       ierr = MatSetType(S_Ej_inv_all,MATAIJ);CHKERRQ(ierr);
713       ierr = MatSeqAIJSetPreallocation(S_Ej_inv_all,0,nnz);CHKERRQ(ierr);
714     }
715 
716     /* S_Ej_all */
717     cum = cum2 = 0;
718     ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
719     for (i=0;i<sub_schurs->n_subs;i++) {
720       PetscInt j;
721 
722       /* get S_E */
723       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
724       if (restore_S && sub_schurs->is_hermitian) { /* When using MUMPS data I need to expand to upper triangular (column oriented) */
725         PetscInt k;
726         for (k=0;k<subset_size;k++) {
727           for (j=k;j<subset_size;j++) {
728             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
729             work[j*subset_size+k] = S_data[cum2+k*size_schur+j];
730           }
731         }
732       } else { /* copy to workspace */
733         PetscInt k;
734         for (k=0;k<subset_size;k++) {
735           for (j=0;j<subset_size;j++) {
736             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
737           }
738         }
739       }
740       /* insert S_E values */
741       for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
742       ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
743 
744       /* if adaptivity is requested, invert S_E block */
745       if (compute_Stilda && ((PetscBTLookup(sub_schurs->is_edge,i) && use_edges) || (!PetscBTLookup(sub_schurs->is_edge,i) && use_faces))) {
746         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
747         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
748         if (!sub_schurs->is_hermitian) { /* TODO add sytrf/i for symmetric non hermitian */
749           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,work,&B_N,pivots,&B_ierr));
750           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
751           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
752           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
753         } else {
754           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,work,&B_N,&B_ierr));
755           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
756           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,work,&B_N,&B_ierr));
757           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
758         }
759         ierr = PetscFPTrapPop();CHKERRQ(ierr);
760         ierr = MatSetValues(S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
761       }
762       cum += subset_size;
763       cum2 += subset_size*(size_schur + 1);
764     }
765     ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
766 #if defined(PETSC_HAVE_MUMPS)
767     if (restore_S) {
768       ierr = MatMumpsRestoreSchurComplement(F,&S_all);CHKERRQ(ierr);
769       ierr = MatMumpsInvertSchurComplement(F);CHKERRQ(ierr);
770       ierr = MatMumpsGetSchurComplement(F,&S_all);CHKERRQ(ierr);
771     } else if (compute_Stilda) { /* we need to invert explicitly since we are not using MUMPS */
772       ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
773       ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
774       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
775       if (!sub_schurs->is_hermitian) { /* TODO add sytrf/i for symmetric non hermitian */
776         PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
777         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
778         PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
779         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
780       } else {
781         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
782         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
783         PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
784         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
785       }
786       ierr = PetscFPTrapPop();CHKERRQ(ierr);
787       ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
788     }
789 #endif
790     /* S_Ej_tilda_all */
791     cum = cum2 = 0;
792     ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
793     for (i=0;i<sub_schurs->n_subs;i++) {
794       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
795       /* if adaptivity is requested, invert S_E and insert St_E^-1 blocks */
796       if (compute_Stilda && ((PetscBTLookup(sub_schurs->is_edge,i) && use_edges) || (!PetscBTLookup(sub_schurs->is_edge,i) && use_faces))) {
797         PetscInt j;
798         /* get (St^-1)_E */
799         if (sub_schurs->is_hermitian) { /* I need to expand to upper triangular (column oriented) */
800           PetscInt k;
801           for (k=0;k<subset_size;k++) {
802             for (j=k;j<subset_size;j++) {
803               work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
804               work[j*subset_size+k] = S_data[cum2+k*size_schur+j];
805             }
806           }
807         } else { /* copy to workspace */
808           PetscInt k;
809           for (k=0;k<subset_size;k++) {
810             for (j=0;j<subset_size;j++) {
811               work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
812             }
813           }
814         }
815         for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
816         ierr = MatSetValues(S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
817         ierr = PetscBTSet(sub_schurs->computed_Stilda_subs,i);CHKERRQ(ierr);
818       }
819       cum += subset_size;
820       cum2 += subset_size*(size_schur + 1);
821     }
822     ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
823     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
824 #if defined(PETSC_HAVE_MUMPS)
825     if (restore_S) {
826       ierr = MatMumpsRestoreSchurComplement(F,&S_all);CHKERRQ(ierr);
827     }
828 #endif
829   }
830   ierr = MatDestroy(&F);CHKERRQ(ierr);
831   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
832   ierr = PetscFree(nnz);CHKERRQ(ierr);
833   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
834   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
835   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
836   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
837   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
838   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
839   if (compute_Stilda) {
840     ierr = MatAssemblyBegin(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
841     ierr = MatAssemblyEnd(S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
842     ierr = MatAssemblyBegin(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
843     ierr = MatAssemblyEnd(S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
844   }
845 
846   /* Global matrix of all assembled Schur on subsets */
847   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
848   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
849   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
850 
851   /* Get local part of (\sum_j S_Ej) */
852   ierr = ISCreateGeneral(comm_n,local_size,all_local_idx_G,PETSC_OWN_POINTER,&temp_is);CHKERRQ(ierr);
853   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
854   ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
855 
856   /* Compute explicitly (\sum_j S_Ej)^-1 (faster scaling during PCApply, needs extra work when doing setup) */
857   if (faster_deluxe) {
858     Mat         tmpmat;
859     PetscScalar *array;
860     PetscInt    cum;
861 
862     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all,&array);CHKERRQ(ierr);
863     cum = 0;
864     for (i=0;i<sub_schurs->n_subs;i++) {
865       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
866       ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
867       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
868       if (!sub_schurs->is_hermitian) {
869         PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
870         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
871         PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
872         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
873       } else {
874         PetscInt j,k;
875 
876         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
877         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
878         PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
879         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
880         for (j=0;j<B_N;j++) {
881           for (k=j+1;k<B_N;k++) {
882             array[k*B_N+j+cum] = array[j*B_N+k+cum];
883           }
884         }
885       }
886       ierr = PetscFPTrapPop();CHKERRQ(ierr);
887       cum += subset_size*subset_size;
888     }
889     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all,&array);CHKERRQ(ierr);
890     ierr = MatMatMult(sub_schurs->S_Ej_all,sub_schurs->sum_S_Ej_all,MAT_INITIAL_MATRIX,1.0,&tmpmat);CHKERRQ(ierr);
891     ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
892     ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
893     sub_schurs->S_Ej_all = tmpmat;
894   }
895 
896   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
897   if (compute_Stilda) {
898     ierr = MatISSetLocalMat(work_mat,S_Ej_tilda_all);CHKERRQ(ierr);
899     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
900     ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
901     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
902     ierr = MatISSetLocalMat(work_mat,S_Ej_inv_all);CHKERRQ(ierr);
903     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
904     ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
905     ierr = MatGetSubMatrixUnsorted(global_schur_subsets,temp_is,temp_is,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
906   }
907 
908   /* free workspace */
909   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
910   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
911   ierr = MatDestroy(&S_Ej_tilda_all);CHKERRQ(ierr);
912   ierr = MatDestroy(&S_Ej_inv_all);CHKERRQ(ierr);
913   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
914   ierr = ISDestroy(&temp_is);CHKERRQ(ierr);
915   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
916   PetscFunctionReturn(0);
917 }
918 
919 #undef __FUNCT__
920 #define __FUNCT__ "PCBDDCSubSchursInit"
921 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap)
922 {
923   IS              *faces,*edges,*all_cc,vertices;
924   PetscInt        i,n_faces,n_edges,n_all_cc;
925   PetscBool       is_sorted;
926   PetscErrorCode  ierr;
927 
928   PetscFunctionBegin;
929   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
930   if (!is_sorted) {
931     SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
932   }
933   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
934   if (!is_sorted) {
935     SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
936   }
937 
938   /* reset any previous data */
939   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
940 
941   /* get index sets for faces and edges (already sorted by global ordering) */
942   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
943   n_all_cc = n_faces+n_edges;
944   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
945   ierr = PetscBTCreate(n_all_cc,&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
946   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
947   for (i=0;i<n_faces;i++) {
948     all_cc[i] = faces[i];
949   }
950   for (i=0;i<n_edges;i++) {
951     all_cc[n_faces+i] = edges[i];
952     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
953   }
954   ierr = PetscFree(faces);CHKERRQ(ierr);
955   ierr = PetscFree(edges);CHKERRQ(ierr);
956   sub_schurs->is_dir = NULL;
957   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
958 
959   /* Determine if MUMPS can be used */
960   sub_schurs->use_mumps = PETSC_FALSE;
961 #if defined(PETSC_HAVE_MUMPS)
962   sub_schurs->use_mumps = PETSC_TRUE;
963 #endif
964 
965   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
966   sub_schurs->is_I = is_I;
967   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
968   sub_schurs->is_B = is_B;
969   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
970   sub_schurs->l2gmap = graph->l2gmap;
971   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
972   sub_schurs->BtoNmap = BtoNmap;
973   sub_schurs->n_subs = n_all_cc;
974   sub_schurs->is_subs = all_cc;
975   if (!sub_schurs->use_mumps) { /* sort by local ordering mumps is not present */
976     for (i=0;i<sub_schurs->n_subs;i++) {
977       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
978     }
979   }
980   sub_schurs->is_vertices = vertices;
981   sub_schurs->S_Ej_all = NULL;
982   sub_schurs->sum_S_Ej_all = NULL;
983   sub_schurs->sum_S_Ej_inv_all = NULL;
984   sub_schurs->sum_S_Ej_tilda_all = NULL;
985   sub_schurs->is_Ej_all = NULL;
986   PetscFunctionReturn(0);
987 }
988 
989 #undef __FUNCT__
990 #define __FUNCT__ "PCBDDCSubSchursCreate"
991 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
992 {
993   PCBDDCSubSchurs schurs_ctx;
994   PetscErrorCode  ierr;
995 
996   PetscFunctionBegin;
997   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
998   schurs_ctx->n_subs = 0;
999   *sub_schurs = schurs_ctx;
1000   PetscFunctionReturn(0);
1001 }
1002 
1003 #undef __FUNCT__
1004 #define __FUNCT__ "PCBDDCSubSchursDestroy"
1005 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs *sub_schurs)
1006 {
1007   PetscErrorCode ierr;
1008 
1009   PetscFunctionBegin;
1010   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
1011   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
1012   PetscFunctionReturn(0);
1013 }
1014 
1015 #undef __FUNCT__
1016 #define __FUNCT__ "PCBDDCSubSchursReset"
1017 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1018 {
1019   PetscInt       i;
1020   PetscErrorCode ierr;
1021 
1022   PetscFunctionBegin;
1023   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1024   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1025   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1026   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1027   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1028   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1029   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1030   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1031   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1032   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1033   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1034   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1035   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1036   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1037   ierr = PetscBTDestroy(&sub_schurs->computed_Stilda_subs);CHKERRQ(ierr);
1038   for (i=0;i<sub_schurs->n_subs;i++) {
1039     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
1040   }
1041   if (sub_schurs->n_subs) {
1042     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1043   }
1044   if (sub_schurs->reuse_mumps) {
1045     ierr = PCBDDCReuseMumpsReset(sub_schurs->reuse_mumps);CHKERRQ(ierr);
1046   }
1047   ierr = PetscFree(sub_schurs->reuse_mumps);CHKERRQ(ierr);
1048   sub_schurs->n_subs = 0;
1049   PetscFunctionReturn(0);
1050 }
1051 
1052 #undef __FUNCT__
1053 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
1054 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1055 {
1056   PetscInt       i,j,n;
1057   PetscErrorCode ierr;
1058 
1059   PetscFunctionBegin;
1060   n = 0;
1061   for (i=-n_prev;i<0;i++) {
1062     PetscInt start_dof = queue_tip[i];
1063     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1064       PetscInt dof = adjncy[j];
1065       if (!PetscBTLookup(touched,dof)) {
1066         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1067         queue_tip[n] = dof;
1068         n++;
1069       }
1070     }
1071   }
1072   *n_added = n;
1073   PetscFunctionReturn(0);
1074 }
1075