xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 8d92b15d0a672d41cd20e20bb23f2fc6d8101cba)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <petscblaslapack.h>
4 
5 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt*,PetscInt,PetscBT,PetscInt*,PetscInt*,PetscInt*);
6 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat,PetscBool,MatReuse,Mat*);
7 static PetscErrorCode PCBDDCReuseSolvers_Interior(PC,Vec,Vec);
8 static PetscErrorCode PCBDDCReuseSolvers_Correction(PC,Vec,Vec);
9 
10 /* if v2 is not present, correction is done in-place */
11 #undef __FUNCT__
12 #define __FUNCT__ "PCBDDCReuseSolversBenignAdapt"
13 PetscErrorCode PCBDDCReuseSolversBenignAdapt(PCBDDCReuseSolvers ctx, Vec v, Vec v2, PetscBool sol, PetscBool full)
14 {
15   PetscScalar    *array;
16   PetscScalar    *array2;
17   PetscErrorCode ierr;
18 
19   PetscFunctionBegin;
20   if (!ctx->benign_n) PetscFunctionReturn(0);
21   if (sol && full) {
22     PetscInt n_I,size_schur;
23 
24     /* get sizes */
25     ierr = MatGetSize(ctx->benign_csAIB,&size_schur,NULL);CHKERRQ(ierr);
26     ierr = VecGetSize(v,&n_I);CHKERRQ(ierr);
27     n_I = n_I - size_schur;
28     /* get schur sol from array */
29     ierr = VecGetArray(v,&array);CHKERRQ(ierr);
30     ierr = VecPlaceArray(ctx->benign_dummy_schur_vec,array+n_I);CHKERRQ(ierr);
31     ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
32     /* apply interior sol correction */
33     ierr = MatMultTranspose(ctx->benign_csAIB,ctx->benign_dummy_schur_vec,ctx->benign_corr_work);CHKERRQ(ierr);
34     ierr = VecResetArray(ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
35     ierr = MatMultAdd(ctx->benign_AIIm1ones,ctx->benign_corr_work,v,v);CHKERRQ(ierr);
36   }
37   if (v2) {
38     PetscInt nl;
39 
40     ierr = VecGetArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
41     ierr = VecGetLocalSize(v2,&nl);CHKERRQ(ierr);
42     ierr = VecGetArray(v2,&array2);CHKERRQ(ierr);
43     ierr = PetscMemcpy(array2,array,nl*sizeof(PetscScalar));CHKERRQ(ierr);
44   } else {
45     ierr = VecGetArray(v,&array);CHKERRQ(ierr);
46     array2 = array;
47   }
48   if (!sol) { /* change rhs */
49     PetscInt n;
50     for (n=0;n<ctx->benign_n;n++) {
51       PetscScalar    sum = 0.;
52       const PetscInt *cols;
53       PetscInt       nz,i;
54 
55       ierr = ISGetLocalSize(ctx->benign_zerodiag_subs[n],&nz);CHKERRQ(ierr);
56       ierr = ISGetIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
57       for (i=0;i<nz-1;i++) sum += array[cols[i]];
58 #if defined(PETSC_USE_COMPLEX)
59       sum = -(PetscRealPart(sum)/nz + PETSC_i*(PetscImaginaryPart(sum)/nz));
60 #else
61       sum = -sum/nz;
62 #endif
63       for (i=0;i<nz-1;i++) array2[cols[i]] += sum;
64       ctx->benign_save_vals[n] = array2[cols[nz-1]];
65       array2[cols[nz-1]] = sum;
66       ierr = ISRestoreIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
67     }
68   } else {
69     PetscInt n;
70     for (n=0;n<ctx->benign_n;n++) {
71       PetscScalar    sum = 0.;
72       const PetscInt *cols;
73       PetscInt       nz,i;
74       ierr = ISGetLocalSize(ctx->benign_zerodiag_subs[n],&nz);CHKERRQ(ierr);
75       ierr = ISGetIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
76       for (i=0;i<nz-1;i++) sum += array[cols[i]];
77 #if defined(PETSC_USE_COMPLEX)
78       sum = -(PetscRealPart(sum)/nz + PETSC_i*(PetscImaginaryPart(sum)/nz));
79 #else
80       sum = -sum/nz;
81 #endif
82       for (i=0;i<nz-1;i++) array2[cols[i]] += sum;
83       array2[cols[nz-1]] = ctx->benign_save_vals[n];
84       ierr = ISRestoreIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
85     }
86   }
87   if (v2) {
88     ierr = VecRestoreArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
89     ierr = VecRestoreArray(v2,&array2);CHKERRQ(ierr);
90   } else {
91     ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
92   }
93   if (!sol && full) {
94     Vec      usedv;
95     PetscInt n_I,size_schur;
96 
97     /* get sizes */
98     ierr = MatGetSize(ctx->benign_csAIB,&size_schur,NULL);CHKERRQ(ierr);
99     ierr = VecGetSize(v,&n_I);CHKERRQ(ierr);
100     n_I = n_I - size_schur;
101     /* compute schur rhs correction */
102     if (v2) {
103       usedv = v2;
104     } else {
105       usedv = v;
106     }
107     /* apply schur rhs correction */
108     ierr = MatMultTranspose(ctx->benign_AIIm1ones,usedv,ctx->benign_corr_work);CHKERRQ(ierr);
109     ierr = VecGetArrayRead(usedv,(const PetscScalar**)&array);CHKERRQ(ierr);
110     ierr = VecPlaceArray(ctx->benign_dummy_schur_vec,array+n_I);CHKERRQ(ierr);
111     ierr = VecRestoreArrayRead(usedv,(const PetscScalar**)&array);CHKERRQ(ierr);
112     ierr = MatMultAdd(ctx->benign_csAIB,ctx->benign_corr_work,ctx->benign_dummy_schur_vec,ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
113     ierr = VecResetArray(ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
114   }
115   PetscFunctionReturn(0);
116 }
117 
118 #undef __FUNCT__
119 #define __FUNCT__ "PCBDDCReuseSolvers_Solve_Private"
120 static PetscErrorCode PCBDDCReuseSolvers_Solve_Private(PC pc, Vec rhs, Vec sol, PetscBool transpose, PetscBool full)
121 {
122   PCBDDCReuseSolvers ctx;
123   PetscBool          copy = PETSC_FALSE;
124   PetscErrorCode     ierr;
125 
126   PetscFunctionBegin;
127   ierr = PCShellGetContext(pc,(void **)&ctx);CHKERRQ(ierr);
128   if (full) {
129 #if defined(PETSC_HAVE_MUMPS)
130     ierr = MatMumpsSetIcntl(ctx->F,26,-1);CHKERRQ(ierr);
131 #endif
132 #if defined(PETSC_HAVE_MKL_PARDISO)
133     ierr = MatMkl_PardisoSetCntl(ctx->F,70,0);CHKERRQ(ierr);
134 #endif
135     copy = ctx->has_vertices;
136   } else { /* interior solver */
137 #if defined(PETSC_HAVE_MUMPS)
138     ierr = MatMumpsSetIcntl(ctx->F,26,0);CHKERRQ(ierr);
139 #endif
140 #if defined(PETSC_HAVE_MKL_PARDISO)
141     ierr = MatMkl_PardisoSetCntl(ctx->F,70,1);CHKERRQ(ierr);
142 #endif
143     copy = PETSC_TRUE;
144   }
145   /* copy rhs into factored matrix workspace */
146   if (copy) {
147     PetscInt    n;
148     PetscScalar *array,*array_solver;
149 
150     ierr = VecGetLocalSize(rhs,&n);CHKERRQ(ierr);
151     ierr = VecGetArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
152     ierr = VecGetArray(ctx->rhs,&array_solver);CHKERRQ(ierr);
153     ierr = PetscMemcpy(array_solver,array,n*sizeof(PetscScalar));CHKERRQ(ierr);
154     ierr = VecRestoreArray(ctx->rhs,&array_solver);CHKERRQ(ierr);
155     ierr = VecRestoreArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
156 
157     ierr = PCBDDCReuseSolversBenignAdapt(ctx,ctx->rhs,NULL,PETSC_FALSE,full);CHKERRQ(ierr);
158     if (transpose) {
159       ierr = MatSolveTranspose(ctx->F,ctx->rhs,ctx->sol);CHKERRQ(ierr);
160     } else {
161       ierr = MatSolve(ctx->F,ctx->rhs,ctx->sol);CHKERRQ(ierr);
162     }
163     ierr = PCBDDCReuseSolversBenignAdapt(ctx,ctx->sol,NULL,PETSC_TRUE,full);CHKERRQ(ierr);
164 
165     /* get back data to caller worskpace */
166     ierr = VecGetArrayRead(ctx->sol,(const PetscScalar**)&array_solver);CHKERRQ(ierr);
167     ierr = VecGetArray(sol,&array);CHKERRQ(ierr);
168     ierr = PetscMemcpy(array,array_solver,n*sizeof(PetscScalar));CHKERRQ(ierr);
169     ierr = VecRestoreArray(sol,&array);CHKERRQ(ierr);
170     ierr = VecRestoreArrayRead(ctx->sol,(const PetscScalar**)&array_solver);CHKERRQ(ierr);
171   } else {
172     if (ctx->benign_n) {
173       ierr = PCBDDCReuseSolversBenignAdapt(ctx,rhs,ctx->rhs,PETSC_FALSE,full);CHKERRQ(ierr);
174       if (transpose) {
175         ierr = MatSolveTranspose(ctx->F,ctx->rhs,sol);CHKERRQ(ierr);
176       } else {
177         ierr = MatSolve(ctx->F,ctx->rhs,sol);CHKERRQ(ierr);
178       }
179       ierr = PCBDDCReuseSolversBenignAdapt(ctx,sol,NULL,PETSC_TRUE,full);CHKERRQ(ierr);
180     } else {
181       if (transpose) {
182         ierr = MatSolveTranspose(ctx->F,rhs,sol);CHKERRQ(ierr);
183       } else {
184         ierr = MatSolve(ctx->F,rhs,sol);CHKERRQ(ierr);
185       }
186     }
187   }
188   /* restore defaults */
189 #if defined(PETSC_HAVE_MUMPS)
190   ierr = MatMumpsSetIcntl(ctx->F,26,-1);CHKERRQ(ierr);
191 #endif
192 #if defined(PETSC_HAVE_MKL_PARDISO)
193   ierr = MatMkl_PardisoSetCntl(ctx->F,70,0);CHKERRQ(ierr);
194 #endif
195   PetscFunctionReturn(0);
196 }
197 
198 #undef __FUNCT__
199 #define __FUNCT__ "PCBDDCReuseSolvers_Correction"
200 static PetscErrorCode PCBDDCReuseSolvers_Correction(PC pc, Vec rhs, Vec sol)
201 {
202   PetscErrorCode   ierr;
203 
204   PetscFunctionBegin;
205   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
206   PetscFunctionReturn(0);
207 }
208 
209 #undef __FUNCT__
210 #define __FUNCT__ "PCBDDCReuseSolvers_CorrectionTranspose"
211 static PetscErrorCode PCBDDCReuseSolvers_CorrectionTranspose(PC pc, Vec rhs, Vec sol)
212 {
213   PetscErrorCode   ierr;
214 
215   PetscFunctionBegin;
216   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_TRUE,PETSC_TRUE);CHKERRQ(ierr);
217   PetscFunctionReturn(0);
218 }
219 
220 #undef __FUNCT__
221 #define __FUNCT__ "PCBDDCReuseSolvers_Interior"
222 static PetscErrorCode PCBDDCReuseSolvers_Interior(PC pc, Vec rhs, Vec sol)
223 {
224   PetscErrorCode   ierr;
225 
226   PetscFunctionBegin;
227   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_FALSE,PETSC_FALSE);CHKERRQ(ierr);
228   PetscFunctionReturn(0);
229 }
230 
231 #undef __FUNCT__
232 #define __FUNCT__ "PCBDDCReuseSolvers_InteriorTranspose"
233 static PetscErrorCode PCBDDCReuseSolvers_InteriorTranspose(PC pc, Vec rhs, Vec sol)
234 {
235   PetscErrorCode   ierr;
236 
237   PetscFunctionBegin;
238   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
239   PetscFunctionReturn(0);
240 }
241 
242 #undef __FUNCT__
243 #define __FUNCT__ "PCBDDCReuseSolversReset"
244 static PetscErrorCode PCBDDCReuseSolversReset(PCBDDCReuseSolvers reuse)
245 {
246   PetscInt       i;
247   PetscErrorCode ierr;
248 
249   PetscFunctionBegin;
250   ierr = MatDestroy(&reuse->F);CHKERRQ(ierr);
251   ierr = VecDestroy(&reuse->sol);CHKERRQ(ierr);
252   ierr = VecDestroy(&reuse->rhs);CHKERRQ(ierr);
253   ierr = PCDestroy(&reuse->interior_solver);CHKERRQ(ierr);
254   ierr = PCDestroy(&reuse->correction_solver);CHKERRQ(ierr);
255   ierr = ISDestroy(&reuse->is_R);CHKERRQ(ierr);
256   ierr = ISDestroy(&reuse->is_B);CHKERRQ(ierr);
257   ierr = VecScatterDestroy(&reuse->correction_scatter_B);CHKERRQ(ierr);
258   ierr = VecDestroy(&reuse->sol_B);CHKERRQ(ierr);
259   ierr = VecDestroy(&reuse->rhs_B);CHKERRQ(ierr);
260   for (i=0;i<reuse->benign_n;i++) {
261     ierr = ISDestroy(&reuse->benign_zerodiag_subs[i]);CHKERRQ(ierr);
262   }
263   ierr = PetscFree(reuse->benign_zerodiag_subs);CHKERRQ(ierr);
264   ierr = PetscFree(reuse->benign_save_vals);CHKERRQ(ierr);
265   ierr = MatDestroy(&reuse->benign_csAIB);CHKERRQ(ierr);
266   ierr = MatDestroy(&reuse->benign_AIIm1ones);CHKERRQ(ierr);
267   ierr = VecDestroy(&reuse->benign_corr_work);CHKERRQ(ierr);
268   ierr = VecDestroy(&reuse->benign_dummy_schur_vec);CHKERRQ(ierr);
269   PetscFunctionReturn(0);
270 }
271 
272 #undef __FUNCT__
273 #define __FUNCT__ "PCBDDCComputeExplicitSchur"
274 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
275 {
276   Mat            B, C, D, Bd, Cd, AinvBd;
277   KSP            ksp;
278   PC             pc;
279   PetscBool      isLU, isILU, isCHOL, Bdense, Cdense;
280   PetscReal      fill = 2.0;
281   PetscInt       n_I;
282   PetscMPIInt    size;
283   PetscErrorCode ierr;
284 
285   PetscFunctionBegin;
286   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);CHKERRQ(ierr);
287   if (size != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not for parallel matrices");
288   if (reuse == MAT_REUSE_MATRIX) {
289     PetscBool Sdense;
290 
291     ierr = PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense);CHKERRQ(ierr);
292     if (!Sdense) SETERRQ(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"S should dense");
293   }
294   ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
295   ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
296   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
297   ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
298   ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
299   ierr = PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);CHKERRQ(ierr);
300   ierr = PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);CHKERRQ(ierr);
301   ierr = PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);CHKERRQ(ierr);
302   ierr = MatGetSize(B,&n_I,NULL);CHKERRQ(ierr);
303   if (n_I) {
304     if (!Bdense) {
305       ierr = MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
306     } else {
307       Bd = B;
308     }
309 
310     if (isLU || isILU || isCHOL) {
311       Mat fact;
312       ierr = KSPSetUp(ksp);CHKERRQ(ierr);
313       ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
314       ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
315       ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
316     } else {
317       PetscBool ex = PETSC_TRUE;
318 
319       if (ex) {
320         Mat Ainvd;
321 
322         ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
323         ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
324         ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
325       } else {
326         Vec         sol,rhs;
327         PetscScalar *arrayrhs,*arraysol;
328         PetscInt    i,nrhs,n;
329 
330         ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
331         ierr = MatGetSize(Bd,&n,&nrhs);CHKERRQ(ierr);
332         ierr = MatDenseGetArray(Bd,&arrayrhs);CHKERRQ(ierr);
333         ierr = MatDenseGetArray(AinvBd,&arraysol);CHKERRQ(ierr);
334         ierr = KSPGetSolution(ksp,&sol);CHKERRQ(ierr);
335         ierr = KSPGetRhs(ksp,&rhs);CHKERRQ(ierr);
336         for (i=0;i<nrhs;i++) {
337           ierr = VecPlaceArray(rhs,arrayrhs+i*n);CHKERRQ(ierr);
338           ierr = VecPlaceArray(sol,arraysol+i*n);CHKERRQ(ierr);
339           ierr = KSPSolve(ksp,rhs,sol);CHKERRQ(ierr);
340           ierr = VecResetArray(rhs);CHKERRQ(ierr);
341           ierr = VecResetArray(sol);CHKERRQ(ierr);
342         }
343         ierr = MatDenseRestoreArray(Bd,&arrayrhs);CHKERRQ(ierr);
344         ierr = MatDenseRestoreArray(AinvBd,&arrayrhs);CHKERRQ(ierr);
345       }
346     }
347     if (!Bdense & !issym) {
348       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
349     }
350 
351     if (!issym) {
352       if (!Cdense) {
353         ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
354       } else {
355         Cd = C;
356       }
357       ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
358       if (!Cdense) {
359         ierr = MatDestroy(&Cd);CHKERRQ(ierr);
360       }
361     } else {
362       ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
363       if (!Bdense) {
364         ierr = MatDestroy(&Bd);CHKERRQ(ierr);
365       }
366     }
367     ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
368   }
369 
370   if (D) {
371     Mat       Dd;
372     PetscBool Ddense;
373 
374     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
375     if (!Ddense) {
376       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
377     } else {
378       Dd = D;
379     }
380     if (n_I) {
381       ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
382     } else {
383       if (reuse == MAT_INITIAL_MATRIX) {
384         ierr = MatDuplicate(Dd,MAT_COPY_VALUES,S);CHKERRQ(ierr);
385       } else {
386         ierr = MatCopy(Dd,*S,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
387       }
388     }
389     if (!Ddense) {
390       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
391     }
392   } else {
393     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
394   }
395   PetscFunctionReturn(0);
396 }
397 
398 #undef __FUNCT__
399 #define __FUNCT__ "PCBDDCSubSchursSetUp"
400 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)
401 {
402   Mat                    F,A_II,A_IB,A_BI,A_BB,AE_II;
403   Mat                    S_all;
404   Mat                    global_schur_subsets,work_mat,*submats;
405   ISLocalToGlobalMapping l2gmap_subsets;
406   IS                     is_I,is_I_layer;
407   IS                     all_subsets,all_subsets_mult,all_subsets_n;
408   PetscInt               *nnz,*all_local_idx_N;
409   PetscInt               *auxnum1,*auxnum2;
410   PetscInt               i,subset_size,max_subset_size;
411   PetscInt               n_B,extra,local_size,global_size;
412   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
413   PetscScalar            *Bwork;
414   PetscSubcomm           subcomm;
415   PetscMPIInt            color,rank;
416   MPI_Comm               comm_n;
417   PetscBool              deluxe = PETSC_TRUE, use_getr = PETSC_FALSE;
418   PetscErrorCode         ierr;
419 
420   PetscFunctionBegin;
421   /* update info in sub_schurs */
422   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
423   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
424   sub_schurs->is_hermitian = PETSC_FALSE;
425   sub_schurs->is_posdef = PETSC_FALSE;
426   if (Ain) {
427     PetscBool isseqaij;
428     /* determine if we are dealing with hermitian positive definite problems */
429 #if !defined(PETSC_USE_COMPLEX)
430     if (Ain->symmetric_set) sub_schurs->is_hermitian = Ain->symmetric;
431 #else
432     if (Ain->hermitian_set) sub_schurs->is_hermitian = Ain->hermitian;
433 #endif
434     if (Ain->spd_set) sub_schurs->is_posdef = Ain->spd;
435 
436     /* check */
437     ierr = PetscObjectTypeCompare((PetscObject)Ain,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
438     if (compute_Stilda && (!Ain->hermitian_set || !Ain->spd_set)) { /* these are lazy checks, maybe I should throw an error if they are not set */
439       PetscInt lsize;
440 
441       ierr = MatGetSize(Ain,&lsize,NULL);CHKERRQ(ierr);
442       if (lsize) {
443         PetscScalar val;
444         PetscReal   norm;
445         Vec         vec1,vec2,vec3;
446 
447         ierr = MatCreateVecs(Ain,&vec1,&vec2);CHKERRQ(ierr);
448         ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
449         ierr = MatMult(Ain,vec1,vec2);CHKERRQ(ierr);
450         if (!Ain->spd_set && !benign_trick) {
451           ierr = VecDot(vec1,vec2,&val);CHKERRQ(ierr);
452           if (PetscRealPart(val) > 0. && PetscAbsReal(PetscImaginaryPart(val)) < PETSC_SMALL) sub_schurs->is_posdef = PETSC_TRUE;
453         }
454         if (!Ain->hermitian_set) {
455           ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
456 #if !defined(PETSC_USE_COMPLEX)
457           ierr = MatMultTranspose(Ain,vec1,vec3);CHKERRQ(ierr);
458 #else
459           ierr = MatMultHermitianTranspose(Ain,vec1,vec3);CHKERRQ(ierr);
460 #endif
461           ierr = VecAXPY(vec3,-1.0,vec2);CHKERRQ(ierr);
462           ierr = VecNorm(vec3,NORM_INFINITY,&norm);CHKERRQ(ierr);
463           if (!Ain->hermitian_set) {
464             if (norm > PetscSqrtReal(PETSC_SMALL)) {
465               sub_schurs->is_hermitian = PETSC_FALSE;
466             } else {
467               sub_schurs->is_hermitian = PETSC_TRUE;
468             }
469           }
470           ierr = VecDestroy(&vec3);CHKERRQ(ierr);
471         }
472         ierr = VecDestroy(&vec1);CHKERRQ(ierr);
473         ierr = VecDestroy(&vec2);CHKERRQ(ierr);
474       } else {
475         sub_schurs->is_hermitian = PETSC_TRUE;
476         sub_schurs->is_posdef = PETSC_TRUE;
477       }
478     }
479     if (isseqaij) {
480       ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
481       sub_schurs->A = Ain;
482     } else {
483       ierr = MatConvert(Ain,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
484     }
485   }
486 
487   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
488   sub_schurs->S = Sin;
489   if (sub_schurs->schur_explicit) {
490     sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
491   }
492 
493   /* preliminary checks */
494   if (!sub_schurs->schur_explicit && compute_Stilda) SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS and/or MKL_PARDISO");
495 
496   /* restrict work on active processes */
497   color = 0;
498   if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
499   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
500   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
501   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
502   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
503   ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
504   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
505   if (!sub_schurs->n_subs) {
506     ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
507     PetscFunctionReturn(0);
508   }
509   /* ierr = PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);CHKERRQ(ierr); */
510 
511   /* get Schur complement matrices */
512   if (!sub_schurs->schur_explicit) {
513     Mat       tA_IB,tA_BI,tA_BB;
514     PetscBool isseqsbaij;
515     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
516     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);CHKERRQ(ierr);
517     if (isseqsbaij) {
518       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
519       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
520       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
521     } else {
522       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
523       A_BB = tA_BB;
524       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
525       A_IB = tA_IB;
526       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
527       A_BI = tA_BI;
528     }
529   } else {
530     A_II = NULL;
531     A_IB = NULL;
532     A_BI = NULL;
533     A_BB = NULL;
534   }
535   S_all = NULL;
536 
537   /* determine interior problems */
538   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
539   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
540     PetscBT                touched;
541     const PetscInt*        idx_B;
542     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
543 
544     if (!xadj || !adjncy) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
545     /* get sizes */
546     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
547     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
548 
549     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
550     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
551     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
552 
553     /* all boundary dofs must be skipped when adding layers */
554     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
555     for (j=0;j<n_B;j++) {
556       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
557     }
558     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
559     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
560 
561     /* add prescribed number of layers of dofs */
562     n_local_dofs = n_B;
563     n_prev_added = n_B;
564     for (layer=0;layer<nlayers;layer++) {
565       PetscInt n_added;
566       if (n_local_dofs == n_I+n_B) break;
567       if (n_local_dofs > n_I+n_B) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error querying layer %D. Out of bound access (%D > %D)",layer,n_local_dofs,n_I+n_B);
568       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
569       n_prev_added = n_added;
570       n_local_dofs += n_added;
571       if (!n_added) break;
572     }
573     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
574 
575     /* IS for I layer dofs in original numbering */
576     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I),n_local_dofs-n_B,local_numbering+n_B,PETSC_COPY_VALUES,&is_I_layer);CHKERRQ(ierr);
577     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
578     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
579     /* IS for I layer dofs in I numbering */
580     if (!sub_schurs->schur_explicit) {
581       ISLocalToGlobalMapping ItoNmap;
582       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
583       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
584       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
585 
586       /* II block */
587       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
588     }
589   } else {
590     PetscInt n_I;
591 
592     /* IS for I dofs in original numbering */
593     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
594     is_I_layer = sub_schurs->is_I;
595 
596     /* IS for I dofs in I numbering (strided 1) */
597     if (!sub_schurs->schur_explicit) {
598       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
599       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
600 
601       /* II block is the same */
602       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
603       AE_II = A_II;
604     }
605   }
606 
607   /* Get info on subset sizes and sum of all subsets sizes */
608   max_subset_size = 0;
609   local_size = 0;
610   for (i=0;i<sub_schurs->n_subs;i++) {
611     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
612     max_subset_size = PetscMax(subset_size,max_subset_size);
613     local_size += subset_size;
614   }
615 
616   /* Work arrays for local indices */
617   extra = 0;
618   ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
619   if (sub_schurs->schur_explicit && is_I_layer) {
620     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
621   }
622   ierr = PetscMalloc1(n_B+extra,&all_local_idx_N);CHKERRQ(ierr);
623   if (extra) {
624     const PetscInt *idxs;
625     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
626     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
627     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
628   }
629   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
630   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum1);CHKERRQ(ierr);
631   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
632 
633   /* Get local indices in local numbering */
634   local_size = 0;
635   for (i=0;i<sub_schurs->n_subs;i++) {
636     PetscInt j;
637     const    PetscInt *idxs;
638 
639     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
640     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
641     /* start (smallest in global ordering) and multiplicity */
642     auxnum1[i] = idxs[0];
643     auxnum2[i] = subset_size;
644     /* subset indices in local numbering */
645     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
646     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
647     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
648     local_size += subset_size;
649   }
650 
651   /* allocate extra workspace needed only for GETRI */
652   Bwork = NULL;
653   pivots = NULL;
654   if (local_size && !benign_trick && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
655     PetscScalar lwork;
656 
657     use_getr = PETSC_TRUE;
658     B_lwork = -1;
659     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
660     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
661     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,Bwork,&B_N,pivots,&lwork,&B_lwork,&B_ierr));
662     ierr = PetscFPTrapPop();CHKERRQ(ierr);
663     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
664     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
665     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
666   }
667 
668   /* prepare parallel matrices for summing up properly schurs on subsets */
669   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);CHKERRQ(ierr);
670   ierr = ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);CHKERRQ(ierr);
671   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
672   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);CHKERRQ(ierr);
673   ierr = PCBDDCSubsetNumbering(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);CHKERRQ(ierr);
674   ierr = ISDestroy(&all_subsets);CHKERRQ(ierr);
675   ierr = ISDestroy(&all_subsets_mult);CHKERRQ(ierr);
676   ierr = ISGetLocalSize(all_subsets_n,&i);CHKERRQ(ierr);
677   if (i != local_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",i,local_size);
678   ierr = ISLocalToGlobalMappingCreateIS(all_subsets_n,&l2gmap_subsets);CHKERRQ(ierr);
679   ierr = MatCreateIS(comm_n,1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,NULL,&work_mat);CHKERRQ(ierr);
680   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
681   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
682   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
683   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
684 
685   /* subset indices in local boundary numbering */
686   if (!sub_schurs->is_Ej_all) {
687     PetscInt *all_local_idx_B;
688 
689     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
690     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
691     if (subset_size != local_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %D != %D\n",subset_size,local_size);
692     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
693   }
694 
695   if (change) {
696     ISLocalToGlobalMapping BtoS;
697     IS                     change_primal_B;
698     IS                     change_primal_all;
699 
700     if (sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
701     if (sub_schurs->change) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
702     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change_primal_sub);CHKERRQ(ierr);
703     for (i=0;i<sub_schurs->n_subs;i++) {
704       ISLocalToGlobalMapping NtoS;
705       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);CHKERRQ(ierr);
706       ierr = ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
707       ierr = ISLocalToGlobalMappingDestroy(&NtoS);CHKERRQ(ierr);
708     }
709     ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);CHKERRQ(ierr);
710     ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);CHKERRQ(ierr);
711     ierr = ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);CHKERRQ(ierr);
712     ierr = ISLocalToGlobalMappingDestroy(&BtoS);CHKERRQ(ierr);
713     ierr = ISDestroy(&change_primal_B);CHKERRQ(ierr);
714     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change);CHKERRQ(ierr);
715     for (i=0;i<sub_schurs->n_subs;i++) {
716       Mat change_sub;
717 
718       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
719       ierr = KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);CHKERRQ(ierr);
720       ierr = KSPSetType(sub_schurs->change[i],KSPPREONLY);CHKERRQ(ierr);
721       if (!sub_schurs->change_with_qr) {
722         ierr = MatGetSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
723       } else {
724         Mat change_subt;
725         ierr = MatGetSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);CHKERRQ(ierr);
726         ierr = MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
727         ierr = MatDestroy(&change_subt);CHKERRQ(ierr);
728       }
729       ierr = KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);CHKERRQ(ierr);
730       ierr = MatDestroy(&change_sub);CHKERRQ(ierr);
731       ierr = KSPSetOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");CHKERRQ(ierr);
732     }
733     ierr = ISDestroy(&change_primal_all);CHKERRQ(ierr);
734   }
735 
736   /* Local matrix of all local Schur on subsets (transposed) */
737   if (!sub_schurs->S_Ej_all) {
738     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
739     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
740     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
741     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
742   }
743 
744   /* Compute Schur complements explicitly */
745   F = NULL;
746   if (!sub_schurs->schur_explicit) { /* this code branch is used when MatFactor with Schur complemnent support is not present; it is not very efficient, unless the economic version of the scaling is required */
747     Mat         S_Ej_expl;
748     PetscScalar *work;
749     PetscInt    j,*dummy_idx;
750     PetscBool   Sdense;
751 
752     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
753     local_size = 0;
754     for (i=0;i<sub_schurs->n_subs;i++) {
755       IS  is_subset_B;
756       Mat AE_EE,AE_IE,AE_EI,S_Ej;
757 
758       /* subsets in original and boundary numbering */
759       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
760       /* EE block */
761       ierr = MatGetSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
762       /* IE block */
763       ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
764       /* EI block */
765       if (sub_schurs->is_hermitian) {
766         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
767       } else {
768         ierr = MatGetSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
769       }
770       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
771       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
772       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
773       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
774       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
775       if (AE_II == A_II) { /* we can reuse the same ksp */
776         KSP ksp;
777         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
778         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
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         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
787         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
788         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
789         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
790         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
791         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
792         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
793         if (!ispcnone) {
794           PCType pc_type;
795           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
796           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
797         } else {
798           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
799         }
800         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
801         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
802           MatSolverPackage solver=NULL;
803           ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
804           if (solver) {
805             ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
806           }
807         }
808         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
809       }
810       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
811       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
812       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
813       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
814       if (Sdense) {
815         for (j=0;j<subset_size;j++) {
816           dummy_idx[j]=local_size+j;
817         }
818         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
819       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
820       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
821       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
822       local_size += subset_size;
823     }
824     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
825     /* free */
826     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
827     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
828     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
829   } else {
830     Mat         A,cs_AIB_mat = NULL,benign_AIIm1_ones_mat = NULL;
831     Vec         Dall = NULL;
832     IS          is_A_all,*is_p_r = NULL;
833     PetscScalar *work,*S_data,*schur_factor,infty = PETSC_MAX_REAL;
834     PetscInt    n,n_I,*dummy_idx,size_schur,size_active_schur,cum,cum2;
835     PetscBool   economic,solver_S,S_lower_triangular = PETSC_FALSE,factor_workaround;
836     char        solver[256];
837 
838     /* get sizes */
839     n_I = 0;
840     if (is_I_layer) {
841       ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
842     }
843     economic = PETSC_FALSE;
844     ierr = ISGetLocalSize(sub_schurs->is_I,&cum);CHKERRQ(ierr);
845     if (cum != n_I) economic = PETSC_TRUE;
846     ierr = MatGetLocalSize(sub_schurs->A,&n,NULL);CHKERRQ(ierr);
847     size_active_schur = local_size;
848 
849     /* import scaling vector (wrong formulation if we have 3D edges) */
850     if (scaling && compute_Stilda) {
851       const PetscScalar *array;
852       PetscScalar       *array2;
853       const PetscInt    *idxs;
854       PetscInt          i;
855 
856       ierr = ISGetIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
857       ierr = VecCreateSeq(PETSC_COMM_SELF,size_active_schur,&Dall);CHKERRQ(ierr);
858       ierr = VecGetArrayRead(scaling,&array);CHKERRQ(ierr);
859       ierr = VecGetArray(Dall,&array2);CHKERRQ(ierr);
860       for (i=0;i<size_active_schur;i++) array2[i] = array[idxs[i]];
861       ierr = VecRestoreArray(Dall,&array2);CHKERRQ(ierr);
862       ierr = VecRestoreArrayRead(scaling,&array);CHKERRQ(ierr);
863       ierr = ISRestoreIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
864       deluxe = PETSC_FALSE;
865     }
866 
867     /* size active schurs does not count any dirichlet or vertex dof on the interface */
868     cum = n_I+size_active_schur;
869     if (sub_schurs->is_dir) {
870       const PetscInt* idxs;
871       PetscInt        n_dir;
872 
873       ierr = ISGetLocalSize(sub_schurs->is_dir,&n_dir);CHKERRQ(ierr);
874       ierr = ISGetIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
875       ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_dir*sizeof(PetscInt));CHKERRQ(ierr);
876       ierr = ISRestoreIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
877       cum += n_dir;
878     }
879     factor_workaround = PETSC_FALSE;
880     /* include the primal vertices in the Schur complement */
881     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
882       PetscInt n_v;
883 
884       ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
885       if (n_v) {
886         const PetscInt* idxs;
887 
888         ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
889         ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_v*sizeof(PetscInt));CHKERRQ(ierr);
890         ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
891         cum += n_v;
892         factor_workaround = PETSC_TRUE;
893       }
894     }
895     size_schur = cum - n_I;
896     ierr = ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);CHKERRQ(ierr);
897     /* get working mat (TODO: factorize without actually permuting)  */
898     if (cum == n) {
899       ierr = ISSetPermutation(is_A_all);CHKERRQ(ierr);
900       ierr = MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
901     } else {
902       ierr = MatGetSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
903     }
904     ierr = MatSetOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
905 
906     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
907        n^2 instead of n^1.5 or something. This is a workaround */
908     if (benign_n) {
909       Vec                    v;
910       ISLocalToGlobalMapping N_to_reor;
911       IS                     is_p0,is_p0_p;
912       PetscScalar            *cs_AIB,*AIIm1_data;
913       PetscInt               sizeA;
914 
915       ierr = ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);CHKERRQ(ierr);
916       ierr = ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
917       ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);CHKERRQ(ierr);
918       ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
919       ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
920       ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
921       ierr = MatCreateSeqDense(PETSC_COMM_SELF,sizeA,benign_n,NULL,&benign_AIIm1_ones_mat);CHKERRQ(ierr);
922       ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,benign_n,NULL,&cs_AIB_mat);CHKERRQ(ierr);
923       ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
924       ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
925       ierr = PetscMalloc1(benign_n,&is_p_r);CHKERRQ(ierr);
926       /* compute colsum of A_IB restricted to pressures */
927       for (i=0;i<benign_n;i++) {
928         Vec            benign_AIIm1_ones;
929         PetscScalar    *array;
930         const PetscInt *idxs;
931         PetscInt       j,nz;
932 
933         ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);CHKERRQ(ierr);
934         ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
935         ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
936         for (j=0;j<nz;j++) AIIm1_data[idxs[j]+sizeA*i] = 1.;
937         ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
938         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
939         ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
940         ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
941         ierr = VecGetArray(v,&array);CHKERRQ(ierr);
942         for (j=0;j<size_schur;j++) {
943 #if defined(PETSC_USE_COMPLEX)
944           cs_AIB[i*size_schur + j] = (PetscRealPart(array[j+n_I])/nz + PETSC_i*(PetscImaginaryPart(array[j+n_I])/nz));
945 #else
946           cs_AIB[i*size_schur + j] = array[j+n_I]/nz;
947 #endif
948         }
949         ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
950       }
951       ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
952       ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
953       ierr = VecDestroy(&v);CHKERRQ(ierr);
954       ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);CHKERRQ(ierr);
955       ierr = MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);CHKERRQ(ierr);
956       ierr = ISDestroy(&is_p0_p);CHKERRQ(ierr);
957       ierr = ISLocalToGlobalMappingDestroy(&N_to_reor);CHKERRQ(ierr);
958     }
959     ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_hermitian);CHKERRQ(ierr);
960     ierr = MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
961     ierr = MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
962 #if defined(PETSC_HAVE_MUMPS)
963     ierr = PetscStrcpy(solver,MATSOLVERMUMPS);CHKERRQ(ierr);
964 #else
965     ierr = PetscStrcpy(solver,MATSOLVERMKL_PARDISO);CHKERRQ(ierr);
966 #endif
967     ierr = PetscOptionsGetString(NULL,"sub_schurs_","-mat_solver_package",solver,256,NULL);CHKERRQ(ierr);
968 
969     /* when using the benign subspace trick, the local Schur complements are SPD */
970     if (benign_trick) sub_schurs->is_posdef = PETSC_TRUE;
971 
972     if (n_I) { /* TODO add ordering from options */
973       IS is_schur;
974 
975       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
976         ierr = MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
977       } else {
978         ierr = MatGetFactor(A,solver,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
979       }
980       /* subsets ordered last */
981       ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is_schur);CHKERRQ(ierr);
982       ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
983       ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
984 
985       /* factorization step */
986       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
987         ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
988 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
989         ierr = MatMumpsSetIcntl(F,19,2);CHKERRQ(ierr);
990 #endif
991         if (sub_schurs->is_posdef) {
992           ierr = MatFactorSetSchurComplementSolverType(F,1);CHKERRQ(ierr);
993         } else {
994           ierr = MatFactorSetSchurComplementSolverType(F,2);CHKERRQ(ierr);
995         }
996         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
997         S_lower_triangular = PETSC_TRUE;
998       } else {
999         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
1000 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
1001         ierr = MatMumpsSetIcntl(F,19,3);CHKERRQ(ierr);
1002 #endif
1003         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
1004       }
1005 
1006       /* get explicit Schur Complement computed during numeric factorization */
1007       ierr = MatFactorGetSchurComplement(F,&S_all);CHKERRQ(ierr);
1008       /* we can reuse the solvers if we are not using the economic version */
1009       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
1010       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
1011       solver_S = PETSC_TRUE;
1012 
1013       /* update the Schur complement with the change of basis on the pressures */
1014       if (benign_n) {
1015         PetscScalar *S_data,*cs_AIB,*AIIm1_data;
1016         Vec         v;
1017         PetscInt    sizeA;
1018 
1019         ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1020         ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
1021         ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
1022 #if defined(PETSC_HAVE_MUMPS)
1023         ierr = MatMumpsSetIcntl(F,26,0);CHKERRQ(ierr);
1024 #endif
1025 #if defined(PETSC_HAVE_MKL_PARDISO)
1026         ierr = MatMkl_PardisoSetCntl(F,70,1);CHKERRQ(ierr);
1027 #endif
1028         ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1029         ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1030         for (i=0;i<benign_n;i++) {
1031           Vec            benign_AIIm1_ones;
1032           PetscScalar    *array,sum = 0.,one = 1.;
1033           const PetscInt *idxs;
1034           PetscInt       j,nz;
1035           PetscBLASInt   B_k,B_n;
1036 
1037           ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
1038           ierr = VecCopy(benign_AIIm1_ones,v);CHKERRQ(ierr);
1039           ierr = MatSolve(F,v,benign_AIIm1_ones);CHKERRQ(ierr);
1040           ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
1041           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1042           /* p0 dof (eliminated) is excluded from the sum */
1043           for (j=0;j<nz-1;j++) sum -= AIIm1_data[idxs[j]+sizeA*i];
1044           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1045           ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
1046           ierr = VecGetArray(v,&array);CHKERRQ(ierr);
1047           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
1048           /* cs_AIB already scaled by 1./nz */
1049           B_k = 1;
1050           ierr = PetscBLASIntCast(size_schur,&B_n);CHKERRQ(ierr);
1051           PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
1052           sum  = 1.;
1053           PetscStackCallBLAS("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));
1054           ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
1055           /* set p0 entry of AIIm1_ones to zero */
1056           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1057           for (j=0;j<benign_n;j++) AIIm1_data[idxs[nz-1]+sizeA*j] = 0.;
1058           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1059           ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
1060         }
1061   /* restore defaults */
1062 #if defined(PETSC_HAVE_MUMPS)
1063         ierr = MatMumpsSetIcntl(F,26,-1);CHKERRQ(ierr);
1064 #endif
1065 #if defined(PETSC_HAVE_MKL_PARDISO)
1066         ierr = MatMkl_PardisoSetCntl(F,70,0);CHKERRQ(ierr);
1067 #endif
1068         ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1069         ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1070         ierr = VecDestroy(&v);CHKERRQ(ierr);
1071         ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1072       }
1073       if (!reuse_solvers) {
1074         for (i=0;i<benign_n;i++) {
1075           ierr = ISDestroy(&is_p_r[i]);CHKERRQ(ierr);
1076         }
1077         ierr = PetscFree(is_p_r);CHKERRQ(ierr);
1078         ierr = MatDestroy(&cs_AIB_mat);CHKERRQ(ierr);
1079         ierr = MatDestroy(&benign_AIIm1_ones_mat);CHKERRQ(ierr);
1080       }
1081     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1082       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
1083       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1084       solver_S = PETSC_FALSE;
1085     }
1086 
1087     if (reuse_solvers) {
1088       Mat                A_II,Afake;
1089       Vec                vec1_B;
1090       PCBDDCReuseSolvers msolv_ctx;
1091       PetscInt           n_R;
1092 
1093       if (sub_schurs->reuse_solver) {
1094         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1095       } else {
1096         ierr = PetscNew(&sub_schurs->reuse_solver);CHKERRQ(ierr);
1097       }
1098       msolv_ctx = sub_schurs->reuse_solver;
1099       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1100       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
1101       msolv_ctx->F = F;
1102       ierr = MatCreateVecs(F,&msolv_ctx->sol,NULL);CHKERRQ(ierr);
1103       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1104       {
1105         PetscScalar *array;
1106         PetscInt    n;
1107 
1108         ierr = VecGetLocalSize(msolv_ctx->sol,&n);CHKERRQ(ierr);
1109         ierr = VecGetArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1110         ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);CHKERRQ(ierr);
1111         ierr = VecRestoreArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1112       }
1113       msolv_ctx->has_vertices = factor_workaround;
1114 
1115       /* interior solver */
1116       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);CHKERRQ(ierr);
1117       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
1118       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
1119       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
1120       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);CHKERRQ(ierr);
1121       ierr = PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);CHKERRQ(ierr);
1122 
1123       /* correction solver */
1124       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->correction_solver);CHKERRQ(ierr);
1125       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
1126       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
1127       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);CHKERRQ(ierr);
1128       ierr = PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);CHKERRQ(ierr);
1129 
1130       /* scatter and vecs for Schur complement solver */
1131       ierr = MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);CHKERRQ(ierr);
1132       ierr = MatCreateVecs(sub_schurs->S,&vec1_B,NULL);CHKERRQ(ierr);
1133       if (!factor_workaround) {
1134         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1135         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1136         ierr = PetscObjectReference((PetscObject)is_A_all);CHKERRQ(ierr);
1137         msolv_ctx->is_R = is_A_all;
1138       } else {
1139         IS              is_B_all;
1140         const PetscInt* idxs;
1141         PetscInt        dual,n_v,n;
1142 
1143         ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
1144         dual = size_schur - n_v;
1145         ierr = ISGetLocalSize(is_A_all,&n);CHKERRQ(ierr);
1146         ierr = ISGetIndices(is_A_all,&idxs);CHKERRQ(ierr);
1147         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);CHKERRQ(ierr);
1148         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1149         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1150         ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);CHKERRQ(ierr);
1151         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1152         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1153         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);CHKERRQ(ierr);
1154         ierr = ISRestoreIndices(is_A_all,&idxs);CHKERRQ(ierr);
1155       }
1156       ierr = ISGetLocalSize(msolv_ctx->is_R,&n_R);CHKERRQ(ierr);
1157       ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,n_R,n_R,0,NULL,&Afake);CHKERRQ(ierr);
1158       ierr = PCSetOperators(msolv_ctx->correction_solver,Afake,Afake);CHKERRQ(ierr);
1159       ierr = MatDestroy(&Afake);CHKERRQ(ierr);
1160       ierr = VecDestroy(&vec1_B);CHKERRQ(ierr);
1161 
1162       /* communicate benign info to solver context */
1163       if (benign_n) {
1164         PetscScalar *array;
1165 
1166         msolv_ctx->benign_n = benign_n;
1167         msolv_ctx->benign_zerodiag_subs = is_p_r;
1168         ierr = PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);CHKERRQ(ierr);
1169         msolv_ctx->benign_csAIB = cs_AIB_mat;
1170         ierr = MatCreateVecs(cs_AIB_mat,&msolv_ctx->benign_corr_work,NULL);CHKERRQ(ierr);
1171         ierr = VecGetArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1172         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array,&msolv_ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
1173         ierr = VecRestoreArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1174         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1175       }
1176     }
1177     ierr = MatDestroy(&A);CHKERRQ(ierr);
1178     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
1179 
1180     /* Work arrays */
1181     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
1182 
1183     /* matrices for adaptive selection */
1184     if (compute_Stilda) {
1185       if (!sub_schurs->sum_S_Ej_tilda_all) {
1186         ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1187         ierr = MatSetSizes(sub_schurs->sum_S_Ej_tilda_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
1188         ierr = MatSetType(sub_schurs->sum_S_Ej_tilda_all,MATAIJ);CHKERRQ(ierr);
1189         ierr = MatSeqAIJSetPreallocation(sub_schurs->sum_S_Ej_tilda_all,0,nnz);CHKERRQ(ierr);
1190       }
1191       if (!sub_schurs->sum_S_Ej_inv_all && deluxe) {
1192         ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1193         ierr = MatSetSizes(sub_schurs->sum_S_Ej_inv_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
1194         ierr = MatSetType(sub_schurs->sum_S_Ej_inv_all,MATAIJ);CHKERRQ(ierr);
1195         ierr = MatSeqAIJSetPreallocation(sub_schurs->sum_S_Ej_inv_all,0,nnz);CHKERRQ(ierr);
1196       }
1197     }
1198 
1199     /* S_Ej_all */
1200     cum = cum2 = 0;
1201     ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1202     for (i=0;i<sub_schurs->n_subs;i++) {
1203       PetscInt j;
1204 
1205       /* get S_E */
1206       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1207       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1208         PetscInt k;
1209         for (k=0;k<subset_size;k++) {
1210           for (j=k;j<subset_size;j++) {
1211             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1212             work[j*subset_size+k] = PetscConj(S_data[cum2+k*size_schur+j]);
1213           }
1214         }
1215       } else { /* just copy to workspace */
1216         PetscInt k;
1217         for (k=0;k<subset_size;k++) {
1218           for (j=0;j<subset_size;j++) {
1219             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1220           }
1221         }
1222       }
1223       /* insert S_E values */
1224       for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1225       if (sub_schurs->change) {
1226         Mat            change_sub,SEj,T;
1227 
1228         /* change basis */
1229         ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1230         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1231         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1232           Mat T2;
1233           ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1234           ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1235           ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1236           ierr = MatDestroy(&T2);CHKERRQ(ierr);
1237         } else {
1238           ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1239         }
1240         ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1241         ierr = MatDestroy(&T);CHKERRQ(ierr);
1242         ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1.0,NULL,NULL);CHKERRQ(ierr);
1243         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1244       }
1245       if (deluxe) {
1246         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1247         /* if adaptivity is requested, invert S_E blocks */
1248         if (compute_Stilda) {
1249           ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1250           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1251           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1252             PetscInt k;
1253             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,work,&B_N,&B_ierr));
1254             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1255             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,work,&B_N,&B_ierr));
1256             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1257             for (k=0;k<subset_size;k++) {
1258               for (j=k;j<subset_size;j++) {
1259                 work[j*subset_size+k] = work[k*subset_size+j];
1260               }
1261             }
1262           } else {
1263             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,work,&B_N,pivots,&B_ierr));
1264             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1265             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1266             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1267           }
1268           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1269           ierr = MatSetValues(sub_schurs->sum_S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1270         }
1271       } else if (compute_Stilda) { /* not using deluxe */
1272         Mat         SEj;
1273         Vec         D;
1274         PetscScalar *array;
1275 
1276         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1277         ierr = VecGetArray(Dall,&array);CHKERRQ(ierr);
1278         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,array+cum,&D);CHKERRQ(ierr);
1279         ierr = VecRestoreArray(Dall,&array);CHKERRQ(ierr);
1280         ierr = VecShift(D,-1.);CHKERRQ(ierr);
1281         ierr = MatDiagonalScale(SEj,D,D);CHKERRQ(ierr);
1282         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1283         ierr = VecDestroy(&D);CHKERRQ(ierr);
1284         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1285       }
1286       cum += subset_size;
1287       cum2 += subset_size*(size_schur + 1);
1288     }
1289     ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1290 
1291     if (solver_S) {
1292       ierr = MatFactorRestoreSchurComplement(F,&S_all);CHKERRQ(ierr);
1293     }
1294 
1295     schur_factor = NULL;
1296     if (compute_Stilda && size_active_schur) {
1297 
1298       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1299         PetscInt j;
1300         for (j=0;j<size_schur;j++) dummy_idx[j] = j;
1301         ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,size_schur,dummy_idx,size_schur,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1302       } else {
1303         Mat S_all_inv=NULL;
1304         if (solver_S) { /* use MatFactor calls to invert S */
1305             /* let MatFactor factor the Schur complement */
1306           ierr = MatFactorFactorizeSchurComplement(F);CHKERRQ(ierr);
1307           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1308              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 */
1309           if (factor_workaround) {
1310             PetscScalar *data;
1311             PetscInt nd = 0;
1312 
1313             if (!sub_schurs->is_posdef) {
1314               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1315             }
1316             ierr = MatFactorGetSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1317             ierr = MatDenseGetArray(S_all_inv,&data);CHKERRQ(ierr);
1318             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1319               ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1320             }
1321             ierr = PetscMalloc1((size_active_schur*(size_active_schur+1))/2+nd,&schur_factor);CHKERRQ(ierr);
1322             cum = 0;
1323             for (i=0;i<size_active_schur;i++) {
1324               ierr = PetscMemcpy(schur_factor+cum,data+i*(size_schur+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1325               cum += size_active_schur-i;
1326             }
1327             for (i=0;i<nd;i++) schur_factor[cum+i] = data[(i+size_active_schur)*(size_schur+1)];
1328             /* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1329             ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1330             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1331             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,data,&B_N,&B_ierr));
1332             ierr = PetscFPTrapPop();CHKERRQ(ierr);
1333             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1334             ierr = MatDenseRestoreArray(S_all_inv,&data);CHKERRQ(ierr);
1335           } else {
1336             ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
1337             ierr = MatFactorGetSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1338           }
1339         } else { /* we need to invert explicitly since we are not using MatFactor for S */
1340           ierr = PetscObjectReference((PetscObject)S_all);CHKERRQ(ierr);
1341           S_all_inv = S_all;
1342           ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1343           ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1344           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1345           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1346             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
1347             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1348             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
1349             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1350           } else {
1351             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
1352             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1353             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1354             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1355           }
1356           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1357           ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1358         }
1359         /* S_Ej_tilda_all */
1360         cum = cum2 = 0;
1361         ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1362         for (i=0;i<sub_schurs->n_subs;i++) {
1363           PetscInt j;
1364 
1365           ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1366           /* get (St^-1)_E */
1367           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1368              will be properly accessed later during adaptive selection */
1369           if (S_lower_triangular) {
1370             PetscInt k;
1371             if (sub_schurs->change) {
1372               for (k=0;k<subset_size;k++) {
1373                 for (j=k;j<subset_size;j++) {
1374                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1375                   work[j*subset_size+k] = work[k*subset_size+j];
1376                 }
1377               }
1378             } else {
1379               for (k=0;k<subset_size;k++) {
1380                 for (j=k;j<subset_size;j++) {
1381                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1382                 }
1383               }
1384             }
1385           } else {
1386             PetscInt k;
1387             for (k=0;k<subset_size;k++) {
1388               for (j=0;j<subset_size;j++) {
1389                 work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1390               }
1391             }
1392           }
1393           if (sub_schurs->change) {
1394             Mat change_sub,SEj,T;
1395 
1396             /* change basis */
1397             ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1398             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1399             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1400               Mat T2;
1401               ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1402               ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1403               ierr = MatDestroy(&T2);CHKERRQ(ierr);
1404               ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1405             } else {
1406               ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1407             }
1408             ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1409             ierr = MatDestroy(&T);CHKERRQ(ierr);
1410             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
1411             ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1./PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
1412             ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1413           }
1414           for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1415           ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1416           cum += subset_size;
1417           cum2 += subset_size*(size_schur + 1);
1418         }
1419         ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1420         if (solver_S) {
1421           ierr = MatFactorRestoreSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1422         }
1423         ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
1424       }
1425 
1426       /* move back factors to Schur data into F */
1427       if (factor_workaround) {
1428         Mat S_tmp;
1429         PetscInt nv,nd=0;
1430 
1431         if (!solver_S) {
1432           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
1433         }
1434         ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
1435         ierr = MatFactorGetSchurComplement(F,&S_tmp);CHKERRQ(ierr);
1436         if (sub_schurs->is_posdef) {
1437           PetscScalar *data;
1438 
1439           ierr = MatZeroEntries(S_tmp);CHKERRQ(ierr);
1440           ierr = MatDenseGetArray(S_tmp,&data);CHKERRQ(ierr);
1441 
1442           if (S_lower_triangular) {
1443             cum = 0;
1444             for (i=0;i<size_active_schur;i++) {
1445               ierr = PetscMemcpy(data+i*(size_schur+1),schur_factor+cum,(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1446               cum += size_active_schur-i;
1447 	    }
1448           } else {
1449             ierr = PetscMemcpy(data,schur_factor,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1450           }
1451           if (sub_schurs->is_dir) {
1452             ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1453 	    for (i=0;i<nd;i++) {
1454 	      data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
1455 	    }
1456           }
1457           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1458              set the diagonal entry of the Schur factor to a very large value */
1459           for (i=size_active_schur+nd;i<size_schur;i++) {
1460             data[i*(size_schur+1)] = infty;
1461           }
1462           ierr = MatDenseRestoreArray(S_tmp,&data);CHKERRQ(ierr);
1463         } else {
1464           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1465         }
1466         ierr = MatFactorRestoreSchurComplement(F,&S_tmp);CHKERRQ(ierr);
1467       }
1468     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
1469       PetscScalar *data;
1470       PetscInt    nd = 0;
1471 
1472       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1473         ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1474       }
1475       ierr = MatFactorGetSchurComplement(F,&S_all);CHKERRQ(ierr);
1476       ierr = MatDenseGetArray(S_all,&data);CHKERRQ(ierr);
1477       for (i=0;i<size_active_schur;i++) {
1478         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1479       }
1480       for (i=size_active_schur+nd;i<size_schur;i++) {
1481         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1482         data[i*(size_schur+1)] = infty;
1483       }
1484       ierr = MatDenseRestoreArray(S_all,&data);CHKERRQ(ierr);
1485       ierr = MatFactorRestoreSchurComplement(F,&S_all);CHKERRQ(ierr);
1486     }
1487     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
1488     ierr = PetscFree(schur_factor);CHKERRQ(ierr);
1489     ierr = VecDestroy(&Dall);CHKERRQ(ierr);
1490   }
1491   ierr = PetscFree(nnz);CHKERRQ(ierr);
1492   ierr = MatDestroy(&F);CHKERRQ(ierr);
1493   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1494   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
1495   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1496   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1497   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1498   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1499   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1500   if (compute_Stilda) {
1501     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1502     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1503     if (deluxe) {
1504       ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1505       ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1506     }
1507   }
1508 
1509   /* Global matrix of all assembled Schur on subsets */
1510   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
1511   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
1512   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1513 
1514   /* Get local part of (\sum_j S_Ej) */
1515   if (!sub_schurs->sum_S_Ej_all) {
1516     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_INITIAL_MATRIX,&submats);CHKERRQ(ierr);
1517     sub_schurs->sum_S_Ej_all = submats[0];
1518   } else {
1519     ierr = PetscMalloc1(1,&submats);CHKERRQ(ierr);
1520     submats[0] = sub_schurs->sum_S_Ej_all;
1521     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1522   }
1523 
1524   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1525   if (compute_Stilda) {
1526     ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1527     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1528     submats[0] = sub_schurs->sum_S_Ej_tilda_all;
1529     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1530     if (deluxe) {
1531       ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1532       ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1533       submats[0] = sub_schurs->sum_S_Ej_inv_all;
1534       ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1535     } else {
1536       PetscScalar *array;
1537       PetscInt    cum;
1538 
1539       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1540       cum = 0;
1541       for (i=0;i<sub_schurs->n_subs;i++) {
1542         ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1543         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1544         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1545         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
1546         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1547         PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
1548         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1549         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1550         cum += subset_size*subset_size;
1551       }
1552       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1553       ierr = PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1554       ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1555       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1556     }
1557   }
1558 
1559   /* free workspace */
1560   ierr = PetscFree(submats);CHKERRQ(ierr);
1561   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
1562   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
1563   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
1564   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
1565   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
1566   PetscFunctionReturn(0);
1567 }
1568 
1569 #undef __FUNCT__
1570 #define __FUNCT__ "PCBDDCSubSchursInit"
1571 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap)
1572 {
1573   IS              *faces,*edges,*all_cc,vertices;
1574   PetscInt        i,n_faces,n_edges,n_all_cc;
1575   PetscBool       is_sorted;
1576   PetscErrorCode  ierr;
1577 
1578   PetscFunctionBegin;
1579   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
1580   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
1581   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
1582   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
1583 
1584   /* reset any previous data */
1585   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
1586 
1587   /* get index sets for faces and edges (already sorted by global ordering) */
1588   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1589   n_all_cc = n_faces+n_edges;
1590   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
1591   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
1592   for (i=0;i<n_faces;i++) {
1593     all_cc[i] = faces[i];
1594   }
1595   for (i=0;i<n_edges;i++) {
1596     all_cc[n_faces+i] = edges[i];
1597     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
1598   }
1599   ierr = PetscFree(faces);CHKERRQ(ierr);
1600   ierr = PetscFree(edges);CHKERRQ(ierr);
1601   sub_schurs->is_dir = NULL;
1602   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
1603 
1604   /* Determine if MatFactor can be used */
1605   sub_schurs->schur_explicit = PETSC_FALSE;
1606 #if defined(PETSC_HAVE_MUMPS)
1607   sub_schurs->schur_explicit = PETSC_TRUE;
1608 #endif
1609 #if defined(PETSC_HAVE_MKL_PARDISO)
1610   sub_schurs->schur_explicit = PETSC_TRUE;
1611 #endif
1612 
1613   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
1614   sub_schurs->is_I = is_I;
1615   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
1616   sub_schurs->is_B = is_B;
1617   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
1618   sub_schurs->l2gmap = graph->l2gmap;
1619   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
1620   sub_schurs->BtoNmap = BtoNmap;
1621   sub_schurs->n_subs = n_all_cc;
1622   sub_schurs->is_subs = all_cc;
1623   if (!sub_schurs->schur_explicit) { /* sort by local ordering if we are not using MatFactor */
1624     for (i=0;i<sub_schurs->n_subs;i++) {
1625       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
1626     }
1627   }
1628   sub_schurs->is_vertices = vertices;
1629   sub_schurs->S_Ej_all = NULL;
1630   sub_schurs->sum_S_Ej_all = NULL;
1631   sub_schurs->sum_S_Ej_inv_all = NULL;
1632   sub_schurs->sum_S_Ej_tilda_all = NULL;
1633   sub_schurs->is_Ej_all = NULL;
1634   PetscFunctionReturn(0);
1635 }
1636 
1637 #undef __FUNCT__
1638 #define __FUNCT__ "PCBDDCSubSchursCreate"
1639 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1640 {
1641   PCBDDCSubSchurs schurs_ctx;
1642   PetscErrorCode  ierr;
1643 
1644   PetscFunctionBegin;
1645   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
1646   schurs_ctx->n_subs = 0;
1647   *sub_schurs = schurs_ctx;
1648   PetscFunctionReturn(0);
1649 }
1650 
1651 #undef __FUNCT__
1652 #define __FUNCT__ "PCBDDCSubSchursReset"
1653 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1654 {
1655   PetscInt       i;
1656   PetscErrorCode ierr;
1657 
1658   PetscFunctionBegin;
1659   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1660   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1661   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1662   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1663   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1664   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1665   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1666   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1667   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1668   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1669   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1670   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1671   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1672   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1673   for (i=0;i<sub_schurs->n_subs;i++) {
1674     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
1675   }
1676   if (sub_schurs->n_subs) {
1677     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1678   }
1679   if (sub_schurs->reuse_solver) {
1680     ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1681   }
1682   ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1683   if (sub_schurs->change) {
1684     for (i=0;i<sub_schurs->n_subs;i++) {
1685       ierr = KSPDestroy(&sub_schurs->change[i]);CHKERRQ(ierr);
1686       ierr = ISDestroy(&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
1687     }
1688   }
1689   ierr = PetscFree(sub_schurs->change);CHKERRQ(ierr);
1690   ierr = PetscFree(sub_schurs->change_primal_sub);CHKERRQ(ierr);
1691   sub_schurs->n_subs = 0;
1692   PetscFunctionReturn(0);
1693 }
1694 
1695 #undef __FUNCT__
1696 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
1697 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1698 {
1699   PetscInt       i,j,n;
1700   PetscErrorCode ierr;
1701 
1702   PetscFunctionBegin;
1703   n = 0;
1704   for (i=-n_prev;i<0;i++) {
1705     PetscInt start_dof = queue_tip[i];
1706     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1707       PetscInt dof = adjncy[j];
1708       if (!PetscBTLookup(touched,dof)) {
1709         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1710         queue_tip[n] = dof;
1711         n++;
1712       }
1713     }
1714   }
1715   *n_added = n;
1716   PetscFunctionReturn(0);
1717 }
1718