xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 3d96e9964ff330fd2a9eee374bcd4376da7efe60)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <../src/mat/impls/dense/seq/dense.h>
4 #include <petscblaslapack.h>
5 
6 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt*,PetscInt,PetscBT,PetscInt*,PetscInt*,PetscInt*);
7 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat,PetscBool,MatReuse,Mat*);
8 static PetscErrorCode PCBDDCReuseSolvers_Interior(PC,Vec,Vec);
9 static PetscErrorCode PCBDDCReuseSolvers_Correction(PC,Vec,Vec);
10 
11 /* if v2 is not present, correction is done in-place */
12 PetscErrorCode PCBDDCReuseSolversBenignAdapt(PCBDDCReuseSolvers ctx, Vec v, Vec v2, PetscBool sol, PetscBool full)
13 {
14   PetscScalar    *array;
15   PetscScalar    *array2;
16   PetscErrorCode ierr;
17 
18   PetscFunctionBegin;
19   if (!ctx->benign_n) PetscFunctionReturn(0);
20   if (sol && full) {
21     PetscInt n_I,size_schur;
22 
23     /* get sizes */
24     ierr = MatGetSize(ctx->benign_csAIB,&size_schur,NULL);CHKERRQ(ierr);
25     ierr = VecGetSize(v,&n_I);CHKERRQ(ierr);
26     n_I = n_I - size_schur;
27     /* get schur sol from array */
28     ierr = VecGetArray(v,&array);CHKERRQ(ierr);
29     ierr = VecPlaceArray(ctx->benign_dummy_schur_vec,array+n_I);CHKERRQ(ierr);
30     ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
31     /* apply interior sol correction */
32     ierr = MatMultTranspose(ctx->benign_csAIB,ctx->benign_dummy_schur_vec,ctx->benign_corr_work);CHKERRQ(ierr);
33     ierr = VecResetArray(ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
34     ierr = MatMultAdd(ctx->benign_AIIm1ones,ctx->benign_corr_work,v,v);CHKERRQ(ierr);
35   }
36   if (v2) {
37     PetscInt nl;
38 
39     ierr = VecGetArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
40     ierr = VecGetLocalSize(v2,&nl);CHKERRQ(ierr);
41     ierr = VecGetArray(v2,&array2);CHKERRQ(ierr);
42     ierr = PetscMemcpy(array2,array,nl*sizeof(PetscScalar));CHKERRQ(ierr);
43   } else {
44     ierr = VecGetArray(v,&array);CHKERRQ(ierr);
45     array2 = array;
46   }
47   if (!sol) { /* change rhs */
48     PetscInt n;
49     for (n=0;n<ctx->benign_n;n++) {
50       PetscScalar    sum = 0.;
51       const PetscInt *cols;
52       PetscInt       nz,i;
53 
54       ierr = ISGetLocalSize(ctx->benign_zerodiag_subs[n],&nz);CHKERRQ(ierr);
55       ierr = ISGetIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
56       for (i=0;i<nz-1;i++) sum += array[cols[i]];
57 #if defined(PETSC_USE_COMPLEX)
58       sum = -(PetscRealPart(sum)/nz + PETSC_i*(PetscImaginaryPart(sum)/nz));
59 #else
60       sum = -sum/nz;
61 #endif
62       for (i=0;i<nz-1;i++) array2[cols[i]] += sum;
63       ctx->benign_save_vals[n] = array2[cols[nz-1]];
64       array2[cols[nz-1]] = sum;
65       ierr = ISRestoreIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
66     }
67   } else {
68     PetscInt n;
69     for (n=0;n<ctx->benign_n;n++) {
70       PetscScalar    sum = 0.;
71       const PetscInt *cols;
72       PetscInt       nz,i;
73       ierr = ISGetLocalSize(ctx->benign_zerodiag_subs[n],&nz);CHKERRQ(ierr);
74       ierr = ISGetIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
75       for (i=0;i<nz-1;i++) sum += array[cols[i]];
76 #if defined(PETSC_USE_COMPLEX)
77       sum = -(PetscRealPart(sum)/nz + PETSC_i*(PetscImaginaryPart(sum)/nz));
78 #else
79       sum = -sum/nz;
80 #endif
81       for (i=0;i<nz-1;i++) array2[cols[i]] += sum;
82       array2[cols[nz-1]] = ctx->benign_save_vals[n];
83       ierr = ISRestoreIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
84     }
85   }
86   if (v2) {
87     ierr = VecRestoreArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
88     ierr = VecRestoreArray(v2,&array2);CHKERRQ(ierr);
89   } else {
90     ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
91   }
92   if (!sol && full) {
93     Vec      usedv;
94     PetscInt n_I,size_schur;
95 
96     /* get sizes */
97     ierr = MatGetSize(ctx->benign_csAIB,&size_schur,NULL);CHKERRQ(ierr);
98     ierr = VecGetSize(v,&n_I);CHKERRQ(ierr);
99     n_I = n_I - size_schur;
100     /* compute schur rhs correction */
101     if (v2) {
102       usedv = v2;
103     } else {
104       usedv = v;
105     }
106     /* apply schur rhs correction */
107     ierr = MatMultTranspose(ctx->benign_AIIm1ones,usedv,ctx->benign_corr_work);CHKERRQ(ierr);
108     ierr = VecGetArrayRead(usedv,(const PetscScalar**)&array);CHKERRQ(ierr);
109     ierr = VecPlaceArray(ctx->benign_dummy_schur_vec,array+n_I);CHKERRQ(ierr);
110     ierr = VecRestoreArrayRead(usedv,(const PetscScalar**)&array);CHKERRQ(ierr);
111     ierr = MatMultAdd(ctx->benign_csAIB,ctx->benign_corr_work,ctx->benign_dummy_schur_vec,ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
112     ierr = VecResetArray(ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
113   }
114   PetscFunctionReturn(0);
115 }
116 
117 static PetscErrorCode PCBDDCReuseSolvers_Solve_Private(PC pc, Vec rhs, Vec sol, PetscBool transpose, PetscBool full)
118 {
119   PCBDDCReuseSolvers ctx;
120   PetscBool          copy = PETSC_FALSE;
121   PetscErrorCode     ierr;
122 
123   PetscFunctionBegin;
124   ierr = PCShellGetContext(pc,(void **)&ctx);CHKERRQ(ierr);
125   if (full) {
126 #if defined(PETSC_HAVE_MUMPS)
127     ierr = MatMumpsSetIcntl(ctx->F,26,-1);CHKERRQ(ierr);
128 #endif
129 #if defined(PETSC_HAVE_MKL_PARDISO)
130     ierr = MatMkl_PardisoSetCntl(ctx->F,70,0);CHKERRQ(ierr);
131 #endif
132     copy = ctx->has_vertices;
133   } else { /* interior solver */
134 #if defined(PETSC_HAVE_MUMPS)
135     ierr = MatMumpsSetIcntl(ctx->F,26,0);CHKERRQ(ierr);
136 #endif
137 #if defined(PETSC_HAVE_MKL_PARDISO)
138     ierr = MatMkl_PardisoSetCntl(ctx->F,70,1);CHKERRQ(ierr);
139 #endif
140     copy = PETSC_TRUE;
141   }
142   /* copy rhs into factored matrix workspace */
143   if (copy) {
144     PetscInt    n;
145     PetscScalar *array,*array_solver;
146 
147     ierr = VecGetLocalSize(rhs,&n);CHKERRQ(ierr);
148     ierr = VecGetArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
149     ierr = VecGetArray(ctx->rhs,&array_solver);CHKERRQ(ierr);
150     ierr = PetscMemcpy(array_solver,array,n*sizeof(PetscScalar));CHKERRQ(ierr);
151     ierr = VecRestoreArray(ctx->rhs,&array_solver);CHKERRQ(ierr);
152     ierr = VecRestoreArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
153 
154     ierr = PCBDDCReuseSolversBenignAdapt(ctx,ctx->rhs,NULL,PETSC_FALSE,full);CHKERRQ(ierr);
155     if (transpose) {
156       ierr = MatSolveTranspose(ctx->F,ctx->rhs,ctx->sol);CHKERRQ(ierr);
157     } else {
158       ierr = MatSolve(ctx->F,ctx->rhs,ctx->sol);CHKERRQ(ierr);
159     }
160     ierr = PCBDDCReuseSolversBenignAdapt(ctx,ctx->sol,NULL,PETSC_TRUE,full);CHKERRQ(ierr);
161 
162     /* get back data to caller worskpace */
163     ierr = VecGetArrayRead(ctx->sol,(const PetscScalar**)&array_solver);CHKERRQ(ierr);
164     ierr = VecGetArray(sol,&array);CHKERRQ(ierr);
165     ierr = PetscMemcpy(array,array_solver,n*sizeof(PetscScalar));CHKERRQ(ierr);
166     ierr = VecRestoreArray(sol,&array);CHKERRQ(ierr);
167     ierr = VecRestoreArrayRead(ctx->sol,(const PetscScalar**)&array_solver);CHKERRQ(ierr);
168   } else {
169     if (ctx->benign_n) {
170       ierr = PCBDDCReuseSolversBenignAdapt(ctx,rhs,ctx->rhs,PETSC_FALSE,full);CHKERRQ(ierr);
171       if (transpose) {
172         ierr = MatSolveTranspose(ctx->F,ctx->rhs,sol);CHKERRQ(ierr);
173       } else {
174         ierr = MatSolve(ctx->F,ctx->rhs,sol);CHKERRQ(ierr);
175       }
176       ierr = PCBDDCReuseSolversBenignAdapt(ctx,sol,NULL,PETSC_TRUE,full);CHKERRQ(ierr);
177     } else {
178       if (transpose) {
179         ierr = MatSolveTranspose(ctx->F,rhs,sol);CHKERRQ(ierr);
180       } else {
181         ierr = MatSolve(ctx->F,rhs,sol);CHKERRQ(ierr);
182       }
183     }
184   }
185   /* restore defaults */
186 #if defined(PETSC_HAVE_MUMPS)
187   ierr = MatMumpsSetIcntl(ctx->F,26,-1);CHKERRQ(ierr);
188 #endif
189 #if defined(PETSC_HAVE_MKL_PARDISO)
190   ierr = MatMkl_PardisoSetCntl(ctx->F,70,0);CHKERRQ(ierr);
191 #endif
192   PetscFunctionReturn(0);
193 }
194 
195 static PetscErrorCode PCBDDCReuseSolvers_Correction(PC pc, Vec rhs, Vec sol)
196 {
197   PetscErrorCode   ierr;
198 
199   PetscFunctionBegin;
200   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
201   PetscFunctionReturn(0);
202 }
203 
204 static PetscErrorCode PCBDDCReuseSolvers_CorrectionTranspose(PC pc, Vec rhs, Vec sol)
205 {
206   PetscErrorCode   ierr;
207 
208   PetscFunctionBegin;
209   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_TRUE,PETSC_TRUE);CHKERRQ(ierr);
210   PetscFunctionReturn(0);
211 }
212 
213 static PetscErrorCode PCBDDCReuseSolvers_Interior(PC pc, Vec rhs, Vec sol)
214 {
215   PetscErrorCode   ierr;
216 
217   PetscFunctionBegin;
218   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_FALSE,PETSC_FALSE);CHKERRQ(ierr);
219   PetscFunctionReturn(0);
220 }
221 
222 static PetscErrorCode PCBDDCReuseSolvers_InteriorTranspose(PC pc, Vec rhs, Vec sol)
223 {
224   PetscErrorCode   ierr;
225 
226   PetscFunctionBegin;
227   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
228   PetscFunctionReturn(0);
229 }
230 
231 static PetscErrorCode PCBDDCReuseSolversReset(PCBDDCReuseSolvers reuse)
232 {
233   PetscInt       i;
234   PetscErrorCode ierr;
235 
236   PetscFunctionBegin;
237   ierr = MatDestroy(&reuse->F);CHKERRQ(ierr);
238   ierr = VecDestroy(&reuse->sol);CHKERRQ(ierr);
239   ierr = VecDestroy(&reuse->rhs);CHKERRQ(ierr);
240   ierr = PCDestroy(&reuse->interior_solver);CHKERRQ(ierr);
241   ierr = PCDestroy(&reuse->correction_solver);CHKERRQ(ierr);
242   ierr = ISDestroy(&reuse->is_R);CHKERRQ(ierr);
243   ierr = ISDestroy(&reuse->is_B);CHKERRQ(ierr);
244   ierr = VecScatterDestroy(&reuse->correction_scatter_B);CHKERRQ(ierr);
245   ierr = VecDestroy(&reuse->sol_B);CHKERRQ(ierr);
246   ierr = VecDestroy(&reuse->rhs_B);CHKERRQ(ierr);
247   for (i=0;i<reuse->benign_n;i++) {
248     ierr = ISDestroy(&reuse->benign_zerodiag_subs[i]);CHKERRQ(ierr);
249   }
250   ierr = PetscFree(reuse->benign_zerodiag_subs);CHKERRQ(ierr);
251   ierr = PetscFree(reuse->benign_save_vals);CHKERRQ(ierr);
252   ierr = MatDestroy(&reuse->benign_csAIB);CHKERRQ(ierr);
253   ierr = MatDestroy(&reuse->benign_AIIm1ones);CHKERRQ(ierr);
254   ierr = VecDestroy(&reuse->benign_corr_work);CHKERRQ(ierr);
255   ierr = VecDestroy(&reuse->benign_dummy_schur_vec);CHKERRQ(ierr);
256   PetscFunctionReturn(0);
257 }
258 
259 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
260 {
261   Mat            B, C, D, Bd, Cd, AinvBd;
262   KSP            ksp;
263   PC             pc;
264   PetscBool      isLU, isILU, isCHOL, Bdense, Cdense;
265   PetscReal      fill = 2.0;
266   PetscInt       n_I;
267   PetscMPIInt    size;
268   PetscErrorCode ierr;
269 
270   PetscFunctionBegin;
271   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);CHKERRQ(ierr);
272   if (size != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not for parallel matrices");
273   if (reuse == MAT_REUSE_MATRIX) {
274     PetscBool Sdense;
275 
276     ierr = PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense);CHKERRQ(ierr);
277     if (!Sdense) SETERRQ(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"S should dense");
278   }
279   ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
280   ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
281   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
282   ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
283   ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
284   ierr = PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);CHKERRQ(ierr);
285   ierr = PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);CHKERRQ(ierr);
286   ierr = PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);CHKERRQ(ierr);
287   ierr = MatGetSize(B,&n_I,NULL);CHKERRQ(ierr);
288   if (n_I) {
289     if (!Bdense) {
290       ierr = MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
291     } else {
292       Bd = B;
293     }
294 
295     if (isLU || isILU || isCHOL) {
296       Mat fact;
297       ierr = KSPSetUp(ksp);CHKERRQ(ierr);
298       ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
299       ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
300       ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
301     } else {
302       PetscBool ex = PETSC_TRUE;
303 
304       if (ex) {
305         Mat Ainvd;
306 
307         ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
308         ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
309         ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
310       } else {
311         Vec         sol,rhs;
312         PetscScalar *arrayrhs,*arraysol;
313         PetscInt    i,nrhs,n;
314 
315         ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
316         ierr = MatGetSize(Bd,&n,&nrhs);CHKERRQ(ierr);
317         ierr = MatDenseGetArray(Bd,&arrayrhs);CHKERRQ(ierr);
318         ierr = MatDenseGetArray(AinvBd,&arraysol);CHKERRQ(ierr);
319         ierr = KSPGetSolution(ksp,&sol);CHKERRQ(ierr);
320         ierr = KSPGetRhs(ksp,&rhs);CHKERRQ(ierr);
321         for (i=0;i<nrhs;i++) {
322           ierr = VecPlaceArray(rhs,arrayrhs+i*n);CHKERRQ(ierr);
323           ierr = VecPlaceArray(sol,arraysol+i*n);CHKERRQ(ierr);
324           ierr = KSPSolve(ksp,rhs,sol);CHKERRQ(ierr);
325           ierr = VecResetArray(rhs);CHKERRQ(ierr);
326           ierr = VecResetArray(sol);CHKERRQ(ierr);
327         }
328         ierr = MatDenseRestoreArray(Bd,&arrayrhs);CHKERRQ(ierr);
329         ierr = MatDenseRestoreArray(AinvBd,&arrayrhs);CHKERRQ(ierr);
330       }
331     }
332     if (!Bdense & !issym) {
333       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
334     }
335 
336     if (!issym) {
337       if (!Cdense) {
338         ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
339       } else {
340         Cd = C;
341       }
342       ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
343       if (!Cdense) {
344         ierr = MatDestroy(&Cd);CHKERRQ(ierr);
345       }
346     } else {
347       ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
348       if (!Bdense) {
349         ierr = MatDestroy(&Bd);CHKERRQ(ierr);
350       }
351     }
352     ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
353   }
354 
355   if (D) {
356     Mat       Dd;
357     PetscBool Ddense;
358 
359     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
360     if (!Ddense) {
361       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
362     } else {
363       Dd = D;
364     }
365     if (n_I) {
366       ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
367     } else {
368       if (reuse == MAT_INITIAL_MATRIX) {
369         ierr = MatDuplicate(Dd,MAT_COPY_VALUES,S);CHKERRQ(ierr);
370       } else {
371         ierr = MatCopy(Dd,*S,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
372       }
373     }
374     if (!Ddense) {
375       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
376     }
377   } else {
378     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
379   }
380   PetscFunctionReturn(0);
381 }
382 
383 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)
384 {
385   Mat                    F,A_II,A_IB,A_BI,A_BB,AE_II;
386   Mat                    S_all;
387   Mat                    global_schur_subsets,work_mat,*submats;
388   ISLocalToGlobalMapping l2gmap_subsets;
389   IS                     is_I,is_I_layer;
390   IS                     all_subsets,all_subsets_mult,all_subsets_n;
391   PetscInt               *nnz,*all_local_idx_N;
392   PetscInt               *auxnum1,*auxnum2;
393   PetscInt               i,subset_size,max_subset_size;
394   PetscInt               n_B,extra,local_size,global_size;
395   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
396   PetscScalar            *Bwork;
397   PetscSubcomm           subcomm;
398   PetscMPIInt            color,rank;
399   MPI_Comm               comm_n;
400   PetscBool              deluxe = PETSC_TRUE, use_getr = PETSC_FALSE;
401   PetscErrorCode         ierr;
402 
403   PetscFunctionBegin;
404   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
405   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
406 
407   sub_schurs->is_hermitian = PETSC_TRUE;
408   sub_schurs->is_posdef    = PETSC_TRUE;
409   if (benign_trick) sub_schurs->is_posdef = PETSC_FALSE;
410   ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)sub_schurs->l2gmap),sub_schurs->prefix,"BDDC sub_schurs options","PC");CHKERRQ(ierr);
411   ierr = PetscOptionsBool("-sub_schurs_hermitian","Hermitian problem",NULL,sub_schurs->is_hermitian,&sub_schurs->is_hermitian,NULL);CHKERRQ(ierr);
412   ierr = PetscOptionsBool("-sub_schurs_posdef","Positive definite problem",NULL,sub_schurs->is_posdef,&sub_schurs->is_posdef,NULL);CHKERRQ(ierr);
413   ierr = PetscOptionsEnd();CHKERRQ(ierr);
414 
415   /* convert matrix if needed */
416   if (Ain) {
417     PetscBool isseqaij;
418     ierr = PetscObjectTypeCompare((PetscObject)Ain,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
419     if (isseqaij) {
420       ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
421       sub_schurs->A = Ain;
422     } else {
423       ierr = MatConvert(Ain,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
424     }
425   }
426 
427   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
428   sub_schurs->S = Sin;
429   if (sub_schurs->schur_explicit) {
430     sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
431   }
432 
433   /* preliminary checks */
434   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");
435 
436   /* restrict work on active processes */
437   color = 0;
438   if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
439   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
440   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
441   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
442   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
443   ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
444   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
445   if (!sub_schurs->n_subs) {
446     ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
447     PetscFunctionReturn(0);
448   }
449   /* ierr = PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);CHKERRQ(ierr); */
450 
451   /* get Schur complement matrices */
452   if (!sub_schurs->schur_explicit) {
453     Mat       tA_IB,tA_BI,tA_BB;
454     PetscBool isseqsbaij;
455     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
456     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);CHKERRQ(ierr);
457     if (isseqsbaij) {
458       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
459       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
460       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
461     } else {
462       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
463       A_BB = tA_BB;
464       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
465       A_IB = tA_IB;
466       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
467       A_BI = tA_BI;
468     }
469   } else {
470     A_II = NULL;
471     A_IB = NULL;
472     A_BI = NULL;
473     A_BB = NULL;
474   }
475   S_all = NULL;
476 
477   /* determine interior problems */
478   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
479   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
480     PetscBT                touched;
481     const PetscInt*        idx_B;
482     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
483 
484     if (!xadj) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
485     /* get sizes */
486     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
487     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
488 
489     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
490     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
491     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
492 
493     /* all boundary dofs must be skipped when adding layers */
494     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
495     for (j=0;j<n_B;j++) {
496       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
497     }
498     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
499     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
500 
501     /* add prescribed number of layers of dofs */
502     n_local_dofs = n_B;
503     n_prev_added = n_B;
504     for (layer=0;layer<nlayers;layer++) {
505       PetscInt n_added;
506       if (n_local_dofs == n_I+n_B) break;
507       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);
508       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
509       n_prev_added = n_added;
510       n_local_dofs += n_added;
511       if (!n_added) break;
512     }
513     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
514 
515     /* IS for I layer dofs in original numbering */
516     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);
517     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
518     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
519     /* IS for I layer dofs in I numbering */
520     if (!sub_schurs->schur_explicit) {
521       ISLocalToGlobalMapping ItoNmap;
522       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
523       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
524       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
525 
526       /* II block */
527       ierr = MatCreateSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
528     }
529   } else {
530     PetscInt n_I;
531 
532     /* IS for I dofs in original numbering */
533     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
534     is_I_layer = sub_schurs->is_I;
535 
536     /* IS for I dofs in I numbering (strided 1) */
537     if (!sub_schurs->schur_explicit) {
538       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
539       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
540 
541       /* II block is the same */
542       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
543       AE_II = A_II;
544     }
545   }
546 
547   /* Get info on subset sizes and sum of all subsets sizes */
548   max_subset_size = 0;
549   local_size = 0;
550   for (i=0;i<sub_schurs->n_subs;i++) {
551     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
552     max_subset_size = PetscMax(subset_size,max_subset_size);
553     local_size += subset_size;
554   }
555 
556   /* Work arrays for local indices */
557   extra = 0;
558   ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
559   if (sub_schurs->schur_explicit && is_I_layer) {
560     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
561   }
562   ierr = PetscMalloc1(n_B+extra,&all_local_idx_N);CHKERRQ(ierr);
563   if (extra) {
564     const PetscInt *idxs;
565     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
566     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
567     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
568   }
569   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
570   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum1);CHKERRQ(ierr);
571   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
572 
573   /* Get local indices in local numbering */
574   local_size = 0;
575   for (i=0;i<sub_schurs->n_subs;i++) {
576     PetscInt j;
577     const    PetscInt *idxs;
578 
579     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
580     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
581     /* start (smallest in global ordering) and multiplicity */
582     auxnum1[i] = idxs[0];
583     auxnum2[i] = subset_size;
584     /* subset indices in local numbering */
585     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
586     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
587     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
588     local_size += subset_size;
589   }
590 
591   /* allocate extra workspace needed only for GETRI */
592   if (local_size && !benign_trick && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
593     PetscScalar  lwork,dummyscalar = 0.;
594     PetscBLASInt dummyint = 0;
595 
596     use_getr = PETSC_TRUE;
597     B_lwork = -1;
598     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
599     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
600     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
601     ierr = PetscFPTrapPop();CHKERRQ(ierr);
602     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
603     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
604     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
605   } else {
606     Bwork = NULL;
607     pivots = NULL;
608   }
609 
610   /* prepare parallel matrices for summing up properly schurs on subsets */
611   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);CHKERRQ(ierr);
612   ierr = ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);CHKERRQ(ierr);
613   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
614   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);CHKERRQ(ierr);
615   ierr = ISRenumber(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);CHKERRQ(ierr);
616   ierr = ISDestroy(&all_subsets);CHKERRQ(ierr);
617   ierr = ISDestroy(&all_subsets_mult);CHKERRQ(ierr);
618   ierr = ISGetLocalSize(all_subsets_n,&i);CHKERRQ(ierr);
619   if (i != local_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",i,local_size);
620   ierr = ISLocalToGlobalMappingCreateIS(all_subsets_n,&l2gmap_subsets);CHKERRQ(ierr);
621   ierr = MatCreateIS(comm_n,1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,NULL,&work_mat);CHKERRQ(ierr);
622   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
623   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
624   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
625   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
626 
627   /* subset indices in local boundary numbering */
628   if (!sub_schurs->is_Ej_all) {
629     PetscInt *all_local_idx_B;
630 
631     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
632     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
633     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);
634     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
635   }
636 
637   if (change) {
638     ISLocalToGlobalMapping BtoS;
639     IS                     change_primal_B;
640     IS                     change_primal_all;
641 
642     if (sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
643     if (sub_schurs->change) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
644     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change_primal_sub);CHKERRQ(ierr);
645     for (i=0;i<sub_schurs->n_subs;i++) {
646       ISLocalToGlobalMapping NtoS;
647       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);CHKERRQ(ierr);
648       ierr = ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
649       ierr = ISLocalToGlobalMappingDestroy(&NtoS);CHKERRQ(ierr);
650     }
651     ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);CHKERRQ(ierr);
652     ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);CHKERRQ(ierr);
653     ierr = ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);CHKERRQ(ierr);
654     ierr = ISLocalToGlobalMappingDestroy(&BtoS);CHKERRQ(ierr);
655     ierr = ISDestroy(&change_primal_B);CHKERRQ(ierr);
656     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change);CHKERRQ(ierr);
657     for (i=0;i<sub_schurs->n_subs;i++) {
658       Mat change_sub;
659 
660       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
661       ierr = KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);CHKERRQ(ierr);
662       ierr = KSPSetType(sub_schurs->change[i],KSPPREONLY);CHKERRQ(ierr);
663       if (!sub_schurs->change_with_qr) {
664         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
665       } else {
666         Mat change_subt;
667         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);CHKERRQ(ierr);
668         ierr = MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
669         ierr = MatDestroy(&change_subt);CHKERRQ(ierr);
670       }
671       ierr = KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);CHKERRQ(ierr);
672       ierr = MatDestroy(&change_sub);CHKERRQ(ierr);
673       ierr = KSPSetOptionsPrefix(sub_schurs->change[i],sub_schurs->prefix);CHKERRQ(ierr);
674       ierr = KSPAppendOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");CHKERRQ(ierr);
675     }
676     ierr = ISDestroy(&change_primal_all);CHKERRQ(ierr);
677   }
678 
679   /* Local matrix of all local Schur on subsets (transposed) */
680   if (!sub_schurs->S_Ej_all) {
681     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
682     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
683     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
684     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
685   }
686 
687   /* Compute Schur complements explicitly */
688   F = NULL;
689   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 */
690     Mat         S_Ej_expl;
691     PetscScalar *work;
692     PetscInt    j,*dummy_idx;
693     PetscBool   Sdense;
694 
695     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
696     local_size = 0;
697     for (i=0;i<sub_schurs->n_subs;i++) {
698       IS  is_subset_B;
699       Mat AE_EE,AE_IE,AE_EI,S_Ej;
700 
701       /* subsets in original and boundary numbering */
702       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
703       /* EE block */
704       ierr = MatCreateSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
705       /* IE block */
706       ierr = MatCreateSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
707       /* EI block */
708       if (sub_schurs->is_hermitian) {
709         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
710       } else {
711         ierr = MatCreateSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
712       }
713       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
714       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
715       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
716       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
717       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
718       if (AE_II == A_II) { /* we can reuse the same ksp */
719         KSP ksp;
720         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
721         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
722       } else { /* build new ksp object which inherits ksp and pc types from the original one */
723         KSP       origksp,schurksp;
724         PC        origpc,schurpc;
725         KSPType   ksp_type;
726         PetscInt  n_internal;
727         PetscBool ispcnone;
728 
729         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
730         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
731         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
732         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
733         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
734         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
735         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
736         if (!ispcnone) {
737           PCType pc_type;
738           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
739           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
740         } else {
741           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
742         }
743         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
744         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
745           MatSolverPackage solver=NULL;
746           ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
747           if (solver) {
748             ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
749           }
750         }
751         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
752       }
753       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
754       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
755       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
756       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
757       if (Sdense) {
758         for (j=0;j<subset_size;j++) {
759           dummy_idx[j]=local_size+j;
760         }
761         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
762       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
763       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
764       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
765       local_size += subset_size;
766     }
767     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
768     /* free */
769     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
770     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
771     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
772   } else {
773     Mat         A,cs_AIB_mat = NULL,benign_AIIm1_ones_mat = NULL;
774     Vec         Dall = NULL;
775     IS          is_A_all,*is_p_r = NULL;
776     PetscScalar *work,*S_data,*schur_factor,infty = PETSC_MAX_REAL;
777     PetscInt    n,n_I,*dummy_idx,size_schur,size_active_schur,cum,cum2;
778     PetscBool   economic,solver_S,S_lower_triangular = PETSC_FALSE;
779     PetscBool   schur_has_vertices,factor_workaround;
780     char        solver[256];
781 
782     /* get sizes */
783     n_I = 0;
784     if (is_I_layer) {
785       ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
786     }
787     economic = PETSC_FALSE;
788     ierr = ISGetLocalSize(sub_schurs->is_I,&cum);CHKERRQ(ierr);
789     if (cum != n_I) economic = PETSC_TRUE;
790     ierr = MatGetLocalSize(sub_schurs->A,&n,NULL);CHKERRQ(ierr);
791     size_active_schur = local_size;
792 
793     /* import scaling vector (wrong formulation if we have 3D edges) */
794     if (scaling && compute_Stilda) {
795       const PetscScalar *array;
796       PetscScalar       *array2;
797       const PetscInt    *idxs;
798       PetscInt          i;
799 
800       ierr = ISGetIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
801       ierr = VecCreateSeq(PETSC_COMM_SELF,size_active_schur,&Dall);CHKERRQ(ierr);
802       ierr = VecGetArrayRead(scaling,&array);CHKERRQ(ierr);
803       ierr = VecGetArray(Dall,&array2);CHKERRQ(ierr);
804       for (i=0;i<size_active_schur;i++) array2[i] = array[idxs[i]];
805       ierr = VecRestoreArray(Dall,&array2);CHKERRQ(ierr);
806       ierr = VecRestoreArrayRead(scaling,&array);CHKERRQ(ierr);
807       ierr = ISRestoreIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
808       deluxe = PETSC_FALSE;
809     }
810 
811     /* size active schurs does not count any dirichlet or vertex dof on the interface */
812     factor_workaround = PETSC_FALSE;
813     schur_has_vertices = PETSC_FALSE;
814     cum = n_I+size_active_schur;
815     if (sub_schurs->is_dir) {
816       const PetscInt* idxs;
817       PetscInt        n_dir;
818 
819       ierr = ISGetLocalSize(sub_schurs->is_dir,&n_dir);CHKERRQ(ierr);
820       ierr = ISGetIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
821       ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_dir*sizeof(PetscInt));CHKERRQ(ierr);
822       ierr = ISRestoreIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
823       cum += n_dir;
824       factor_workaround = PETSC_TRUE;
825     }
826     /* include the primal vertices in the Schur complement */
827     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
828       PetscInt n_v;
829 
830       ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
831       if (n_v) {
832         const PetscInt* idxs;
833 
834         ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
835         ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_v*sizeof(PetscInt));CHKERRQ(ierr);
836         ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
837         cum += n_v;
838         factor_workaround = PETSC_TRUE;
839         schur_has_vertices = PETSC_TRUE;
840       }
841     }
842     size_schur = cum - n_I;
843     ierr = ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);CHKERRQ(ierr);
844     /* get working mat (TODO: factorize without actually permuting)  */
845     if (cum == n) {
846       ierr = ISSetPermutation(is_A_all);CHKERRQ(ierr);
847       ierr = MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
848     } else {
849       ierr = MatCreateSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
850     }
851     ierr = MatSetOptionsPrefix(A,sub_schurs->prefix);CHKERRQ(ierr);
852     ierr = MatAppendOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
853 
854     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
855        n^2 instead of n^1.5 or something. This is a workaround */
856     if (benign_n) {
857       Vec                    v;
858       ISLocalToGlobalMapping N_to_reor;
859       IS                     is_p0,is_p0_p;
860       PetscScalar            *cs_AIB,*AIIm1_data;
861       PetscInt               sizeA;
862 
863       ierr = ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);CHKERRQ(ierr);
864       ierr = ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
865       ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);CHKERRQ(ierr);
866       ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
867       ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
868       ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
869       ierr = MatCreateSeqDense(PETSC_COMM_SELF,sizeA,benign_n,NULL,&benign_AIIm1_ones_mat);CHKERRQ(ierr);
870       ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,benign_n,NULL,&cs_AIB_mat);CHKERRQ(ierr);
871       ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
872       ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
873       ierr = PetscMalloc1(benign_n,&is_p_r);CHKERRQ(ierr);
874       /* compute colsum of A_IB restricted to pressures */
875       for (i=0;i<benign_n;i++) {
876         Vec            benign_AIIm1_ones;
877         PetscScalar    *array;
878         const PetscInt *idxs;
879         PetscInt       j,nz;
880 
881         ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);CHKERRQ(ierr);
882         ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
883         ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
884         for (j=0;j<nz;j++) AIIm1_data[idxs[j]+sizeA*i] = 1.;
885         ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
886         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
887         ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
888         ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
889         ierr = VecGetArray(v,&array);CHKERRQ(ierr);
890         for (j=0;j<size_schur;j++) {
891 #if defined(PETSC_USE_COMPLEX)
892           cs_AIB[i*size_schur + j] = (PetscRealPart(array[j+n_I])/nz + PETSC_i*(PetscImaginaryPart(array[j+n_I])/nz));
893 #else
894           cs_AIB[i*size_schur + j] = array[j+n_I]/nz;
895 #endif
896         }
897         ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
898       }
899       ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
900       ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
901       ierr = VecDestroy(&v);CHKERRQ(ierr);
902       ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);CHKERRQ(ierr);
903       ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
904       ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
905       ierr = MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);CHKERRQ(ierr);
906       ierr = ISDestroy(&is_p0_p);CHKERRQ(ierr);
907       ierr = ISLocalToGlobalMappingDestroy(&N_to_reor);CHKERRQ(ierr);
908     }
909     ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_hermitian);CHKERRQ(ierr);
910     ierr = MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
911     ierr = MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
912 #if defined(PETSC_HAVE_MUMPS)
913     ierr = PetscStrcpy(solver,MATSOLVERMUMPS);CHKERRQ(ierr);
914 #else
915     ierr = PetscStrcpy(solver,MATSOLVERMKL_PARDISO);CHKERRQ(ierr);
916 #endif
917     ierr = PetscOptionsGetString(NULL,((PetscObject)A)->prefix,"-mat_solver_package",solver,256,NULL);CHKERRQ(ierr);
918 
919     /* when using the benign subspace trick, the local Schur complements are SPD */
920     if (benign_trick) sub_schurs->is_posdef = PETSC_TRUE;
921 
922     if (n_I) { /* TODO add ordering from options */
923       IS is_schur;
924 
925       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
926         ierr = MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
927       } else {
928         ierr = MatGetFactor(A,solver,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
929       }
930       ierr = MatSetErrorIfFailure(A,PETSC_TRUE);CHKERRQ(ierr);
931 
932       /* subsets ordered last */
933       ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is_schur);CHKERRQ(ierr);
934       ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
935       ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
936 
937       /* factorization step */
938       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
939         ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
940 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
941         ierr = MatMumpsSetIcntl(F,19,2);CHKERRQ(ierr);
942 #endif
943         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
944         S_lower_triangular = PETSC_TRUE;
945       } else {
946         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
947 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
948         ierr = MatMumpsSetIcntl(F,19,3);CHKERRQ(ierr);
949 #endif
950         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
951       }
952       ierr = MatViewFromOptions(F,(PetscObject)A,"-mat_factor_view");CHKERRQ(ierr);
953 
954       /* get explicit Schur Complement computed during numeric factorization */
955       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
956       ierr = MatSetOption(S_all,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
957       ierr = MatSetOption(S_all,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
958 
959       /* we can reuse the solvers if we are not using the economic version */
960       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
961       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
962       solver_S = PETSC_TRUE;
963 
964       /* update the Schur complement with the change of basis on the pressures */
965       if (benign_n) {
966         PetscScalar *S_data,*cs_AIB,*AIIm1_data;
967         Vec         v;
968         PetscInt    sizeA;
969 
970         ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
971         ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
972         ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
973 #if defined(PETSC_HAVE_MUMPS)
974         ierr = MatMumpsSetIcntl(F,26,0);CHKERRQ(ierr);
975 #endif
976 #if defined(PETSC_HAVE_MKL_PARDISO)
977         ierr = MatMkl_PardisoSetCntl(F,70,1);CHKERRQ(ierr);
978 #endif
979         ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
980         ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
981         for (i=0;i<benign_n;i++) {
982           Vec            benign_AIIm1_ones;
983           PetscScalar    *array,sum = 0.,one = 1.;
984           const PetscInt *idxs;
985           PetscInt       j,nz;
986           PetscBLASInt   B_k,B_n;
987 
988           ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
989           ierr = VecCopy(benign_AIIm1_ones,v);CHKERRQ(ierr);
990           ierr = MatSolve(F,v,benign_AIIm1_ones);CHKERRQ(ierr);
991           ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
992           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
993           /* p0 dof (eliminated) is excluded from the sum */
994           for (j=0;j<nz-1;j++) sum -= AIIm1_data[idxs[j]+sizeA*i];
995           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
996           ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
997           ierr = VecGetArray(v,&array);CHKERRQ(ierr);
998           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
999           /* cs_AIB already scaled by 1./nz */
1000           B_k = 1;
1001           ierr = PetscBLASIntCast(size_schur,&B_n);CHKERRQ(ierr);
1002           PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
1003           sum  = 1.;
1004           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));
1005           ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
1006           /* set p0 entry of AIIm1_ones to zero */
1007           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1008           for (j=0;j<benign_n;j++) AIIm1_data[idxs[nz-1]+sizeA*j] = 0.;
1009           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1010           ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
1011         }
1012   /* restore defaults */
1013 #if defined(PETSC_HAVE_MUMPS)
1014         ierr = MatMumpsSetIcntl(F,26,-1);CHKERRQ(ierr);
1015 #endif
1016 #if defined(PETSC_HAVE_MKL_PARDISO)
1017         ierr = MatMkl_PardisoSetCntl(F,70,0);CHKERRQ(ierr);
1018 #endif
1019         ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1020         ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1021         ierr = VecDestroy(&v);CHKERRQ(ierr);
1022         ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1023       }
1024       if (!reuse_solvers) {
1025         for (i=0;i<benign_n;i++) {
1026           ierr = ISDestroy(&is_p_r[i]);CHKERRQ(ierr);
1027         }
1028         ierr = PetscFree(is_p_r);CHKERRQ(ierr);
1029         ierr = MatDestroy(&cs_AIB_mat);CHKERRQ(ierr);
1030         ierr = MatDestroy(&benign_AIIm1_ones_mat);CHKERRQ(ierr);
1031       }
1032     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1033       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
1034       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1035       factor_workaround = PETSC_FALSE;
1036       solver_S = PETSC_FALSE;
1037     }
1038 
1039     if (reuse_solvers) {
1040       Mat                A_II,Afake;
1041       Vec                vec1_B;
1042       PCBDDCReuseSolvers msolv_ctx;
1043       PetscInt           n_R;
1044 
1045       if (sub_schurs->reuse_solver) {
1046         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1047       } else {
1048         ierr = PetscNew(&sub_schurs->reuse_solver);CHKERRQ(ierr);
1049       }
1050       msolv_ctx = sub_schurs->reuse_solver;
1051       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1052       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
1053       msolv_ctx->F = F;
1054       ierr = MatCreateVecs(F,&msolv_ctx->sol,NULL);CHKERRQ(ierr);
1055       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1056       {
1057         PetscScalar *array;
1058         PetscInt    n;
1059 
1060         ierr = VecGetLocalSize(msolv_ctx->sol,&n);CHKERRQ(ierr);
1061         ierr = VecGetArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1062         ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);CHKERRQ(ierr);
1063         ierr = VecRestoreArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1064       }
1065       msolv_ctx->has_vertices = schur_has_vertices;
1066 
1067       /* interior solver */
1068       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);CHKERRQ(ierr);
1069       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
1070       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
1071       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
1072       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);CHKERRQ(ierr);
1073       ierr = PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);CHKERRQ(ierr);
1074 
1075       /* correction solver */
1076       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->correction_solver);CHKERRQ(ierr);
1077       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
1078       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
1079       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);CHKERRQ(ierr);
1080       ierr = PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);CHKERRQ(ierr);
1081 
1082       /* scatter and vecs for Schur complement solver */
1083       ierr = MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);CHKERRQ(ierr);
1084       ierr = MatCreateVecs(sub_schurs->S,&vec1_B,NULL);CHKERRQ(ierr);
1085       if (!schur_has_vertices) {
1086         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1087         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1088         ierr = PetscObjectReference((PetscObject)is_A_all);CHKERRQ(ierr);
1089         msolv_ctx->is_R = is_A_all;
1090       } else {
1091         IS              is_B_all;
1092         const PetscInt* idxs;
1093         PetscInt        dual,n_v,n;
1094 
1095         ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
1096         dual = size_schur - n_v;
1097         ierr = ISGetLocalSize(is_A_all,&n);CHKERRQ(ierr);
1098         ierr = ISGetIndices(is_A_all,&idxs);CHKERRQ(ierr);
1099         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);CHKERRQ(ierr);
1100         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1101         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1102         ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);CHKERRQ(ierr);
1103         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1104         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1105         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);CHKERRQ(ierr);
1106         ierr = ISRestoreIndices(is_A_all,&idxs);CHKERRQ(ierr);
1107       }
1108       ierr = ISGetLocalSize(msolv_ctx->is_R,&n_R);CHKERRQ(ierr);
1109       ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,n_R,n_R,0,NULL,&Afake);CHKERRQ(ierr);
1110       ierr = MatAssemblyBegin(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1111       ierr = MatAssemblyEnd(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1112       ierr = PCSetOperators(msolv_ctx->correction_solver,Afake,Afake);CHKERRQ(ierr);
1113       ierr = MatDestroy(&Afake);CHKERRQ(ierr);
1114       ierr = VecDestroy(&vec1_B);CHKERRQ(ierr);
1115 
1116       /* communicate benign info to solver context */
1117       if (benign_n) {
1118         PetscScalar *array;
1119 
1120         msolv_ctx->benign_n = benign_n;
1121         msolv_ctx->benign_zerodiag_subs = is_p_r;
1122         ierr = PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);CHKERRQ(ierr);
1123         msolv_ctx->benign_csAIB = cs_AIB_mat;
1124         ierr = MatCreateVecs(cs_AIB_mat,&msolv_ctx->benign_corr_work,NULL);CHKERRQ(ierr);
1125         ierr = VecGetArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1126         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array,&msolv_ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
1127         ierr = VecRestoreArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1128         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1129       }
1130     } else {
1131       if (sub_schurs->reuse_solver) {
1132         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1133       }
1134       ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1135     }
1136     ierr = MatDestroy(&A);CHKERRQ(ierr);
1137     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
1138 
1139     /* Work arrays */
1140     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
1141 
1142     /* matrices for deluxe scaling and adaptive selection */
1143     if (!sub_schurs->sum_S_Ej_all) {
1144       ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1145       ierr = MatSetSizes(sub_schurs->sum_S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
1146       ierr = MatSetType(sub_schurs->sum_S_Ej_all,MATAIJ);CHKERRQ(ierr);
1147       ierr = MatSeqAIJSetPreallocation(sub_schurs->sum_S_Ej_all,0,nnz);CHKERRQ(ierr);
1148     }
1149     if (compute_Stilda) {
1150       if (!sub_schurs->sum_S_Ej_tilda_all) {
1151         ierr = MatDuplicate(sub_schurs->sum_S_Ej_all,MAT_SHARE_NONZERO_PATTERN,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1152       }
1153       if (!sub_schurs->sum_S_Ej_inv_all && deluxe) {
1154         ierr = MatDuplicate(sub_schurs->sum_S_Ej_all,MAT_SHARE_NONZERO_PATTERN,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1155       }
1156     }
1157 
1158     /* S_Ej_all */
1159     cum = cum2 = 0;
1160     ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1161     for (i=0;i<sub_schurs->n_subs;i++) {
1162       PetscInt j;
1163 
1164       /* get S_E */
1165       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1166       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1167         PetscInt k;
1168         for (k=0;k<subset_size;k++) {
1169           for (j=k;j<subset_size;j++) {
1170             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1171             work[j*subset_size+k] = PetscConj(S_data[cum2+k*size_schur+j]);
1172           }
1173         }
1174       } else { /* just copy to workspace */
1175         PetscInt k;
1176         for (k=0;k<subset_size;k++) {
1177           for (j=0;j<subset_size;j++) {
1178             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1179           }
1180         }
1181       }
1182       /* insert S_E values */
1183       for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1184       if (sub_schurs->change) {
1185         Mat            change_sub,SEj,T;
1186 
1187         /* change basis */
1188         ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1189         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1190         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1191           Mat T2;
1192           ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1193           ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1194           ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1195           ierr = MatDestroy(&T2);CHKERRQ(ierr);
1196         } else {
1197           ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1198         }
1199         ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1200         ierr = MatDestroy(&T);CHKERRQ(ierr);
1201         ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1.0,NULL,NULL);CHKERRQ(ierr);
1202         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1203       }
1204       if (deluxe) {
1205         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1206         /* if adaptivity is requested, invert S_E blocks */
1207         if (compute_Stilda) {
1208           ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1209           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1210           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1211             PetscInt k;
1212             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,work,&B_N,&B_ierr));
1213             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1214             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,work,&B_N,&B_ierr));
1215             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1216             for (k=0;k<subset_size;k++) {
1217               for (j=k;j<subset_size;j++) {
1218                 work[j*subset_size+k] = work[k*subset_size+j];
1219               }
1220             }
1221           } else {
1222             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,work,&B_N,pivots,&B_ierr));
1223             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1224             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1225             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1226           }
1227           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1228           ierr = MatSetValues(sub_schurs->sum_S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1229         }
1230       } else if (compute_Stilda) { /* not using deluxe */
1231         Mat         SEj;
1232         Vec         D;
1233         PetscScalar *array;
1234 
1235         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1236         ierr = VecGetArray(Dall,&array);CHKERRQ(ierr);
1237         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,array+cum,&D);CHKERRQ(ierr);
1238         ierr = VecRestoreArray(Dall,&array);CHKERRQ(ierr);
1239         ierr = VecShift(D,-1.);CHKERRQ(ierr);
1240         ierr = MatDiagonalScale(SEj,D,D);CHKERRQ(ierr);
1241         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1242         ierr = VecDestroy(&D);CHKERRQ(ierr);
1243         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1244       }
1245       cum += subset_size;
1246       cum2 += subset_size*(size_schur + 1);
1247     }
1248     ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1249 
1250     if (solver_S) {
1251       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1252     }
1253 
1254     schur_factor = NULL;
1255     if (compute_Stilda && size_active_schur) {
1256 
1257       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1258         PetscInt j;
1259         for (j=0;j<size_schur;j++) dummy_idx[j] = j;
1260         ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,size_schur,dummy_idx,size_schur,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1261       } else {
1262         Mat S_all_inv=NULL;
1263         if (solver_S) {
1264           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1265              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 */
1266           if (factor_workaround) {/* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1267             PetscScalar *data;
1268             PetscInt     nd = 0;
1269 
1270             if (!sub_schurs->is_posdef) {
1271               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1272             }
1273             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1274             ierr = MatDenseGetArray(S_all_inv,&data);CHKERRQ(ierr);
1275             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1276               ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1277             }
1278 
1279             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
1280             if (schur_has_vertices) {
1281               Mat          M;
1282               PetscScalar *tdata;
1283               PetscInt     nv = 0, news;
1284 
1285               ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
1286               news = size_active_schur + nv;
1287               ierr = PetscCalloc1(news*news,&tdata);CHKERRQ(ierr);
1288               for (i=0;i<size_active_schur;i++) {
1289                 ierr = PetscMemcpy(tdata+i*(news+1),data+i*(size_schur+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1290                 ierr = PetscMemcpy(tdata+i*(news+1)+size_active_schur-i,data+i*size_schur+size_active_schur+nd,nv*sizeof(PetscScalar));CHKERRQ(ierr);
1291               }
1292               for (i=0;i<nv;i++) {
1293                 PetscInt k = i+size_active_schur;
1294                 ierr = PetscMemcpy(tdata+k*(news+1),data+(k+nd)*(size_schur+1),(nv-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1295               }
1296 
1297               ierr = MatCreateSeqDense(PETSC_COMM_SELF,news,news,tdata,&M);CHKERRQ(ierr);
1298               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1299               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1300               /* save the factors */
1301               cum = 0;
1302               ierr = PetscMalloc1((size_active_schur*(size_active_schur +1))/2+nd,&schur_factor);CHKERRQ(ierr);
1303               for (i=0;i<size_active_schur;i++) {
1304                 ierr = PetscMemcpy(schur_factor+cum,tdata+i*(news+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1305                 cum += size_active_schur - i;
1306               }
1307               for (i=0;i<nd;i++) schur_factor[cum+i] = PetscSqrtReal(PetscRealPart(data[(i+size_active_schur)*(size_schur+1)]));
1308               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1309               /* move back just the active dofs to the Schur complement */
1310               for (i=0;i<size_active_schur;i++) {
1311                 ierr = PetscMemcpy(data+i*size_schur,tdata+i*news,size_active_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1312               }
1313               ierr = PetscFree(tdata);CHKERRQ(ierr);
1314               ierr = MatDestroy(&M);CHKERRQ(ierr);
1315             } else { /* we can factorize and invert just the activedofs */
1316               Mat M;
1317 
1318               ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_active_schur,size_active_schur,data,&M);CHKERRQ(ierr);
1319               ierr = MatSeqDenseSetLDA(M,size_schur);CHKERRQ(ierr);
1320               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1321               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1322               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1323               ierr = MatDestroy(&M);CHKERRQ(ierr);
1324               for (i=0;i<nd;i++) data[(i+size_active_schur)*(size_schur+1)] = 1.0/data[(i+size_active_schur)*(size_schur+1)];
1325             }
1326             ierr = MatDenseRestoreArray(S_all_inv,&data);CHKERRQ(ierr);
1327           } else { /* use MatFactor calls to invert S */
1328             ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
1329             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1330           }
1331         } else { /* we need to invert explicitly since we are not using MatFactor for S */
1332           ierr = PetscObjectReference((PetscObject)S_all);CHKERRQ(ierr);
1333           S_all_inv = S_all;
1334           ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1335           ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1336           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1337           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1338             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
1339             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1340             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
1341             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1342           } else {
1343             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
1344             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1345             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1346             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1347           }
1348           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1349           ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1350         }
1351         /* S_Ej_tilda_all */
1352         cum = cum2 = 0;
1353         ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1354         for (i=0;i<sub_schurs->n_subs;i++) {
1355           PetscInt j;
1356 
1357           ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1358           /* get (St^-1)_E */
1359           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1360              will be properly accessed later during adaptive selection */
1361           if (S_lower_triangular) {
1362             PetscInt k;
1363             if (sub_schurs->change) {
1364               for (k=0;k<subset_size;k++) {
1365                 for (j=k;j<subset_size;j++) {
1366                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1367                   work[j*subset_size+k] = work[k*subset_size+j];
1368                 }
1369               }
1370             } else {
1371               for (k=0;k<subset_size;k++) {
1372                 for (j=k;j<subset_size;j++) {
1373                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1374                 }
1375               }
1376             }
1377           } else {
1378             PetscInt k;
1379             for (k=0;k<subset_size;k++) {
1380               for (j=0;j<subset_size;j++) {
1381                 work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1382               }
1383             }
1384           }
1385           if (sub_schurs->change) {
1386             Mat change_sub,SEj,T;
1387 
1388             /* change basis */
1389             ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1390             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1391             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1392               Mat T2;
1393               ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1394               ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1395               ierr = MatDestroy(&T2);CHKERRQ(ierr);
1396               ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1397             } else {
1398               ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1399             }
1400             ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1401             ierr = MatDestroy(&T);CHKERRQ(ierr);
1402             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
1403             ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1./PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
1404             ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1405           }
1406           for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1407           ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1408           cum += subset_size;
1409           cum2 += subset_size*(size_schur + 1);
1410         }
1411         ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1412         if (solver_S) {
1413           if (schur_has_vertices) {
1414             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1415           } else {
1416             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_INVERTED);CHKERRQ(ierr);
1417           }
1418         }
1419         ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
1420       }
1421 
1422       /* move back factors if needed */
1423       if (schur_has_vertices) {
1424         Mat      S_tmp;
1425         PetscInt nd = 0;
1426 
1427         if (!solver_S) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
1428         ierr = MatFactorGetSchurComplement(F,&S_tmp,NULL);CHKERRQ(ierr);
1429         if (sub_schurs->is_posdef) {
1430           PetscScalar *data;
1431 
1432           ierr = MatDenseGetArray(S_tmp,&data);CHKERRQ(ierr);
1433           ierr = PetscMemzero(data,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1434 
1435           if (S_lower_triangular) {
1436             cum = 0;
1437             for (i=0;i<size_active_schur;i++) {
1438               ierr = PetscMemcpy(data+i*(size_schur+1),schur_factor+cum,(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1439               cum += size_active_schur-i;
1440 	    }
1441           } else {
1442             ierr = PetscMemcpy(data,schur_factor,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1443           }
1444           if (sub_schurs->is_dir) {
1445             ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1446 	    for (i=0;i<nd;i++) {
1447 	      data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
1448 	    }
1449           }
1450           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1451              set the diagonal entry of the Schur factor to a very large value */
1452           for (i=size_active_schur+nd;i<size_schur;i++) {
1453             data[i*(size_schur+1)] = infty;
1454           }
1455           ierr = MatDenseRestoreArray(S_tmp,&data);CHKERRQ(ierr);
1456         } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1457         ierr = MatFactorRestoreSchurComplement(F,&S_tmp,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1458       }
1459     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
1460       PetscScalar *data;
1461       PetscInt    nd = 0;
1462 
1463       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1464         ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1465       }
1466       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1467       ierr = MatDenseGetArray(S_all,&data);CHKERRQ(ierr);
1468       for (i=0;i<size_active_schur;i++) {
1469         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1470       }
1471       for (i=size_active_schur+nd;i<size_schur;i++) {
1472         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1473         data[i*(size_schur+1)] = infty;
1474       }
1475       ierr = MatDenseRestoreArray(S_all,&data);CHKERRQ(ierr);
1476       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1477     }
1478     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
1479     ierr = PetscFree(schur_factor);CHKERRQ(ierr);
1480     ierr = VecDestroy(&Dall);CHKERRQ(ierr);
1481   }
1482   ierr = PetscFree(nnz);CHKERRQ(ierr);
1483   ierr = MatDestroy(&F);CHKERRQ(ierr);
1484   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1485   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
1486   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1487   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1488   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1489   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1490   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1491   if (compute_Stilda) {
1492     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1493     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1494     if (deluxe) {
1495       ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1496       ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1497     }
1498   }
1499 
1500   /* Global matrix of all assembled Schur on subsets */
1501   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
1502   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
1503   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1504 
1505   /* Get local part of (\sum_j S_Ej) */
1506   ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_INITIAL_MATRIX,&submats);CHKERRQ(ierr);
1507   ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1508 
1509   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1510   if (compute_Stilda) {
1511     ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1512     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1513     ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1514     ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_tilda_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1515     if (deluxe) {
1516       ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1517       ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1518       ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1519       ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_inv_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1520     } else {
1521       PetscScalar *array;
1522       PetscInt    cum;
1523 
1524       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1525       cum = 0;
1526       for (i=0;i<sub_schurs->n_subs;i++) {
1527         ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1528         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1529         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1530         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
1531         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1532         PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
1533         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1534         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1535         cum += subset_size*subset_size;
1536       }
1537       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1538       ierr = PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1539       ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1540       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1541     }
1542   }
1543   ierr = MatDestroySubMatrices(1,&submats);CHKERRQ(ierr);
1544 
1545   /* free workspace */
1546   ierr = PetscFree(submats);CHKERRQ(ierr);
1547   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
1548   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
1549   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
1550   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
1551   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
1552   PetscFunctionReturn(0);
1553 }
1554 
1555 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc)
1556 {
1557   IS              *faces,*edges,*all_cc,vertices;
1558   PetscInt        i,n_faces,n_edges,n_all_cc;
1559   PetscBool       is_sorted;
1560   PetscErrorCode  ierr;
1561 
1562   PetscFunctionBegin;
1563   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
1564   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
1565   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
1566   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
1567 
1568   /* reset any previous data */
1569   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
1570 
1571   /* get index sets for faces and edges (already sorted by global ordering) */
1572   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1573   n_all_cc = n_faces+n_edges;
1574   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
1575   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
1576   for (i=0;i<n_faces;i++) {
1577     if (copycc) {
1578       ierr = ISDuplicate(faces[i],&all_cc[i]);CHKERRQ(ierr);
1579     } else {
1580       ierr = PetscObjectReference((PetscObject)faces[i]);CHKERRQ(ierr);
1581       all_cc[i] = faces[i];
1582     }
1583   }
1584   for (i=0;i<n_edges;i++) {
1585     if (copycc) {
1586       ierr = ISDuplicate(edges[i],&all_cc[n_faces+i]);CHKERRQ(ierr);
1587     } else {
1588       ierr = PetscObjectReference((PetscObject)edges[i]);CHKERRQ(ierr);
1589       all_cc[n_faces+i] = edges[i];
1590     }
1591     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
1592   }
1593   ierr = PetscObjectReference((PetscObject)vertices);CHKERRQ(ierr);
1594   sub_schurs->is_vertices = vertices;
1595   ierr = PCBDDCGraphRestoreCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1596   sub_schurs->is_dir = NULL;
1597   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
1598 
1599   /* Determine if MatFactor can be used */
1600   sub_schurs->schur_explicit = PETSC_FALSE;
1601 #if defined(PETSC_HAVE_MUMPS)
1602   sub_schurs->schur_explicit = PETSC_TRUE;
1603 #endif
1604 #if defined(PETSC_HAVE_MKL_PARDISO)
1605   sub_schurs->schur_explicit = PETSC_TRUE;
1606 #endif
1607 
1608   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
1609   sub_schurs->is_I = is_I;
1610   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
1611   sub_schurs->is_B = is_B;
1612   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
1613   sub_schurs->l2gmap = graph->l2gmap;
1614   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
1615   sub_schurs->BtoNmap = BtoNmap;
1616   sub_schurs->n_subs = n_all_cc;
1617   sub_schurs->is_subs = all_cc;
1618   if (!sub_schurs->schur_explicit) { /* sort by local ordering if we are not using MatFactor */
1619     for (i=0;i<sub_schurs->n_subs;i++) {
1620       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
1621     }
1622   }
1623   sub_schurs->S_Ej_all = NULL;
1624   sub_schurs->sum_S_Ej_all = NULL;
1625   sub_schurs->sum_S_Ej_inv_all = NULL;
1626   sub_schurs->sum_S_Ej_tilda_all = NULL;
1627   sub_schurs->is_Ej_all = NULL;
1628   PetscFunctionReturn(0);
1629 }
1630 
1631 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1632 {
1633   PCBDDCSubSchurs schurs_ctx;
1634   PetscErrorCode  ierr;
1635 
1636   PetscFunctionBegin;
1637   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
1638   schurs_ctx->n_subs = 0;
1639   *sub_schurs = schurs_ctx;
1640   PetscFunctionReturn(0);
1641 }
1642 
1643 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1644 {
1645   PetscInt       i;
1646   PetscErrorCode ierr;
1647 
1648   PetscFunctionBegin;
1649   if (!sub_schurs) PetscFunctionReturn(0);
1650   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1651   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1652   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1653   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1654   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1655   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1656   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1657   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1658   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1659   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1660   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1661   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1662   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1663   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1664   for (i=0;i<sub_schurs->n_subs;i++) {
1665     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
1666   }
1667   if (sub_schurs->n_subs) {
1668     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1669   }
1670   if (sub_schurs->reuse_solver) {
1671     ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1672   }
1673   ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1674   if (sub_schurs->change) {
1675     for (i=0;i<sub_schurs->n_subs;i++) {
1676       ierr = KSPDestroy(&sub_schurs->change[i]);CHKERRQ(ierr);
1677       ierr = ISDestroy(&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
1678     }
1679   }
1680   ierr = PetscFree(sub_schurs->change);CHKERRQ(ierr);
1681   ierr = PetscFree(sub_schurs->change_primal_sub);CHKERRQ(ierr);
1682   sub_schurs->n_subs = 0;
1683   PetscFunctionReturn(0);
1684 }
1685 
1686 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs* sub_schurs)
1687 {
1688   PetscErrorCode ierr;
1689 
1690   PetscFunctionBegin;
1691   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
1692   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
1693   PetscFunctionReturn(0);
1694 }
1695 
1696 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1697 {
1698   PetscInt       i,j,n;
1699   PetscErrorCode ierr;
1700 
1701   PetscFunctionBegin;
1702   n = 0;
1703   for (i=-n_prev;i<0;i++) {
1704     PetscInt start_dof = queue_tip[i];
1705     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1706       PetscInt dof = adjncy[j];
1707       if (!PetscBTLookup(touched,dof)) {
1708         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1709         queue_tip[n] = dof;
1710         n++;
1711       }
1712     }
1713   }
1714   *n_added = n;
1715   PetscFunctionReturn(0);
1716 }
1717