xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 79329b78a0a78fcd57733e7fa9724ece5ee4cbb6)
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     PetscCall(MatMumpsSetIcntl(ctx->F, 26, -1));
125 #if defined(PETSC_HAVE_MKL_PARDISO)
126     PetscCall(MatMkl_PardisoSetCntl(ctx->F, 70, 0));
127 #endif
128     copy = ctx->has_vertices;
129   } else { /* interior solver */
130     PetscCall(MatMumpsSetIcntl(ctx->F, 26, 0));
131 #if defined(PETSC_HAVE_MKL_PARDISO)
132     PetscCall(MatMkl_PardisoSetCntl(ctx->F, 70, 1));
133 #endif
134     copy = PETSC_TRUE;
135   }
136   /* copy rhs into factored matrix workspace */
137   if (copy) {
138     PetscInt     n;
139     PetscScalar *array, *array_solver;
140 
141     PetscCall(VecGetLocalSize(rhs, &n));
142     PetscCall(VecGetArrayRead(rhs, (const PetscScalar **)&array));
143     PetscCall(VecGetArray(ctx->rhs, &array_solver));
144     PetscCall(PetscArraycpy(array_solver, array, n));
145     PetscCall(VecRestoreArray(ctx->rhs, &array_solver));
146     PetscCall(VecRestoreArrayRead(rhs, (const PetscScalar **)&array));
147 
148     PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, ctx->rhs, NULL, PETSC_FALSE, full));
149     if (transpose) {
150       PetscCall(MatSolveTranspose(ctx->F, ctx->rhs, ctx->sol));
151     } else {
152       PetscCall(MatSolve(ctx->F, ctx->rhs, ctx->sol));
153     }
154     PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, ctx->sol, NULL, PETSC_TRUE, full));
155 
156     /* get back data to caller worskpace */
157     PetscCall(VecGetArrayRead(ctx->sol, (const PetscScalar **)&array_solver));
158     PetscCall(VecGetArray(sol, &array));
159     PetscCall(PetscArraycpy(array, array_solver, n));
160     PetscCall(VecRestoreArray(sol, &array));
161     PetscCall(VecRestoreArrayRead(ctx->sol, (const PetscScalar **)&array_solver));
162   } else {
163     if (ctx->benign_n) {
164       PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, rhs, ctx->rhs, PETSC_FALSE, full));
165       if (transpose) {
166         PetscCall(MatSolveTranspose(ctx->F, ctx->rhs, sol));
167       } else {
168         PetscCall(MatSolve(ctx->F, ctx->rhs, sol));
169       }
170       PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, sol, NULL, PETSC_TRUE, full));
171     } else {
172       if (transpose) {
173         PetscCall(MatSolveTranspose(ctx->F, rhs, sol));
174       } else {
175         PetscCall(MatSolve(ctx->F, rhs, sol));
176       }
177     }
178   }
179   /* restore defaults */
180   PetscCall(MatMumpsSetIcntl(ctx->F, 26, -1));
181 #if defined(PETSC_HAVE_MKL_PARDISO)
182   PetscCall(MatMkl_PardisoSetCntl(ctx->F, 70, 0));
183 #endif
184   PetscFunctionReturn(PETSC_SUCCESS);
185 }
186 
187 static PetscErrorCode PCBDDCReuseSolvers_Correction(PC pc, Vec rhs, Vec sol)
188 {
189   PetscFunctionBegin;
190   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_FALSE, PETSC_TRUE));
191   PetscFunctionReturn(PETSC_SUCCESS);
192 }
193 
194 static PetscErrorCode PCBDDCReuseSolvers_CorrectionTranspose(PC pc, Vec rhs, Vec sol)
195 {
196   PetscFunctionBegin;
197   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_TRUE, PETSC_TRUE));
198   PetscFunctionReturn(PETSC_SUCCESS);
199 }
200 
201 static PetscErrorCode PCBDDCReuseSolvers_Interior(PC pc, Vec rhs, Vec sol)
202 {
203   PetscFunctionBegin;
204   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_FALSE, PETSC_FALSE));
205   PetscFunctionReturn(PETSC_SUCCESS);
206 }
207 
208 static PetscErrorCode PCBDDCReuseSolvers_InteriorTranspose(PC pc, Vec rhs, Vec sol)
209 {
210   PetscFunctionBegin;
211   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_TRUE, PETSC_FALSE));
212   PetscFunctionReturn(PETSC_SUCCESS);
213 }
214 
215 static PetscErrorCode PCBDDCReuseSolvers_View(PC pc, PetscViewer viewer)
216 {
217   PCBDDCReuseSolvers ctx;
218   PetscBool          isascii;
219 
220   PetscFunctionBegin;
221   PetscCall(PCShellGetContext(pc, &ctx));
222   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
223   if (isascii) PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_INFO));
224   PetscCall(MatView(ctx->F, viewer));
225   if (isascii) PetscCall(PetscViewerPopFormat(viewer));
226   PetscFunctionReturn(PETSC_SUCCESS);
227 }
228 
229 static PetscErrorCode PCBDDCReuseSolversReset(PCBDDCReuseSolvers reuse)
230 {
231   PetscInt i;
232 
233   PetscFunctionBegin;
234   PetscCall(MatDestroy(&reuse->F));
235   PetscCall(VecDestroy(&reuse->sol));
236   PetscCall(VecDestroy(&reuse->rhs));
237   PetscCall(PCDestroy(&reuse->interior_solver));
238   PetscCall(PCDestroy(&reuse->correction_solver));
239   PetscCall(ISDestroy(&reuse->is_R));
240   PetscCall(ISDestroy(&reuse->is_B));
241   PetscCall(VecScatterDestroy(&reuse->correction_scatter_B));
242   PetscCall(VecDestroy(&reuse->sol_B));
243   PetscCall(VecDestroy(&reuse->rhs_B));
244   for (i = 0; i < reuse->benign_n; i++) PetscCall(ISDestroy(&reuse->benign_zerodiag_subs[i]));
245   PetscCall(PetscFree(reuse->benign_zerodiag_subs));
246   PetscCall(PetscFree(reuse->benign_save_vals));
247   PetscCall(MatDestroy(&reuse->benign_csAIB));
248   PetscCall(MatDestroy(&reuse->benign_AIIm1ones));
249   PetscCall(VecDestroy(&reuse->benign_corr_work));
250   PetscCall(VecDestroy(&reuse->benign_dummy_schur_vec));
251   PetscFunctionReturn(PETSC_SUCCESS);
252 }
253 
254 static PetscErrorCode PCBDDCReuseSolvers_Destroy(PC pc)
255 {
256   PCBDDCReuseSolvers ctx;
257 
258   PetscFunctionBegin;
259   PetscCall(PCShellGetContext(pc, &ctx));
260   PetscCall(PCBDDCReuseSolversReset(ctx));
261   PetscCall(PetscFree(ctx));
262   PetscCall(PCShellSetContext(pc, NULL));
263   PetscFunctionReturn(PETSC_SUCCESS);
264 }
265 
266 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
267 {
268   Mat         B, C, D, Bd, Cd, AinvBd;
269   KSP         ksp;
270   PC          pc;
271   PetscBool   isLU, isILU, isCHOL, Bdense, Cdense;
272   PetscReal   fill = 2.0;
273   PetscInt    n_I;
274   PetscMPIInt size;
275 
276   PetscFunctionBegin;
277   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)M), &size));
278   PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not for parallel matrices");
279   if (reuse == MAT_REUSE_MATRIX) {
280     PetscBool Sdense;
281 
282     PetscCall(PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense));
283     PetscCheck(Sdense, PetscObjectComm((PetscObject)M), PETSC_ERR_SUP, "S should dense");
284   }
285   PetscCall(MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D));
286   PetscCall(MatSchurComplementGetKSP(M, &ksp));
287   PetscCall(KSPGetPC(ksp, &pc));
288   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCLU, &isLU));
289   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCILU, &isILU));
290   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
291   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQDENSE, &Bdense));
292   PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQDENSE, &Cdense));
293   PetscCall(MatGetSize(B, &n_I, NULL));
294   if (n_I) {
295     if (!Bdense) {
296       PetscCall(MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd));
297     } else {
298       Bd = B;
299     }
300 
301     if (isLU || isILU || isCHOL) {
302       Mat fact;
303       PetscCall(KSPSetUp(ksp));
304       PetscCall(PCFactorGetMatrix(pc, &fact));
305       PetscCall(MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd));
306       PetscCall(MatMatSolve(fact, Bd, AinvBd));
307     } else {
308       PetscBool ex = PETSC_TRUE;
309 
310       if (ex) {
311         Mat Ainvd;
312 
313         PetscCall(PCComputeOperator(pc, MATDENSE, &Ainvd));
314         PetscCall(MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd));
315         PetscCall(MatDestroy(&Ainvd));
316       } else {
317         Vec          sol, rhs;
318         PetscScalar *arrayrhs, *arraysol;
319         PetscInt     i, nrhs, n;
320 
321         PetscCall(MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd));
322         PetscCall(MatGetSize(Bd, &n, &nrhs));
323         PetscCall(MatDenseGetArray(Bd, &arrayrhs));
324         PetscCall(MatDenseGetArray(AinvBd, &arraysol));
325         PetscCall(KSPGetSolution(ksp, &sol));
326         PetscCall(KSPGetRhs(ksp, &rhs));
327         for (i = 0; i < nrhs; i++) {
328           PetscCall(VecPlaceArray(rhs, arrayrhs + i * n));
329           PetscCall(VecPlaceArray(sol, arraysol + i * n));
330           PetscCall(KSPSolve(ksp, rhs, sol));
331           PetscCall(VecResetArray(rhs));
332           PetscCall(VecResetArray(sol));
333         }
334         PetscCall(MatDenseRestoreArray(Bd, &arrayrhs));
335         PetscCall(MatDenseRestoreArray(AinvBd, &arrayrhs));
336       }
337     }
338     if (!Bdense & !issym) PetscCall(MatDestroy(&Bd));
339 
340     if (!issym) {
341       if (!Cdense) {
342         PetscCall(MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd));
343       } else {
344         Cd = C;
345       }
346       PetscCall(MatMatMult(Cd, AinvBd, reuse, fill, S));
347       if (!Cdense) PetscCall(MatDestroy(&Cd));
348     } else {
349       PetscCall(MatTransposeMatMult(Bd, AinvBd, reuse, fill, S));
350       if (!Bdense) PetscCall(MatDestroy(&Bd));
351     }
352     PetscCall(MatDestroy(&AinvBd));
353   }
354 
355   if (D) {
356     Mat       Dd;
357     PetscBool Ddense;
358 
359     PetscCall(PetscObjectTypeCompare((PetscObject)D, MATSEQDENSE, &Ddense));
360     if (!Ddense) {
361       PetscCall(MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd));
362     } else {
363       Dd = D;
364     }
365     if (n_I) {
366       PetscCall(MatAYPX(*S, -1.0, Dd, SAME_NONZERO_PATTERN));
367     } else {
368       if (reuse == MAT_INITIAL_MATRIX) {
369         PetscCall(MatDuplicate(Dd, MAT_COPY_VALUES, S));
370       } else {
371         PetscCall(MatCopy(Dd, *S, SAME_NONZERO_PATTERN));
372       }
373     }
374     if (!Ddense) PetscCall(MatDestroy(&Dd));
375   } else {
376     PetscCall(MatScale(*S, -1.0));
377   }
378   PetscFunctionReturn(PETSC_SUCCESS);
379 }
380 
381 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)
382 {
383   Mat          F, A_II, A_IB, A_BI, A_BB, AE_II;
384   Mat          S_all;
385   Vec          gstash, lstash;
386   VecScatter   sstash;
387   IS           is_I, is_I_layer;
388   IS           all_subsets, all_subsets_mult, all_subsets_n;
389   PetscScalar *stasharray, *Bwork;
390   PetscInt    *nnz, *all_local_idx_N;
391   PetscInt    *auxnum1, *auxnum2;
392   PetscInt     i, subset_size, max_subset_size;
393   PetscInt     n_B, extra, local_size, global_size;
394   PetscInt     local_stash_size;
395   PetscBLASInt B_N, B_ierr, B_lwork, *pivots;
396   MPI_Comm     comm_n;
397   PetscBool    deluxe   = PETSC_TRUE;
398   PetscBool    use_potr = PETSC_FALSE, use_sytr = PETSC_FALSE;
399   PetscViewer  matl_dbg_viewer = NULL;
400   PetscBool    flg;
401 
402   PetscFunctionBegin;
403   PetscCall(MatDestroy(&sub_schurs->A));
404   PetscCall(MatDestroy(&sub_schurs->S));
405   if (Ain) {
406     PetscCall(PetscObjectReference((PetscObject)Ain));
407     sub_schurs->A = Ain;
408   }
409 
410   PetscCall(PetscObjectReference((PetscObject)Sin));
411   sub_schurs->S = Sin;
412   if (sub_schurs->schur_explicit) sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
413 
414   /* preliminary checks */
415   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");
416 
417   if (benign_trick) sub_schurs->is_posdef = PETSC_FALSE;
418 
419   /* debug (MATLAB) */
420   if (sub_schurs->debug) {
421     PetscMPIInt size, rank;
422     PetscInt    nr, *print_schurs_ranks, print_schurs = PETSC_FALSE;
423 
424     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &size));
425     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &rank));
426     nr = size;
427     PetscCall(PetscMalloc1(nr, &print_schurs_ranks));
428     PetscOptionsBegin(PetscObjectComm((PetscObject)sub_schurs->l2gmap), sub_schurs->prefix, "BDDC sub_schurs options", "PC");
429     PetscCall(PetscOptionsIntArray("-sub_schurs_debug_ranks", "Ranks to debug (all if the option is not used)", NULL, print_schurs_ranks, &nr, &flg));
430     if (!flg) print_schurs = PETSC_TRUE;
431     else {
432       print_schurs = PETSC_FALSE;
433       for (i = 0; i < nr; i++)
434         if (print_schurs_ranks[i] == rank) {
435           print_schurs = PETSC_TRUE;
436           break;
437         }
438     }
439     PetscOptionsEnd();
440     PetscCall(PetscFree(print_schurs_ranks));
441     if (print_schurs) {
442       char filename[256];
443 
444       PetscCall(PetscSNPrintf(filename, sizeof(filename), "sub_schurs_Schur_r%d.m", PetscGlobalRank));
445       PetscCall(PetscViewerASCIIOpen(PETSC_COMM_SELF, filename, &matl_dbg_viewer));
446       PetscCall(PetscViewerPushFormat(matl_dbg_viewer, PETSC_VIEWER_ASCII_MATLAB));
447     }
448   }
449 
450   /* restrict work on active processes */
451   if (sub_schurs->restrict_comm) {
452     PetscSubcomm subcomm;
453     PetscMPIInt  color, rank;
454 
455     color = 0;
456     if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
457     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &rank));
458     PetscCall(PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &subcomm));
459     PetscCall(PetscSubcommSetNumber(subcomm, 2));
460     PetscCall(PetscSubcommSetTypeGeneral(subcomm, color, rank));
461     PetscCall(PetscCommDuplicate(PetscSubcommChild(subcomm), &comm_n, NULL));
462     PetscCall(PetscSubcommDestroy(&subcomm));
463     if (!sub_schurs->n_subs) {
464       PetscCall(PetscCommDestroy(&comm_n));
465       PetscFunctionReturn(PETSC_SUCCESS);
466     }
467   } else {
468     PetscCall(PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &comm_n, NULL));
469   }
470 
471   /* get Schur complement matrices */
472   if (!sub_schurs->schur_explicit) {
473     Mat       tA_IB, tA_BI, tA_BB;
474     PetscBool isseqsbaij;
475     PetscCall(MatSchurComplementGetSubMatrices(sub_schurs->S, &A_II, NULL, &tA_IB, &tA_BI, &tA_BB));
476     PetscCall(PetscObjectTypeCompare((PetscObject)tA_BB, MATSEQSBAIJ, &isseqsbaij));
477     if (isseqsbaij) {
478       PetscCall(MatConvert(tA_BB, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_BB));
479       PetscCall(MatConvert(tA_IB, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_IB));
480       PetscCall(MatConvert(tA_BI, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_BI));
481     } else {
482       PetscCall(PetscObjectReference((PetscObject)tA_BB));
483       A_BB = tA_BB;
484       PetscCall(PetscObjectReference((PetscObject)tA_IB));
485       A_IB = tA_IB;
486       PetscCall(PetscObjectReference((PetscObject)tA_BI));
487       A_BI = tA_BI;
488     }
489   } else {
490     A_II = NULL;
491     A_IB = NULL;
492     A_BI = NULL;
493     A_BB = NULL;
494   }
495   S_all = NULL;
496 
497   /* determine interior problems */
498   PetscCall(ISGetLocalSize(sub_schurs->is_I, &i));
499   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
500     PetscBT         touched;
501     const PetscInt *idx_B;
502     PetscInt        n_I, n_B, n_local_dofs, n_prev_added, j, layer, *local_numbering;
503 
504     PetscCheck(xadj, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot request layering without adjacency");
505     /* get sizes */
506     PetscCall(ISGetLocalSize(sub_schurs->is_I, &n_I));
507     PetscCall(ISGetLocalSize(sub_schurs->is_B, &n_B));
508 
509     PetscCall(PetscMalloc1(n_I + n_B, &local_numbering));
510     PetscCall(PetscBTCreate(n_I + n_B, &touched));
511     PetscCall(PetscBTMemzero(n_I + n_B, touched));
512 
513     /* all boundary dofs must be skipped when adding layers */
514     PetscCall(ISGetIndices(sub_schurs->is_B, &idx_B));
515     for (j = 0; j < n_B; j++) PetscCall(PetscBTSet(touched, idx_B[j]));
516     PetscCall(PetscArraycpy(local_numbering, idx_B, n_B));
517     PetscCall(ISRestoreIndices(sub_schurs->is_B, &idx_B));
518 
519     /* add prescribed number of layers of dofs */
520     n_local_dofs = n_B;
521     n_prev_added = n_B;
522     for (layer = 0; layer < nlayers; layer++) {
523       PetscInt n_added = 0;
524       if (n_local_dofs == n_I + n_B) break;
525       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);
526       PetscCall(PCBDDCAdjGetNextLayer_Private(local_numbering + n_local_dofs, n_prev_added, touched, xadj, adjncy, &n_added));
527       n_prev_added = n_added;
528       n_local_dofs += n_added;
529       if (!n_added) break;
530     }
531     PetscCall(PetscBTDestroy(&touched));
532 
533     /* IS for I layer dofs in original numbering */
534     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I), n_local_dofs - n_B, local_numbering + n_B, PETSC_COPY_VALUES, &is_I_layer));
535     PetscCall(PetscFree(local_numbering));
536     PetscCall(ISSort(is_I_layer));
537     /* IS for I layer dofs in I numbering */
538     if (!sub_schurs->schur_explicit) {
539       ISLocalToGlobalMapping ItoNmap;
540       PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_I, &ItoNmap));
541       PetscCall(ISGlobalToLocalMappingApplyIS(ItoNmap, IS_GTOLM_DROP, is_I_layer, &is_I));
542       PetscCall(ISLocalToGlobalMappingDestroy(&ItoNmap));
543 
544       /* II block */
545       PetscCall(MatCreateSubMatrix(A_II, is_I, is_I, MAT_INITIAL_MATRIX, &AE_II));
546     }
547   } else {
548     PetscInt n_I;
549 
550     /* IS for I dofs in original numbering */
551     PetscCall(PetscObjectReference((PetscObject)sub_schurs->is_I));
552     is_I_layer = sub_schurs->is_I;
553 
554     /* IS for I dofs in I numbering (strided 1) */
555     if (!sub_schurs->schur_explicit) {
556       PetscCall(ISGetSize(sub_schurs->is_I, &n_I));
557       PetscCall(ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I), n_I, 0, 1, &is_I));
558 
559       /* II block is the same */
560       PetscCall(PetscObjectReference((PetscObject)A_II));
561       AE_II = A_II;
562     }
563   }
564 
565   /* Get info on subset sizes and sum of all subsets sizes */
566   max_subset_size = 0;
567   local_size      = 0;
568   for (i = 0; i < sub_schurs->n_subs; i++) {
569     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
570     max_subset_size = PetscMax(subset_size, max_subset_size);
571     local_size += subset_size;
572   }
573 
574   /* Work arrays for local indices */
575   extra = 0;
576   PetscCall(ISGetLocalSize(sub_schurs->is_B, &n_B));
577   if (sub_schurs->schur_explicit && is_I_layer) PetscCall(ISGetLocalSize(is_I_layer, &extra));
578   PetscCall(PetscMalloc1(n_B + extra, &all_local_idx_N));
579   if (extra) {
580     const PetscInt *idxs;
581     PetscCall(ISGetIndices(is_I_layer, &idxs));
582     PetscCall(PetscArraycpy(all_local_idx_N, idxs, extra));
583     PetscCall(ISRestoreIndices(is_I_layer, &idxs));
584   }
585   PetscCall(PetscMalloc1(sub_schurs->n_subs, &auxnum1));
586   PetscCall(PetscMalloc1(sub_schurs->n_subs, &auxnum2));
587 
588   /* Get local indices in local numbering */
589   local_size       = 0;
590   local_stash_size = 0;
591   for (i = 0; i < sub_schurs->n_subs; i++) {
592     const PetscInt *idxs;
593 
594     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
595     PetscCall(ISGetIndices(sub_schurs->is_subs[i], &idxs));
596     /* start (smallest in global ordering) and multiplicity */
597     auxnum1[i] = idxs[0];
598     auxnum2[i] = subset_size * subset_size;
599     /* subset indices in local numbering */
600     PetscCall(PetscArraycpy(all_local_idx_N + local_size + extra, idxs, subset_size));
601     PetscCall(ISRestoreIndices(sub_schurs->is_subs[i], &idxs));
602     local_size += subset_size;
603     local_stash_size += subset_size * subset_size;
604   }
605 
606   /* allocate extra workspace needed only for GETRI or SYTRF when inverting the blocks or the entire Schur complement */
607   use_potr = use_sytr = PETSC_FALSE;
608   if (benign_trick || (sub_schurs->is_hermitian && sub_schurs->is_posdef)) {
609     use_potr = PETSC_TRUE;
610   } else if (sub_schurs->is_symmetric) {
611     use_sytr = PETSC_TRUE;
612   }
613   if (local_size && !use_potr && compute_Stilda) {
614     PetscScalar  lwork, dummyscalar = 0.;
615     PetscBLASInt dummyint = 0;
616 
617     B_lwork = -1;
618     PetscCall(PetscBLASIntCast(local_size, &B_N));
619     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
620     if (use_sytr) {
621       PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, &dummyscalar, &B_N, &dummyint, &lwork, &B_lwork, &B_ierr));
622       PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
623     } else {
624       PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, &dummyscalar, &B_N, &dummyint, &lwork, &B_lwork, &B_ierr));
625       PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
626     }
627     PetscCall(PetscFPTrapPop());
628     PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(lwork), &B_lwork));
629     PetscCall(PetscMalloc2(B_lwork, &Bwork, B_N, &pivots));
630   } else {
631     Bwork  = NULL;
632     pivots = NULL;
633   }
634 
635   /* prepare data for summing up properly schurs on subsets */
636   PetscCall(ISCreateGeneral(comm_n, sub_schurs->n_subs, auxnum1, PETSC_OWN_POINTER, &all_subsets_n));
637   PetscCall(ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap, all_subsets_n, &all_subsets));
638   PetscCall(ISDestroy(&all_subsets_n));
639   PetscCall(ISCreateGeneral(comm_n, sub_schurs->n_subs, auxnum2, PETSC_OWN_POINTER, &all_subsets_mult));
640   PetscCall(ISRenumber(all_subsets, all_subsets_mult, &global_size, &all_subsets_n));
641   PetscCall(ISDestroy(&all_subsets));
642   PetscCall(ISDestroy(&all_subsets_mult));
643   PetscCall(ISGetLocalSize(all_subsets_n, &i));
644   PetscCheck(i == local_stash_size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid size of new subset! %" PetscInt_FMT " != %" PetscInt_FMT, i, local_stash_size);
645   PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, local_stash_size, NULL, &lstash));
646   PetscCall(VecCreateMPI(comm_n, PETSC_DECIDE, global_size, &gstash));
647   PetscCall(VecScatterCreate(lstash, NULL, gstash, all_subsets_n, &sstash));
648   PetscCall(ISDestroy(&all_subsets_n));
649 
650   /* subset indices in local boundary numbering */
651   if (!sub_schurs->is_Ej_all) {
652     PetscInt *all_local_idx_B;
653 
654     PetscCall(PetscMalloc1(local_size, &all_local_idx_B));
655     PetscCall(ISGlobalToLocalMappingApply(sub_schurs->BtoNmap, IS_GTOLM_DROP, local_size, all_local_idx_N + extra, &subset_size, all_local_idx_B));
656     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);
657     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, local_size, all_local_idx_B, PETSC_OWN_POINTER, &sub_schurs->is_Ej_all));
658   }
659 
660   if (change) {
661     ISLocalToGlobalMapping BtoS;
662     IS                     change_primal_B;
663     IS                     change_primal_all;
664 
665     PetscCheck(!sub_schurs->change_primal_sub, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
666     PetscCheck(!sub_schurs->change, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
667     PetscCall(PetscMalloc1(sub_schurs->n_subs, &sub_schurs->change_primal_sub));
668     for (i = 0; i < sub_schurs->n_subs; i++) {
669       ISLocalToGlobalMapping NtoS;
670       PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i], &NtoS));
671       PetscCall(ISGlobalToLocalMappingApplyIS(NtoS, IS_GTOLM_DROP, change_primal, &sub_schurs->change_primal_sub[i]));
672       PetscCall(ISLocalToGlobalMappingDestroy(&NtoS));
673     }
674     PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, change_primal, &change_primal_B));
675     PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all, &BtoS));
676     PetscCall(ISGlobalToLocalMappingApplyIS(BtoS, IS_GTOLM_DROP, change_primal_B, &change_primal_all));
677     PetscCall(ISLocalToGlobalMappingDestroy(&BtoS));
678     PetscCall(ISDestroy(&change_primal_B));
679     PetscCall(PetscMalloc1(sub_schurs->n_subs, &sub_schurs->change));
680     for (i = 0; i < sub_schurs->n_subs; i++) {
681       Mat change_sub;
682 
683       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
684       PetscCall(KSPCreate(PETSC_COMM_SELF, &sub_schurs->change[i]));
685       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 */
686       PetscCall(KSPSetType(sub_schurs->change[i], KSPPREONLY));
687       if (!sub_schurs->change_with_qr) {
688         PetscCall(MatCreateSubMatrix(change, sub_schurs->is_subs[i], sub_schurs->is_subs[i], MAT_INITIAL_MATRIX, &change_sub));
689       } else {
690         Mat change_subt;
691         PetscCall(MatCreateSubMatrix(change, sub_schurs->is_subs[i], sub_schurs->is_subs[i], MAT_INITIAL_MATRIX, &change_subt));
692         PetscCall(MatConvert(change_subt, MATSEQDENSE, MAT_INITIAL_MATRIX, &change_sub));
693         PetscCall(MatDestroy(&change_subt));
694       }
695       PetscCall(KSPSetOperators(sub_schurs->change[i], change_sub, change_sub));
696       PetscCall(MatDestroy(&change_sub));
697       PetscCall(KSPSetOptionsPrefix(sub_schurs->change[i], sub_schurs->prefix));
698       PetscCall(KSPAppendOptionsPrefix(sub_schurs->change[i], "sub_schurs_change_"));
699     }
700     PetscCall(ISDestroy(&change_primal_all));
701   }
702 
703   /* Local matrix of all local Schur on subsets (transposed) */
704   if (!sub_schurs->S_Ej_all) {
705     Mat          T;
706     PetscScalar *v;
707     PetscInt    *ii, *jj;
708     PetscInt     cum, i, j, k;
709 
710     /* MatSeqAIJSetPreallocation + MatSetValues is slow for these kind of matrices (may have large blocks)
711        Allocate properly a representative matrix and duplicate */
712     PetscCall(PetscMalloc3(local_size + 1, &ii, local_stash_size, &jj, local_stash_size, &v));
713     ii[0] = 0;
714     cum   = 0;
715     for (i = 0; i < sub_schurs->n_subs; i++) {
716       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
717       for (j = 0; j < subset_size; j++) {
718         const PetscInt row = cum + j;
719         PetscInt       col = cum;
720 
721         ii[row + 1] = ii[row] + subset_size;
722         for (k = ii[row]; k < ii[row + 1]; k++) {
723           jj[k] = col;
724           col++;
725         }
726       }
727       cum += subset_size;
728     }
729     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, local_size, local_size, ii, jj, v, &T));
730     PetscCall(MatDuplicate(T, MAT_DO_NOT_COPY_VALUES, &sub_schurs->S_Ej_all));
731     PetscCall(MatDestroy(&T));
732     PetscCall(PetscFree3(ii, jj, v));
733   }
734   /* matrices for deluxe scaling and adaptive selection */
735   if (compute_Stilda) {
736     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));
737     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));
738   }
739 
740   /* Compute Schur complements explicitly */
741   F = NULL;
742   if (!sub_schurs->schur_explicit) {
743     /* this code branch is used when MatFactor with Schur complement support is not present or when explicitly requested;
744        it is not efficient, unless the economic version of the scaling is used */
745     Mat          S_Ej_expl;
746     PetscScalar *work;
747     PetscInt     j, *dummy_idx;
748     PetscBool    Sdense;
749 
750     PetscCall(PetscMalloc2(max_subset_size, &dummy_idx, max_subset_size * max_subset_size, &work));
751     local_size = 0;
752     for (i = 0; i < sub_schurs->n_subs; i++) {
753       IS  is_subset_B;
754       Mat AE_EE, AE_IE, AE_EI, S_Ej;
755 
756       /* subsets in original and boundary numbering */
757       PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, sub_schurs->is_subs[i], &is_subset_B));
758       /* EE block */
759       PetscCall(MatCreateSubMatrix(A_BB, is_subset_B, is_subset_B, MAT_INITIAL_MATRIX, &AE_EE));
760       /* IE block */
761       PetscCall(MatCreateSubMatrix(A_IB, is_I, is_subset_B, MAT_INITIAL_MATRIX, &AE_IE));
762       /* EI block */
763       if (sub_schurs->is_symmetric) {
764         PetscCall(MatCreateTranspose(AE_IE, &AE_EI));
765       } else if (sub_schurs->is_hermitian) {
766         PetscCall(MatCreateHermitianTranspose(AE_IE, &AE_EI));
767       } else {
768         PetscCall(MatCreateSubMatrix(A_BI, is_subset_B, is_I, MAT_INITIAL_MATRIX, &AE_EI));
769       }
770       PetscCall(ISDestroy(&is_subset_B));
771       PetscCall(MatCreateSchurComplement(AE_II, AE_II, AE_IE, AE_EI, AE_EE, &S_Ej));
772       PetscCall(MatDestroy(&AE_EE));
773       PetscCall(MatDestroy(&AE_IE));
774       PetscCall(MatDestroy(&AE_EI));
775       if (AE_II == A_II) { /* we can reuse the same ksp */
776         KSP ksp;
777         PetscCall(MatSchurComplementGetKSP(sub_schurs->S, &ksp));
778         PetscCall(MatSchurComplementSetKSP(S_Ej, ksp));
779       } else { /* build new ksp object which inherits ksp and pc types from the original one */
780         KSP       origksp, schurksp;
781         PC        origpc, schurpc;
782         KSPType   ksp_type;
783         PetscInt  n_internal;
784         PetscBool ispcnone;
785 
786         PetscCall(MatSchurComplementGetKSP(sub_schurs->S, &origksp));
787         PetscCall(MatSchurComplementGetKSP(S_Ej, &schurksp));
788         PetscCall(KSPGetType(origksp, &ksp_type));
789         PetscCall(KSPSetType(schurksp, ksp_type));
790         PetscCall(KSPGetPC(schurksp, &schurpc));
791         PetscCall(KSPGetPC(origksp, &origpc));
792         PetscCall(PetscObjectTypeCompare((PetscObject)origpc, PCNONE, &ispcnone));
793         if (!ispcnone) {
794           PCType pc_type;
795           PetscCall(PCGetType(origpc, &pc_type));
796           PetscCall(PCSetType(schurpc, pc_type));
797         } else {
798           PetscCall(PCSetType(schurpc, PCLU));
799         }
800         PetscCall(ISGetSize(is_I, &n_internal));
801         if (!n_internal) { /* UMFPACK gives error with 0 sized problems */
802           MatSolverType solver = NULL;
803           PetscCall(PCFactorGetMatSolverType(origpc, &solver));
804           if (solver) PetscCall(PCFactorSetMatSolverType(schurpc, solver));
805         }
806         PetscCall(KSPSetUp(schurksp));
807       }
808       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
809       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &S_Ej_expl));
810       PetscCall(PCBDDCComputeExplicitSchur(S_Ej, sub_schurs->is_symmetric, MAT_REUSE_MATRIX, &S_Ej_expl));
811       PetscCall(PetscObjectTypeCompare((PetscObject)S_Ej_expl, MATSEQDENSE, &Sdense));
812       PetscCheck(Sdense, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for sparse matrices");
813       for (j = 0; j < subset_size; j++) dummy_idx[j] = local_size + j;
814       PetscCall(MatSetValues(sub_schurs->S_Ej_all, subset_size, dummy_idx, subset_size, dummy_idx, work, INSERT_VALUES));
815       PetscCall(MatDestroy(&S_Ej));
816       PetscCall(MatDestroy(&S_Ej_expl));
817       local_size += subset_size;
818     }
819     PetscCall(PetscFree2(dummy_idx, work));
820     /* free */
821     PetscCall(ISDestroy(&is_I));
822     PetscCall(MatDestroy(&AE_II));
823     PetscCall(PetscFree(all_local_idx_N));
824   } else {
825     Mat                A, cs_AIB_mat = NULL, benign_AIIm1_ones_mat = NULL;
826     Mat               *gdswA;
827     Vec                Dall = NULL;
828     IS                 is_A_all, *is_p_r = NULL;
829     MatType            Stype;
830     PetscScalar       *work, *S_data, *schur_factor, infty = PETSC_MAX_REAL;
831     PetscScalar       *SEj_arr = NULL, *SEjinv_arr = NULL;
832     const PetscScalar *rS_data;
833     PetscInt           n, n_I, size_schur, size_active_schur, cum, cum2;
834     PetscBool          economic, solver_S, S_lower_triangular = PETSC_FALSE;
835     PetscBool          schur_has_vertices, factor_workaround;
836     PetscBool          use_cholesky;
837 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
838     PetscBool oldpin;
839 #endif
840 
841     /* get sizes */
842     n_I = 0;
843     if (is_I_layer) PetscCall(ISGetLocalSize(is_I_layer, &n_I));
844     economic = PETSC_FALSE;
845     PetscCall(ISGetLocalSize(sub_schurs->is_I, &cum));
846     if (cum != n_I) economic = PETSC_TRUE;
847     PetscCall(MatGetLocalSize(sub_schurs->A, &n, NULL));
848     size_active_schur = local_size;
849 
850     /* import scaling vector (wrong formulation if we have 3D edges) */
851     if (scaling && compute_Stilda) {
852       const PetscScalar *array;
853       PetscScalar       *array2;
854       const PetscInt    *idxs;
855       PetscInt           i;
856 
857       PetscCall(ISGetIndices(sub_schurs->is_Ej_all, &idxs));
858       PetscCall(VecCreateSeq(PETSC_COMM_SELF, size_active_schur, &Dall));
859       PetscCall(VecGetArrayRead(scaling, &array));
860       PetscCall(VecGetArray(Dall, &array2));
861       for (i = 0; i < size_active_schur; i++) array2[i] = array[idxs[i]];
862       PetscCall(VecRestoreArray(Dall, &array2));
863       PetscCall(VecRestoreArrayRead(scaling, &array));
864       PetscCall(ISRestoreIndices(sub_schurs->is_Ej_all, &idxs));
865       deluxe = PETSC_FALSE;
866     }
867 
868     /* size active schurs does not count any dirichlet or vertex dof on the interface */
869     factor_workaround  = PETSC_FALSE;
870     schur_has_vertices = PETSC_FALSE;
871     cum                = n_I + size_active_schur;
872     if (sub_schurs->is_dir) {
873       const PetscInt *idxs;
874       PetscInt        n_dir;
875 
876       PetscCall(ISGetLocalSize(sub_schurs->is_dir, &n_dir));
877       PetscCall(ISGetIndices(sub_schurs->is_dir, &idxs));
878       PetscCall(PetscArraycpy(all_local_idx_N + cum, idxs, n_dir));
879       PetscCall(ISRestoreIndices(sub_schurs->is_dir, &idxs));
880       cum += n_dir;
881       if (!sub_schurs->gdsw) factor_workaround = PETSC_TRUE;
882     }
883     /* include the primal vertices in the Schur complement */
884     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
885       PetscInt n_v;
886 
887       PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &n_v));
888       if (n_v) {
889         const PetscInt *idxs;
890 
891         PetscCall(ISGetIndices(sub_schurs->is_vertices, &idxs));
892         PetscCall(PetscArraycpy(all_local_idx_N + cum, idxs, n_v));
893         PetscCall(ISRestoreIndices(sub_schurs->is_vertices, &idxs));
894         cum += n_v;
895         if (!sub_schurs->gdsw) factor_workaround = PETSC_TRUE;
896         schur_has_vertices = PETSC_TRUE;
897       }
898     }
899     size_schur = cum - n_I;
900     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, cum, all_local_idx_N, PETSC_OWN_POINTER, &is_A_all));
901 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
902     oldpin = sub_schurs->A->boundtocpu;
903     PetscCall(MatBindToCPU(sub_schurs->A, PETSC_TRUE));
904 #endif
905     if (cum == n) {
906       PetscCall(ISSetPermutation(is_A_all));
907       PetscCall(MatPermute(sub_schurs->A, is_A_all, is_A_all, &A));
908     } else {
909       PetscCall(MatCreateSubMatrix(sub_schurs->A, is_A_all, is_A_all, MAT_INITIAL_MATRIX, &A));
910     }
911 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
912     PetscCall(MatBindToCPU(sub_schurs->A, oldpin));
913 #endif
914     PetscCall(MatSetOptionsPrefixFactor(A, sub_schurs->prefix));
915     PetscCall(MatAppendOptionsPrefixFactor(A, "sub_schurs_"));
916 
917     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
918        this is a workaround */
919     if (benign_n) {
920       Vec                    v, benign_AIIm1_ones;
921       ISLocalToGlobalMapping N_to_reor;
922       IS                     is_p0, is_p0_p;
923       PetscScalar           *cs_AIB, *AIIm1_data;
924       PetscInt               sizeA;
925 
926       PetscCall(ISLocalToGlobalMappingCreateIS(is_A_all, &N_to_reor));
927       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, benign_n, benign_p0_lidx, PETSC_COPY_VALUES, &is_p0));
928       PetscCall(ISGlobalToLocalMappingApplyIS(N_to_reor, IS_GTOLM_DROP, is_p0, &is_p0_p));
929       PetscCall(ISDestroy(&is_p0));
930       PetscCall(MatCreateVecs(A, &v, &benign_AIIm1_ones));
931       PetscCall(VecGetSize(v, &sizeA));
932       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, sizeA, benign_n, NULL, &benign_AIIm1_ones_mat));
933       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size_schur, benign_n, NULL, &cs_AIB_mat));
934       PetscCall(MatDenseGetArray(cs_AIB_mat, &cs_AIB));
935       PetscCall(MatDenseGetArray(benign_AIIm1_ones_mat, &AIIm1_data));
936       PetscCall(PetscMalloc1(benign_n, &is_p_r));
937       /* compute colsum of A_IB restricted to pressures */
938       for (i = 0; i < benign_n; i++) {
939         const PetscScalar *array;
940         const PetscInt    *idxs;
941         PetscInt           j, nz;
942 
943         PetscCall(ISGlobalToLocalMappingApplyIS(N_to_reor, IS_GTOLM_DROP, benign_zerodiag_subs[i], &is_p_r[i]));
944         PetscCall(ISGetLocalSize(is_p_r[i], &nz));
945         PetscCall(ISGetIndices(is_p_r[i], &idxs));
946         for (j = 0; j < nz; j++) AIIm1_data[idxs[j] + sizeA * i] = 1.;
947         PetscCall(ISRestoreIndices(is_p_r[i], &idxs));
948         PetscCall(VecPlaceArray(benign_AIIm1_ones, AIIm1_data + sizeA * i));
949         PetscCall(MatMult(A, benign_AIIm1_ones, v));
950         PetscCall(VecResetArray(benign_AIIm1_ones));
951         PetscCall(VecGetArrayRead(v, &array));
952         for (j = 0; j < size_schur; j++) {
953 #if defined(PETSC_USE_COMPLEX)
954           cs_AIB[i * size_schur + j] = (PetscRealPart(array[j + n_I]) / nz + PETSC_i * (PetscImaginaryPart(array[j + n_I]) / nz));
955 #else
956           cs_AIB[i * size_schur + j] = array[j + n_I] / nz;
957 #endif
958         }
959         PetscCall(VecRestoreArrayRead(v, &array));
960       }
961       PetscCall(MatDenseRestoreArray(cs_AIB_mat, &cs_AIB));
962       PetscCall(MatDenseRestoreArray(benign_AIIm1_ones_mat, &AIIm1_data));
963       PetscCall(VecDestroy(&v));
964       PetscCall(VecDestroy(&benign_AIIm1_ones));
965       PetscCall(MatSetOption(A, MAT_KEEP_NONZERO_PATTERN, PETSC_FALSE));
966       PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));
967       PetscCall(MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
968       PetscCall(MatZeroRowsColumnsIS(A, is_p0_p, 1.0, NULL, NULL));
969       PetscCall(ISDestroy(&is_p0_p));
970       PetscCall(ISLocalToGlobalMappingDestroy(&N_to_reor));
971     }
972     PetscCall(MatSetOption(A, MAT_SYMMETRIC, sub_schurs->is_symmetric));
973     PetscCall(MatSetOption(A, MAT_HERMITIAN, sub_schurs->is_hermitian));
974     PetscCall(MatSetOption(A, MAT_SPD, sub_schurs->is_posdef));
975 
976     /* for complexes, symmetric and hermitian at the same time implies null imaginary part */
977     use_cholesky = (PetscBool)((use_potr || use_sytr) && sub_schurs->is_hermitian && sub_schurs->is_symmetric);
978 
979     /* when using the benign subspace trick, the local Schur complements are SPD */
980     /* MKL_PARDISO does not handle well the computation of a Schur complement from a symmetric indefinite factorization
981        Use LU and adapt pivoting perturbation (still, solution is not as accurate as with using MUMPS) */
982     if (benign_trick) {
983       sub_schurs->is_posdef = PETSC_TRUE;
984       PetscCall(PetscStrcmp(sub_schurs->mat_solver_type, MATSOLVERMKL_PARDISO, &flg));
985       if (flg) use_cholesky = PETSC_FALSE;
986     }
987     if (sub_schurs->mat_factor_type == MAT_FACTOR_NONE) sub_schurs->mat_factor_type = use_cholesky ? MAT_FACTOR_CHOLESKY : MAT_FACTOR_LU;
988 
989     if (n_I) {
990       IS        is_schur;
991       char      stype[64];
992       PetscBool gpu = PETSC_FALSE;
993 
994       PetscCall(MatGetFactor(A, sub_schurs->mat_solver_type, sub_schurs->mat_factor_type, &F));
995       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);
996       PetscCall(MatSetErrorIfFailure(A, PETSC_TRUE));
997 #if defined(PETSC_HAVE_MKL_PARDISO)
998       if (benign_trick) PetscCall(MatMkl_PardisoSetCntl(F, 10, 10));
999 #endif
1000       /* subsets ordered last */
1001       PetscCall(ISCreateStride(PETSC_COMM_SELF, size_schur, n_I, 1, &is_schur));
1002       PetscCall(MatFactorSetSchurIS(F, is_schur));
1003       PetscCall(ISDestroy(&is_schur));
1004 
1005       /* factorization step */
1006       switch (sub_schurs->mat_factor_type) {
1007       case MAT_FACTOR_CHOLESKY:
1008         PetscCall(MatCholeskyFactorSymbolic(F, A, NULL, NULL));
1009         /* be sure that icntl 19 is not set by command line */
1010         PetscCall(MatMumpsSetIcntl(F, 19, 2));
1011         PetscCall(MatCholeskyFactorNumeric(F, A, NULL));
1012         S_lower_triangular = PETSC_TRUE;
1013         break;
1014       case MAT_FACTOR_LU:
1015         PetscCall(MatLUFactorSymbolic(F, A, NULL, NULL, NULL));
1016         /* be sure that icntl 19 is not set by command line */
1017         PetscCall(MatMumpsSetIcntl(F, 19, 3));
1018         PetscCall(MatLUFactorNumeric(F, A, NULL));
1019         break;
1020       default:
1021         SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unsupported factor type %s", MatFactorTypes[sub_schurs->mat_factor_type]);
1022       }
1023       PetscCall(MatViewFromOptions(F, (PetscObject)A, "-mat_factor_view"));
1024 
1025       if (matl_dbg_viewer) {
1026         Mat S;
1027         IS  is;
1028 
1029         PetscCall(PetscObjectSetName((PetscObject)A, "A"));
1030         PetscCall(MatView(A, matl_dbg_viewer));
1031         PetscCall(MatFactorCreateSchurComplement(F, &S, NULL));
1032         PetscCall(PetscObjectSetName((PetscObject)S, "S"));
1033         PetscCall(MatView(S, matl_dbg_viewer));
1034         PetscCall(MatDestroy(&S));
1035         PetscCall(ISCreateStride(PETSC_COMM_SELF, n_I, 0, 1, &is));
1036         PetscCall(PetscObjectSetName((PetscObject)is, "I"));
1037         PetscCall(ISView(is, matl_dbg_viewer));
1038         PetscCall(ISDestroy(&is));
1039         PetscCall(ISCreateStride(PETSC_COMM_SELF, size_schur, n_I, 1, &is));
1040         PetscCall(PetscObjectSetName((PetscObject)is, "B"));
1041         PetscCall(ISView(is, matl_dbg_viewer));
1042         PetscCall(ISDestroy(&is));
1043         PetscCall(PetscObjectSetName((PetscObject)is_A_all, "IA"));
1044         PetscCall(ISView(is_A_all, matl_dbg_viewer));
1045         for (i = 0, cum = 0; i < sub_schurs->n_subs; i++) {
1046           IS   is;
1047           char name[16];
1048 
1049           PetscCall(PetscSNPrintf(name, sizeof(name), "IE%" PetscInt_FMT, i));
1050           PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1051           PetscCall(ISCreateStride(PETSC_COMM_SELF, subset_size, cum, 1, &is));
1052           PetscCall(PetscObjectSetName((PetscObject)is, name));
1053           PetscCall(ISView(is, matl_dbg_viewer));
1054           PetscCall(ISDestroy(&is));
1055           if (sub_schurs->change) {
1056             Mat T;
1057 
1058             PetscCall(PetscSNPrintf(name, sizeof(name), "TE%" PetscInt_FMT, i));
1059             PetscCall(KSPGetOperators(sub_schurs->change[i], &T, NULL));
1060             PetscCall(PetscObjectSetName((PetscObject)T, name));
1061             PetscCall(MatView(T, matl_dbg_viewer));
1062             PetscCall(PetscSNPrintf(name, sizeof(name), "ITE%" PetscInt_FMT, i));
1063             PetscCall(PetscObjectSetName((PetscObject)sub_schurs->change_primal_sub[i], name));
1064             PetscCall(ISView(sub_schurs->change_primal_sub[i], matl_dbg_viewer));
1065           }
1066           cum += subset_size;
1067         }
1068         PetscCall(PetscViewerFlush(matl_dbg_viewer));
1069       }
1070 
1071       /* get explicit Schur Complement computed during numeric factorization */
1072       PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
1073       PetscCall(PetscStrncpy(stype, MATSEQDENSE, sizeof(stype)));
1074 #if defined(PETSC_HAVE_CUDA)
1075       PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &gpu, MATSEQAIJVIENNACL, MATSEQAIJCUSPARSE, ""));
1076 #endif
1077       if (gpu) PetscCall(PetscStrncpy(stype, MATSEQDENSECUDA, sizeof(stype)));
1078       PetscCall(PetscOptionsGetString(NULL, sub_schurs->prefix, "-sub_schurs_schur_mat_type", stype, sizeof(stype), NULL));
1079       PetscCall(MatConvert(S_all, stype, MAT_INPLACE_MATRIX, &S_all));
1080       PetscCall(MatSetOption(S_all, MAT_SPD, sub_schurs->is_posdef));
1081       PetscCall(MatSetOption(S_all, MAT_HERMITIAN, sub_schurs->is_hermitian));
1082       PetscCall(MatGetType(S_all, &Stype));
1083 
1084       /* we can reuse the solvers if we are not using the economic version */
1085       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
1086       if (!sub_schurs->gdsw) {
1087         factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
1088         if (!sub_schurs->is_posdef && factor_workaround && compute_Stilda && size_active_schur) reuse_solvers = factor_workaround = PETSC_FALSE;
1089       }
1090       solver_S = PETSC_TRUE;
1091 
1092       /* update the Schur complement with the change of basis on the pressures */
1093       if (benign_n) {
1094         const PetscScalar *cs_AIB;
1095         PetscScalar       *S_data, *AIIm1_data;
1096         Mat                S2 = NULL, S3 = NULL; /* dbg */
1097         PetscScalar       *S2_data, *S3_data;    /* dbg */
1098         Vec                v, benign_AIIm1_ones;
1099         PetscInt           sizeA;
1100 
1101         PetscCall(MatDenseGetArray(S_all, &S_data));
1102         PetscCall(MatCreateVecs(A, &v, &benign_AIIm1_ones));
1103         PetscCall(VecGetSize(v, &sizeA));
1104         PetscCall(MatMumpsSetIcntl(F, 26, 0));
1105 #if defined(PETSC_HAVE_MKL_PARDISO)
1106         PetscCall(MatMkl_PardisoSetCntl(F, 70, 1));
1107 #endif
1108         PetscCall(MatDenseGetArrayRead(cs_AIB_mat, &cs_AIB));
1109         PetscCall(MatDenseGetArray(benign_AIIm1_ones_mat, &AIIm1_data));
1110         if (matl_dbg_viewer) {
1111           PetscCall(MatDuplicate(S_all, MAT_DO_NOT_COPY_VALUES, &S2));
1112           PetscCall(MatDuplicate(S_all, MAT_DO_NOT_COPY_VALUES, &S3));
1113           PetscCall(MatDenseGetArray(S2, &S2_data));
1114           PetscCall(MatDenseGetArray(S3, &S3_data));
1115         }
1116         for (i = 0; i < benign_n; i++) {
1117           PetscScalar    *array, sum = 0., one = 1., *sums;
1118           const PetscInt *idxs;
1119           PetscInt        k, j, nz;
1120           PetscBLASInt    B_k, B_n;
1121 
1122           PetscCall(PetscCalloc1(benign_n, &sums));
1123           PetscCall(VecPlaceArray(benign_AIIm1_ones, AIIm1_data + sizeA * i));
1124           PetscCall(VecCopy(benign_AIIm1_ones, v));
1125           PetscCall(MatSolve(F, v, benign_AIIm1_ones));
1126           PetscCall(MatMult(A, benign_AIIm1_ones, v));
1127           PetscCall(VecResetArray(benign_AIIm1_ones));
1128           /* p0 dofs (eliminated) are excluded from the sums */
1129           for (k = 0; k < benign_n; k++) {
1130             PetscCall(ISGetLocalSize(is_p_r[k], &nz));
1131             PetscCall(ISGetIndices(is_p_r[k], &idxs));
1132             for (j = 0; j < nz - 1; j++) sums[k] -= AIIm1_data[idxs[j] + sizeA * i];
1133             PetscCall(ISRestoreIndices(is_p_r[k], &idxs));
1134           }
1135           PetscCall(VecGetArrayRead(v, (const PetscScalar **)&array));
1136           if (matl_dbg_viewer) {
1137             Vec  vv;
1138             char name[16];
1139 
1140             PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, size_schur, array + n_I, &vv));
1141             PetscCall(PetscSNPrintf(name, sizeof(name), "Pvs%" PetscInt_FMT, i));
1142             PetscCall(PetscObjectSetName((PetscObject)vv, name));
1143             PetscCall(VecView(vv, matl_dbg_viewer));
1144           }
1145           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
1146           /* cs_AIB already scaled by 1./nz */
1147           B_k = 1;
1148           PetscCall(PetscBLASIntCast(size_schur, &B_n));
1149           for (k = 0; k < benign_n; k++) {
1150             sum = sums[k];
1151 
1152             if (PetscAbsScalar(sum) == 0.0) continue;
1153             if (k == i) {
1154               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));
1155               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));
1156             } else { /* XXX Is it correct to use symmetric rank-2 update with half of the sum? */
1157               sum /= 2.0;
1158               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));
1159               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));
1160             }
1161           }
1162           sum = 1.;
1163           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));
1164           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));
1165           PetscCall(VecRestoreArrayRead(v, (const PetscScalar **)&array));
1166           /* set p0 entry of AIIm1_ones to zero */
1167           PetscCall(ISGetLocalSize(is_p_r[i], &nz));
1168           PetscCall(ISGetIndices(is_p_r[i], &idxs));
1169           for (j = 0; j < benign_n; j++) AIIm1_data[idxs[nz - 1] + sizeA * j] = 0.;
1170           PetscCall(ISRestoreIndices(is_p_r[i], &idxs));
1171           PetscCall(PetscFree(sums));
1172         }
1173         PetscCall(VecDestroy(&benign_AIIm1_ones));
1174         if (matl_dbg_viewer) {
1175           PetscCall(MatDenseRestoreArray(S2, &S2_data));
1176           PetscCall(MatDenseRestoreArray(S3, &S3_data));
1177         }
1178         if (!S_lower_triangular) { /* I need to expand the upper triangular data (column-oriented) */
1179           PetscInt k, j;
1180           for (k = 0; k < size_schur; k++) {
1181             for (j = k; j < size_schur; j++) S_data[j * size_schur + k] = PetscConj(S_data[k * size_schur + j]);
1182           }
1183         }
1184 
1185         /* restore defaults */
1186         PetscCall(MatMumpsSetIcntl(F, 26, -1));
1187 #if defined(PETSC_HAVE_MKL_PARDISO)
1188         PetscCall(MatMkl_PardisoSetCntl(F, 70, 0));
1189 #endif
1190         PetscCall(MatDenseRestoreArrayRead(cs_AIB_mat, &cs_AIB));
1191         PetscCall(MatDenseRestoreArray(benign_AIIm1_ones_mat, &AIIm1_data));
1192         PetscCall(VecDestroy(&v));
1193         PetscCall(MatDenseRestoreArray(S_all, &S_data));
1194         if (matl_dbg_viewer) {
1195           Mat S;
1196 
1197           PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));
1198           PetscCall(MatFactorCreateSchurComplement(F, &S, NULL));
1199           PetscCall(PetscObjectSetName((PetscObject)S, "Sb"));
1200           PetscCall(MatView(S, matl_dbg_viewer));
1201           PetscCall(MatDestroy(&S));
1202           PetscCall(PetscObjectSetName((PetscObject)S2, "S2P"));
1203           PetscCall(MatView(S2, matl_dbg_viewer));
1204           PetscCall(PetscObjectSetName((PetscObject)S3, "S3P"));
1205           PetscCall(MatView(S3, matl_dbg_viewer));
1206           PetscCall(PetscObjectSetName((PetscObject)cs_AIB_mat, "cs"));
1207           PetscCall(MatView(cs_AIB_mat, matl_dbg_viewer));
1208           PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
1209         }
1210         PetscCall(MatDestroy(&S2));
1211         PetscCall(MatDestroy(&S3));
1212       }
1213       if (!reuse_solvers) {
1214         for (i = 0; i < benign_n; i++) PetscCall(ISDestroy(&is_p_r[i]));
1215         PetscCall(PetscFree(is_p_r));
1216         PetscCall(MatDestroy(&cs_AIB_mat));
1217         PetscCall(MatDestroy(&benign_AIIm1_ones_mat));
1218       }
1219     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1220       PetscCall(MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &S_all));
1221       PetscCall(MatGetType(S_all, &Stype));
1222       reuse_solvers     = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1223       factor_workaround = PETSC_FALSE;
1224       solver_S          = PETSC_FALSE;
1225     }
1226 
1227     if (reuse_solvers) {
1228       Mat                A_II, pA_II, Afake;
1229       Vec                vec1_B;
1230       PCBDDCReuseSolvers msolv_ctx;
1231       PetscInt           n_R;
1232 
1233       if (sub_schurs->reuse_solver) {
1234         PetscCall(PCBDDCReuseSolversReset(sub_schurs->reuse_solver));
1235       } else {
1236         PetscCall(PetscNew(&sub_schurs->reuse_solver));
1237       }
1238       msolv_ctx = sub_schurs->reuse_solver;
1239       PetscCall(MatSchurComplementGetSubMatrices(sub_schurs->S, &A_II, &pA_II, NULL, NULL, NULL));
1240       PetscCall(PetscObjectReference((PetscObject)F));
1241       msolv_ctx->F = F;
1242       PetscCall(MatCreateVecs(F, &msolv_ctx->sol, NULL));
1243       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1244       {
1245         PetscScalar *array;
1246         PetscInt     n;
1247 
1248         PetscCall(VecGetLocalSize(msolv_ctx->sol, &n));
1249         PetscCall(VecGetArray(msolv_ctx->sol, &array));
1250         PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol), 1, n, array, &msolv_ctx->rhs));
1251         PetscCall(VecRestoreArray(msolv_ctx->sol, &array));
1252       }
1253       msolv_ctx->has_vertices = schur_has_vertices;
1254 
1255       /* interior solver */
1256       PetscCall(PCCreate(PetscObjectComm((PetscObject)A_II), &msolv_ctx->interior_solver));
1257       PetscCall(PCSetOperators(msolv_ctx->interior_solver, A_II, pA_II));
1258       PetscCall(PCSetType(msolv_ctx->interior_solver, PCSHELL));
1259       PetscCall(PCShellSetName(msolv_ctx->interior_solver, "Interior solver (w/o Schur factorization)"));
1260       PetscCall(PCShellSetContext(msolv_ctx->interior_solver, msolv_ctx));
1261       PetscCall(PCShellSetView(msolv_ctx->interior_solver, PCBDDCReuseSolvers_View));
1262       PetscCall(PCShellSetApply(msolv_ctx->interior_solver, PCBDDCReuseSolvers_Interior));
1263       PetscCall(PCShellSetApplyTranspose(msolv_ctx->interior_solver, PCBDDCReuseSolvers_InteriorTranspose));
1264       if (sub_schurs->gdsw) PetscCall(PCShellSetDestroy(msolv_ctx->interior_solver, PCBDDCReuseSolvers_Destroy));
1265 
1266       /* correction solver */
1267       if (!sub_schurs->gdsw) {
1268         PetscCall(PCCreate(PetscObjectComm((PetscObject)A_II), &msolv_ctx->correction_solver));
1269         PetscCall(PCSetType(msolv_ctx->correction_solver, PCSHELL));
1270         PetscCall(PCShellSetName(msolv_ctx->correction_solver, "Correction solver (with Schur factorization)"));
1271         PetscCall(PCShellSetContext(msolv_ctx->correction_solver, msolv_ctx));
1272         PetscCall(PCShellSetView(msolv_ctx->interior_solver, PCBDDCReuseSolvers_View));
1273         PetscCall(PCShellSetApply(msolv_ctx->correction_solver, PCBDDCReuseSolvers_Correction));
1274         PetscCall(PCShellSetApplyTranspose(msolv_ctx->correction_solver, PCBDDCReuseSolvers_CorrectionTranspose));
1275 
1276         /* scatter and vecs for Schur complement solver */
1277         PetscCall(MatCreateVecs(S_all, &msolv_ctx->sol_B, &msolv_ctx->rhs_B));
1278         PetscCall(MatCreateVecs(sub_schurs->S, &vec1_B, NULL));
1279         if (!schur_has_vertices) {
1280           PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, is_A_all, &msolv_ctx->is_B));
1281           PetscCall(VecScatterCreate(vec1_B, msolv_ctx->is_B, msolv_ctx->sol_B, NULL, &msolv_ctx->correction_scatter_B));
1282           PetscCall(PetscObjectReference((PetscObject)is_A_all));
1283           msolv_ctx->is_R = is_A_all;
1284         } else {
1285           IS              is_B_all;
1286           const PetscInt *idxs;
1287           PetscInt        dual, n_v, n;
1288 
1289           PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &n_v));
1290           dual = size_schur - n_v;
1291           PetscCall(ISGetLocalSize(is_A_all, &n));
1292           PetscCall(ISGetIndices(is_A_all, &idxs));
1293           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all), dual, idxs + n_I, PETSC_COPY_VALUES, &is_B_all));
1294           PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, is_B_all, &msolv_ctx->is_B));
1295           PetscCall(ISDestroy(&is_B_all));
1296           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)is_A_all), dual, 0, 1, &is_B_all));
1297           PetscCall(VecScatterCreate(vec1_B, msolv_ctx->is_B, msolv_ctx->sol_B, is_B_all, &msolv_ctx->correction_scatter_B));
1298           PetscCall(ISDestroy(&is_B_all));
1299           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all), n - n_v, idxs, PETSC_COPY_VALUES, &msolv_ctx->is_R));
1300           PetscCall(ISRestoreIndices(is_A_all, &idxs));
1301         }
1302         PetscCall(ISGetLocalSize(msolv_ctx->is_R, &n_R));
1303         PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, n_R, n_R, 0, NULL, &Afake));
1304         PetscCall(MatAssemblyBegin(Afake, MAT_FINAL_ASSEMBLY));
1305         PetscCall(MatAssemblyEnd(Afake, MAT_FINAL_ASSEMBLY));
1306         PetscCall(PCSetOperators(msolv_ctx->correction_solver, Afake, Afake));
1307         PetscCall(MatDestroy(&Afake));
1308         PetscCall(VecDestroy(&vec1_B));
1309       }
1310       /* communicate benign info to solver context */
1311       if (benign_n) {
1312         PetscScalar *array;
1313 
1314         msolv_ctx->benign_n             = benign_n;
1315         msolv_ctx->benign_zerodiag_subs = is_p_r;
1316         PetscCall(PetscMalloc1(benign_n, &msolv_ctx->benign_save_vals));
1317         msolv_ctx->benign_csAIB = cs_AIB_mat;
1318         PetscCall(MatCreateVecs(cs_AIB_mat, &msolv_ctx->benign_corr_work, NULL));
1319         PetscCall(VecGetArray(msolv_ctx->benign_corr_work, &array));
1320         PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, size_schur, array, &msolv_ctx->benign_dummy_schur_vec));
1321         PetscCall(VecRestoreArray(msolv_ctx->benign_corr_work, &array));
1322         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1323       }
1324     } else {
1325       if (sub_schurs->reuse_solver) PetscCall(PCBDDCReuseSolversReset(sub_schurs->reuse_solver));
1326       PetscCall(PetscFree(sub_schurs->reuse_solver));
1327     }
1328     PetscCall(MatDestroy(&A));
1329     PetscCall(ISDestroy(&is_A_all));
1330 
1331     /* Work arrays */
1332     PetscCall(PetscMalloc1(max_subset_size * max_subset_size, &work));
1333 
1334     /* S_Ej_all */
1335     cum = cum2 = 0;
1336     PetscCall(MatDenseGetArrayRead(S_all, &rS_data));
1337     PetscCall(MatSeqAIJGetArray(sub_schurs->S_Ej_all, &SEj_arr));
1338     if (sub_schurs->sum_S_Ej_inv_all) PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all, &SEjinv_arr));
1339     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));
1340     for (i = 0; i < sub_schurs->n_subs; i++) {
1341       PetscInt j;
1342 
1343       /* get S_E (or K^i_EE for GDSW) */
1344       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1345       if (sub_schurs->gdsw) {
1346         Mat T;
1347 
1348         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &T));
1349         PetscCall(MatConvert(gdswA[i], MATDENSE, MAT_REUSE_MATRIX, &T));
1350         PetscCall(MatDestroy(&T));
1351       } else {
1352         if (S_lower_triangular) { /* I need to expand the upper triangular data (column-oriented) */
1353           PetscInt k;
1354           for (k = 0; k < subset_size; k++) {
1355             for (j = k; j < subset_size; j++) {
1356               work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1357               work[j * subset_size + k] = PetscConj(rS_data[cum2 + k * size_schur + j]);
1358             }
1359           }
1360         } else { /* just copy to workspace */
1361           PetscInt k;
1362           for (k = 0; k < subset_size; k++) {
1363             for (j = 0; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1364           }
1365         }
1366       }
1367       /* insert S_E values */
1368       if (sub_schurs->change) {
1369         Mat change_sub, SEj, T;
1370 
1371         /* change basis */
1372         PetscCall(KSPGetOperators(sub_schurs->change[i], &change_sub, NULL));
1373         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &SEj));
1374         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1375           Mat T2;
1376           PetscCall(MatTransposeMatMult(change_sub, SEj, MAT_INITIAL_MATRIX, 1.0, &T2));
1377           PetscCall(MatMatMult(T2, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
1378           PetscCall(MatConvert(T, MATSEQDENSE, MAT_INPLACE_MATRIX, &T));
1379           PetscCall(MatDestroy(&T2));
1380         } else {
1381           PetscCall(MatPtAP(SEj, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
1382         }
1383         PetscCall(MatCopy(T, SEj, SAME_NONZERO_PATTERN));
1384         PetscCall(MatDestroy(&T));
1385         PetscCall(MatZeroRowsColumnsIS(SEj, sub_schurs->change_primal_sub[i], 1.0, NULL, NULL));
1386         PetscCall(MatDestroy(&SEj));
1387       }
1388       PetscCall(PetscArraycpy(SEj_arr, work, subset_size * subset_size));
1389       if (compute_Stilda) {
1390         if (deluxe) { /* if adaptivity is requested, invert S_E blocks */
1391           Mat                M;
1392           const PetscScalar *vals;
1393           PetscBool          isdense, isdensecuda;
1394 
1395           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &M));
1396           PetscCall(MatSetOption(M, MAT_SPD, sub_schurs->is_posdef));
1397           PetscCall(MatSetOption(M, MAT_HERMITIAN, sub_schurs->is_hermitian));
1398           if (!PetscBTLookup(sub_schurs->is_edge, i)) PetscCall(MatSetType(M, Stype));
1399           PetscCall(PetscObjectTypeCompare((PetscObject)M, MATSEQDENSE, &isdense));
1400           PetscCall(PetscObjectTypeCompare((PetscObject)M, MATSEQDENSECUDA, &isdensecuda));
1401           switch (sub_schurs->mat_factor_type) {
1402           case MAT_FACTOR_CHOLESKY:
1403             PetscCall(MatCholeskyFactor(M, NULL, NULL));
1404             break;
1405           case MAT_FACTOR_LU:
1406             PetscCall(MatLUFactor(M, NULL, NULL, NULL));
1407             break;
1408           default:
1409             SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unsupported factor type %s", MatFactorTypes[sub_schurs->mat_factor_type]);
1410           }
1411           if (isdense) {
1412             PetscCall(MatSeqDenseInvertFactors_Private(M));
1413 #if defined(PETSC_HAVE_CUDA)
1414           } else if (isdensecuda) {
1415             PetscCall(MatSeqDenseCUDAInvertFactors_Internal(M));
1416 #endif
1417           } else SETERRQ(PetscObjectComm((PetscObject)M), PETSC_ERR_SUP, "Not implemented for type %s", Stype);
1418           PetscCall(MatDenseGetArrayRead(M, &vals));
1419           PetscCall(PetscArraycpy(SEjinv_arr, vals, subset_size * subset_size));
1420           PetscCall(MatDenseRestoreArrayRead(M, &vals));
1421           PetscCall(MatDestroy(&M));
1422         } else if (scaling) { /* not using deluxe */
1423           Mat          SEj;
1424           Vec          D;
1425           PetscScalar *array;
1426 
1427           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &SEj));
1428           PetscCall(VecGetArray(Dall, &array));
1429           PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, subset_size, array + cum, &D));
1430           PetscCall(VecRestoreArray(Dall, &array));
1431           PetscCall(VecShift(D, -1.));
1432           PetscCall(MatDiagonalScale(SEj, D, D));
1433           PetscCall(MatDestroy(&SEj));
1434           PetscCall(VecDestroy(&D));
1435           PetscCall(PetscArraycpy(SEj_arr, work, subset_size * subset_size));
1436         }
1437       }
1438       cum += subset_size;
1439       cum2 += subset_size * (size_schur + 1);
1440       SEj_arr += subset_size * subset_size;
1441       if (SEjinv_arr) SEjinv_arr += subset_size * subset_size;
1442     }
1443     if (sub_schurs->gdsw) PetscCall(MatDestroySubMatrices(sub_schurs->n_subs, &gdswA));
1444     PetscCall(MatDenseRestoreArrayRead(S_all, &rS_data));
1445     PetscCall(MatSeqAIJRestoreArray(sub_schurs->S_Ej_all, &SEj_arr));
1446     if (sub_schurs->sum_S_Ej_inv_all) PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all, &SEjinv_arr));
1447     if (solver_S) PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));
1448 
1449     /* may prevent from unneeded copies, since MUMPS or MKL_Pardiso always use CPU memory
1450        however, preliminary tests indicate using GPUs is still faster in the solve phase */
1451 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
1452     if (reuse_solvers) {
1453       Mat                  St;
1454       MatFactorSchurStatus st;
1455 
1456       flg = PETSC_FALSE;
1457       PetscCall(PetscOptionsGetBool(NULL, sub_schurs->prefix, "-sub_schurs_schur_pin_to_cpu", &flg, NULL));
1458       PetscCall(MatFactorGetSchurComplement(F, &St, &st));
1459       PetscCall(MatBindToCPU(St, flg));
1460       PetscCall(MatFactorRestoreSchurComplement(F, &St, st));
1461     }
1462 #endif
1463 
1464     schur_factor = NULL;
1465     if (compute_Stilda && size_active_schur) {
1466       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1467         PetscCall(MatSeqAIJGetArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1468         PetscCall(PetscArraycpy(SEjinv_arr, work, size_schur * size_schur));
1469         PetscCall(MatSeqAIJRestoreArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1470       } else {
1471         Mat S_all_inv = NULL;
1472 
1473         if (solver_S && !sub_schurs->gdsw) {
1474           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1475              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 */
1476           if (factor_workaround) { /* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1477             PetscScalar *data;
1478             PetscInt     nd = 0;
1479 
1480             PetscCheck(use_potr, PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor update not yet implemented for non SPD matrices");
1481             PetscCall(MatFactorGetSchurComplement(F, &S_all_inv, NULL));
1482             PetscCall(MatDenseGetArray(S_all_inv, &data));
1483             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1484               PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
1485             }
1486 
1487             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
1488             if (schur_has_vertices) {
1489               Mat          M;
1490               PetscScalar *tdata;
1491               PetscInt     nv = 0, news;
1492 
1493               PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &nv));
1494               news = size_active_schur + nv;
1495               PetscCall(PetscCalloc1(news * news, &tdata));
1496               for (i = 0; i < size_active_schur; i++) {
1497                 PetscCall(PetscArraycpy(tdata + i * (news + 1), data + i * (size_schur + 1), size_active_schur - i));
1498                 PetscCall(PetscArraycpy(tdata + i * (news + 1) + size_active_schur - i, data + i * size_schur + size_active_schur + nd, nv));
1499               }
1500               for (i = 0; i < nv; i++) {
1501                 PetscInt k = i + size_active_schur;
1502                 PetscCall(PetscArraycpy(tdata + k * (news + 1), data + (k + nd) * (size_schur + 1), nv - i));
1503               }
1504 
1505               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, news, news, tdata, &M));
1506               PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE));
1507               PetscCall(MatCholeskyFactor(M, NULL, NULL));
1508               /* save the factors */
1509               cum = 0;
1510               PetscCall(PetscMalloc1((size_active_schur * (size_active_schur + 1)) / 2 + nd, &schur_factor));
1511               for (i = 0; i < size_active_schur; i++) {
1512                 PetscCall(PetscArraycpy(schur_factor + cum, tdata + i * (news + 1), size_active_schur - i));
1513                 cum += size_active_schur - i;
1514               }
1515               for (i = 0; i < nd; i++) schur_factor[cum + i] = PetscSqrtReal(PetscRealPart(data[(i + size_active_schur) * (size_schur + 1)]));
1516               PetscCall(MatSeqDenseInvertFactors_Private(M));
1517               /* move back just the active dofs to the Schur complement */
1518               for (i = 0; i < size_active_schur; i++) PetscCall(PetscArraycpy(data + i * size_schur, tdata + i * news, size_active_schur));
1519               PetscCall(PetscFree(tdata));
1520               PetscCall(MatDestroy(&M));
1521             } else { /* we can factorize and invert just the activedofs */
1522               Mat          M;
1523               PetscScalar *aux;
1524 
1525               PetscCall(PetscMalloc1(nd, &aux));
1526               for (i = 0; i < nd; i++) aux[i] = 1.0 / data[(i + size_active_schur) * (size_schur + 1)];
1527               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size_active_schur, size_active_schur, data, &M));
1528               PetscCall(MatDenseSetLDA(M, size_schur));
1529               PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE));
1530               PetscCall(MatCholeskyFactor(M, NULL, NULL));
1531               PetscCall(MatSeqDenseInvertFactors_Private(M));
1532               PetscCall(MatDestroy(&M));
1533               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size_schur, nd, data + size_active_schur * size_schur, &M));
1534               PetscCall(MatZeroEntries(M));
1535               PetscCall(MatDestroy(&M));
1536               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nd, size_schur, data + size_active_schur, &M));
1537               PetscCall(MatDenseSetLDA(M, size_schur));
1538               PetscCall(MatZeroEntries(M));
1539               PetscCall(MatDestroy(&M));
1540               for (i = 0; i < nd; i++) data[(i + size_active_schur) * (size_schur + 1)] = aux[i];
1541               PetscCall(PetscFree(aux));
1542             }
1543             PetscCall(MatDenseRestoreArray(S_all_inv, &data));
1544           } else { /* use MatFactor calls to invert S */
1545             PetscCall(MatFactorInvertSchurComplement(F));
1546             PetscCall(MatFactorGetSchurComplement(F, &S_all_inv, NULL));
1547           }
1548         } else if (!sub_schurs->gdsw) { /* we need to invert explicitly since we are not using MatFactor for S */
1549           PetscCall(PetscObjectReference((PetscObject)S_all));
1550           S_all_inv = S_all;
1551           PetscCall(MatDenseGetArray(S_all_inv, &S_data));
1552           PetscCall(PetscBLASIntCast(size_schur, &B_N));
1553           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
1554           if (use_potr) {
1555             PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("L", &B_N, S_data, &B_N, &B_ierr));
1556             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1557             PetscCallBLAS("LAPACKpotri", LAPACKpotri_("L", &B_N, S_data, &B_N, &B_ierr));
1558             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1559           } else if (use_sytr) {
1560             PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, S_data, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
1561             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1562             PetscCallBLAS("LAPACKsytri", LAPACKsytri_("L", &B_N, S_data, &B_N, pivots, Bwork, &B_ierr));
1563             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1564           } else {
1565             PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&B_N, &B_N, S_data, &B_N, pivots, &B_ierr));
1566             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1567             PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, S_data, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
1568             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1569           }
1570           PetscCall(PetscLogFlops(1.0 * size_schur * size_schur * size_schur));
1571           PetscCall(PetscFPTrapPop());
1572           PetscCall(MatDenseRestoreArray(S_all_inv, &S_data));
1573         } else if (sub_schurs->gdsw) {
1574           Mat      tS, tX, SEj, S_II, S_IE, S_EE;
1575           KSP      pS_II;
1576           PC       pS_II_pc;
1577           IS       EE, II;
1578           PetscInt nS;
1579 
1580           PetscCall(MatFactorCreateSchurComplement(F, &tS, NULL));
1581           PetscCall(MatGetSize(tS, &nS, NULL));
1582           PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1583           for (i = 0, cum = 0; i < sub_schurs->n_subs; i++) { /* naive implementation */
1584             PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1585             PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, SEjinv_arr, &SEj));
1586 
1587             PetscCall(ISCreateStride(PETSC_COMM_SELF, subset_size, cum, 1, &EE));
1588             PetscCall(ISComplement(EE, 0, nS, &II));
1589             PetscCall(MatCreateSubMatrix(tS, II, II, MAT_INITIAL_MATRIX, &S_II));
1590             PetscCall(MatCreateSubMatrix(tS, II, EE, MAT_INITIAL_MATRIX, &S_IE));
1591             PetscCall(MatCreateSubMatrix(tS, EE, EE, MAT_INITIAL_MATRIX, &S_EE));
1592             PetscCall(ISDestroy(&II));
1593             PetscCall(ISDestroy(&EE));
1594 
1595             PetscCall(KSPCreate(PETSC_COMM_SELF, &pS_II));
1596             PetscCall(KSPSetNestLevel(pS_II, 1)); /* do not have direct access to a PC to provide the level of nesting of the KSP */
1597             PetscCall(KSPSetType(pS_II, KSPPREONLY));
1598             PetscCall(KSPGetPC(pS_II, &pS_II_pc));
1599             PetscCall(PCSetType(pS_II_pc, PCSVD));
1600             PetscCall(KSPSetOptionsPrefix(pS_II, sub_schurs->prefix));
1601             PetscCall(KSPAppendOptionsPrefix(pS_II, "pseudo_"));
1602             PetscCall(KSPSetOperators(pS_II, S_II, S_II));
1603             PetscCall(MatDestroy(&S_II));
1604             PetscCall(KSPSetFromOptions(pS_II));
1605             PetscCall(KSPSetUp(pS_II));
1606             PetscCall(MatDuplicate(S_IE, MAT_DO_NOT_COPY_VALUES, &tX));
1607             PetscCall(KSPMatSolve(pS_II, S_IE, tX));
1608             PetscCall(KSPDestroy(&pS_II));
1609 
1610             PetscCall(MatTransposeMatMult(S_IE, tX, MAT_REUSE_MATRIX, PETSC_DETERMINE, &SEj));
1611             PetscCall(MatDestroy(&S_IE));
1612             PetscCall(MatDestroy(&tX));
1613             PetscCall(MatAYPX(SEj, -1, S_EE, SAME_NONZERO_PATTERN));
1614             PetscCall(MatDestroy(&S_EE));
1615 
1616             PetscCall(MatDestroy(&SEj));
1617             cum += subset_size;
1618             SEjinv_arr += subset_size * subset_size;
1619           }
1620           PetscCall(MatDestroy(&tS));
1621           PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1622         }
1623         /* S_Ej_tilda_all */
1624         cum = cum2 = 0;
1625         rS_data    = NULL;
1626         if (S_all_inv) PetscCall(MatDenseGetArrayRead(S_all_inv, &rS_data));
1627         PetscCall(MatSeqAIJGetArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1628         for (i = 0; i < sub_schurs->n_subs; i++) {
1629           PetscInt j;
1630 
1631           PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1632           /* get (St^-1)_E */
1633           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1634              will be properly accessed later during adaptive selection */
1635           if (rS_data) {
1636             if (S_lower_triangular) {
1637               PetscInt k;
1638               if (sub_schurs->change) {
1639                 for (k = 0; k < subset_size; k++) {
1640                   for (j = k; j < subset_size; j++) {
1641                     work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1642                     work[j * subset_size + k] = work[k * subset_size + j];
1643                   }
1644                 }
1645               } else {
1646                 for (k = 0; k < subset_size; k++) {
1647                   for (j = k; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1648                 }
1649               }
1650             } else {
1651               PetscInt k;
1652               for (k = 0; k < subset_size; k++) {
1653                 for (j = 0; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
1654               }
1655             }
1656           }
1657           if (sub_schurs->change) {
1658             Mat         change_sub, SEj, T;
1659             PetscScalar val = sub_schurs->gdsw ? PETSC_SMALL : 1. / PETSC_SMALL;
1660 
1661             /* change basis */
1662             PetscCall(KSPGetOperators(sub_schurs->change[i], &change_sub, NULL));
1663             PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, rS_data ? work : SEjinv_arr, &SEj));
1664             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1665               Mat T2;
1666               PetscCall(MatTransposeMatMult(change_sub, SEj, MAT_INITIAL_MATRIX, 1.0, &T2));
1667               PetscCall(MatMatMult(T2, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
1668               PetscCall(MatDestroy(&T2));
1669               PetscCall(MatConvert(T, MATSEQDENSE, MAT_INPLACE_MATRIX, &T));
1670             } else {
1671               PetscCall(MatPtAP(SEj, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
1672             }
1673             PetscCall(MatCopy(T, SEj, SAME_NONZERO_PATTERN));
1674             PetscCall(MatDestroy(&T));
1675             PetscCall(MatZeroRowsColumnsIS(SEj, sub_schurs->change_primal_sub[i], val, NULL, NULL));
1676             PetscCall(MatDestroy(&SEj));
1677           }
1678           if (rS_data) PetscCall(PetscArraycpy(SEjinv_arr, work, subset_size * subset_size));
1679           cum += subset_size;
1680           cum2 += subset_size * (size_schur + 1);
1681           SEjinv_arr += subset_size * subset_size;
1682         }
1683         PetscCall(MatSeqAIJRestoreArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
1684         if (S_all_inv) {
1685           PetscCall(MatDenseRestoreArrayRead(S_all_inv, &rS_data));
1686           if (solver_S) {
1687             if (schur_has_vertices) {
1688               PetscCall(MatFactorRestoreSchurComplement(F, &S_all_inv, MAT_FACTOR_SCHUR_FACTORED));
1689             } else {
1690               PetscCall(MatFactorRestoreSchurComplement(F, &S_all_inv, MAT_FACTOR_SCHUR_INVERTED));
1691             }
1692           }
1693         }
1694         PetscCall(MatDestroy(&S_all_inv));
1695       }
1696 
1697       /* move back factors if needed */
1698       if (schur_has_vertices && factor_workaround && !sub_schurs->gdsw) {
1699         Mat          S_tmp;
1700         PetscInt     nd = 0;
1701         PetscScalar *data;
1702 
1703         PetscCheck(use_potr, PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor update not yet implemented for non SPD matrices");
1704         PetscCheck(solver_S, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
1705         PetscCall(MatFactorGetSchurComplement(F, &S_tmp, NULL));
1706         PetscCall(MatDenseGetArray(S_tmp, &data));
1707         PetscCall(PetscArrayzero(data, size_schur * size_schur));
1708 
1709         if (S_lower_triangular) {
1710           cum = 0;
1711           for (i = 0; i < size_active_schur; i++) {
1712             PetscCall(PetscArraycpy(data + i * (size_schur + 1), schur_factor + cum, size_active_schur - i));
1713             cum += size_active_schur - i;
1714           }
1715         } else {
1716           PetscCall(PetscArraycpy(data, schur_factor, size_schur * size_schur));
1717         }
1718         if (sub_schurs->is_dir) {
1719           PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
1720           for (i = 0; i < nd; i++) data[(i + size_active_schur) * (size_schur + 1)] = schur_factor[cum + i];
1721         }
1722         /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1723              set the diagonal entry of the Schur factor to a very large value */
1724         for (i = size_active_schur + nd; i < size_schur; i++) data[i * (size_schur + 1)] = infty;
1725         PetscCall(MatDenseRestoreArray(S_tmp, &data));
1726         PetscCall(MatFactorRestoreSchurComplement(F, &S_tmp, MAT_FACTOR_SCHUR_FACTORED));
1727       }
1728     } else if (factor_workaround && !sub_schurs->gdsw) { /* we need to eliminate any unneeded coupling */
1729       PetscScalar *data;
1730       PetscInt     nd = 0;
1731 
1732       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1733         PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
1734       }
1735       PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
1736       PetscCall(MatDenseGetArray(S_all, &data));
1737       for (i = 0; i < size_active_schur; i++) PetscCall(PetscArrayzero(data + i * size_schur + size_active_schur, size_schur - size_active_schur));
1738       for (i = size_active_schur + nd; i < size_schur; i++) {
1739         PetscCall(PetscArrayzero(data + i * size_schur + size_active_schur, size_schur - size_active_schur));
1740         data[i * (size_schur + 1)] = infty;
1741       }
1742       PetscCall(MatDenseRestoreArray(S_all, &data));
1743       PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));
1744     }
1745     PetscCall(PetscFree(work));
1746     PetscCall(PetscFree(schur_factor));
1747     PetscCall(VecDestroy(&Dall));
1748   }
1749   PetscCall(ISDestroy(&is_I_layer));
1750   PetscCall(MatDestroy(&S_all));
1751   PetscCall(MatDestroy(&A_BB));
1752   PetscCall(MatDestroy(&A_IB));
1753   PetscCall(MatDestroy(&A_BI));
1754   PetscCall(MatDestroy(&F));
1755 
1756   PetscCall(PetscMalloc1(sub_schurs->n_subs, &nnz));
1757   for (i = 0; i < sub_schurs->n_subs; i++) PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &nnz[i]));
1758   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, sub_schurs->n_subs, nnz, PETSC_OWN_POINTER, &is_I_layer));
1759   PetscCall(MatSetVariableBlockSizes(sub_schurs->S_Ej_all, sub_schurs->n_subs, nnz));
1760   PetscCall(MatAssemblyBegin(sub_schurs->S_Ej_all, MAT_FINAL_ASSEMBLY));
1761   PetscCall(MatAssemblyEnd(sub_schurs->S_Ej_all, MAT_FINAL_ASSEMBLY));
1762   if (compute_Stilda) {
1763     PetscCall(MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_tilda_all, sub_schurs->n_subs, nnz));
1764     PetscCall(MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all, MAT_FINAL_ASSEMBLY));
1765     PetscCall(MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all, MAT_FINAL_ASSEMBLY));
1766     if (deluxe) {
1767       PetscCall(MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_inv_all, sub_schurs->n_subs, nnz));
1768       PetscCall(MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all, MAT_FINAL_ASSEMBLY));
1769       PetscCall(MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all, MAT_FINAL_ASSEMBLY));
1770     }
1771   }
1772   PetscCall(ISDestroy(&is_I_layer));
1773 
1774   /* Get local part of (\sum_j S_Ej) */
1775   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));
1776   PetscCall(VecSet(gstash, 0.0));
1777   PetscCall(MatSeqAIJGetArray(sub_schurs->S_Ej_all, &stasharray));
1778   PetscCall(VecPlaceArray(lstash, stasharray));
1779   PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1780   PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1781   PetscCall(MatSeqAIJRestoreArray(sub_schurs->S_Ej_all, &stasharray));
1782   PetscCall(VecResetArray(lstash));
1783   PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all, &stasharray));
1784   PetscCall(VecPlaceArray(lstash, stasharray));
1785   PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1786   PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1787   PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all, &stasharray));
1788   PetscCall(VecResetArray(lstash));
1789 
1790   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1791   if (compute_Stilda) {
1792     PetscCall(VecSet(gstash, 0.0));
1793     PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &stasharray));
1794     PetscCall(VecPlaceArray(lstash, stasharray));
1795     PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1796     PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1797     PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1798     PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1799     PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &stasharray));
1800     PetscCall(VecResetArray(lstash));
1801     if (deluxe) {
1802       PetscCall(VecSet(gstash, 0.0));
1803       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all, &stasharray));
1804       PetscCall(VecPlaceArray(lstash, stasharray));
1805       PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1806       PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
1807       PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1808       PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
1809       PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all, &stasharray));
1810       PetscCall(VecResetArray(lstash));
1811     } else if (!sub_schurs->gdsw) {
1812       PetscScalar *array;
1813       PetscInt     cum;
1814 
1815       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &array));
1816       cum = 0;
1817       for (i = 0; i < sub_schurs->n_subs; i++) {
1818         PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
1819         PetscCall(PetscBLASIntCast(subset_size, &B_N));
1820         PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
1821         if (use_potr) {
1822           PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("L", &B_N, array + cum, &B_N, &B_ierr));
1823           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1824           PetscCallBLAS("LAPACKpotri", LAPACKpotri_("L", &B_N, array + cum, &B_N, &B_ierr));
1825           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1826         } else if (use_sytr) {
1827           PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, array + cum, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
1828           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1829           PetscCallBLAS("LAPACKsytri", LAPACKsytri_("L", &B_N, array + cum, &B_N, pivots, Bwork, &B_ierr));
1830           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1831         } else {
1832           PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&B_N, &B_N, array + cum, &B_N, pivots, &B_ierr));
1833           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
1834           PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, array + cum, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
1835           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
1836         }
1837         PetscCall(PetscLogFlops(1.0 * subset_size * subset_size * subset_size));
1838         PetscCall(PetscFPTrapPop());
1839         cum += subset_size * subset_size;
1840       }
1841       PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &array));
1842       PetscCall(PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all));
1843       PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_inv_all));
1844       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1845     }
1846   }
1847   PetscCall(VecDestroy(&lstash));
1848   PetscCall(VecDestroy(&gstash));
1849   PetscCall(VecScatterDestroy(&sstash));
1850 
1851   if (matl_dbg_viewer) {
1852     if (sub_schurs->S_Ej_all) {
1853       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->S_Ej_all, "SE"));
1854       PetscCall(MatView(sub_schurs->S_Ej_all, matl_dbg_viewer));
1855     }
1856     if (sub_schurs->sum_S_Ej_all) {
1857       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_all, "SSE"));
1858       PetscCall(MatView(sub_schurs->sum_S_Ej_all, matl_dbg_viewer));
1859     }
1860     if (sub_schurs->sum_S_Ej_inv_all) {
1861       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_inv_all, "SSEm"));
1862       PetscCall(MatView(sub_schurs->sum_S_Ej_inv_all, matl_dbg_viewer));
1863     }
1864     if (sub_schurs->sum_S_Ej_tilda_all) {
1865       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_tilda_all, "SSEt"));
1866       PetscCall(MatView(sub_schurs->sum_S_Ej_tilda_all, matl_dbg_viewer));
1867     }
1868   }
1869 
1870   /* when not explicit, we need to set the factor type */
1871   if (sub_schurs->mat_factor_type == MAT_FACTOR_NONE) sub_schurs->mat_factor_type = sub_schurs->is_hermitian ? MAT_FACTOR_CHOLESKY : MAT_FACTOR_LU;
1872 
1873   /* free workspace */
1874   if (matl_dbg_viewer) PetscCall(PetscViewerFlush(matl_dbg_viewer));
1875   if (sub_schurs->debug) PetscCallMPI(MPI_Barrier(comm_n));
1876   PetscCall(PetscViewerDestroy(&matl_dbg_viewer));
1877   PetscCall(PetscFree2(Bwork, pivots));
1878   PetscCall(PetscCommDestroy(&comm_n));
1879   PetscFunctionReturn(PETSC_SUCCESS);
1880 }
1881 
1882 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, const char *prefix, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc, PetscBool gdsw)
1883 {
1884   IS       *faces, *edges, *all_cc, vertices;
1885   PetscInt  s, i, n_faces, n_edges, n_all_cc;
1886   PetscBool is_sorted, ispardiso, ismumps;
1887 
1888   PetscFunctionBegin;
1889   PetscCall(ISSorted(is_I, &is_sorted));
1890   PetscCheck(is_sorted, PetscObjectComm((PetscObject)is_I), PETSC_ERR_PLIB, "IS for I dofs should be shorted");
1891   PetscCall(ISSorted(is_B, &is_sorted));
1892   PetscCheck(is_sorted, PetscObjectComm((PetscObject)is_B), PETSC_ERR_PLIB, "IS for B dofs should be shorted");
1893 
1894   /* reset any previous data */
1895   PetscCall(PCBDDCSubSchursReset(sub_schurs));
1896 
1897   sub_schurs->gdsw = gdsw;
1898 
1899   /* get index sets for faces and edges (already sorted by global ordering) */
1900   PetscCall(PCBDDCGraphGetCandidatesIS(graph, &n_faces, &faces, &n_edges, &edges, &vertices));
1901   n_all_cc = n_faces + n_edges;
1902   PetscCall(PetscBTCreate(n_all_cc, &sub_schurs->is_edge));
1903   PetscCall(PetscMalloc1(n_all_cc, &all_cc));
1904   n_all_cc = 0;
1905   for (i = 0; i < n_faces; i++) {
1906     PetscCall(ISGetSize(faces[i], &s));
1907     if (!s) continue;
1908     if (copycc) {
1909       PetscCall(ISDuplicate(faces[i], &all_cc[n_all_cc]));
1910     } else {
1911       PetscCall(PetscObjectReference((PetscObject)faces[i]));
1912       all_cc[n_all_cc] = faces[i];
1913     }
1914     n_all_cc++;
1915   }
1916   for (i = 0; i < n_edges; i++) {
1917     PetscCall(ISGetSize(edges[i], &s));
1918     if (!s) continue;
1919     if (copycc) {
1920       PetscCall(ISDuplicate(edges[i], &all_cc[n_all_cc]));
1921     } else {
1922       PetscCall(PetscObjectReference((PetscObject)edges[i]));
1923       all_cc[n_all_cc] = edges[i];
1924     }
1925     PetscCall(PetscBTSet(sub_schurs->is_edge, n_all_cc));
1926     n_all_cc++;
1927   }
1928   PetscCall(PetscObjectReference((PetscObject)vertices));
1929   sub_schurs->is_vertices = vertices;
1930   PetscCall(PCBDDCGraphRestoreCandidatesIS(graph, &n_faces, &faces, &n_edges, &edges, &vertices));
1931   sub_schurs->is_dir = NULL;
1932   PetscCall(PCBDDCGraphGetDirichletDofsB(graph, &sub_schurs->is_dir));
1933 
1934   /* Determine if MatFactor can be used */
1935   PetscCall(PetscStrallocpy(prefix, &sub_schurs->prefix));
1936 #if defined(PETSC_HAVE_MUMPS)
1937   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERMUMPS, sizeof(sub_schurs->mat_solver_type)));
1938 #elif defined(PETSC_HAVE_MKL_PARDISO)
1939   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERMKL_PARDISO, sizeof(sub_schurs->mat_solver_type)));
1940 #else
1941   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERPETSC, sizeof(sub_schurs->mat_solver_type)));
1942 #endif
1943   sub_schurs->mat_factor_type = MAT_FACTOR_NONE;
1944 #if defined(PETSC_USE_COMPLEX)
1945   sub_schurs->is_hermitian = PETSC_FALSE; /* Hermitian Cholesky is not supported by PETSc and external packages */
1946 #else
1947   sub_schurs->is_hermitian = PETSC_TRUE;
1948 #endif
1949   sub_schurs->is_posdef     = PETSC_TRUE;
1950   sub_schurs->is_symmetric  = PETSC_TRUE;
1951   sub_schurs->debug         = PETSC_FALSE;
1952   sub_schurs->restrict_comm = PETSC_FALSE;
1953   PetscOptionsBegin(PetscObjectComm((PetscObject)graph->l2gmap), sub_schurs->prefix, "BDDC sub_schurs options", "PC");
1954   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));
1955   PetscCall(PetscOptionsEnum("-sub_schurs_mat_factor_type", "Factor type to use. Use MAT_FACTOR_NONE for automatic selection", NULL, MatFactorTypes, (PetscEnum)sub_schurs->mat_factor_type, (PetscEnum *)&sub_schurs->mat_factor_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