xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 35d705712e4e30cc2db45fcc137e266709f373c9)
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) {
431       sub_schurs->is_hermitian = Ain->symmetric;
432     }
433 #else
434     if (Ain->hermitian_set) {
435       sub_schurs->is_hermitian = Ain->hermitian;
436     }
437 #endif
438     if (Ain->spd_set) {
439       sub_schurs->is_posdef = Ain->spd;
440     }
441 
442     /* check */
443     ierr = PetscObjectTypeCompare((PetscObject)Ain,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
444     if (compute_Stilda && (!Ain->hermitian_set || !Ain->spd_set)) { /* these are lazy checks, maybe I should throw an error if they are not set */
445       PetscInt lsize;
446 
447       ierr = MatGetSize(Ain,&lsize,NULL);CHKERRQ(ierr);
448       if (lsize) {
449         PetscScalar val;
450         PetscReal   norm;
451         Vec         vec1,vec2,vec3;
452 
453         ierr = MatCreateVecs(Ain,&vec1,&vec2);CHKERRQ(ierr);
454         ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
455         ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
456         ierr = MatMult(Ain,vec1,vec2);CHKERRQ(ierr);
457 #if !defined(PETSC_USE_COMPLEX)
458         ierr = MatMultTranspose(Ain,vec1,vec3);CHKERRQ(ierr);
459 #else
460         ierr = MatMultHermitianTranspose(Ain,vec1,vec3);CHKERRQ(ierr);
461 #endif
462         ierr = VecAXPY(vec3,-1.0,vec2);CHKERRQ(ierr);
463         ierr = VecNorm(vec3,NORM_INFINITY,&norm);CHKERRQ(ierr);
464         if (!Ain->hermitian_set) {
465           if (norm > PetscSqrtReal(PETSC_SMALL)) {
466             sub_schurs->is_hermitian = PETSC_FALSE;
467           } else {
468             sub_schurs->is_hermitian = PETSC_TRUE;
469           }
470         }
471         if (!Ain->spd_set && !benign_trick) {
472           ierr = VecDot(vec1,vec2,&val);CHKERRQ(ierr);
473           if (PetscRealPart(val) > 0. && PetscAbsReal(PetscImaginaryPart(val)) < PETSC_SMALL) sub_schurs->is_posdef = PETSC_TRUE;
474         }
475         ierr = VecDestroy(&vec1);CHKERRQ(ierr);
476         ierr = VecDestroy(&vec2);CHKERRQ(ierr);
477         ierr = VecDestroy(&vec3);CHKERRQ(ierr);
478       } else {
479         sub_schurs->is_hermitian = PETSC_TRUE;
480         sub_schurs->is_posdef = PETSC_TRUE;
481       }
482     }
483     if (isseqaij) {
484       ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
485       sub_schurs->A = Ain;
486     } else {
487       ierr = MatConvert(Ain,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
488     }
489   }
490 
491   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
492   sub_schurs->S = Sin;
493   if (sub_schurs->schur_explicit) {
494     sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
495   }
496 
497   /* preliminary checks */
498   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");
499 
500   /* restrict work on active processes */
501   color = 0;
502   if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
503   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
504   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
505   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
506   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
507   ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
508   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
509   if (!sub_schurs->n_subs) {
510     ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
511     PetscFunctionReturn(0);
512   }
513   /* ierr = PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);CHKERRQ(ierr); */
514 
515   /* get Schur complement matrices */
516   if (!sub_schurs->schur_explicit) {
517     Mat       tA_IB,tA_BI,tA_BB;
518     PetscBool isseqsbaij;
519     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
520     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);CHKERRQ(ierr);
521     if (isseqsbaij) {
522       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
523       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
524       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
525     } else {
526       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
527       A_BB = tA_BB;
528       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
529       A_IB = tA_IB;
530       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
531       A_BI = tA_BI;
532     }
533   } else {
534     A_II = NULL;
535     A_IB = NULL;
536     A_BI = NULL;
537     A_BB = NULL;
538   }
539   S_all = NULL;
540 
541   /* determine interior problems */
542   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
543   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
544     PetscBT                touched;
545     const PetscInt*        idx_B;
546     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
547 
548     if (!xadj || !adjncy) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
549     /* get sizes */
550     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
551     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
552 
553     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
554     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
555     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
556 
557     /* all boundary dofs must be skipped when adding layers */
558     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
559     for (j=0;j<n_B;j++) {
560       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
561     }
562     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
563     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
564 
565     /* add prescribed number of layers of dofs */
566     n_local_dofs = n_B;
567     n_prev_added = n_B;
568     for (layer=0;layer<nlayers;layer++) {
569       PetscInt n_added;
570       if (n_local_dofs == n_I+n_B) break;
571       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);
572       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
573       n_prev_added = n_added;
574       n_local_dofs += n_added;
575       if (!n_added) break;
576     }
577     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
578 
579     /* IS for I layer dofs in original numbering */
580     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);
581     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
582     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
583     /* IS for I layer dofs in I numbering */
584     if (!sub_schurs->schur_explicit) {
585       ISLocalToGlobalMapping ItoNmap;
586       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
587       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
588       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
589 
590       /* II block */
591       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
592     }
593   } else {
594     PetscInt n_I;
595 
596     /* IS for I dofs in original numbering */
597     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
598     is_I_layer = sub_schurs->is_I;
599 
600     /* IS for I dofs in I numbering (strided 1) */
601     if (!sub_schurs->schur_explicit) {
602       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
603       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
604 
605       /* II block is the same */
606       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
607       AE_II = A_II;
608     }
609   }
610 
611   /* Get info on subset sizes and sum of all subsets sizes */
612   max_subset_size = 0;
613   local_size = 0;
614   for (i=0;i<sub_schurs->n_subs;i++) {
615     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
616     max_subset_size = PetscMax(subset_size,max_subset_size);
617     local_size += subset_size;
618   }
619 
620   /* Work arrays for local indices */
621   extra = 0;
622   ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
623   if (sub_schurs->schur_explicit && is_I_layer) {
624     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
625   }
626   ierr = PetscMalloc1(n_B+extra,&all_local_idx_N);CHKERRQ(ierr);
627   if (extra) {
628     const PetscInt *idxs;
629     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
630     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
631     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
632   }
633   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
634   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum1);CHKERRQ(ierr);
635   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
636 
637   /* Get local indices in local numbering */
638   local_size = 0;
639   for (i=0;i<sub_schurs->n_subs;i++) {
640     PetscInt j;
641     const    PetscInt *idxs;
642 
643     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
644     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
645     /* start (smallest in global ordering) and multiplicity */
646     auxnum1[i] = idxs[0];
647     auxnum2[i] = subset_size;
648     /* subset indices in local numbering */
649     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
650     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
651     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
652     local_size += subset_size;
653   }
654 
655   /* allocate extra workspace needed only for GETRI */
656   Bwork = NULL;
657   pivots = NULL;
658   if (local_size && !benign_trick && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
659     PetscScalar lwork;
660 
661     use_getr = PETSC_TRUE;
662     B_lwork = -1;
663     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
664     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
665     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,Bwork,&B_N,pivots,&lwork,&B_lwork,&B_ierr));
666     ierr = PetscFPTrapPop();CHKERRQ(ierr);
667     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
668     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
669     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
670   }
671 
672   /* prepare parallel matrices for summing up properly schurs on subsets */
673   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);CHKERRQ(ierr);
674   ierr = ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);CHKERRQ(ierr);
675   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
676   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);CHKERRQ(ierr);
677   ierr = PCBDDCSubsetNumbering(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);CHKERRQ(ierr);
678   ierr = ISDestroy(&all_subsets);CHKERRQ(ierr);
679   ierr = ISDestroy(&all_subsets_mult);CHKERRQ(ierr);
680   ierr = ISGetLocalSize(all_subsets_n,&i);CHKERRQ(ierr);
681   if (i != local_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",i,local_size);
682   ierr = ISLocalToGlobalMappingCreateIS(all_subsets_n,&l2gmap_subsets);CHKERRQ(ierr);
683   ierr = MatCreateIS(comm_n,1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,NULL,&work_mat);CHKERRQ(ierr);
684   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
685   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
686   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
687   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
688 
689   /* subset indices in local boundary numbering */
690   if (!sub_schurs->is_Ej_all) {
691     PetscInt *all_local_idx_B;
692 
693     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
694     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
695     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);
696     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
697   }
698 
699   if (change) {
700     ISLocalToGlobalMapping BtoS;
701     IS                     change_primal_B;
702     IS                     change_primal_all;
703 
704     if (sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
705     if (sub_schurs->change) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
706     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change_primal_sub);CHKERRQ(ierr);
707     for (i=0;i<sub_schurs->n_subs;i++) {
708       ISLocalToGlobalMapping NtoS;
709       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);CHKERRQ(ierr);
710       ierr = ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
711       ierr = ISLocalToGlobalMappingDestroy(&NtoS);CHKERRQ(ierr);
712     }
713     ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);CHKERRQ(ierr);
714     ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);CHKERRQ(ierr);
715     ierr = ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);CHKERRQ(ierr);
716     ierr = ISLocalToGlobalMappingDestroy(&BtoS);CHKERRQ(ierr);
717     ierr = ISDestroy(&change_primal_B);CHKERRQ(ierr);
718     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change);CHKERRQ(ierr);
719     for (i=0;i<sub_schurs->n_subs;i++) {
720       Mat change_sub;
721 
722       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
723       ierr = KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);CHKERRQ(ierr);
724       ierr = KSPSetType(sub_schurs->change[i],KSPPREONLY);CHKERRQ(ierr);
725       if (!sub_schurs->change_with_qr) {
726         ierr = MatGetSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
727       } else {
728         Mat change_subt;
729         ierr = MatGetSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);CHKERRQ(ierr);
730         ierr = MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
731         ierr = MatDestroy(&change_subt);CHKERRQ(ierr);
732       }
733       ierr = KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);CHKERRQ(ierr);
734       ierr = MatDestroy(&change_sub);CHKERRQ(ierr);
735       ierr = KSPSetOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");CHKERRQ(ierr);
736     }
737     ierr = ISDestroy(&change_primal_all);CHKERRQ(ierr);
738   }
739 
740   /* Local matrix of all local Schur on subsets (transposed) */
741   if (!sub_schurs->S_Ej_all) {
742     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
743     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
744     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
745     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
746   }
747 
748   /* Compute Schur complements explicitly */
749   F = NULL;
750   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 */
751     Mat         S_Ej_expl;
752     PetscScalar *work;
753     PetscInt    j,*dummy_idx;
754     PetscBool   Sdense;
755 
756     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
757     local_size = 0;
758     for (i=0;i<sub_schurs->n_subs;i++) {
759       IS  is_subset_B;
760       Mat AE_EE,AE_IE,AE_EI,S_Ej;
761 
762       /* subsets in original and boundary numbering */
763       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
764       /* EE block */
765       ierr = MatGetSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
766       /* IE block */
767       ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
768       /* EI block */
769       if (sub_schurs->is_hermitian) {
770         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
771       } else {
772         ierr = MatGetSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
773       }
774       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
775       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
776       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
777       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
778       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
779       if (AE_II == A_II) { /* we can reuse the same ksp */
780         KSP ksp;
781         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
782         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
783       } else { /* build new ksp object which inherits ksp and pc types from the original one */
784         KSP       origksp,schurksp;
785         PC        origpc,schurpc;
786         KSPType   ksp_type;
787         PetscInt  n_internal;
788         PetscBool ispcnone;
789 
790         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
791         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
792         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
793         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
794         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
795         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
796         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
797         if (!ispcnone) {
798           PCType pc_type;
799           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
800           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
801         } else {
802           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
803         }
804         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
805         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
806           MatSolverPackage solver=NULL;
807           ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
808           if (solver) {
809             ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
810           }
811         }
812         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
813       }
814       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
815       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
816       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
817       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
818       if (Sdense) {
819         for (j=0;j<subset_size;j++) {
820           dummy_idx[j]=local_size+j;
821         }
822         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
823       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
824       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
825       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
826       local_size += subset_size;
827     }
828     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
829     /* free */
830     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
831     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
832     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
833   } else {
834     Mat         A,cs_AIB_mat = NULL,benign_AIIm1_ones_mat = NULL;
835     Vec         Dall = NULL;
836     IS          is_A_all,*is_p_r = NULL;
837     PetscScalar *work,*S_data,*schur_factor,infty = PETSC_MAX_REAL;
838     PetscInt    n,n_I,*dummy_idx,size_schur,size_active_schur,cum,cum2;
839     PetscBool   economic,solver_S,S_lower_triangular = PETSC_FALSE,factor_workaround;
840     char        solver[256];
841 
842     /* get sizes */
843     n_I = 0;
844     if (is_I_layer) {
845       ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
846     }
847     economic = PETSC_FALSE;
848     ierr = ISGetLocalSize(sub_schurs->is_I,&cum);CHKERRQ(ierr);
849     if (cum != n_I) economic = PETSC_TRUE;
850     ierr = MatGetLocalSize(sub_schurs->A,&n,NULL);CHKERRQ(ierr);
851     size_active_schur = local_size;
852 
853     /* import scaling vector (wrong formulation if we have 3D edges) */
854     if (scaling && compute_Stilda) {
855       const PetscScalar *array;
856       PetscScalar       *array2;
857       const PetscInt    *idxs;
858       PetscInt          i;
859 
860       ierr = ISGetIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
861       ierr = VecCreateSeq(PETSC_COMM_SELF,size_active_schur,&Dall);CHKERRQ(ierr);
862       ierr = VecGetArrayRead(scaling,&array);CHKERRQ(ierr);
863       ierr = VecGetArray(Dall,&array2);CHKERRQ(ierr);
864       for (i=0;i<size_active_schur;i++) array2[i] = array[idxs[i]];
865       ierr = VecRestoreArray(Dall,&array2);CHKERRQ(ierr);
866       ierr = VecRestoreArrayRead(scaling,&array);CHKERRQ(ierr);
867       ierr = ISRestoreIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
868       deluxe = PETSC_FALSE;
869     }
870 
871     /* size active schurs does not count any dirichlet or vertex dof on the interface */
872     cum = n_I+size_active_schur;
873     if (sub_schurs->is_dir) {
874       const PetscInt* idxs;
875       PetscInt        n_dir;
876 
877       ierr = ISGetLocalSize(sub_schurs->is_dir,&n_dir);CHKERRQ(ierr);
878       ierr = ISGetIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
879       ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_dir*sizeof(PetscInt));CHKERRQ(ierr);
880       ierr = ISRestoreIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
881       cum += n_dir;
882     }
883     factor_workaround = PETSC_FALSE;
884     /* include the primal vertices in the Schur complement */
885     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
886       PetscInt n_v;
887 
888       ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
889       if (n_v) {
890         const PetscInt* idxs;
891 
892         ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
893         ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_v*sizeof(PetscInt));CHKERRQ(ierr);
894         ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
895         cum += n_v;
896         factor_workaround = PETSC_TRUE;
897       }
898     }
899     size_schur = cum - n_I;
900     ierr = ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);CHKERRQ(ierr);
901     /* get working mat (TODO: factorize without actually permuting)  */
902     if (cum == n) {
903       ierr = ISSetPermutation(is_A_all);CHKERRQ(ierr);
904       ierr = MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
905     } else {
906       ierr = MatGetSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
907     }
908     ierr = MatSetOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
909 
910     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
911        n^2 instead of n^1.5 or something. This is a workaround */
912     if (benign_n) {
913       Vec                    v;
914       ISLocalToGlobalMapping N_to_reor;
915       IS                     is_p0,is_p0_p;
916       PetscScalar            *cs_AIB,*AIIm1_data;
917       PetscInt               sizeA;
918 
919       ierr = ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);CHKERRQ(ierr);
920       ierr = ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
921       ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);CHKERRQ(ierr);
922       ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
923       ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
924       ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
925       ierr = MatCreateSeqDense(PETSC_COMM_SELF,sizeA,benign_n,NULL,&benign_AIIm1_ones_mat);CHKERRQ(ierr);
926       ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,benign_n,NULL,&cs_AIB_mat);CHKERRQ(ierr);
927       ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
928       ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
929       ierr = PetscMalloc1(benign_n,&is_p_r);CHKERRQ(ierr);
930       /* compute colsum of A_IB restricted to pressures */
931       for (i=0;i<benign_n;i++) {
932         Vec            benign_AIIm1_ones;
933         PetscScalar    *array;
934         const PetscInt *idxs;
935         PetscInt       j,nz;
936 
937         ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);CHKERRQ(ierr);
938         ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
939         ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
940         for (j=0;j<nz;j++) AIIm1_data[idxs[j]+sizeA*i] = 1.;
941         ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
942         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
943         ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
944         ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
945         ierr = VecGetArray(v,&array);CHKERRQ(ierr);
946         for (j=0;j<size_schur;j++) {
947 #if defined(PETSC_USE_COMPLEX)
948           cs_AIB[i*size_schur + j] = (PetscRealPart(array[j+n_I])/nz + PETSC_i*(PetscImaginaryPart(array[j+n_I])/nz));
949 #else
950           cs_AIB[i*size_schur + j] = array[j+n_I]/nz;
951 #endif
952         }
953         ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
954       }
955       ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
956       ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
957       ierr = VecDestroy(&v);CHKERRQ(ierr);
958       ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);CHKERRQ(ierr);
959       ierr = MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);CHKERRQ(ierr);
960       ierr = ISDestroy(&is_p0_p);CHKERRQ(ierr);
961       ierr = ISLocalToGlobalMappingDestroy(&N_to_reor);CHKERRQ(ierr);
962     }
963     ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_hermitian);CHKERRQ(ierr);
964     ierr = MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
965     ierr = MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
966 #if defined(PETSC_HAVE_MUMPS)
967     ierr = PetscStrcpy(solver,MATSOLVERMUMPS);CHKERRQ(ierr);
968 #else
969     ierr = PetscStrcpy(solver,MATSOLVERMKL_PARDISO);CHKERRQ(ierr);
970 #endif
971     ierr = PetscOptionsGetString(NULL,"sub_schurs_","-mat_solver_package",solver,256,NULL);CHKERRQ(ierr);
972 
973     /* when using the benign subspace trick, the local Schur complements are SPD */
974     if (benign_trick) sub_schurs->is_posdef = PETSC_TRUE;
975 
976     if (n_I) { /* TODO add ordering from options */
977       IS is_schur;
978 
979       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
980         ierr = MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
981       } else {
982         ierr = MatGetFactor(A,solver,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
983       }
984       /* subsets ordered last */
985       ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is_schur);CHKERRQ(ierr);
986       ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
987       ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
988 
989       /* factorization step */
990       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
991         ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
992 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
993         ierr = MatMumpsSetIcntl(F,19,2);CHKERRQ(ierr);
994 #endif
995         if (sub_schurs->is_posdef) {
996           ierr = MatFactorSetSchurComplementSolverType(F,1);CHKERRQ(ierr);
997         } else {
998           ierr = MatFactorSetSchurComplementSolverType(F,2);CHKERRQ(ierr);
999         }
1000         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
1001         S_lower_triangular = PETSC_TRUE;
1002       } else {
1003         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
1004 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
1005         ierr = MatMumpsSetIcntl(F,19,3);CHKERRQ(ierr);
1006 #endif
1007         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
1008       }
1009 
1010       /* get explicit Schur Complement computed during numeric factorization */
1011       ierr = MatFactorGetSchurComplement(F,&S_all);CHKERRQ(ierr);
1012       /* we can reuse the solvers if we are not using the economic version */
1013       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
1014       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
1015       solver_S = PETSC_TRUE;
1016 
1017       /* update the Schur complement with the change of basis on the pressures */
1018       if (benign_n) {
1019         PetscScalar *S_data,*cs_AIB,*AIIm1_data;
1020         Vec         v;
1021         PetscInt    sizeA;
1022 
1023         ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1024         ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
1025         ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
1026 #if defined(PETSC_HAVE_MUMPS)
1027         ierr = MatMumpsSetIcntl(F,26,0);CHKERRQ(ierr);
1028 #endif
1029 #if defined(PETSC_HAVE_MKL_PARDISO)
1030         ierr = MatMkl_PardisoSetCntl(F,70,1);CHKERRQ(ierr);
1031 #endif
1032         ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1033         ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1034         for (i=0;i<benign_n;i++) {
1035           Vec            benign_AIIm1_ones;
1036           PetscScalar    *array,sum = 0.,one = 1.;
1037           const PetscInt *idxs;
1038           PetscInt       j,nz;
1039           PetscBLASInt   B_k,B_n;
1040 
1041           ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
1042           ierr = VecCopy(benign_AIIm1_ones,v);CHKERRQ(ierr);
1043           ierr = MatSolve(F,v,benign_AIIm1_ones);CHKERRQ(ierr);
1044           ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
1045           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1046           /* p0 dof (eliminated) is excluded from the sum */
1047           for (j=0;j<nz-1;j++) sum -= AIIm1_data[idxs[j]+sizeA*i];
1048           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1049           ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
1050           ierr = VecGetArray(v,&array);CHKERRQ(ierr);
1051           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
1052           /* cs_AIB already scaled by 1./nz */
1053           B_k = 1;
1054           ierr = PetscBLASIntCast(size_schur,&B_n);CHKERRQ(ierr);
1055           PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
1056           sum  = 1.;
1057           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));
1058           ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
1059           /* set p0 entry of AIIm1_ones to zero */
1060           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1061           for (j=0;j<benign_n;j++) AIIm1_data[idxs[nz-1]+sizeA*j] = 0.;
1062           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1063           ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
1064         }
1065   /* restore defaults */
1066 #if defined(PETSC_HAVE_MUMPS)
1067         ierr = MatMumpsSetIcntl(F,26,-1);CHKERRQ(ierr);
1068 #endif
1069 #if defined(PETSC_HAVE_MKL_PARDISO)
1070         ierr = MatMkl_PardisoSetCntl(F,70,0);CHKERRQ(ierr);
1071 #endif
1072         ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1073         ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1074         ierr = VecDestroy(&v);CHKERRQ(ierr);
1075         ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1076       }
1077       if (!reuse_solvers) {
1078         for (i=0;i<benign_n;i++) {
1079           ierr = ISDestroy(&is_p_r[i]);CHKERRQ(ierr);
1080         }
1081         ierr = PetscFree(is_p_r);CHKERRQ(ierr);
1082         ierr = MatDestroy(&cs_AIB_mat);CHKERRQ(ierr);
1083         ierr = MatDestroy(&benign_AIIm1_ones_mat);CHKERRQ(ierr);
1084       }
1085     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1086       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
1087       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1088       solver_S = PETSC_FALSE;
1089     }
1090 
1091     if (reuse_solvers) {
1092       Mat                A_II,Afake;
1093       Vec                vec1_B;
1094       PCBDDCReuseSolvers msolv_ctx;
1095       PetscInt           n_R;
1096 
1097       if (sub_schurs->reuse_solver) {
1098         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1099       } else {
1100         ierr = PetscNew(&sub_schurs->reuse_solver);CHKERRQ(ierr);
1101       }
1102       msolv_ctx = sub_schurs->reuse_solver;
1103       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1104       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
1105       msolv_ctx->F = F;
1106       ierr = MatCreateVecs(F,&msolv_ctx->sol,NULL);CHKERRQ(ierr);
1107       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1108       {
1109         PetscScalar *array;
1110         PetscInt    n;
1111 
1112         ierr = VecGetLocalSize(msolv_ctx->sol,&n);CHKERRQ(ierr);
1113         ierr = VecGetArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1114         ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);CHKERRQ(ierr);
1115         ierr = VecRestoreArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1116       }
1117       msolv_ctx->has_vertices = factor_workaround;
1118 
1119       /* interior solver */
1120       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);CHKERRQ(ierr);
1121       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
1122       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
1123       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
1124       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);CHKERRQ(ierr);
1125       ierr = PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);CHKERRQ(ierr);
1126 
1127       /* correction solver */
1128       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->correction_solver);CHKERRQ(ierr);
1129       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
1130       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
1131       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);CHKERRQ(ierr);
1132       ierr = PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);CHKERRQ(ierr);
1133 
1134       /* scatter and vecs for Schur complement solver */
1135       ierr = MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);CHKERRQ(ierr);
1136       ierr = MatCreateVecs(sub_schurs->S,&vec1_B,NULL);CHKERRQ(ierr);
1137       if (!factor_workaround) {
1138         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1139         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1140         ierr = PetscObjectReference((PetscObject)is_A_all);CHKERRQ(ierr);
1141         msolv_ctx->is_R = is_A_all;
1142       } else {
1143         IS              is_B_all;
1144         const PetscInt* idxs;
1145         PetscInt        dual,n_v,n;
1146 
1147         ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
1148         dual = size_schur - n_v;
1149         ierr = ISGetLocalSize(is_A_all,&n);CHKERRQ(ierr);
1150         ierr = ISGetIndices(is_A_all,&idxs);CHKERRQ(ierr);
1151         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);CHKERRQ(ierr);
1152         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1153         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1154         ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);CHKERRQ(ierr);
1155         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1156         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1157         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);CHKERRQ(ierr);
1158         ierr = ISRestoreIndices(is_A_all,&idxs);CHKERRQ(ierr);
1159       }
1160       ierr = ISGetLocalSize(msolv_ctx->is_R,&n_R);CHKERRQ(ierr);
1161       ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,n_R,n_R,0,NULL,&Afake);CHKERRQ(ierr);
1162       ierr = PCSetOperators(msolv_ctx->correction_solver,Afake,Afake);CHKERRQ(ierr);
1163       ierr = MatDestroy(&Afake);CHKERRQ(ierr);
1164       ierr = VecDestroy(&vec1_B);CHKERRQ(ierr);
1165 
1166       /* communicate benign info to solver context */
1167       if (benign_n) {
1168         PetscScalar *array;
1169 
1170         msolv_ctx->benign_n = benign_n;
1171         msolv_ctx->benign_zerodiag_subs = is_p_r;
1172         ierr = PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);CHKERRQ(ierr);
1173         msolv_ctx->benign_csAIB = cs_AIB_mat;
1174         ierr = MatCreateVecs(cs_AIB_mat,&msolv_ctx->benign_corr_work,NULL);CHKERRQ(ierr);
1175         ierr = VecGetArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1176         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array,&msolv_ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
1177         ierr = VecRestoreArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1178         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1179       }
1180     }
1181     ierr = MatDestroy(&A);CHKERRQ(ierr);
1182     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
1183 
1184     /* Work arrays */
1185     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
1186 
1187     /* matrices for adaptive selection */
1188     if (compute_Stilda) {
1189       if (!sub_schurs->sum_S_Ej_tilda_all) {
1190         ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1191         ierr = MatSetSizes(sub_schurs->sum_S_Ej_tilda_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
1192         ierr = MatSetType(sub_schurs->sum_S_Ej_tilda_all,MATAIJ);CHKERRQ(ierr);
1193         ierr = MatSeqAIJSetPreallocation(sub_schurs->sum_S_Ej_tilda_all,0,nnz);CHKERRQ(ierr);
1194       }
1195       if (!sub_schurs->sum_S_Ej_inv_all && deluxe) {
1196         ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1197         ierr = MatSetSizes(sub_schurs->sum_S_Ej_inv_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
1198         ierr = MatSetType(sub_schurs->sum_S_Ej_inv_all,MATAIJ);CHKERRQ(ierr);
1199         ierr = MatSeqAIJSetPreallocation(sub_schurs->sum_S_Ej_inv_all,0,nnz);CHKERRQ(ierr);
1200       }
1201     }
1202 
1203     /* S_Ej_all */
1204     cum = cum2 = 0;
1205     ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1206     for (i=0;i<sub_schurs->n_subs;i++) {
1207       PetscInt j;
1208 
1209       /* get S_E */
1210       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1211       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1212         PetscInt k;
1213         for (k=0;k<subset_size;k++) {
1214           for (j=k;j<subset_size;j++) {
1215             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1216             work[j*subset_size+k] = PetscConj(S_data[cum2+k*size_schur+j]);
1217           }
1218         }
1219       } else { /* just copy to workspace */
1220         PetscInt k;
1221         for (k=0;k<subset_size;k++) {
1222           for (j=0;j<subset_size;j++) {
1223             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1224           }
1225         }
1226       }
1227       /* insert S_E values */
1228       for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1229       if (sub_schurs->change) {
1230         Mat            change_sub,SEj,T;
1231 
1232         /* change basis */
1233         ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1234         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1235         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1236           Mat T2;
1237           ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1238           ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1239           ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1240           ierr = MatDestroy(&T2);CHKERRQ(ierr);
1241         } else {
1242           ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1243         }
1244         ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1245         ierr = MatDestroy(&T);CHKERRQ(ierr);
1246         ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1.0,NULL,NULL);CHKERRQ(ierr);
1247         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1248       }
1249       if (deluxe) {
1250         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1251         /* if adaptivity is requested, invert S_E blocks */
1252         if (compute_Stilda) {
1253           ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1254           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1255           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1256             PetscInt k;
1257             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,work,&B_N,&B_ierr));
1258             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1259             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,work,&B_N,&B_ierr));
1260             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1261             for (k=0;k<subset_size;k++) {
1262               for (j=k;j<subset_size;j++) {
1263                 work[j*subset_size+k] = work[k*subset_size+j];
1264               }
1265             }
1266           } else {
1267             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,work,&B_N,pivots,&B_ierr));
1268             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1269             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1270             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1271           }
1272           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1273           ierr = MatSetValues(sub_schurs->sum_S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1274         }
1275       } else if (compute_Stilda) { /* not using deluxe */
1276         Mat         SEj;
1277         Vec         D;
1278         PetscScalar *array;
1279 
1280         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1281         ierr = VecGetArray(Dall,&array);CHKERRQ(ierr);
1282         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,array+cum,&D);CHKERRQ(ierr);
1283         ierr = VecRestoreArray(Dall,&array);CHKERRQ(ierr);
1284         ierr = VecShift(D,-1.);CHKERRQ(ierr);
1285         ierr = MatDiagonalScale(SEj,D,D);CHKERRQ(ierr);
1286         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1287         ierr = VecDestroy(&D);CHKERRQ(ierr);
1288         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1289       }
1290       cum += subset_size;
1291       cum2 += subset_size*(size_schur + 1);
1292     }
1293     ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1294 
1295     if (solver_S) {
1296       ierr = MatFactorRestoreSchurComplement(F,&S_all);CHKERRQ(ierr);
1297     }
1298 
1299     schur_factor = NULL;
1300     if (compute_Stilda && size_active_schur) {
1301 
1302       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1303         PetscInt j;
1304         for (j=0;j<size_schur;j++) dummy_idx[j] = j;
1305         ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,size_schur,dummy_idx,size_schur,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1306       } else {
1307         Mat S_all_inv=NULL;
1308         if (solver_S) { /* use MatFactor calls to invert S */
1309             /* let MatFactor factor the Schur complement */
1310           ierr = MatFactorFactorizeSchurComplement(F);CHKERRQ(ierr);
1311           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1312              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 */
1313           if (factor_workaround) {
1314             PetscScalar *data;
1315             PetscInt nd = 0;
1316 
1317             if (!sub_schurs->is_posdef) {
1318               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1319             }
1320             ierr = MatFactorGetSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1321             ierr = MatDenseGetArray(S_all_inv,&data);CHKERRQ(ierr);
1322             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1323               ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1324             }
1325             ierr = PetscMalloc1((size_active_schur*(size_active_schur+1))/2+nd,&schur_factor);CHKERRQ(ierr);
1326             cum = 0;
1327             for (i=0;i<size_active_schur;i++) {
1328               ierr = PetscMemcpy(schur_factor+cum,data+i*(size_schur+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1329               cum += size_active_schur-i;
1330             }
1331             for (i=0;i<nd;i++) schur_factor[cum+i] = data[(i+size_active_schur)*(size_schur+1)];
1332             /* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1333             ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1334             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1335             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,data,&B_N,&B_ierr));
1336             ierr = PetscFPTrapPop();CHKERRQ(ierr);
1337             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1338             ierr = MatDenseRestoreArray(S_all_inv,&data);CHKERRQ(ierr);
1339           } else {
1340             ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
1341             ierr = MatFactorGetSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1342           }
1343         } else { /* we need to invert explicitly since we are not using MatFactor for S */
1344           ierr = PetscObjectReference((PetscObject)S_all);CHKERRQ(ierr);
1345           S_all_inv = S_all;
1346           ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1347           ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1348           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1349           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1350             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
1351             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1352             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
1353             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1354           } else {
1355             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
1356             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1357             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1358             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1359           }
1360           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1361           ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1362         }
1363         /* S_Ej_tilda_all */
1364         cum = cum2 = 0;
1365         ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1366         for (i=0;i<sub_schurs->n_subs;i++) {
1367           PetscInt j;
1368 
1369           ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1370           /* get (St^-1)_E */
1371           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1372              will be properly accessed later during adaptive selection */
1373           if (S_lower_triangular) {
1374             PetscInt k;
1375             if (sub_schurs->change) {
1376               for (k=0;k<subset_size;k++) {
1377                 for (j=k;j<subset_size;j++) {
1378                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1379                   work[j*subset_size+k] = work[k*subset_size+j];
1380                 }
1381               }
1382             } else {
1383               for (k=0;k<subset_size;k++) {
1384                 for (j=k;j<subset_size;j++) {
1385                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1386                 }
1387               }
1388             }
1389           } else {
1390             PetscInt k;
1391             for (k=0;k<subset_size;k++) {
1392               for (j=0;j<subset_size;j++) {
1393                 work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1394               }
1395             }
1396           }
1397           if (sub_schurs->change) {
1398             Mat change_sub,SEj,T;
1399 
1400             /* change basis */
1401             ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1402             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1403             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1404               Mat T2;
1405               ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1406               ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1407               ierr = MatDestroy(&T2);CHKERRQ(ierr);
1408               ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1409             } else {
1410               ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1411             }
1412             ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1413             ierr = MatDestroy(&T);CHKERRQ(ierr);
1414             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
1415             ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1./PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
1416             ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1417           }
1418           for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1419           ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1420           cum += subset_size;
1421           cum2 += subset_size*(size_schur + 1);
1422         }
1423         ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1424         if (solver_S) {
1425           ierr = MatFactorRestoreSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1426         }
1427         ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
1428       }
1429 
1430       /* move back factors to Schur data into F */
1431       if (factor_workaround) {
1432         Mat S_tmp;
1433         PetscInt nv,nd=0;
1434 
1435         if (!solver_S) {
1436           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
1437         }
1438         ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
1439         ierr = MatFactorGetSchurComplement(F,&S_tmp);CHKERRQ(ierr);
1440         if (sub_schurs->is_posdef) {
1441           PetscScalar *data;
1442 
1443           ierr = MatZeroEntries(S_tmp);CHKERRQ(ierr);
1444           ierr = MatDenseGetArray(S_tmp,&data);CHKERRQ(ierr);
1445 
1446           if (S_lower_triangular) {
1447             cum = 0;
1448             for (i=0;i<size_active_schur;i++) {
1449               ierr = PetscMemcpy(data+i*(size_schur+1),schur_factor+cum,(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1450               cum += size_active_schur-i;
1451 	    }
1452           } else {
1453             ierr = PetscMemcpy(data,schur_factor,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1454           }
1455           if (sub_schurs->is_dir) {
1456             ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1457 	    for (i=0;i<nd;i++) {
1458 	      data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
1459 	    }
1460           }
1461           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1462              set the diagonal entry of the Schur factor to a very large value */
1463           for (i=size_active_schur+nd;i<size_schur;i++) {
1464             data[i*(size_schur+1)] = infty;
1465           }
1466           ierr = MatDenseRestoreArray(S_tmp,&data);CHKERRQ(ierr);
1467         } else {
1468           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1469         }
1470         ierr = MatFactorRestoreSchurComplement(F,&S_tmp);CHKERRQ(ierr);
1471       }
1472     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
1473       PetscScalar *data;
1474       PetscInt    nd = 0;
1475 
1476       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1477         ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1478       }
1479       ierr = MatFactorGetSchurComplement(F,&S_all);CHKERRQ(ierr);
1480       ierr = MatDenseGetArray(S_all,&data);CHKERRQ(ierr);
1481       for (i=0;i<size_active_schur;i++) {
1482         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1483       }
1484       for (i=size_active_schur+nd;i<size_schur;i++) {
1485         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1486         data[i*(size_schur+1)] = infty;
1487       }
1488       ierr = MatDenseRestoreArray(S_all,&data);CHKERRQ(ierr);
1489       ierr = MatFactorRestoreSchurComplement(F,&S_all);CHKERRQ(ierr);
1490     }
1491     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
1492     ierr = PetscFree(schur_factor);CHKERRQ(ierr);
1493     ierr = VecDestroy(&Dall);CHKERRQ(ierr);
1494   }
1495   ierr = PetscFree(nnz);CHKERRQ(ierr);
1496   ierr = MatDestroy(&F);CHKERRQ(ierr);
1497   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1498   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
1499   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1500   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1501   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1502   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1503   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1504   if (compute_Stilda) {
1505     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1506     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1507     if (deluxe) {
1508       ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1509       ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1510     }
1511   }
1512 
1513   /* Global matrix of all assembled Schur on subsets */
1514   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
1515   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
1516   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1517 
1518   /* Get local part of (\sum_j S_Ej) */
1519   if (!sub_schurs->sum_S_Ej_all) {
1520     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_INITIAL_MATRIX,&submats);CHKERRQ(ierr);
1521     sub_schurs->sum_S_Ej_all = submats[0];
1522   } else {
1523     ierr = PetscMalloc1(1,&submats);CHKERRQ(ierr);
1524     submats[0] = sub_schurs->sum_S_Ej_all;
1525     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1526   }
1527 
1528   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1529   if (compute_Stilda) {
1530     ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1531     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1532     submats[0] = sub_schurs->sum_S_Ej_tilda_all;
1533     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1534     if (deluxe) {
1535       ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1536       ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1537       submats[0] = sub_schurs->sum_S_Ej_inv_all;
1538       ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1539     } else {
1540       PetscScalar *array;
1541       PetscInt    cum;
1542 
1543       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1544       cum = 0;
1545       for (i=0;i<sub_schurs->n_subs;i++) {
1546         ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1547         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1548         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1549         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
1550         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1551         PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
1552         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1553         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1554         cum += subset_size*subset_size;
1555       }
1556       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1557       ierr = PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1558       ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1559       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1560     }
1561   }
1562 
1563   /* free workspace */
1564   ierr = PetscFree(submats);CHKERRQ(ierr);
1565   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
1566   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
1567   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
1568   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
1569   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
1570   PetscFunctionReturn(0);
1571 }
1572 
1573 #undef __FUNCT__
1574 #define __FUNCT__ "PCBDDCSubSchursInit"
1575 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap)
1576 {
1577   IS              *faces,*edges,*all_cc,vertices;
1578   PetscInt        i,n_faces,n_edges,n_all_cc;
1579   PetscBool       is_sorted;
1580   PetscErrorCode  ierr;
1581 
1582   PetscFunctionBegin;
1583   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
1584   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
1585   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
1586   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
1587 
1588   /* reset any previous data */
1589   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
1590 
1591   /* get index sets for faces and edges (already sorted by global ordering) */
1592   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1593   n_all_cc = n_faces+n_edges;
1594   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
1595   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
1596   for (i=0;i<n_faces;i++) {
1597     all_cc[i] = faces[i];
1598   }
1599   for (i=0;i<n_edges;i++) {
1600     all_cc[n_faces+i] = edges[i];
1601     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
1602   }
1603   ierr = PetscFree(faces);CHKERRQ(ierr);
1604   ierr = PetscFree(edges);CHKERRQ(ierr);
1605   sub_schurs->is_dir = NULL;
1606   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
1607 
1608   /* Determine if MatFactor can be used */
1609   sub_schurs->schur_explicit = PETSC_FALSE;
1610 #if defined(PETSC_HAVE_MUMPS)
1611   sub_schurs->schur_explicit = PETSC_TRUE;
1612 #endif
1613 #if defined(PETSC_HAVE_MKL_PARDISO)
1614   sub_schurs->schur_explicit = PETSC_TRUE;
1615 #endif
1616 
1617   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
1618   sub_schurs->is_I = is_I;
1619   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
1620   sub_schurs->is_B = is_B;
1621   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
1622   sub_schurs->l2gmap = graph->l2gmap;
1623   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
1624   sub_schurs->BtoNmap = BtoNmap;
1625   sub_schurs->n_subs = n_all_cc;
1626   sub_schurs->is_subs = all_cc;
1627   if (!sub_schurs->schur_explicit) { /* sort by local ordering if we are not using MatFactor */
1628     for (i=0;i<sub_schurs->n_subs;i++) {
1629       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
1630     }
1631   }
1632   sub_schurs->is_vertices = vertices;
1633   sub_schurs->S_Ej_all = NULL;
1634   sub_schurs->sum_S_Ej_all = NULL;
1635   sub_schurs->sum_S_Ej_inv_all = NULL;
1636   sub_schurs->sum_S_Ej_tilda_all = NULL;
1637   sub_schurs->is_Ej_all = NULL;
1638   PetscFunctionReturn(0);
1639 }
1640 
1641 #undef __FUNCT__
1642 #define __FUNCT__ "PCBDDCSubSchursCreate"
1643 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1644 {
1645   PCBDDCSubSchurs schurs_ctx;
1646   PetscErrorCode  ierr;
1647 
1648   PetscFunctionBegin;
1649   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
1650   schurs_ctx->n_subs = 0;
1651   *sub_schurs = schurs_ctx;
1652   PetscFunctionReturn(0);
1653 }
1654 
1655 #undef __FUNCT__
1656 #define __FUNCT__ "PCBDDCSubSchursReset"
1657 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1658 {
1659   PetscInt       i;
1660   PetscErrorCode ierr;
1661 
1662   PetscFunctionBegin;
1663   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1664   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1665   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1666   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1667   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1668   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1669   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1670   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1671   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1672   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1673   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1674   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1675   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1676   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1677   for (i=0;i<sub_schurs->n_subs;i++) {
1678     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
1679   }
1680   if (sub_schurs->n_subs) {
1681     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1682   }
1683   if (sub_schurs->reuse_solver) {
1684     ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1685   }
1686   ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1687   if (sub_schurs->change) {
1688     for (i=0;i<sub_schurs->n_subs;i++) {
1689       ierr = KSPDestroy(&sub_schurs->change[i]);CHKERRQ(ierr);
1690       ierr = ISDestroy(&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
1691     }
1692   }
1693   ierr = PetscFree(sub_schurs->change);CHKERRQ(ierr);
1694   ierr = PetscFree(sub_schurs->change_primal_sub);CHKERRQ(ierr);
1695   sub_schurs->n_subs = 0;
1696   PetscFunctionReturn(0);
1697 }
1698 
1699 #undef __FUNCT__
1700 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
1701 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1702 {
1703   PetscInt       i,j,n;
1704   PetscErrorCode ierr;
1705 
1706   PetscFunctionBegin;
1707   n = 0;
1708   for (i=-n_prev;i<0;i++) {
1709     PetscInt start_dof = queue_tip[i];
1710     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1711       PetscInt dof = adjncy[j];
1712       if (!PetscBTLookup(touched,dof)) {
1713         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1714         queue_tip[n] = dof;
1715         n++;
1716       }
1717     }
1718   }
1719   *n_added = n;
1720   PetscFunctionReturn(0);
1721 }
1722