xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision e91c04dfc8a52dee1965211bb1cc8e5bf775178f)
1 #include <petsc/private/pcbddcimpl.h>
2 #include <petsc/private/pcbddcprivateimpl.h>
3 #include <../src/mat/impls/dense/seq/dense.h>
4 #include <petscblaslapack.h>
5 
6 static inline PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt *, PetscInt, PetscBT, PetscInt *, PetscInt *, PetscInt *);
7 static PetscErrorCode        PCBDDCComputeExplicitSchur(Mat, PetscBool, MatReuse, Mat *);
8 static PetscErrorCode        PCBDDCReuseSolvers_Interior(PC, Vec, Vec);
9 static PetscErrorCode        PCBDDCReuseSolvers_Correction(PC, Vec, Vec);
10 
11 /* if v2 is not present, correction is done in-place */
12 PetscErrorCode PCBDDCReuseSolversBenignAdapt(PCBDDCReuseSolvers ctx, Vec v, Vec v2, PetscBool sol, PetscBool full)
13 {
14   PetscScalar *array;
15   PetscScalar *array2;
16 
17   PetscFunctionBegin;
18   if (!ctx->benign_n) PetscFunctionReturn(PETSC_SUCCESS);
19   if (sol && full) {
20     PetscInt n_I, size_schur;
21 
22     /* get sizes */
23     PetscCall(MatGetSize(ctx->benign_csAIB, &size_schur, NULL));
24     PetscCall(VecGetSize(v, &n_I));
25     n_I = n_I - size_schur;
26     /* get schur sol from array */
27     PetscCall(VecGetArray(v, &array));
28     PetscCall(VecPlaceArray(ctx->benign_dummy_schur_vec, array + n_I));
29     PetscCall(VecRestoreArray(v, &array));
30     /* apply interior sol correction */
31     PetscCall(MatMultTranspose(ctx->benign_csAIB, ctx->benign_dummy_schur_vec, ctx->benign_corr_work));
32     PetscCall(VecResetArray(ctx->benign_dummy_schur_vec));
33     PetscCall(MatMultAdd(ctx->benign_AIIm1ones, ctx->benign_corr_work, v, v));
34   }
35   if (v2) {
36     PetscInt nl;
37 
38     PetscCall(VecGetArrayRead(v, (const PetscScalar **)&array));
39     PetscCall(VecGetLocalSize(v2, &nl));
40     PetscCall(VecGetArray(v2, &array2));
41     PetscCall(PetscArraycpy(array2, array, nl));
42   } else {
43     PetscCall(VecGetArray(v, &array));
44     array2 = array;
45   }
46   if (!sol) { /* change rhs */
47     PetscInt n;
48     for (n = 0; n < ctx->benign_n; n++) {
49       PetscScalar     sum = 0.;
50       const PetscInt *cols;
51       PetscInt        nz, i;
52 
53       PetscCall(ISGetLocalSize(ctx->benign_zerodiag_subs[n], &nz));
54       PetscCall(ISGetIndices(ctx->benign_zerodiag_subs[n], &cols));
55       for (i = 0; i < nz - 1; i++) sum += array[cols[i]];
56 #if defined(PETSC_USE_COMPLEX)
57       sum = -(PetscRealPart(sum) / nz + PETSC_i * (PetscImaginaryPart(sum) / nz));
58 #else
59       sum = -sum / nz;
60 #endif
61       for (i = 0; i < nz - 1; i++) array2[cols[i]] += sum;
62       ctx->benign_save_vals[n] = array2[cols[nz - 1]];
63       array2[cols[nz - 1]]     = sum;
64       PetscCall(ISRestoreIndices(ctx->benign_zerodiag_subs[n], &cols));
65     }
66   } else {
67     PetscInt n;
68     for (n = 0; n < ctx->benign_n; n++) {
69       PetscScalar     sum = 0.;
70       const PetscInt *cols;
71       PetscInt        nz, i;
72       PetscCall(ISGetLocalSize(ctx->benign_zerodiag_subs[n], &nz));
73       PetscCall(ISGetIndices(ctx->benign_zerodiag_subs[n], &cols));
74       for (i = 0; i < nz - 1; i++) sum += array[cols[i]];
75 #if defined(PETSC_USE_COMPLEX)
76       sum = -(PetscRealPart(sum) / nz + PETSC_i * (PetscImaginaryPart(sum) / nz));
77 #else
78       sum = -sum / nz;
79 #endif
80       for (i = 0; i < nz - 1; i++) array2[cols[i]] += sum;
81       array2[cols[nz - 1]] = ctx->benign_save_vals[n];
82       PetscCall(ISRestoreIndices(ctx->benign_zerodiag_subs[n], &cols));
83     }
84   }
85   if (v2) {
86     PetscCall(VecRestoreArrayRead(v, (const PetscScalar **)&array));
87     PetscCall(VecRestoreArray(v2, &array2));
88   } else {
89     PetscCall(VecRestoreArray(v, &array));
90   }
91   if (!sol && full) {
92     Vec      usedv;
93     PetscInt n_I, size_schur;
94 
95     /* get sizes */
96     PetscCall(MatGetSize(ctx->benign_csAIB, &size_schur, NULL));
97     PetscCall(VecGetSize(v, &n_I));
98     n_I = n_I - size_schur;
99     /* compute schur rhs correction */
100     if (v2) {
101       usedv = v2;
102     } else {
103       usedv = v;
104     }
105     /* apply schur rhs correction */
106     PetscCall(MatMultTranspose(ctx->benign_AIIm1ones, usedv, ctx->benign_corr_work));
107     PetscCall(VecGetArrayRead(usedv, (const PetscScalar **)&array));
108     PetscCall(VecPlaceArray(ctx->benign_dummy_schur_vec, array + n_I));
109     PetscCall(VecRestoreArrayRead(usedv, (const PetscScalar **)&array));
110     PetscCall(MatMultAdd(ctx->benign_csAIB, ctx->benign_corr_work, ctx->benign_dummy_schur_vec, ctx->benign_dummy_schur_vec));
111     PetscCall(VecResetArray(ctx->benign_dummy_schur_vec));
112   }
113   PetscFunctionReturn(PETSC_SUCCESS);
114 }
115 
116 static PetscErrorCode PCBDDCReuseSolvers_Solve_Private(PC pc, Vec rhs, Vec sol, PetscBool transpose, PetscBool full)
117 {
118   PCBDDCReuseSolvers ctx;
119   PetscBool          copy = PETSC_FALSE;
120 
121   PetscFunctionBegin;
122   PetscCall(PCShellGetContext(pc, &ctx));
123   if (full) {
124 #if defined(PETSC_HAVE_MUMPS)
125     PetscCall(MatMumpsSetIcntl(ctx->F, 26, -1));
126 #endif
127 #if defined(PETSC_HAVE_MKL_PARDISO)
128     PetscCall(MatMkl_PardisoSetCntl(ctx->F, 70, 0));
129 #endif
130     copy = ctx->has_vertices;
131   } else { /* interior solver */
132 #if defined(PETSC_HAVE_MUMPS)
133     PetscCall(MatMumpsSetIcntl(ctx->F, 26, 0));
134 #endif
135 #if defined(PETSC_HAVE_MKL_PARDISO)
136     PetscCall(MatMkl_PardisoSetCntl(ctx->F, 70, 1));
137 #endif
138     copy = PETSC_TRUE;
139   }
140   /* copy rhs into factored matrix workspace */
141   if (copy) {
142     PetscInt     n;
143     PetscScalar *array, *array_solver;
144 
145     PetscCall(VecGetLocalSize(rhs, &n));
146     PetscCall(VecGetArrayRead(rhs, (const PetscScalar **)&array));
147     PetscCall(VecGetArray(ctx->rhs, &array_solver));
148     PetscCall(PetscArraycpy(array_solver, array, n));
149     PetscCall(VecRestoreArray(ctx->rhs, &array_solver));
150     PetscCall(VecRestoreArrayRead(rhs, (const PetscScalar **)&array));
151 
152     PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, ctx->rhs, NULL, PETSC_FALSE, full));
153     if (transpose) {
154       PetscCall(MatSolveTranspose(ctx->F, ctx->rhs, ctx->sol));
155     } else {
156       PetscCall(MatSolve(ctx->F, ctx->rhs, ctx->sol));
157     }
158     PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, ctx->sol, NULL, PETSC_TRUE, full));
159 
160     /* get back data to caller worskpace */
161     PetscCall(VecGetArrayRead(ctx->sol, (const PetscScalar **)&array_solver));
162     PetscCall(VecGetArray(sol, &array));
163     PetscCall(PetscArraycpy(array, array_solver, n));
164     PetscCall(VecRestoreArray(sol, &array));
165     PetscCall(VecRestoreArrayRead(ctx->sol, (const PetscScalar **)&array_solver));
166   } else {
167     if (ctx->benign_n) {
168       PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, rhs, ctx->rhs, PETSC_FALSE, full));
169       if (transpose) {
170         PetscCall(MatSolveTranspose(ctx->F, ctx->rhs, sol));
171       } else {
172         PetscCall(MatSolve(ctx->F, ctx->rhs, sol));
173       }
174       PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, sol, NULL, PETSC_TRUE, full));
175     } else {
176       if (transpose) {
177         PetscCall(MatSolveTranspose(ctx->F, rhs, sol));
178       } else {
179         PetscCall(MatSolve(ctx->F, rhs, sol));
180       }
181     }
182   }
183   /* restore defaults */
184 #if defined(PETSC_HAVE_MUMPS)
185   PetscCall(MatMumpsSetIcntl(ctx->F, 26, -1));
186 #endif
187 #if defined(PETSC_HAVE_MKL_PARDISO)
188   PetscCall(MatMkl_PardisoSetCntl(ctx->F, 70, 0));
189 #endif
190   PetscFunctionReturn(PETSC_SUCCESS);
191 }
192 
193 static PetscErrorCode PCBDDCReuseSolvers_Correction(PC pc, Vec rhs, Vec sol)
194 {
195   PetscFunctionBegin;
196   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_FALSE, PETSC_TRUE));
197   PetscFunctionReturn(PETSC_SUCCESS);
198 }
199 
200 static PetscErrorCode PCBDDCReuseSolvers_CorrectionTranspose(PC pc, Vec rhs, Vec sol)
201 {
202   PetscFunctionBegin;
203   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_TRUE, PETSC_TRUE));
204   PetscFunctionReturn(PETSC_SUCCESS);
205 }
206 
207 static PetscErrorCode PCBDDCReuseSolvers_Interior(PC pc, Vec rhs, Vec sol)
208 {
209   PetscFunctionBegin;
210   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_FALSE, PETSC_FALSE));
211   PetscFunctionReturn(PETSC_SUCCESS);
212 }
213 
214 static PetscErrorCode PCBDDCReuseSolvers_InteriorTranspose(PC pc, Vec rhs, Vec sol)
215 {
216   PetscFunctionBegin;
217   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_TRUE, PETSC_FALSE));
218   PetscFunctionReturn(PETSC_SUCCESS);
219 }
220 
221 static PetscErrorCode PCBDDCReuseSolvers_View(PC pc, PetscViewer viewer)
222 {
223   PCBDDCReuseSolvers ctx;
224   PetscBool          iascii;
225 
226   PetscFunctionBegin;
227   PetscCall(PCShellGetContext(pc, &ctx));
228   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
229   if (iascii) PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_INFO));
230   PetscCall(MatView(ctx->F, viewer));
231   if (iascii) PetscCall(PetscViewerPopFormat(viewer));
232   PetscFunctionReturn(PETSC_SUCCESS);
233 }
234 
235 static PetscErrorCode PCBDDCReuseSolversReset(PCBDDCReuseSolvers reuse)
236 {
237   PetscInt i;
238 
239   PetscFunctionBegin;
240   PetscCall(MatDestroy(&reuse->F));
241   PetscCall(VecDestroy(&reuse->sol));
242   PetscCall(VecDestroy(&reuse->rhs));
243   PetscCall(PCDestroy(&reuse->interior_solver));
244   PetscCall(PCDestroy(&reuse->correction_solver));
245   PetscCall(ISDestroy(&reuse->is_R));
246   PetscCall(ISDestroy(&reuse->is_B));
247   PetscCall(VecScatterDestroy(&reuse->correction_scatter_B));
248   PetscCall(VecDestroy(&reuse->sol_B));
249   PetscCall(VecDestroy(&reuse->rhs_B));
250   for (i = 0; i < reuse->benign_n; i++) PetscCall(ISDestroy(&reuse->benign_zerodiag_subs[i]));
251   PetscCall(PetscFree(reuse->benign_zerodiag_subs));
252   PetscCall(PetscFree(reuse->benign_save_vals));
253   PetscCall(MatDestroy(&reuse->benign_csAIB));
254   PetscCall(MatDestroy(&reuse->benign_AIIm1ones));
255   PetscCall(VecDestroy(&reuse->benign_corr_work));
256   PetscCall(VecDestroy(&reuse->benign_dummy_schur_vec));
257   PetscFunctionReturn(PETSC_SUCCESS);
258 }
259 
260 static PetscErrorCode PCBDDCReuseSolvers_Destroy(PC pc)
261 {
262   PCBDDCReuseSolvers ctx;
263 
264   PetscFunctionBegin;
265   PetscCall(PCShellGetContext(pc, &ctx));
266   PetscCall(PCBDDCReuseSolversReset(ctx));
267   PetscCall(PetscFree(ctx));
268   PetscCall(PCShellSetContext(pc, NULL));
269   PetscFunctionReturn(PETSC_SUCCESS);
270 }
271 
272 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
273 {
274   Mat         B, C, D, Bd, Cd, AinvBd;
275   KSP         ksp;
276   PC          pc;
277   PetscBool   isLU, isILU, isCHOL, Bdense, Cdense;
278   PetscReal   fill = 2.0;
279   PetscInt    n_I;
280   PetscMPIInt size;
281 
282   PetscFunctionBegin;
283   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)M), &size));
284   PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not for parallel matrices");
285   if (reuse == MAT_REUSE_MATRIX) {
286     PetscBool Sdense;
287 
288     PetscCall(PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense));
289     PetscCheck(Sdense, PetscObjectComm((PetscObject)M), PETSC_ERR_SUP, "S should dense");
290   }
291   PetscCall(MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D));
292   PetscCall(MatSchurComplementGetKSP(M, &ksp));
293   PetscCall(KSPGetPC(ksp, &pc));
294   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCLU, &isLU));
295   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCILU, &isILU));
296   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
297   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQDENSE, &Bdense));
298   PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQDENSE, &Cdense));
299   PetscCall(MatGetSize(B, &n_I, NULL));
300   if (n_I) {
301     if (!Bdense) {
302       PetscCall(MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd));
303     } else {
304       Bd = B;
305     }
306 
307     if (isLU || isILU || isCHOL) {
308       Mat fact;
309       PetscCall(KSPSetUp(ksp));
310       PetscCall(PCFactorGetMatrix(pc, &fact));
311       PetscCall(MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd));
312       PetscCall(MatMatSolve(fact, Bd, AinvBd));
313     } else {
314       PetscBool ex = PETSC_TRUE;
315 
316       if (ex) {
317         Mat Ainvd;
318 
319         PetscCall(PCComputeOperator(pc, MATDENSE, &Ainvd));
320         PetscCall(MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd));
321         PetscCall(MatDestroy(&Ainvd));
322       } else {
323         Vec          sol, rhs;
324         PetscScalar *arrayrhs, *arraysol;
325         PetscInt     i, nrhs, n;
326 
327         PetscCall(MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd));
328         PetscCall(MatGetSize(Bd, &n, &nrhs));
329         PetscCall(MatDenseGetArray(Bd, &arrayrhs));
330         PetscCall(MatDenseGetArray(AinvBd, &arraysol));
331         PetscCall(KSPGetSolution(ksp, &sol));
332         PetscCall(KSPGetRhs(ksp, &rhs));
333         for (i = 0; i < nrhs; i++) {
334           PetscCall(VecPlaceArray(rhs, arrayrhs + i * n));
335           PetscCall(VecPlaceArray(sol, arraysol + i * n));
336           PetscCall(KSPSolve(ksp, rhs, sol));
337           PetscCall(VecResetArray(rhs));
338           PetscCall(VecResetArray(sol));
339         }
340         PetscCall(MatDenseRestoreArray(Bd, &arrayrhs));
341         PetscCall(MatDenseRestoreArray(AinvBd, &arrayrhs));
342       }
343     }
344     if (!Bdense & !issym) PetscCall(MatDestroy(&Bd));
345 
346     if (!issym) {
347       if (!Cdense) {
348         PetscCall(MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd));
349       } else {
350         Cd = C;
351       }
352       PetscCall(MatMatMult(Cd, AinvBd, reuse, fill, S));
353       if (!Cdense) PetscCall(MatDestroy(&Cd));
354     } else {
355       PetscCall(MatTransposeMatMult(Bd, AinvBd, reuse, fill, S));
356       if (!Bdense) PetscCall(MatDestroy(&Bd));
357     }
358     PetscCall(MatDestroy(&AinvBd));
359   }
360 
361   if (D) {
362     Mat       Dd;
363     PetscBool Ddense;
364 
365     PetscCall(PetscObjectTypeCompare((PetscObject)D, MATSEQDENSE, &Ddense));
366     if (!Ddense) {
367       PetscCall(MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd));
368     } else {
369       Dd = D;
370     }
371     if (n_I) {
372       PetscCall(MatAYPX(*S, -1.0, Dd, SAME_NONZERO_PATTERN));
373     } else {
374       if (reuse == MAT_INITIAL_MATRIX) {
375         PetscCall(MatDuplicate(Dd, MAT_COPY_VALUES, S));
376       } else {
377         PetscCall(MatCopy(Dd, *S, SAME_NONZERO_PATTERN));
378       }
379     }
380     if (!Ddense) PetscCall(MatDestroy(&Dd));
381   } else {
382     PetscCall(MatScale(*S, -1.0));
383   }
384   PetscFunctionReturn(PETSC_SUCCESS);
385 }
386 
387 PetscErrorCode PCBDDCSubSchursSetUp(PCBDDCSubSchurs sub_schurs, Mat Ain, Mat Sin, PetscBool exact_schur, PetscInt xadj[], PetscInt adjncy[], PetscInt nlayers, Vec scaling, PetscBool compute_Stilda, PetscBool reuse_solvers, PetscBool benign_trick, PetscInt benign_n, PetscInt benign_p0_lidx[], IS benign_zerodiag_subs[], Mat change, IS change_primal)
388 {
389   Mat          F, A_II, A_IB, A_BI, A_BB, AE_II;
390   Mat          S_all;
391   Vec          gstash, lstash;
392   VecScatter   sstash;
393   IS           is_I, is_I_layer;
394   IS           all_subsets, all_subsets_mult, all_subsets_n;
395   PetscScalar *stasharray, *Bwork;
396   PetscInt    *nnz, *all_local_idx_N;
397   PetscInt    *auxnum1, *auxnum2;
398   PetscInt     i, subset_size, max_subset_size;
399   PetscInt     n_B, extra, local_size, global_size;
400   PetscInt     local_stash_size;
401   PetscBLASInt B_N, B_ierr, B_lwork, *pivots;
402   MPI_Comm     comm_n;
403   PetscBool    deluxe   = PETSC_TRUE;
404   PetscBool    use_potr = PETSC_FALSE, use_sytr = PETSC_FALSE;
405   PetscViewer  matl_dbg_viewer = NULL;
406   PetscBool    flg;
407 
408   PetscFunctionBegin;
409   PetscCall(MatDestroy(&sub_schurs->A));
410   PetscCall(MatDestroy(&sub_schurs->S));
411   if (Ain) {
412     PetscCall(PetscObjectReference((PetscObject)Ain));
413     sub_schurs->A = Ain;
414   }
415 
416   PetscCall(PetscObjectReference((PetscObject)Sin));
417   sub_schurs->S = Sin;
418   if (sub_schurs->schur_explicit) sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
419 
420   /* preliminary checks */
421   PetscCheck(sub_schurs->schur_explicit || !compute_Stilda, PetscObjectComm((PetscObject)sub_schurs->l2gmap), PETSC_ERR_SUP, "Adaptive selection of constraints requires MUMPS and/or MKL_PARDISO");
422 
423   if (benign_trick) sub_schurs->is_posdef = PETSC_FALSE;
424 
425   /* debug (MATLAB) */
426   if (sub_schurs->debug) {
427     PetscMPIInt size, rank;
428     PetscInt    nr, *print_schurs_ranks, print_schurs = PETSC_FALSE;
429 
430     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &size));
431     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &rank));
432     nr = size;
433     PetscCall(PetscMalloc1(nr, &print_schurs_ranks));
434     PetscOptionsBegin(PetscObjectComm((PetscObject)sub_schurs->l2gmap), sub_schurs->prefix, "BDDC sub_schurs options", "PC");
435     PetscCall(PetscOptionsIntArray("-sub_schurs_debug_ranks", "Ranks to debug (all if the option is not used)", NULL, print_schurs_ranks, &nr, &flg));
436     if (!flg) print_schurs = PETSC_TRUE;
437     else {
438       print_schurs = PETSC_FALSE;
439       for (i = 0; i < nr; i++)
440         if (print_schurs_ranks[i] == rank) {
441           print_schurs = PETSC_TRUE;
442           break;
443         }
444     }
445     PetscOptionsEnd();
446     PetscCall(PetscFree(print_schurs_ranks));
447     if (print_schurs) {
448       char filename[256];
449 
450       PetscCall(PetscSNPrintf(filename, sizeof(filename), "sub_schurs_Schur_r%d.m", PetscGlobalRank));
451       PetscCall(PetscViewerASCIIOpen(PETSC_COMM_SELF, filename, &matl_dbg_viewer));
452       PetscCall(PetscViewerPushFormat(matl_dbg_viewer, PETSC_VIEWER_ASCII_MATLAB));
453     }
454   }
455 
456   /* restrict work on active processes */
457   if (sub_schurs->restrict_comm) {
458     PetscSubcomm subcomm;
459     PetscMPIInt  color, rank;
460 
461     color = 0;
462     if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
463     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &rank));
464     PetscCall(PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &subcomm));
465     PetscCall(PetscSubcommSetNumber(subcomm, 2));
466     PetscCall(PetscSubcommSetTypeGeneral(subcomm, color, rank));
467     PetscCall(PetscCommDuplicate(PetscSubcommChild(subcomm), &comm_n, NULL));
468     PetscCall(PetscSubcommDestroy(&subcomm));
469     if (!sub_schurs->n_subs) {
470       PetscCall(PetscCommDestroy(&comm_n));
471       PetscFunctionReturn(PETSC_SUCCESS);
472     }
473   } else {
474     PetscCall(PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &comm_n, NULL));
475   }
476 
477   /* get Schur complement matrices */
478   if (!sub_schurs->schur_explicit) {
479     Mat       tA_IB, tA_BI, tA_BB;
480     PetscBool isseqsbaij;
481     PetscCall(MatSchurComplementGetSubMatrices(sub_schurs->S, &A_II, NULL, &tA_IB, &tA_BI, &tA_BB));
482     PetscCall(PetscObjectTypeCompare((PetscObject)tA_BB, MATSEQSBAIJ, &isseqsbaij));
483     if (isseqsbaij) {
484       PetscCall(MatConvert(tA_BB, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_BB));
485       PetscCall(MatConvert(tA_IB, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_IB));
486       PetscCall(MatConvert(tA_BI, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_BI));
487     } else {
488       PetscCall(PetscObjectReference((PetscObject)tA_BB));
489       A_BB = tA_BB;
490       PetscCall(PetscObjectReference((PetscObject)tA_IB));
491       A_IB = tA_IB;
492       PetscCall(PetscObjectReference((PetscObject)tA_BI));
493       A_BI = tA_BI;
494     }
495   } else {
496     A_II = NULL;
497     A_IB = NULL;
498     A_BI = NULL;
499     A_BB = NULL;
500   }
501   S_all = NULL;
502 
503   /* determine interior problems */
504   PetscCall(ISGetLocalSize(sub_schurs->is_I, &i));
505   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
506     PetscBT         touched;
507     const PetscInt *idx_B;
508     PetscInt        n_I, n_B, n_local_dofs, n_prev_added, j, layer, *local_numbering;
509 
510     PetscCheck(xadj, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot request layering without adjacency");
511     /* get sizes */
512     PetscCall(ISGetLocalSize(sub_schurs->is_I, &n_I));
513     PetscCall(ISGetLocalSize(sub_schurs->is_B, &n_B));
514 
515     PetscCall(PetscMalloc1(n_I + n_B, &local_numbering));
516     PetscCall(PetscBTCreate(n_I + n_B, &touched));
517     PetscCall(PetscBTMemzero(n_I + n_B, touched));
518 
519     /* all boundary dofs must be skipped when adding layers */
520     PetscCall(ISGetIndices(sub_schurs->is_B, &idx_B));
521     for (j = 0; j < n_B; j++) PetscCall(PetscBTSet(touched, idx_B[j]));
522     PetscCall(PetscArraycpy(local_numbering, idx_B, n_B));
523     PetscCall(ISRestoreIndices(sub_schurs->is_B, &idx_B));
524 
525     /* add prescribed number of layers of dofs */
526     n_local_dofs = n_B;
527     n_prev_added = n_B;
528     for (layer = 0; layer < nlayers; layer++) {
529       PetscInt n_added = 0;
530       if (n_local_dofs == n_I + n_B) break;
531       PetscCheck(n_local_dofs <= n_I + n_B, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error querying layer %" PetscInt_FMT ". Out of bound access (%" PetscInt_FMT " > %" PetscInt_FMT ")", layer, n_local_dofs, n_I + n_B);
532       PetscCall(PCBDDCAdjGetNextLayer_Private(local_numbering + n_local_dofs, n_prev_added, touched, xadj, adjncy, &n_added));
533       n_prev_added = n_added;
534       n_local_dofs += n_added;
535       if (!n_added) break;
536     }
537     PetscCall(PetscBTDestroy(&touched));
538 
539     /* IS for I layer dofs in original numbering */
540     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I), n_local_dofs - n_B, local_numbering + n_B, PETSC_COPY_VALUES, &is_I_layer));
541     PetscCall(PetscFree(local_numbering));
542     PetscCall(ISSort(is_I_layer));
543     /* IS for I layer dofs in I numbering */
544     if (!sub_schurs->schur_explicit) {
545       ISLocalToGlobalMapping ItoNmap;
546       PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_I, &ItoNmap));
547       PetscCall(ISGlobalToLocalMappingApplyIS(ItoNmap, IS_GTOLM_DROP, is_I_layer, &is_I));
548       PetscCall(ISLocalToGlobalMappingDestroy(&ItoNmap));
549 
550       /* II block */
551       PetscCall(MatCreateSubMatrix(A_II, is_I, is_I, MAT_INITIAL_MATRIX, &AE_II));
552     }
553   } else {
554     PetscInt n_I;
555 
556     /* IS for I dofs in original numbering */
557     PetscCall(PetscObjectReference((PetscObject)sub_schurs->is_I));
558     is_I_layer = sub_schurs->is_I;
559 
560     /* IS for I dofs in I numbering (strided 1) */
561     if (!sub_schurs->schur_explicit) {
562       PetscCall(ISGetSize(sub_schurs->is_I, &n_I));
563       PetscCall(ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I), n_I, 0, 1, &is_I));
564 
565       /* II block is the same */
566       PetscCall(PetscObjectReference((PetscObject)A_II));
567       AE_II = A_II;
568     }
569   }
570 
571   /* Get info on subset sizes and sum of all subsets sizes */
572   max_subset_size = 0;
573   local_size      = 0;
574   for (i = 0; i < sub_schurs->n_subs; i++) {
575     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
576     max_subset_size = PetscMax(subset_size, max_subset_size);
577     local_size += subset_size;
578   }
579 
580   /* Work arrays for local indices */
581   extra = 0;
582   PetscCall(ISGetLocalSize(sub_schurs->is_B, &n_B));
583   if (sub_schurs->schur_explicit && is_I_layer) PetscCall(ISGetLocalSize(is_I_layer, &extra));
584   PetscCall(PetscMalloc1(n_B + extra, &all_local_idx_N));
585   if (extra) {
586     const PetscInt *idxs;
587     PetscCall(ISGetIndices(is_I_layer, &idxs));
588     PetscCall(PetscArraycpy(all_local_idx_N, idxs, extra));
589     PetscCall(ISRestoreIndices(is_I_layer, &idxs));
590   }
591   PetscCall(PetscMalloc1(sub_schurs->n_subs, &auxnum1));
592   PetscCall(PetscMalloc1(sub_schurs->n_subs, &auxnum2));
593 
594   /* Get local indices in local numbering */
595   local_size       = 0;
596   local_stash_size = 0;
597   for (i = 0; i < sub_schurs->n_subs; i++) {
598     const PetscInt *idxs;
599 
600     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
601     PetscCall(ISGetIndices(sub_schurs->is_subs[i], &idxs));
602     /* start (smallest in global ordering) and multiplicity */
603     auxnum1[i] = idxs[0];
604     auxnum2[i] = subset_size * subset_size;
605     /* subset indices in local numbering */
606     PetscCall(PetscArraycpy(all_local_idx_N + local_size + extra, idxs, subset_size));
607     PetscCall(ISRestoreIndices(sub_schurs->is_subs[i], &idxs));
608     local_size += subset_size;
609     local_stash_size += subset_size * subset_size;
610   }
611 
612   /* allocate extra workspace needed only for GETRI or SYTRF */
613   use_potr = use_sytr = PETSC_FALSE;
614   if (benign_trick || (sub_schurs->is_hermitian && sub_schurs->is_posdef)) {
615     use_potr = PETSC_TRUE;
616   } else if (sub_schurs->is_symmetric) {
617     use_sytr = PETSC_TRUE;
618   }
619   if (local_size && !use_potr) {
620     PetscScalar  lwork, dummyscalar = 0.;
621     PetscBLASInt dummyint = 0;
622 
623     B_lwork = -1;
624     PetscCall(PetscBLASIntCast(local_size, &B_N));
625     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
626     if (use_sytr) {
627       PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, &dummyscalar, &B_N, &dummyint, &lwork, &B_lwork, &B_ierr));
628       PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
629     } else {
630       PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, &dummyscalar, &B_N, &dummyint, &lwork, &B_lwork, &B_ierr));
631       PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
632     }
633     PetscCall(PetscFPTrapPop());
634     PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(lwork), &B_lwork));
635     PetscCall(PetscMalloc2(B_lwork, &Bwork, B_N, &pivots));
636   } else {
637     Bwork  = NULL;
638     pivots = NULL;
639   }
640 
641   /* prepare data for summing up properly schurs on subsets */
642   PetscCall(ISCreateGeneral(comm_n, sub_schurs->n_subs, auxnum1, PETSC_OWN_POINTER, &all_subsets_n));
643   PetscCall(ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap, all_subsets_n, &all_subsets));
644   PetscCall(ISDestroy(&all_subsets_n));
645   PetscCall(ISCreateGeneral(comm_n, sub_schurs->n_subs, auxnum2, PETSC_OWN_POINTER, &all_subsets_mult));
646   PetscCall(ISRenumber(all_subsets, all_subsets_mult, &global_size, &all_subsets_n));
647   PetscCall(ISDestroy(&all_subsets));
648   PetscCall(ISDestroy(&all_subsets_mult));
649   PetscCall(ISGetLocalSize(all_subsets_n, &i));
650   PetscCheck(i == local_stash_size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid size of new subset! %" PetscInt_FMT " != %" PetscInt_FMT, i, local_stash_size);
651   PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, local_stash_size, NULL, &lstash));
652   PetscCall(VecCreateMPI(comm_n, PETSC_DECIDE, global_size, &gstash));
653   PetscCall(VecScatterCreate(lstash, NULL, gstash, all_subsets_n, &sstash));
654   PetscCall(ISDestroy(&all_subsets_n));
655 
656   /* subset indices in local boundary numbering */
657   if (!sub_schurs->is_Ej_all) {
658     PetscInt *all_local_idx_B;
659 
660     PetscCall(PetscMalloc1(local_size, &all_local_idx_B));
661     PetscCall(ISGlobalToLocalMappingApply(sub_schurs->BtoNmap, IS_GTOLM_DROP, local_size, all_local_idx_N + extra, &subset_size, all_local_idx_B));
662     PetscCheck(subset_size == local_size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error in sub_schurs serial (BtoNmap)! %" PetscInt_FMT " != %" PetscInt_FMT, subset_size, local_size);
663     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, local_size, all_local_idx_B, PETSC_OWN_POINTER, &sub_schurs->is_Ej_all));
664   }
665 
666   if (change) {
667     ISLocalToGlobalMapping BtoS;
668     IS                     change_primal_B;
669     IS                     change_primal_all;
670 
671     PetscCheck(!sub_schurs->change_primal_sub, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
672     PetscCheck(!sub_schurs->change, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
673     PetscCall(PetscMalloc1(sub_schurs->n_subs, &sub_schurs->change_primal_sub));
674     for (i = 0; i < sub_schurs->n_subs; i++) {
675       ISLocalToGlobalMapping NtoS;
676       PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i], &NtoS));
677       PetscCall(ISGlobalToLocalMappingApplyIS(NtoS, IS_GTOLM_DROP, change_primal, &sub_schurs->change_primal_sub[i]));
678       PetscCall(ISLocalToGlobalMappingDestroy(&NtoS));
679     }
680     PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, change_primal, &change_primal_B));
681     PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all, &BtoS));
682     PetscCall(ISGlobalToLocalMappingApplyIS(BtoS, IS_GTOLM_DROP, change_primal_B, &change_primal_all));
683     PetscCall(ISLocalToGlobalMappingDestroy(&BtoS));
684     PetscCall(ISDestroy(&change_primal_B));
685     PetscCall(PetscMalloc1(sub_schurs->n_subs, &sub_schurs->change));
686     for (i = 0; i < sub_schurs->n_subs; i++) {
687       Mat change_sub;
688 
689       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
690       PetscCall(KSPCreate(PETSC_COMM_SELF, &sub_schurs->change[i]));
691       PetscCall(KSPSetNestLevel(sub_schurs->change[i], 1)); /* do not seem to have direct access to a PC from which to get the level of nests */
692       PetscCall(KSPSetType(sub_schurs->change[i], KSPPREONLY));
693       if (!sub_schurs->change_with_qr) {
694         PetscCall(MatCreateSubMatrix(change, sub_schurs->is_subs[i], sub_schurs->is_subs[i], MAT_INITIAL_MATRIX, &change_sub));
695       } else {
696         Mat change_subt;
697         PetscCall(MatCreateSubMatrix(change, sub_schurs->is_subs[i], sub_schurs->is_subs[i], MAT_INITIAL_MATRIX, &change_subt));
698         PetscCall(MatConvert(change_subt, MATSEQDENSE, MAT_INITIAL_MATRIX, &change_sub));
699         PetscCall(MatDestroy(&change_subt));
700       }
701       PetscCall(KSPSetOperators(sub_schurs->change[i], change_sub, change_sub));
702       PetscCall(MatDestroy(&change_sub));
703       PetscCall(KSPSetOptionsPrefix(sub_schurs->change[i], sub_schurs->prefix));
704       PetscCall(KSPAppendOptionsPrefix(sub_schurs->change[i], "sub_schurs_change_"));
705     }
706     PetscCall(ISDestroy(&change_primal_all));
707   }
708 
709   /* Local matrix of all local Schur on subsets (transposed) */
710   if (!sub_schurs->S_Ej_all) {
711     Mat          T;
712     PetscScalar *v;
713     PetscInt    *ii, *jj;
714     PetscInt     cum, i, j, k;
715 
716     /* MatSeqAIJSetPreallocation + MatSetValues is slow for these kind of matrices (may have large blocks)
717        Allocate properly a representative matrix and duplicate */
718     PetscCall(PetscMalloc3(local_size + 1, &ii, local_stash_size, &jj, local_stash_size, &v));
719     ii[0] = 0;
720     cum   = 0;
721     for (i = 0; i < sub_schurs->n_subs; i++) {
722       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
723       for (j = 0; j < subset_size; j++) {
724         const PetscInt row = cum + j;
725         PetscInt       col = cum;
726 
727         ii[row + 1] = ii[row] + subset_size;
728         for (k = ii[row]; k < ii[row + 1]; k++) {
729           jj[k] = col;
730           col++;
731         }
732       }
733       cum += subset_size;
734     }
735     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, local_size, local_size, ii, jj, v, &T));
736     PetscCall(MatDuplicate(T, MAT_DO_NOT_COPY_VALUES, &sub_schurs->S_Ej_all));
737     PetscCall(MatDestroy(&T));
738     PetscCall(PetscFree3(ii, jj, v));
739   }
740   /* matrices for deluxe scaling and adaptive selection */
741   if (compute_Stilda) {
742     if (!sub_schurs->sum_S_Ej_tilda_all) PetscCall(MatDuplicate(sub_schurs->S_Ej_all, MAT_DO_NOT_COPY_VALUES, &sub_schurs->sum_S_Ej_tilda_all));
743     if (!sub_schurs->sum_S_Ej_inv_all && deluxe) PetscCall(MatDuplicate(sub_schurs->S_Ej_all, MAT_DO_NOT_COPY_VALUES, &sub_schurs->sum_S_Ej_inv_all));
744   }
745 
746   /* Compute Schur complements explicitly */
747   F = NULL;
748   if (!sub_schurs->schur_explicit) {
749     /* this code branch is used when MatFactor with Schur complement support is not present or when explicitly requested;
750        it is not efficient, unless the economic version of the scaling is used */
751     Mat          S_Ej_expl;
752     PetscScalar *work;
753     PetscInt     j, *dummy_idx;
754     PetscBool    Sdense;
755 
756     PetscCall(PetscMalloc2(max_subset_size, &dummy_idx, max_subset_size * max_subset_size, &work));
757     local_size = 0;
758     for (i = 0; i < sub_schurs->n_subs; i++) {
759       IS  is_subset_B;
760       Mat AE_EE, AE_IE, AE_EI, S_Ej;
761 
762       /* subsets in original and boundary numbering */
763       PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, sub_schurs->is_subs[i], &is_subset_B));
764       /* EE block */
765       PetscCall(MatCreateSubMatrix(A_BB, is_subset_B, is_subset_B, MAT_INITIAL_MATRIX, &AE_EE));
766       /* IE block */
767       PetscCall(MatCreateSubMatrix(A_IB, is_I, is_subset_B, MAT_INITIAL_MATRIX, &AE_IE));
768       /* EI block */
769       if (sub_schurs->is_symmetric) {
770         PetscCall(MatCreateTranspose(AE_IE, &AE_EI));
771       } else if (sub_schurs->is_hermitian) {
772         PetscCall(MatCreateHermitianTranspose(AE_IE, &AE_EI));
773       } else {
774         PetscCall(MatCreateSubMatrix(A_BI, is_subset_B, is_I, MAT_INITIAL_MATRIX, &AE_EI));
775       }
776       PetscCall(ISDestroy(&is_subset_B));
777       PetscCall(MatCreateSchurComplement(AE_II, AE_II, AE_IE, AE_EI, AE_EE, &S_Ej));
778       PetscCall(MatDestroy(&AE_EE));
779       PetscCall(MatDestroy(&AE_IE));
780       PetscCall(MatDestroy(&AE_EI));
781       if (AE_II == A_II) { /* we can reuse the same ksp */
782         KSP ksp;
783         PetscCall(MatSchurComplementGetKSP(sub_schurs->S, &ksp));
784         PetscCall(MatSchurComplementSetKSP(S_Ej, ksp));
785       } else { /* build new ksp object which inherits ksp and pc types from the original one */
786         KSP       origksp, schurksp;
787         PC        origpc, schurpc;
788         KSPType   ksp_type;
789         PetscInt  n_internal;
790         PetscBool ispcnone;
791 
792         PetscCall(MatSchurComplementGetKSP(sub_schurs->S, &origksp));
793         PetscCall(MatSchurComplementGetKSP(S_Ej, &schurksp));
794         PetscCall(KSPGetType(origksp, &ksp_type));
795         PetscCall(KSPSetType(schurksp, ksp_type));
796         PetscCall(KSPGetPC(schurksp, &schurpc));
797         PetscCall(KSPGetPC(origksp, &origpc));
798         PetscCall(PetscObjectTypeCompare((PetscObject)origpc, PCNONE, &ispcnone));
799         if (!ispcnone) {
800           PCType pc_type;
801           PetscCall(PCGetType(origpc, &pc_type));
802           PetscCall(PCSetType(schurpc, pc_type));
803         } else {
804           PetscCall(PCSetType(schurpc, PCLU));
805         }
806         PetscCall(ISGetSize(is_I, &n_internal));
807         if (!n_internal) { /* UMFPACK gives error with 0 sized problems */
808           MatSolverType solver = NULL;
809           PetscCall(PCFactorGetMatSolverType(origpc, &solver));
810           if (solver) PetscCall(PCFactorSetMatSolverType(schurpc, solver));
811         }
812         PetscCall(KSPSetUp(schurksp));
813       }
814       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
815       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &S_Ej_expl));
816       PetscCall(PCBDDCComputeExplicitSchur(S_Ej, sub_schurs->is_symmetric, MAT_REUSE_MATRIX, &S_Ej_expl));
817       PetscCall(PetscObjectTypeCompare((PetscObject)S_Ej_expl, MATSEQDENSE, &Sdense));
818       PetscCheck(Sdense, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for sparse matrices");
819       for (j = 0; j < subset_size; j++) dummy_idx[j] = local_size + j;
820       PetscCall(MatSetValues(sub_schurs->S_Ej_all, subset_size, dummy_idx, subset_size, dummy_idx, work, INSERT_VALUES));
821       PetscCall(MatDestroy(&S_Ej));
822       PetscCall(MatDestroy(&S_Ej_expl));
823       local_size += subset_size;
824     }
825     PetscCall(PetscFree2(dummy_idx, work));
826     /* free */
827     PetscCall(ISDestroy(&is_I));
828     PetscCall(MatDestroy(&AE_II));
829     PetscCall(PetscFree(all_local_idx_N));
830   } else {
831     Mat                A, cs_AIB_mat = NULL, benign_AIIm1_ones_mat = NULL;
832     Mat               *gdswA;
833     Vec                Dall = NULL;
834     IS                 is_A_all, *is_p_r = NULL;
835     MatType            Stype;
836     PetscScalar       *work, *S_data, *schur_factor, infty = PETSC_MAX_REAL;
837     PetscScalar       *SEj_arr = NULL, *SEjinv_arr = NULL;
838     const PetscScalar *rS_data;
839     PetscInt           n, n_I, size_schur, size_active_schur, cum, cum2;
840     PetscBool          economic, solver_S, S_lower_triangular = PETSC_FALSE;
841     PetscBool          schur_has_vertices, factor_workaround;
842     PetscBool          use_cholesky;
843 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
844     PetscBool oldpin;
845 #endif
846 
847     /* get sizes */
848     n_I = 0;
849     if (is_I_layer) PetscCall(ISGetLocalSize(is_I_layer, &n_I));
850     economic = PETSC_FALSE;
851     PetscCall(ISGetLocalSize(sub_schurs->is_I, &cum));
852     if (cum != n_I) economic = PETSC_TRUE;
853     PetscCall(MatGetLocalSize(sub_schurs->A, &n, NULL));
854     size_active_schur = local_size;
855 
856     /* import scaling vector (wrong formulation if we have 3D edges) */
857     if (scaling && compute_Stilda) {
858       const PetscScalar *array;
859       PetscScalar       *array2;
860       const PetscInt    *idxs;
861       PetscInt           i;
862 
863       PetscCall(ISGetIndices(sub_schurs->is_Ej_all, &idxs));
864       PetscCall(VecCreateSeq(PETSC_COMM_SELF, size_active_schur, &Dall));
865       PetscCall(VecGetArrayRead(scaling, &array));
866       PetscCall(VecGetArray(Dall, &array2));
867       for (i = 0; i < size_active_schur; i++) array2[i] = array[idxs[i]];
868       PetscCall(VecRestoreArray(Dall, &array2));
869       PetscCall(VecRestoreArrayRead(scaling, &array));
870       PetscCall(ISRestoreIndices(sub_schurs->is_Ej_all, &idxs));
871       deluxe = PETSC_FALSE;
872     }
873 
874     /* size active schurs does not count any dirichlet or vertex dof on the interface */
875     factor_workaround  = PETSC_FALSE;
876     schur_has_vertices = PETSC_FALSE;
877     cum                = n_I + size_active_schur;
878     if (sub_schurs->is_dir) {
879       const PetscInt *idxs;
880       PetscInt        n_dir;
881 
882       PetscCall(ISGetLocalSize(sub_schurs->is_dir, &n_dir));
883       PetscCall(ISGetIndices(sub_schurs->is_dir, &idxs));
884       PetscCall(PetscArraycpy(all_local_idx_N + cum, idxs, n_dir));
885       PetscCall(ISRestoreIndices(sub_schurs->is_dir, &idxs));
886       cum += n_dir;
887       if (!sub_schurs->gdsw) factor_workaround = PETSC_TRUE;
888     }
889     /* include the primal vertices in the Schur complement */
890     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
891       PetscInt n_v;
892 
893       PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &n_v));
894       if (n_v) {
895         const PetscInt *idxs;
896 
897         PetscCall(ISGetIndices(sub_schurs->is_vertices, &idxs));
898         PetscCall(PetscArraycpy(all_local_idx_N + cum, idxs, n_v));
899         PetscCall(ISRestoreIndices(sub_schurs->is_vertices, &idxs));
900         cum += n_v;
901         if (!sub_schurs->gdsw) factor_workaround = PETSC_TRUE;
902         schur_has_vertices = PETSC_TRUE;
903       }
904     }
905     size_schur = cum - n_I;
906     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cum, all_local_idx_N, PETSC_OWN_POINTER, &is_A_all));
907 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
908     oldpin = sub_schurs->A->boundtocpu;
909     PetscCall(MatBindToCPU(sub_schurs->A, PETSC_TRUE));
910 #endif
911     if (cum == n) {
912       PetscCall(ISSetPermutation(is_A_all));
913       PetscCall(MatPermute(sub_schurs->A, is_A_all, is_A_all, &A));
914     } else {
915       PetscCall(MatCreateSubMatrix(sub_schurs->A, is_A_all, is_A_all, MAT_INITIAL_MATRIX, &A));
916     }
917 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
918     PetscCall(MatBindToCPU(sub_schurs->A, oldpin));
919 #endif
920     PetscCall(MatSetOptionsPrefixFactor(A, sub_schurs->prefix));
921     PetscCall(MatAppendOptionsPrefixFactor(A, "sub_schurs_"));
922 
923     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
924        this is a workaround */
925     if (benign_n) {
926       Vec                    v, benign_AIIm1_ones;
927       ISLocalToGlobalMapping N_to_reor;
928       IS                     is_p0, is_p0_p;
929       PetscScalar           *cs_AIB, *AIIm1_data;
930       PetscInt               sizeA;
931 
932       PetscCall(ISLocalToGlobalMappingCreateIS(is_A_all, &N_to_reor));
933       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, benign_n, benign_p0_lidx, PETSC_COPY_VALUES, &is_p0));
934       PetscCall(ISGlobalToLocalMappingApplyIS(N_to_reor, IS_GTOLM_DROP, is_p0, &is_p0_p));
935       PetscCall(ISDestroy(&is_p0));
936       PetscCall(MatCreateVecs(A, &v, &benign_AIIm1_ones));
937       PetscCall(VecGetSize(v, &sizeA));
938       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, sizeA, benign_n, NULL, &benign_AIIm1_ones_mat));
939       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size_schur, benign_n, NULL, &cs_AIB_mat));
940       PetscCall(MatDenseGetArray(cs_AIB_mat, &cs_AIB));
941       PetscCall(MatDenseGetArray(benign_AIIm1_ones_mat, &AIIm1_data));
942       PetscCall(PetscMalloc1(benign_n, &is_p_r));
943       /* compute colsum of A_IB restricted to pressures */
944       for (i = 0; i < benign_n; i++) {
945         const PetscScalar *array;
946         const PetscInt    *idxs;
947         PetscInt           j, nz;
948 
949         PetscCall(ISGlobalToLocalMappingApplyIS(N_to_reor, IS_GTOLM_DROP, benign_zerodiag_subs[i], &is_p_r[i]));
950         PetscCall(ISGetLocalSize(is_p_r[i], &nz));
951         PetscCall(ISGetIndices(is_p_r[i], &idxs));
952         for (j = 0; j < nz; j++) AIIm1_data[idxs[j] + sizeA * i] = 1.;
953         PetscCall(ISRestoreIndices(is_p_r[i], &idxs));
954         PetscCall(VecPlaceArray(benign_AIIm1_ones, AIIm1_data + sizeA * i));
955         PetscCall(MatMult(A, benign_AIIm1_ones, v));
956         PetscCall(VecResetArray(benign_AIIm1_ones));
957         PetscCall(VecGetArrayRead(v, &array));
958         for (j = 0; j < size_schur; j++) {
959 #if defined(PETSC_USE_COMPLEX)
960           cs_AIB[i * size_schur + j] = (PetscRealPart(array[j + n_I]) / nz + PETSC_i * (PetscImaginaryPart(array[j + n_I]) / nz));
961 #else
962           cs_AIB[i * size_schur + j] = array[j + n_I] / nz;
963 #endif
964         }
965         PetscCall(VecRestoreArrayRead(v, &array));
966       }
967       PetscCall(MatDenseRestoreArray(cs_AIB_mat, &cs_AIB));
968       PetscCall(MatDenseRestoreArray(benign_AIIm1_ones_mat, &AIIm1_data));
969       PetscCall(VecDestroy(&v));
970       PetscCall(VecDestroy(&benign_AIIm1_ones));
971       PetscCall(MatSetOption(A, MAT_KEEP_NONZERO_PATTERN, PETSC_FALSE));
972       PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));
973       PetscCall(MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
974       PetscCall(MatZeroRowsColumnsIS(A, is_p0_p, 1.0, NULL, NULL));
975       PetscCall(ISDestroy(&is_p0_p));
976       PetscCall(ISLocalToGlobalMappingDestroy(&N_to_reor));
977     }
978     PetscCall(MatSetOption(A, MAT_SYMMETRIC, sub_schurs->is_symmetric));
979     PetscCall(MatSetOption(A, MAT_HERMITIAN, sub_schurs->is_hermitian));
980     PetscCall(MatSetOption(A, MAT_SPD, sub_schurs->is_posdef));
981 
982     /* for complexes, symmetric and hermitian at the same time implies null imaginary part */
983     use_cholesky = (PetscBool)((use_potr || use_sytr) && sub_schurs->is_hermitian && sub_schurs->is_symmetric);
984 
985     /* when using the benign subspace trick, the local Schur complements are SPD */
986     /* MKL_PARDISO does not handle well the computation of a Schur complement from a symmetric indefinite factorization
987        Use LU and adapt pivoting perturbation (still, solution is not as accurate as with using MUMPS) */
988     if (benign_trick) {
989       sub_schurs->is_posdef = PETSC_TRUE;
990       PetscCall(PetscStrcmp(sub_schurs->mat_solver_type, MATSOLVERMKL_PARDISO, &flg));
991       if (flg) use_cholesky = PETSC_FALSE;
992     }
993 
994     if (n_I) {
995       IS        is_schur;
996       char      stype[64];
997       PetscBool gpu = PETSC_FALSE;
998 
999       if (use_cholesky) {
1000         PetscCall(MatGetFactor(A, sub_schurs->mat_solver_type, MAT_FACTOR_CHOLESKY, &F));
1001       } else {
1002         PetscCall(MatGetFactor(A, sub_schurs->mat_solver_type, MAT_FACTOR_LU, &F));
1003       }
1004       PetscCheck(F, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MatGetFactor not supported by matrix instance of type %s. Rerun with \"-info :mat | grep MatGetFactor_\" for additional information", ((PetscObject)A)->type_name);
1005       PetscCall(MatSetErrorIfFailure(A, PETSC_TRUE));
1006 #if defined(PETSC_HAVE_MKL_PARDISO)
1007       if (benign_trick) PetscCall(MatMkl_PardisoSetCntl(F, 10, 10));
1008 #endif
1009       /* subsets ordered last */
1010       PetscCall(ISCreateStride(PETSC_COMM_SELF, size_schur, n_I, 1, &is_schur));
1011       PetscCall(MatFactorSetSchurIS(F, is_schur));
1012       PetscCall(ISDestroy(&is_schur));
1013 
1014       /* factorization step */
1015       if (use_cholesky) {
1016         PetscCall(MatCholeskyFactorSymbolic(F, A, NULL, NULL));
1017 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
1018         PetscCall(MatMumpsSetIcntl(F, 19, 2));
1019 #endif
1020         PetscCall(MatCholeskyFactorNumeric(F, A, NULL));
1021         S_lower_triangular = PETSC_TRUE;
1022       } else {
1023         PetscCall(MatLUFactorSymbolic(F, A, NULL, NULL, NULL));
1024 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
1025         PetscCall(MatMumpsSetIcntl(F, 19, 3));
1026 #endif
1027         PetscCall(MatLUFactorNumeric(F, A, NULL));
1028       }
1029       PetscCall(MatViewFromOptions(F, (PetscObject)A, "-mat_factor_view"));
1030 
1031       if (matl_dbg_viewer) {
1032         Mat S;
1033         IS  is;
1034 
1035         PetscCall(PetscObjectSetName((PetscObject)A, "A"));
1036         PetscCall(MatView(A, matl_dbg_viewer));
1037         PetscCall(MatFactorCreateSchurComplement(F, &S, NULL));
1038         PetscCall(PetscObjectSetName((PetscObject)S, "S"));
1039         PetscCall(MatView(S, matl_dbg_viewer));
1040         PetscCall(MatDestroy(&S));
1041         PetscCall(ISCreateStride(PETSC_COMM_SELF, n_I, 0, 1, &is));
1042         PetscCall(PetscObjectSetName((PetscObject)is, "I"));
1043         PetscCall(ISView(is, matl_dbg_viewer));
1044         PetscCall(ISDestroy(&is));
1045         PetscCall(ISCreateStride(PETSC_COMM_SELF, size_schur, n_I, 1, &is));
1046         PetscCall(PetscObjectSetName((PetscObject)is, "B"));
1047         PetscCall(ISView(is, matl_dbg_viewer));
1048         PetscCall(ISDestroy(&is));
1049         PetscCall(PetscObjectSetName((PetscObject)is_A_all, "IA"));
1050         PetscCall(ISView(is_A_all, matl_dbg_viewer));
1051         for (i = 0, cum = 0; i < sub_schurs->n_subs; i++) {
1052           IS   is;
1053           char name[16];
1054 
1055           PetscCall(PetscSNPrintf(name, sizeof(name), "IE%" PetscInt_FMT, i));
1056           PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1057           PetscCall(ISCreateStride(PETSC_COMM_SELF, subset_size, cum, 1, &is));
1058           PetscCall(PetscObjectSetName((PetscObject)is, name));
1059           PetscCall(ISView(is, matl_dbg_viewer));
1060           PetscCall(ISDestroy(&is));
1061           if (sub_schurs->change) {
1062             Mat T;
1063 
1064             PetscCall(PetscSNPrintf(name, sizeof(name), "TE%" PetscInt_FMT, i));
1065             PetscCall(KSPGetOperators(sub_schurs->change[i], &T, NULL));
1066             PetscCall(PetscObjectSetName((PetscObject)T, name));
1067             PetscCall(MatView(T, matl_dbg_viewer));
1068             PetscCall(PetscSNPrintf(name, sizeof(name), "ITE%" PetscInt_FMT, i));
1069             PetscCall(PetscObjectSetName((PetscObject)sub_schurs->change_primal_sub[i], name));
1070             PetscCall(ISView(sub_schurs->change_primal_sub[i], matl_dbg_viewer));
1071           }
1072           cum += subset_size;
1073         }
1074         PetscCall(PetscViewerFlush(matl_dbg_viewer));
1075       }
1076 
1077       /* get explicit Schur Complement computed during numeric factorization */
1078       PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
1079       PetscCall(PetscStrncpy(stype, MATSEQDENSE, sizeof(stype)));
1080 #if defined(PETSC_HAVE_CUDA)
1081       PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &gpu, MATSEQAIJVIENNACL, MATSEQAIJCUSPARSE, ""));
1082 #endif
1083       if (gpu) PetscCall(PetscStrncpy(stype, MATSEQDENSECUDA, sizeof(stype)));
1084       PetscCall(PetscOptionsGetString(NULL, sub_schurs->prefix, "-sub_schurs_schur_mat_type", stype, sizeof(stype), NULL));
1085       PetscCall(MatConvert(S_all, stype, MAT_INPLACE_MATRIX, &S_all));
1086       PetscCall(MatSetOption(S_all, MAT_SPD, sub_schurs->is_posdef));
1087       PetscCall(MatSetOption(S_all, MAT_HERMITIAN, sub_schurs->is_hermitian));
1088       PetscCall(MatGetType(S_all, &Stype));
1089 
1090       /* we can reuse the solvers if we are not using the economic version */
1091       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
1092       if (!sub_schurs->gdsw) {
1093         factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
1094         if (!sub_schurs->is_posdef && factor_workaround && compute_Stilda && size_active_schur) reuse_solvers = factor_workaround = PETSC_FALSE;
1095       }
1096       solver_S = PETSC_TRUE;
1097 
1098       /* update the Schur complement with the change of basis on the pressures */
1099       if (benign_n) {
1100         const PetscScalar *cs_AIB;
1101         PetscScalar       *S_data, *AIIm1_data;
1102         Mat                S2 = NULL, S3 = NULL; /* dbg */
1103         PetscScalar       *S2_data, *S3_data;    /* dbg */
1104         Vec                v, benign_AIIm1_ones;
1105         PetscInt           sizeA;
1106 
1107         PetscCall(MatDenseGetArray(S_all, &S_data));
1108         PetscCall(MatCreateVecs(A, &v, &benign_AIIm1_ones));
1109         PetscCall(VecGetSize(v, &sizeA));
1110 #if defined(PETSC_HAVE_MUMPS)
1111         PetscCall(MatMumpsSetIcntl(F, 26, 0));
1112 #endif
1113 #if defined(PETSC_HAVE_MKL_PARDISO)
1114         PetscCall(MatMkl_PardisoSetCntl(F, 70, 1));
1115 #endif
1116         PetscCall(MatDenseGetArrayRead(cs_AIB_mat, &cs_AIB));
1117         PetscCall(MatDenseGetArray(benign_AIIm1_ones_mat, &AIIm1_data));
1118         if (matl_dbg_viewer) {
1119           PetscCall(MatDuplicate(S_all, MAT_DO_NOT_COPY_VALUES, &S2));
1120           PetscCall(MatDuplicate(S_all, MAT_DO_NOT_COPY_VALUES, &S3));
1121           PetscCall(MatDenseGetArray(S2, &S2_data));
1122           PetscCall(MatDenseGetArray(S3, &S3_data));
1123         }
1124         for (i = 0; i < benign_n; i++) {
1125           PetscScalar    *array, sum = 0., one = 1., *sums;
1126           const PetscInt *idxs;
1127           PetscInt        k, j, nz;
1128           PetscBLASInt    B_k, B_n;
1129 
1130           PetscCall(PetscCalloc1(benign_n, &sums));
1131           PetscCall(VecPlaceArray(benign_AIIm1_ones, AIIm1_data + sizeA * i));
1132           PetscCall(VecCopy(benign_AIIm1_ones, v));
1133           PetscCall(MatSolve(F, v, benign_AIIm1_ones));
1134           PetscCall(MatMult(A, benign_AIIm1_ones, v));
1135           PetscCall(VecResetArray(benign_AIIm1_ones));
1136           /* p0 dofs (eliminated) are excluded from the sums */
1137           for (k = 0; k < benign_n; k++) {
1138             PetscCall(ISGetLocalSize(is_p_r[k], &nz));
1139             PetscCall(ISGetIndices(is_p_r[k], &idxs));
1140             for (j = 0; j < nz - 1; j++) sums[k] -= AIIm1_data[idxs[j] + sizeA * i];
1141             PetscCall(ISRestoreIndices(is_p_r[k], &idxs));
1142           }
1143           PetscCall(VecGetArrayRead(v, (const PetscScalar **)&array));
1144           if (matl_dbg_viewer) {
1145             Vec  vv;
1146             char name[16];
1147 
1148             PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, size_schur, array + n_I, &vv));
1149             PetscCall(PetscSNPrintf(name, sizeof(name), "Pvs%" PetscInt_FMT, i));
1150             PetscCall(PetscObjectSetName((PetscObject)vv, name));
1151             PetscCall(VecView(vv, matl_dbg_viewer));
1152           }
1153           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
1154           /* cs_AIB already scaled by 1./nz */
1155           B_k = 1;
1156           PetscCall(PetscBLASIntCast(size_schur, &B_n));
1157           for (k = 0; k < benign_n; k++) {
1158             sum = sums[k];
1159 
1160             if (PetscAbsScalar(sum) == 0.0) continue;
1161             if (k == i) {
1162               if (B_n) PetscCallBLAS("BLASsyrk", BLASsyrk_("L", "N", &B_n, &B_k, &sum, cs_AIB + i * size_schur, &B_n, &one, S_data, &B_n));
1163               if (matl_dbg_viewer && B_n) PetscCallBLAS("BLASsyrk", BLASsyrk_("L", "N", &B_n, &B_k, &sum, cs_AIB + i * size_schur, &B_n, &one, S3_data, &B_n));
1164             } else { /* XXX Is it correct to use symmetric rank-2 update with half of the sum? */
1165               sum /= 2.0;
1166               if (B_n) PetscCallBLAS("BLASsyr2k", BLASsyr2k_("L", "N", &B_n, &B_k, &sum, cs_AIB + k * size_schur, &B_n, cs_AIB + i * size_schur, &B_n, &one, S_data, &B_n));
1167               if (matl_dbg_viewer && B_n) PetscCallBLAS("BLASsyr2k", BLASsyr2k_("L", "N", &B_n, &B_k, &sum, cs_AIB + k * size_schur, &B_n, cs_AIB + i * size_schur, &B_n, &one, S3_data, &B_n));
1168             }
1169           }
1170           sum = 1.;
1171           if (B_n) PetscCallBLAS("BLASsyr2k", BLASsyr2k_("L", "N", &B_n, &B_k, &sum, array + n_I, &B_n, cs_AIB + i * size_schur, &B_n, &one, S_data, &B_n));
1172           if (matl_dbg_viewer && B_n) PetscCallBLAS("BLASsyr2k", BLASsyr2k_("L", "N", &B_n, &B_k, &sum, array + n_I, &B_n, cs_AIB + i * size_schur, &B_n, &one, S2_data, &B_n));
1173           PetscCall(VecRestoreArrayRead(v, (const PetscScalar **)&array));
1174           /* set p0 entry of AIIm1_ones to zero */
1175           PetscCall(ISGetLocalSize(is_p_r[i], &nz));
1176           PetscCall(ISGetIndices(is_p_r[i], &idxs));
1177           for (j = 0; j < benign_n; j++) AIIm1_data[idxs[nz - 1] + sizeA * j] = 0.;
1178           PetscCall(ISRestoreIndices(is_p_r[i], &idxs));
1179           PetscCall(PetscFree(sums));
1180         }
1181         PetscCall(VecDestroy(&benign_AIIm1_ones));
1182         if (matl_dbg_viewer) {
1183           PetscCall(MatDenseRestoreArray(S2, &S2_data));
1184           PetscCall(MatDenseRestoreArray(S3, &S3_data));
1185         }
1186         if (!S_lower_triangular) { /* I need to expand the upper triangular data (column-oriented) */
1187           PetscInt k, j;
1188           for (k = 0; k < size_schur; k++) {
1189             for (j = k; j < size_schur; j++) S_data[j * size_schur + k] = PetscConj(S_data[k * size_schur + j]);
1190           }
1191         }
1192 
1193         /* restore defaults */
1194 #if defined(PETSC_HAVE_MUMPS)
1195         PetscCall(MatMumpsSetIcntl(F, 26, -1));
1196 #endif
1197 #if defined(PETSC_HAVE_MKL_PARDISO)
1198         PetscCall(MatMkl_PardisoSetCntl(F, 70, 0));
1199 #endif
1200         PetscCall(MatDenseRestoreArrayRead(cs_AIB_mat, &cs_AIB));
1201         PetscCall(MatDenseRestoreArray(benign_AIIm1_ones_mat, &AIIm1_data));
1202         PetscCall(VecDestroy(&v));
1203         PetscCall(MatDenseRestoreArray(S_all, &S_data));
1204         if (matl_dbg_viewer) {
1205           Mat S;
1206 
1207           PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));
1208           PetscCall(MatFactorCreateSchurComplement(F, &S, NULL));
1209           PetscCall(PetscObjectSetName((PetscObject)S, "Sb"));
1210           PetscCall(MatView(S, matl_dbg_viewer));
1211           PetscCall(MatDestroy(&S));
1212           PetscCall(PetscObjectSetName((PetscObject)S2, "S2P"));
1213           PetscCall(MatView(S2, matl_dbg_viewer));
1214           PetscCall(PetscObjectSetName((PetscObject)S3, "S3P"));
1215           PetscCall(MatView(S3, matl_dbg_viewer));
1216           PetscCall(PetscObjectSetName((PetscObject)cs_AIB_mat, "cs"));
1217           PetscCall(MatView(cs_AIB_mat, matl_dbg_viewer));
1218           PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
1219         }
1220         PetscCall(MatDestroy(&S2));
1221         PetscCall(MatDestroy(&S3));
1222       }
1223       if (!reuse_solvers) {
1224         for (i = 0; i < benign_n; i++) PetscCall(ISDestroy(&is_p_r[i]));
1225         PetscCall(PetscFree(is_p_r));
1226         PetscCall(MatDestroy(&cs_AIB_mat));
1227         PetscCall(MatDestroy(&benign_AIIm1_ones_mat));
1228       }
1229     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1230       PetscCall(MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &S_all));
1231       PetscCall(MatGetType(S_all, &Stype));
1232       reuse_solvers     = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1233       factor_workaround = PETSC_FALSE;
1234       solver_S          = PETSC_FALSE;
1235     }
1236 
1237     if (reuse_solvers) {
1238       Mat                A_II, pA_II, Afake;
1239       Vec                vec1_B;
1240       PCBDDCReuseSolvers msolv_ctx;
1241       PetscInt           n_R;
1242 
1243       if (sub_schurs->reuse_solver) {
1244         PetscCall(PCBDDCReuseSolversReset(sub_schurs->reuse_solver));
1245       } else {
1246         PetscCall(PetscNew(&sub_schurs->reuse_solver));
1247       }
1248       msolv_ctx = sub_schurs->reuse_solver;
1249       PetscCall(MatSchurComplementGetSubMatrices(sub_schurs->S, &A_II, &pA_II, NULL, NULL, NULL));
1250       PetscCall(PetscObjectReference((PetscObject)F));
1251       msolv_ctx->F = F;
1252       PetscCall(MatCreateVecs(F, &msolv_ctx->sol, NULL));
1253       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1254       {
1255         PetscScalar *array;
1256         PetscInt     n;
1257 
1258         PetscCall(VecGetLocalSize(msolv_ctx->sol, &n));
1259         PetscCall(VecGetArray(msolv_ctx->sol, &array));
1260         PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol), 1, n, array, &msolv_ctx->rhs));
1261         PetscCall(VecRestoreArray(msolv_ctx->sol, &array));
1262       }
1263       msolv_ctx->has_vertices = schur_has_vertices;
1264 
1265       /* interior solver */
1266       PetscCall(PCCreate(PetscObjectComm((PetscObject)A_II), &msolv_ctx->interior_solver));
1267       PetscCall(PCSetOperators(msolv_ctx->interior_solver, A_II, pA_II));
1268       PetscCall(PCSetType(msolv_ctx->interior_solver, PCSHELL));
1269       PetscCall(PCShellSetName(msolv_ctx->interior_solver, "Interior solver (w/o Schur factorization)"));
1270       PetscCall(PCShellSetContext(msolv_ctx->interior_solver, msolv_ctx));
1271       PetscCall(PCShellSetView(msolv_ctx->interior_solver, PCBDDCReuseSolvers_View));
1272       PetscCall(PCShellSetApply(msolv_ctx->interior_solver, PCBDDCReuseSolvers_Interior));
1273       PetscCall(PCShellSetApplyTranspose(msolv_ctx->interior_solver, PCBDDCReuseSolvers_InteriorTranspose));
1274       if (sub_schurs->gdsw) PetscCall(PCShellSetDestroy(msolv_ctx->interior_solver, PCBDDCReuseSolvers_Destroy));
1275 
1276       /* correction solver */
1277       if (!sub_schurs->gdsw) {
1278         PetscCall(PCCreate(PetscObjectComm((PetscObject)A_II), &msolv_ctx->correction_solver));
1279         PetscCall(PCSetType(msolv_ctx->correction_solver, PCSHELL));
1280         PetscCall(PCShellSetName(msolv_ctx->correction_solver, "Correction solver (with Schur factorization)"));
1281         PetscCall(PCShellSetContext(msolv_ctx->correction_solver, msolv_ctx));
1282         PetscCall(PCShellSetView(msolv_ctx->interior_solver, PCBDDCReuseSolvers_View));
1283         PetscCall(PCShellSetApply(msolv_ctx->correction_solver, PCBDDCReuseSolvers_Correction));
1284         PetscCall(PCShellSetApplyTranspose(msolv_ctx->correction_solver, PCBDDCReuseSolvers_CorrectionTranspose));
1285 
1286         /* scatter and vecs for Schur complement solver */
1287         PetscCall(MatCreateVecs(S_all, &msolv_ctx->sol_B, &msolv_ctx->rhs_B));
1288         PetscCall(MatCreateVecs(sub_schurs->S, &vec1_B, NULL));
1289         if (!schur_has_vertices) {
1290           PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, is_A_all, &msolv_ctx->is_B));
1291           PetscCall(VecScatterCreate(vec1_B, msolv_ctx->is_B, msolv_ctx->sol_B, NULL, &msolv_ctx->correction_scatter_B));
1292           PetscCall(PetscObjectReference((PetscObject)is_A_all));
1293           msolv_ctx->is_R = is_A_all;
1294         } else {
1295           IS              is_B_all;
1296           const PetscInt *idxs;
1297           PetscInt        dual, n_v, n;
1298 
1299           PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &n_v));
1300           dual = size_schur - n_v;
1301           PetscCall(ISGetLocalSize(is_A_all, &n));
1302           PetscCall(ISGetIndices(is_A_all, &idxs));
1303           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all), dual, idxs + n_I, PETSC_COPY_VALUES, &is_B_all));
1304           PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, is_B_all, &msolv_ctx->is_B));
1305           PetscCall(ISDestroy(&is_B_all));
1306           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)is_A_all), dual, 0, 1, &is_B_all));
1307           PetscCall(VecScatterCreate(vec1_B, msolv_ctx->is_B, msolv_ctx->sol_B, is_B_all, &msolv_ctx->correction_scatter_B));
1308           PetscCall(ISDestroy(&is_B_all));
1309           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all), n - n_v, idxs, PETSC_COPY_VALUES, &msolv_ctx->is_R));
1310           PetscCall(ISRestoreIndices(is_A_all, &idxs));
1311         }
1312         PetscCall(ISGetLocalSize(msolv_ctx->is_R, &n_R));
1313         PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, n_R, n_R, 0, NULL, &Afake));
1314         PetscCall(MatAssemblyBegin(Afake, MAT_FINAL_ASSEMBLY));
1315         PetscCall(MatAssemblyEnd(Afake, MAT_FINAL_ASSEMBLY));
1316         PetscCall(PCSetOperators(msolv_ctx->correction_solver, Afake, Afake));
1317         PetscCall(MatDestroy(&Afake));
1318         PetscCall(VecDestroy(&vec1_B));
1319       }
1320       /* communicate benign info to solver context */
1321       if (benign_n) {
1322         PetscScalar *array;
1323 
1324         msolv_ctx->benign_n             = benign_n;
1325         msolv_ctx->benign_zerodiag_subs = is_p_r;
1326         PetscCall(PetscMalloc1(benign_n, &msolv_ctx->benign_save_vals));
1327         msolv_ctx->benign_csAIB = cs_AIB_mat;
1328         PetscCall(MatCreateVecs(cs_AIB_mat, &msolv_ctx->benign_corr_work, NULL));
1329         PetscCall(VecGetArray(msolv_ctx->benign_corr_work, &array));
1330         PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, size_schur, array, &msolv_ctx->benign_dummy_schur_vec));
1331         PetscCall(VecRestoreArray(msolv_ctx->benign_corr_work, &array));
1332         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1333       }
1334     } else {
1335       if (sub_schurs->reuse_solver) PetscCall(PCBDDCReuseSolversReset(sub_schurs->reuse_solver));
1336       PetscCall(PetscFree(sub_schurs->reuse_solver));
1337     }
1338     PetscCall(MatDestroy(&A));
1339     PetscCall(ISDestroy(&is_A_all));
1340 
1341     /* Work arrays */
1342     PetscCall(PetscMalloc1(max_subset_size * max_subset_size, &work));
1343 
1344     /* S_Ej_all */
1345     cum = cum2 = 0;
1346     PetscCall(MatDenseGetArrayRead(S_all, &rS_data));
1347     PetscCall(MatSeqAIJGetArray(sub_schurs->S_Ej_all, &SEj_arr));
1348     if (sub_schurs->sum_S_Ej_inv_all) PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all, &SEjinv_arr));
1349     if (sub_schurs->gdsw) PetscCall(MatCreateSubMatrices(sub_schurs->A, sub_schurs->n_subs, sub_schurs->is_subs, sub_schurs->is_subs, MAT_INITIAL_MATRIX, &gdswA));
1350     for (i = 0; i < sub_schurs->n_subs; i++) {
1351       PetscInt j;
1352 
1353       /* get S_E (or K^i_EE for GDSW) */
1354       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1355       if (sub_schurs->gdsw) {
1356         Mat T;
1357 
1358         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &T));
1359         PetscCall(MatConvert(gdswA[i], MATDENSE, MAT_REUSE_MATRIX, &T));
1360         PetscCall(MatDestroy(&T));
1361       } else {
1362         if (S_lower_triangular) { /* I need to expand the upper triangular data (column-oriented) */
1363           PetscInt k;
1364           for (k = 0; k < subset_size; k++) {
1365             for (j = k; j < subset_size; j++) {
1366               work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1367               work[j * subset_size + k] = PetscConj(rS_data[cum2 + k * size_schur + j]);
1368             }
1369           }
1370         } else { /* just copy to workspace */
1371           PetscInt k;
1372           for (k = 0; k < subset_size; k++) {
1373             for (j = 0; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1374           }
1375         }
1376       }
1377       /* insert S_E values */
1378       if (sub_schurs->change) {
1379         Mat change_sub, SEj, T;
1380 
1381         /* change basis */
1382         PetscCall(KSPGetOperators(sub_schurs->change[i], &change_sub, NULL));
1383         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &SEj));
1384         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1385           Mat T2;
1386           PetscCall(MatTransposeMatMult(change_sub, SEj, MAT_INITIAL_MATRIX, 1.0, &T2));
1387           PetscCall(MatMatMult(T2, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
1388           PetscCall(MatConvert(T, MATSEQDENSE, MAT_INPLACE_MATRIX, &T));
1389           PetscCall(MatDestroy(&T2));
1390         } else {
1391           PetscCall(MatPtAP(SEj, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
1392         }
1393         PetscCall(MatCopy(T, SEj, SAME_NONZERO_PATTERN));
1394         PetscCall(MatDestroy(&T));
1395         PetscCall(MatZeroRowsColumnsIS(SEj, sub_schurs->change_primal_sub[i], 1.0, NULL, NULL));
1396         PetscCall(MatDestroy(&SEj));
1397       }
1398       PetscCall(PetscArraycpy(SEj_arr, work, subset_size * subset_size));
1399       if (compute_Stilda) {
1400         if (deluxe) { /* if adaptivity is requested, invert S_E blocks */
1401           Mat                M;
1402           const PetscScalar *vals;
1403           PetscBool          isdense, isdensecuda;
1404 
1405           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &M));
1406           PetscCall(MatSetOption(M, MAT_SPD, sub_schurs->is_posdef));
1407           PetscCall(MatSetOption(M, MAT_HERMITIAN, sub_schurs->is_hermitian));
1408           if (!PetscBTLookup(sub_schurs->is_edge, i)) PetscCall(MatSetType(M, Stype));
1409           PetscCall(PetscObjectTypeCompare((PetscObject)M, MATSEQDENSE, &isdense));
1410           PetscCall(PetscObjectTypeCompare((PetscObject)M, MATSEQDENSECUDA, &isdensecuda));
1411           if (use_cholesky) {
1412             PetscCall(MatCholeskyFactor(M, NULL, NULL));
1413           } else {
1414             PetscCall(MatLUFactor(M, NULL, NULL, NULL));
1415           }
1416           if (isdense) {
1417             PetscCall(MatSeqDenseInvertFactors_Private(M));
1418 #if defined(PETSC_HAVE_CUDA)
1419           } else if (isdensecuda) {
1420             PetscCall(MatSeqDenseCUDAInvertFactors_Internal(M));
1421 #endif
1422           } else SETERRQ(PetscObjectComm((PetscObject)M), PETSC_ERR_SUP, "Not implemented for type %s", Stype);
1423           PetscCall(MatDenseGetArrayRead(M, &vals));
1424           PetscCall(PetscArraycpy(SEjinv_arr, vals, subset_size * subset_size));
1425           PetscCall(MatDenseRestoreArrayRead(M, &vals));
1426           PetscCall(MatDestroy(&M));
1427         } else if (scaling) { /* not using deluxe */
1428           Mat          SEj;
1429           Vec          D;
1430           PetscScalar *array;
1431 
1432           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &SEj));
1433           PetscCall(VecGetArray(Dall, &array));
1434           PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, subset_size, array + cum, &D));
1435           PetscCall(VecRestoreArray(Dall, &array));
1436           PetscCall(VecShift(D, -1.));
1437           PetscCall(MatDiagonalScale(SEj, D, D));
1438           PetscCall(MatDestroy(&SEj));
1439           PetscCall(VecDestroy(&D));
1440           PetscCall(PetscArraycpy(SEj_arr, work, subset_size * subset_size));
1441         }
1442       }
1443       cum += subset_size;
1444       cum2 += subset_size * (size_schur + 1);
1445       SEj_arr += subset_size * subset_size;
1446       if (SEjinv_arr) SEjinv_arr += subset_size * subset_size;
1447     }
1448     if (sub_schurs->gdsw) PetscCall(MatDestroySubMatrices(sub_schurs->n_subs, &gdswA));
1449     PetscCall(MatDenseRestoreArrayRead(S_all, &rS_data));
1450     PetscCall(MatSeqAIJRestoreArray(sub_schurs->S_Ej_all, &SEj_arr));
1451     if (sub_schurs->sum_S_Ej_inv_all) PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all, &SEjinv_arr));
1452     if (solver_S) PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));
1453 
1454     /* may prevent from unneeded copies, since MUMPS or MKL_Pardiso always use CPU memory
1455        however, preliminary tests indicate using GPUs is still faster in the solve phase */
1456 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
1457     if (reuse_solvers) {
1458       Mat                  St;
1459       MatFactorSchurStatus st;
1460 
1461       flg = PETSC_FALSE;
1462       PetscCall(PetscOptionsGetBool(NULL, sub_schurs->prefix, "-sub_schurs_schur_pin_to_cpu", &flg, NULL));
1463       PetscCall(MatFactorGetSchurComplement(F, &St, &st));
1464       PetscCall(MatBindToCPU(St, flg));
1465       PetscCall(MatFactorRestoreSchurComplement(F, &St, st));
1466     }
1467 #endif
1468 
1469     schur_factor = NULL;
1470     if (compute_Stilda && size_active_schur) {
1471       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1472         PetscCall(MatSeqAIJGetArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1473         PetscCall(PetscArraycpy(SEjinv_arr, work, size_schur * size_schur));
1474         PetscCall(MatSeqAIJRestoreArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1475       } else {
1476         Mat S_all_inv = NULL;
1477 
1478         if (solver_S && !sub_schurs->gdsw) {
1479           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1480              The latter is not the principal subminor for S^-1. However, the factors can be reused since S_\Delta\Delta is the leading principal submatrix of S */
1481           if (factor_workaround) { /* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1482             PetscScalar *data;
1483             PetscInt     nd = 0;
1484 
1485             PetscCheck(use_potr, PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor update not yet implemented for non SPD matrices");
1486             PetscCall(MatFactorGetSchurComplement(F, &S_all_inv, NULL));
1487             PetscCall(MatDenseGetArray(S_all_inv, &data));
1488             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1489               PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
1490             }
1491 
1492             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
1493             if (schur_has_vertices) {
1494               Mat          M;
1495               PetscScalar *tdata;
1496               PetscInt     nv = 0, news;
1497 
1498               PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &nv));
1499               news = size_active_schur + nv;
1500               PetscCall(PetscCalloc1(news * news, &tdata));
1501               for (i = 0; i < size_active_schur; i++) {
1502                 PetscCall(PetscArraycpy(tdata + i * (news + 1), data + i * (size_schur + 1), size_active_schur - i));
1503                 PetscCall(PetscArraycpy(tdata + i * (news + 1) + size_active_schur - i, data + i * size_schur + size_active_schur + nd, nv));
1504               }
1505               for (i = 0; i < nv; i++) {
1506                 PetscInt k = i + size_active_schur;
1507                 PetscCall(PetscArraycpy(tdata + k * (news + 1), data + (k + nd) * (size_schur + 1), nv - i));
1508               }
1509 
1510               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, news, news, tdata, &M));
1511               PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE));
1512               PetscCall(MatCholeskyFactor(M, NULL, NULL));
1513               /* save the factors */
1514               cum = 0;
1515               PetscCall(PetscMalloc1((size_active_schur * (size_active_schur + 1)) / 2 + nd, &schur_factor));
1516               for (i = 0; i < size_active_schur; i++) {
1517                 PetscCall(PetscArraycpy(schur_factor + cum, tdata + i * (news + 1), size_active_schur - i));
1518                 cum += size_active_schur - i;
1519               }
1520               for (i = 0; i < nd; i++) schur_factor[cum + i] = PetscSqrtReal(PetscRealPart(data[(i + size_active_schur) * (size_schur + 1)]));
1521               PetscCall(MatSeqDenseInvertFactors_Private(M));
1522               /* move back just the active dofs to the Schur complement */
1523               for (i = 0; i < size_active_schur; i++) PetscCall(PetscArraycpy(data + i * size_schur, tdata + i * news, size_active_schur));
1524               PetscCall(PetscFree(tdata));
1525               PetscCall(MatDestroy(&M));
1526             } else { /* we can factorize and invert just the activedofs */
1527               Mat          M;
1528               PetscScalar *aux;
1529 
1530               PetscCall(PetscMalloc1(nd, &aux));
1531               for (i = 0; i < nd; i++) aux[i] = 1.0 / data[(i + size_active_schur) * (size_schur + 1)];
1532               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size_active_schur, size_active_schur, data, &M));
1533               PetscCall(MatDenseSetLDA(M, size_schur));
1534               PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE));
1535               PetscCall(MatCholeskyFactor(M, NULL, NULL));
1536               PetscCall(MatSeqDenseInvertFactors_Private(M));
1537               PetscCall(MatDestroy(&M));
1538               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size_schur, nd, data + size_active_schur * size_schur, &M));
1539               PetscCall(MatZeroEntries(M));
1540               PetscCall(MatDestroy(&M));
1541               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nd, size_schur, data + size_active_schur, &M));
1542               PetscCall(MatDenseSetLDA(M, size_schur));
1543               PetscCall(MatZeroEntries(M));
1544               PetscCall(MatDestroy(&M));
1545               for (i = 0; i < nd; i++) data[(i + size_active_schur) * (size_schur + 1)] = aux[i];
1546               PetscCall(PetscFree(aux));
1547             }
1548             PetscCall(MatDenseRestoreArray(S_all_inv, &data));
1549           } else { /* use MatFactor calls to invert S */
1550             PetscCall(MatFactorInvertSchurComplement(F));
1551             PetscCall(MatFactorGetSchurComplement(F, &S_all_inv, NULL));
1552           }
1553         } else if (!sub_schurs->gdsw) { /* we need to invert explicitly since we are not using MatFactor for S */
1554           PetscCall(PetscObjectReference((PetscObject)S_all));
1555           S_all_inv = S_all;
1556           PetscCall(MatDenseGetArray(S_all_inv, &S_data));
1557           PetscCall(PetscBLASIntCast(size_schur, &B_N));
1558           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
1559           if (use_potr) {
1560             PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("L", &B_N, S_data, &B_N, &B_ierr));
1561             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1562             PetscCallBLAS("LAPACKpotri", LAPACKpotri_("L", &B_N, S_data, &B_N, &B_ierr));
1563             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1564           } else if (use_sytr) {
1565             PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, S_data, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
1566             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1567             PetscCallBLAS("LAPACKsytri", LAPACKsytri_("L", &B_N, S_data, &B_N, pivots, Bwork, &B_ierr));
1568             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1569           } else {
1570             PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&B_N, &B_N, S_data, &B_N, pivots, &B_ierr));
1571             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1572             PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, S_data, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
1573             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1574           }
1575           PetscCall(PetscLogFlops(1.0 * size_schur * size_schur * size_schur));
1576           PetscCall(PetscFPTrapPop());
1577           PetscCall(MatDenseRestoreArray(S_all_inv, &S_data));
1578         } else if (sub_schurs->gdsw) {
1579           Mat      tS, tX, SEj, S_II, S_IE, S_EE;
1580           KSP      pS_II;
1581           PC       pS_II_pc;
1582           IS       EE, II;
1583           PetscInt nS;
1584 
1585           PetscCall(MatFactorCreateSchurComplement(F, &tS, NULL));
1586           PetscCall(MatGetSize(tS, &nS, NULL));
1587           PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1588           for (i = 0, cum = 0; i < sub_schurs->n_subs; i++) { /* naive implementation */
1589             PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1590             PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, SEjinv_arr, &SEj));
1591 
1592             PetscCall(ISCreateStride(PETSC_COMM_SELF, subset_size, cum, 1, &EE));
1593             PetscCall(ISComplement(EE, 0, nS, &II));
1594             PetscCall(MatCreateSubMatrix(tS, II, II, MAT_INITIAL_MATRIX, &S_II));
1595             PetscCall(MatCreateSubMatrix(tS, II, EE, MAT_INITIAL_MATRIX, &S_IE));
1596             PetscCall(MatCreateSubMatrix(tS, EE, EE, MAT_INITIAL_MATRIX, &S_EE));
1597             PetscCall(ISDestroy(&II));
1598             PetscCall(ISDestroy(&EE));
1599 
1600             PetscCall(KSPCreate(PETSC_COMM_SELF, &pS_II));
1601             PetscCall(KSPSetNestLevel(pS_II, 1)); /* do not have direct access to a PC to provide the level of nesting of the KSP */
1602             PetscCall(KSPSetType(pS_II, KSPPREONLY));
1603             PetscCall(KSPGetPC(pS_II, &pS_II_pc));
1604             PetscCall(PCSetType(pS_II_pc, PCSVD));
1605             PetscCall(KSPSetOptionsPrefix(pS_II, sub_schurs->prefix));
1606             PetscCall(KSPAppendOptionsPrefix(pS_II, "pseudo_"));
1607             PetscCall(KSPSetOperators(pS_II, S_II, S_II));
1608             PetscCall(MatDestroy(&S_II));
1609             PetscCall(KSPSetFromOptions(pS_II));
1610             PetscCall(KSPSetUp(pS_II));
1611             PetscCall(MatDuplicate(S_IE, MAT_DO_NOT_COPY_VALUES, &tX));
1612             PetscCall(KSPMatSolve(pS_II, S_IE, tX));
1613             PetscCall(KSPDestroy(&pS_II));
1614 
1615             PetscCall(MatTransposeMatMult(S_IE, tX, MAT_REUSE_MATRIX, PETSC_DETERMINE, &SEj));
1616             PetscCall(MatDestroy(&S_IE));
1617             PetscCall(MatDestroy(&tX));
1618             PetscCall(MatAYPX(SEj, -1, S_EE, SAME_NONZERO_PATTERN));
1619             PetscCall(MatDestroy(&S_EE));
1620 
1621             PetscCall(MatDestroy(&SEj));
1622             cum += subset_size;
1623             SEjinv_arr += subset_size * subset_size;
1624           }
1625           PetscCall(MatDestroy(&tS));
1626           PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1627         }
1628         /* S_Ej_tilda_all */
1629         cum = cum2 = 0;
1630         rS_data    = NULL;
1631         if (S_all_inv) PetscCall(MatDenseGetArrayRead(S_all_inv, &rS_data));
1632         PetscCall(MatSeqAIJGetArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1633         for (i = 0; i < sub_schurs->n_subs; i++) {
1634           PetscInt j;
1635 
1636           PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1637           /* get (St^-1)_E */
1638           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1639              will be properly accessed later during adaptive selection */
1640           if (rS_data) {
1641             if (S_lower_triangular) {
1642               PetscInt k;
1643               if (sub_schurs->change) {
1644                 for (k = 0; k < subset_size; k++) {
1645                   for (j = k; j < subset_size; j++) {
1646                     work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1647                     work[j * subset_size + k] = work[k * subset_size + j];
1648                   }
1649                 }
1650               } else {
1651                 for (k = 0; k < subset_size; k++) {
1652                   for (j = k; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1653                 }
1654               }
1655             } else {
1656               PetscInt k;
1657               for (k = 0; k < subset_size; k++) {
1658                 for (j = 0; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1659               }
1660             }
1661           }
1662           if (sub_schurs->change) {
1663             Mat         change_sub, SEj, T;
1664             PetscScalar val = sub_schurs->gdsw ? PETSC_SMALL : 1. / PETSC_SMALL;
1665 
1666             /* change basis */
1667             PetscCall(KSPGetOperators(sub_schurs->change[i], &change_sub, NULL));
1668             PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, rS_data ? work : SEjinv_arr, &SEj));
1669             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1670               Mat T2;
1671               PetscCall(MatTransposeMatMult(change_sub, SEj, MAT_INITIAL_MATRIX, 1.0, &T2));
1672               PetscCall(MatMatMult(T2, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
1673               PetscCall(MatDestroy(&T2));
1674               PetscCall(MatConvert(T, MATSEQDENSE, MAT_INPLACE_MATRIX, &T));
1675             } else {
1676               PetscCall(MatPtAP(SEj, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
1677             }
1678             PetscCall(MatCopy(T, SEj, SAME_NONZERO_PATTERN));
1679             PetscCall(MatDestroy(&T));
1680             PetscCall(MatZeroRowsColumnsIS(SEj, sub_schurs->change_primal_sub[i], val, NULL, NULL));
1681             PetscCall(MatDestroy(&SEj));
1682           }
1683           if (rS_data) PetscCall(PetscArraycpy(SEjinv_arr, work, subset_size * subset_size));
1684           cum += subset_size;
1685           cum2 += subset_size * (size_schur + 1);
1686           SEjinv_arr += subset_size * subset_size;
1687         }
1688         PetscCall(MatSeqAIJRestoreArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1689         if (S_all_inv) {
1690           PetscCall(MatDenseRestoreArrayRead(S_all_inv, &rS_data));
1691           if (solver_S) {
1692             if (schur_has_vertices) {
1693               PetscCall(MatFactorRestoreSchurComplement(F, &S_all_inv, MAT_FACTOR_SCHUR_FACTORED));
1694             } else {
1695               PetscCall(MatFactorRestoreSchurComplement(F, &S_all_inv, MAT_FACTOR_SCHUR_INVERTED));
1696             }
1697           }
1698         }
1699         PetscCall(MatDestroy(&S_all_inv));
1700       }
1701 
1702       /* move back factors if needed */
1703       if (schur_has_vertices && factor_workaround && !sub_schurs->gdsw) {
1704         Mat          S_tmp;
1705         PetscInt     nd = 0;
1706         PetscScalar *data;
1707 
1708         PetscCheck(use_potr, PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor update not yet implemented for non SPD matrices");
1709         PetscCheck(solver_S, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
1710         PetscCall(MatFactorGetSchurComplement(F, &S_tmp, NULL));
1711         PetscCall(MatDenseGetArray(S_tmp, &data));
1712         PetscCall(PetscArrayzero(data, size_schur * size_schur));
1713 
1714         if (S_lower_triangular) {
1715           cum = 0;
1716           for (i = 0; i < size_active_schur; i++) {
1717             PetscCall(PetscArraycpy(data + i * (size_schur + 1), schur_factor + cum, size_active_schur - i));
1718             cum += size_active_schur - i;
1719           }
1720         } else {
1721           PetscCall(PetscArraycpy(data, schur_factor, size_schur * size_schur));
1722         }
1723         if (sub_schurs->is_dir) {
1724           PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
1725           for (i = 0; i < nd; i++) data[(i + size_active_schur) * (size_schur + 1)] = schur_factor[cum + i];
1726         }
1727         /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1728              set the diagonal entry of the Schur factor to a very large value */
1729         for (i = size_active_schur + nd; i < size_schur; i++) data[i * (size_schur + 1)] = infty;
1730         PetscCall(MatDenseRestoreArray(S_tmp, &data));
1731         PetscCall(MatFactorRestoreSchurComplement(F, &S_tmp, MAT_FACTOR_SCHUR_FACTORED));
1732       }
1733     } else if (factor_workaround && !sub_schurs->gdsw) { /* we need to eliminate any unneeded coupling */
1734       PetscScalar *data;
1735       PetscInt     nd = 0;
1736 
1737       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1738         PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
1739       }
1740       PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
1741       PetscCall(MatDenseGetArray(S_all, &data));
1742       for (i = 0; i < size_active_schur; i++) PetscCall(PetscArrayzero(data + i * size_schur + size_active_schur, size_schur - size_active_schur));
1743       for (i = size_active_schur + nd; i < size_schur; i++) {
1744         PetscCall(PetscArrayzero(data + i * size_schur + size_active_schur, size_schur - size_active_schur));
1745         data[i * (size_schur + 1)] = infty;
1746       }
1747       PetscCall(MatDenseRestoreArray(S_all, &data));
1748       PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));
1749     }
1750     PetscCall(PetscFree(work));
1751     PetscCall(PetscFree(schur_factor));
1752     PetscCall(VecDestroy(&Dall));
1753   }
1754   PetscCall(ISDestroy(&is_I_layer));
1755   PetscCall(MatDestroy(&S_all));
1756   PetscCall(MatDestroy(&A_BB));
1757   PetscCall(MatDestroy(&A_IB));
1758   PetscCall(MatDestroy(&A_BI));
1759   PetscCall(MatDestroy(&F));
1760 
1761   PetscCall(PetscMalloc1(sub_schurs->n_subs, &nnz));
1762   for (i = 0; i < sub_schurs->n_subs; i++) PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &nnz[i]));
1763   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, sub_schurs->n_subs, nnz, PETSC_OWN_POINTER, &is_I_layer));
1764   PetscCall(MatSetVariableBlockSizes(sub_schurs->S_Ej_all, sub_schurs->n_subs, nnz));
1765   PetscCall(MatAssemblyBegin(sub_schurs->S_Ej_all, MAT_FINAL_ASSEMBLY));
1766   PetscCall(MatAssemblyEnd(sub_schurs->S_Ej_all, MAT_FINAL_ASSEMBLY));
1767   if (compute_Stilda) {
1768     PetscCall(MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_tilda_all, sub_schurs->n_subs, nnz));
1769     PetscCall(MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all, MAT_FINAL_ASSEMBLY));
1770     PetscCall(MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all, MAT_FINAL_ASSEMBLY));
1771     if (deluxe) {
1772       PetscCall(MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_inv_all, sub_schurs->n_subs, nnz));
1773       PetscCall(MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all, MAT_FINAL_ASSEMBLY));
1774       PetscCall(MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all, MAT_FINAL_ASSEMBLY));
1775     }
1776   }
1777   PetscCall(ISDestroy(&is_I_layer));
1778 
1779   /* Get local part of (\sum_j S_Ej) */
1780   if (!sub_schurs->sum_S_Ej_all) PetscCall(MatDuplicate(sub_schurs->S_Ej_all, MAT_DO_NOT_COPY_VALUES, &sub_schurs->sum_S_Ej_all));
1781   PetscCall(VecSet(gstash, 0.0));
1782   PetscCall(MatSeqAIJGetArray(sub_schurs->S_Ej_all, &stasharray));
1783   PetscCall(VecPlaceArray(lstash, stasharray));
1784   PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1785   PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1786   PetscCall(MatSeqAIJRestoreArray(sub_schurs->S_Ej_all, &stasharray));
1787   PetscCall(VecResetArray(lstash));
1788   PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all, &stasharray));
1789   PetscCall(VecPlaceArray(lstash, stasharray));
1790   PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1791   PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1792   PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all, &stasharray));
1793   PetscCall(VecResetArray(lstash));
1794 
1795   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1796   if (compute_Stilda) {
1797     PetscCall(VecSet(gstash, 0.0));
1798     PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &stasharray));
1799     PetscCall(VecPlaceArray(lstash, stasharray));
1800     PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1801     PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1802     PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1803     PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1804     PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &stasharray));
1805     PetscCall(VecResetArray(lstash));
1806     if (deluxe) {
1807       PetscCall(VecSet(gstash, 0.0));
1808       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all, &stasharray));
1809       PetscCall(VecPlaceArray(lstash, stasharray));
1810       PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1811       PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1812       PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1813       PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1814       PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all, &stasharray));
1815       PetscCall(VecResetArray(lstash));
1816     } else if (!sub_schurs->gdsw) {
1817       PetscScalar *array;
1818       PetscInt     cum;
1819 
1820       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &array));
1821       cum = 0;
1822       for (i = 0; i < sub_schurs->n_subs; i++) {
1823         PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1824         PetscCall(PetscBLASIntCast(subset_size, &B_N));
1825         PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
1826         if (use_potr) {
1827           PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("L", &B_N, array + cum, &B_N, &B_ierr));
1828           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1829           PetscCallBLAS("LAPACKpotri", LAPACKpotri_("L", &B_N, array + cum, &B_N, &B_ierr));
1830           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1831         } else if (use_sytr) {
1832           PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, array + cum, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
1833           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1834           PetscCallBLAS("LAPACKsytri", LAPACKsytri_("L", &B_N, array + cum, &B_N, pivots, Bwork, &B_ierr));
1835           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1836         } else {
1837           PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&B_N, &B_N, array + cum, &B_N, pivots, &B_ierr));
1838           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1839           PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, array + cum, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
1840           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1841         }
1842         PetscCall(PetscLogFlops(1.0 * subset_size * subset_size * subset_size));
1843         PetscCall(PetscFPTrapPop());
1844         cum += subset_size * subset_size;
1845       }
1846       PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &array));
1847       PetscCall(PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all));
1848       PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_inv_all));
1849       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1850     }
1851   }
1852   PetscCall(VecDestroy(&lstash));
1853   PetscCall(VecDestroy(&gstash));
1854   PetscCall(VecScatterDestroy(&sstash));
1855 
1856   if (matl_dbg_viewer) {
1857     if (sub_schurs->S_Ej_all) {
1858       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->S_Ej_all, "SE"));
1859       PetscCall(MatView(sub_schurs->S_Ej_all, matl_dbg_viewer));
1860     }
1861     if (sub_schurs->sum_S_Ej_all) {
1862       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_all, "SSE"));
1863       PetscCall(MatView(sub_schurs->sum_S_Ej_all, matl_dbg_viewer));
1864     }
1865     if (sub_schurs->sum_S_Ej_inv_all) {
1866       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_inv_all, "SSEm"));
1867       PetscCall(MatView(sub_schurs->sum_S_Ej_inv_all, matl_dbg_viewer));
1868     }
1869     if (sub_schurs->sum_S_Ej_tilda_all) {
1870       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_tilda_all, "SSEt"));
1871       PetscCall(MatView(sub_schurs->sum_S_Ej_tilda_all, matl_dbg_viewer));
1872     }
1873   }
1874 
1875   /* free workspace */
1876   if (matl_dbg_viewer) PetscCall(PetscViewerFlush(matl_dbg_viewer));
1877   if (sub_schurs->debug) PetscCallMPI(MPI_Barrier(comm_n));
1878   PetscCall(PetscViewerDestroy(&matl_dbg_viewer));
1879   PetscCall(PetscFree2(Bwork, pivots));
1880   PetscCall(PetscCommDestroy(&comm_n));
1881   PetscFunctionReturn(PETSC_SUCCESS);
1882 }
1883 
1884 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, const char *prefix, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc, PetscBool gdsw)
1885 {
1886   IS       *faces, *edges, *all_cc, vertices;
1887   PetscInt  s, i, n_faces, n_edges, n_all_cc;
1888   PetscBool is_sorted, ispardiso, ismumps;
1889 
1890   PetscFunctionBegin;
1891   PetscCall(ISSorted(is_I, &is_sorted));
1892   PetscCheck(is_sorted, PetscObjectComm((PetscObject)is_I), PETSC_ERR_PLIB, "IS for I dofs should be shorted");
1893   PetscCall(ISSorted(is_B, &is_sorted));
1894   PetscCheck(is_sorted, PetscObjectComm((PetscObject)is_B), PETSC_ERR_PLIB, "IS for B dofs should be shorted");
1895 
1896   /* reset any previous data */
1897   PetscCall(PCBDDCSubSchursReset(sub_schurs));
1898 
1899   sub_schurs->gdsw = gdsw;
1900 
1901   /* get index sets for faces and edges (already sorted by global ordering) */
1902   PetscCall(PCBDDCGraphGetCandidatesIS(graph, &n_faces, &faces, &n_edges, &edges, &vertices));
1903   n_all_cc = n_faces + n_edges;
1904   PetscCall(PetscBTCreate(n_all_cc, &sub_schurs->is_edge));
1905   PetscCall(PetscMalloc1(n_all_cc, &all_cc));
1906   n_all_cc = 0;
1907   for (i = 0; i < n_faces; i++) {
1908     PetscCall(ISGetSize(faces[i], &s));
1909     if (!s) continue;
1910     if (copycc) {
1911       PetscCall(ISDuplicate(faces[i], &all_cc[n_all_cc]));
1912     } else {
1913       PetscCall(PetscObjectReference((PetscObject)faces[i]));
1914       all_cc[n_all_cc] = faces[i];
1915     }
1916     n_all_cc++;
1917   }
1918   for (i = 0; i < n_edges; i++) {
1919     PetscCall(ISGetSize(edges[i], &s));
1920     if (!s) continue;
1921     if (copycc) {
1922       PetscCall(ISDuplicate(edges[i], &all_cc[n_all_cc]));
1923     } else {
1924       PetscCall(PetscObjectReference((PetscObject)edges[i]));
1925       all_cc[n_all_cc] = edges[i];
1926     }
1927     PetscCall(PetscBTSet(sub_schurs->is_edge, n_all_cc));
1928     n_all_cc++;
1929   }
1930   PetscCall(PetscObjectReference((PetscObject)vertices));
1931   sub_schurs->is_vertices = vertices;
1932   PetscCall(PCBDDCGraphRestoreCandidatesIS(graph, &n_faces, &faces, &n_edges, &edges, &vertices));
1933   sub_schurs->is_dir = NULL;
1934   PetscCall(PCBDDCGraphGetDirichletDofsB(graph, &sub_schurs->is_dir));
1935 
1936   /* Determine if MatFactor can be used */
1937   PetscCall(PetscStrallocpy(prefix, &sub_schurs->prefix));
1938 #if defined(PETSC_HAVE_MUMPS)
1939   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERMUMPS, sizeof(sub_schurs->mat_solver_type)));
1940 #elif defined(PETSC_HAVE_MKL_PARDISO)
1941   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERMKL_PARDISO, sizeof(sub_schurs->mat_solver_type)));
1942 #else
1943   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERPETSC, sizeof(sub_schurs->mat_solver_type)));
1944 #endif
1945 #if defined(PETSC_USE_COMPLEX)
1946   sub_schurs->is_hermitian = PETSC_FALSE; /* Hermitian Cholesky is not supported by PETSc and external packages */
1947 #else
1948   sub_schurs->is_hermitian = PETSC_TRUE;
1949 #endif
1950   sub_schurs->is_posdef     = PETSC_TRUE;
1951   sub_schurs->is_symmetric  = PETSC_TRUE;
1952   sub_schurs->debug         = PETSC_FALSE;
1953   sub_schurs->restrict_comm = PETSC_FALSE;
1954   PetscOptionsBegin(PetscObjectComm((PetscObject)graph->l2gmap), sub_schurs->prefix, "BDDC sub_schurs options", "PC");
1955   PetscCall(PetscOptionsString("-sub_schurs_mat_solver_type", "Specific direct solver to use", NULL, sub_schurs->mat_solver_type, sub_schurs->mat_solver_type, sizeof(sub_schurs->mat_solver_type), NULL));
1956   PetscCall(PetscOptionsBool("-sub_schurs_symmetric", "Symmetric problem", NULL, sub_schurs->is_symmetric, &sub_schurs->is_symmetric, NULL));
1957   PetscCall(PetscOptionsBool("-sub_schurs_hermitian", "Hermitian problem", NULL, sub_schurs->is_hermitian, &sub_schurs->is_hermitian, NULL));
1958   PetscCall(PetscOptionsBool("-sub_schurs_posdef", "Positive definite problem", NULL, sub_schurs->is_posdef, &sub_schurs->is_posdef, NULL));
1959   PetscCall(PetscOptionsBool("-sub_schurs_restrictcomm", "Restrict communicator on active processes only", NULL, sub_schurs->restrict_comm, &sub_schurs->restrict_comm, NULL));
1960   PetscCall(PetscOptionsBool("-sub_schurs_debug", "Debug output", NULL, sub_schurs->debug, &sub_schurs->debug, NULL));
1961   PetscOptionsEnd();
1962   PetscCall(PetscStrcmp(sub_schurs->mat_solver_type, MATSOLVERMUMPS, &ismumps));
1963   PetscCall(PetscStrcmp(sub_schurs->mat_solver_type, MATSOLVERMKL_PARDISO, &ispardiso));
1964   sub_schurs->schur_explicit = (PetscBool)(ispardiso || ismumps);
1965 
1966   /* for reals, symmetric and Hermitian are synonyms */
1967 #if !defined(PETSC_USE_COMPLEX)
1968   sub_schurs->is_symmetric = (PetscBool)(sub_schurs->is_symmetric && sub_schurs->is_hermitian);
1969   sub_schurs->is_hermitian = sub_schurs->is_symmetric;
1970 #endif
1971 
1972   PetscCall(PetscObjectReference((PetscObject)is_I));
1973   sub_schurs->is_I = is_I;
1974   PetscCall(PetscObjectReference((PetscObject)is_B));
1975   sub_schurs->is_B = is_B;
1976   PetscCall(PetscObjectReference((PetscObject)graph->l2gmap));
1977   sub_schurs->l2gmap = graph->l2gmap;
1978   PetscCall(PetscObjectReference((PetscObject)BtoNmap));
1979   sub_schurs->BtoNmap            = BtoNmap;
1980   sub_schurs->n_subs             = n_all_cc;
1981   sub_schurs->is_subs            = all_cc;
1982   sub_schurs->S_Ej_all           = NULL;
1983   sub_schurs->sum_S_Ej_all       = NULL;
1984   sub_schurs->sum_S_Ej_inv_all   = NULL;
1985   sub_schurs->sum_S_Ej_tilda_all = NULL;
1986   sub_schurs->is_Ej_all          = NULL;
1987   PetscFunctionReturn(PETSC_SUCCESS);
1988 }
1989 
1990 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1991 {
1992   PCBDDCSubSchurs schurs_ctx;
1993 
1994   PetscFunctionBegin;
1995   PetscCall(PetscNew(&schurs_ctx));
1996   schurs_ctx->n_subs = 0;
1997   *sub_schurs        = schurs_ctx;
1998   PetscFunctionReturn(PETSC_SUCCESS);
1999 }
2000 
2001 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
2002 {
2003   PetscInt i;
2004 
2005   PetscFunctionBegin;
2006   if (!sub_schurs) PetscFunctionReturn(PETSC_SUCCESS);
2007   PetscCall(PetscFree(sub_schurs->prefix));
2008   PetscCall(MatDestroy(&sub_schurs->A));
2009   PetscCall(MatDestroy(&sub_schurs->S));
2010   PetscCall(ISDestroy(&sub_schurs->is_I));
2011   PetscCall(ISDestroy(&sub_schurs->is_B));
2012   PetscCall(ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap));
2013   PetscCall(ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap));
2014   PetscCall(MatDestroy(&sub_schurs->S_Ej_all));
2015   PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_all));
2016   PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_inv_all));
2017   PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_tilda_all));
2018   PetscCall(ISDestroy(&sub_schurs->is_Ej_all));
2019   PetscCall(ISDestroy(&sub_schurs->is_vertices));
2020   PetscCall(ISDestroy(&sub_schurs->is_dir));
2021   PetscCall(PetscBTDestroy(&sub_schurs->is_edge));
2022   for (i = 0; i < sub_schurs->n_subs; i++) PetscCall(ISDestroy(&sub_schurs->is_subs[i]));
2023   if (sub_schurs->n_subs) PetscCall(PetscFree(sub_schurs->is_subs));
2024   if (sub_schurs->reuse_solver) PetscCall(PCBDDCReuseSolversReset(sub_schurs->reuse_solver));
2025   PetscCall(PetscFree(sub_schurs->reuse_solver));
2026   if (sub_schurs->change) {
2027     for (i = 0; i < sub_schurs->n_subs; i++) {
2028       PetscCall(KSPDestroy(&sub_schurs->change[i]));
2029       PetscCall(ISDestroy(&sub_schurs->change_primal_sub[i]));
2030     }
2031   }
2032   PetscCall(PetscFree(sub_schurs->change));
2033   PetscCall(PetscFree(sub_schurs->change_primal_sub));
2034   sub_schurs->n_subs = 0;
2035   PetscFunctionReturn(PETSC_SUCCESS);
2036 }
2037 
2038 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs *sub_schurs)
2039 {
2040   PetscFunctionBegin;
2041   PetscCall(PCBDDCSubSchursReset(*sub_schurs));
2042   PetscCall(PetscFree(*sub_schurs));
2043   PetscFunctionReturn(PETSC_SUCCESS);
2044 }
2045 
2046 static inline PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt *queue_tip, PetscInt n_prev, PetscBT touched, PetscInt *xadj, PetscInt *adjncy, PetscInt *n_added)
2047 {
2048   PetscInt i, j, n;
2049 
2050   PetscFunctionBegin;
2051   n = 0;
2052   for (i = -n_prev; i < 0; i++) {
2053     PetscInt start_dof = queue_tip[i];
2054     for (j = xadj[start_dof]; j < xadj[start_dof + 1]; j++) {
2055       PetscInt dof = adjncy[j];
2056       if (!PetscBTLookup(touched, dof)) {
2057         PetscCall(PetscBTSet(touched, dof));
2058         queue_tip[n] = dof;
2059         n++;
2060       }
2061     }
2062   }
2063   *n_added = n;
2064   PetscFunctionReturn(PETSC_SUCCESS);
2065 }
2066