xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision f72e1d794beb6e111ffcdcf7032cfb587762bde1)
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 #if defined(PETSC_USE_COMPLEX)
408   sub_schurs->is_hermitian = PETSC_FALSE; /* Hermitian Cholesky is not supported by PETSc and external packages */
409 #else
410   sub_schurs->is_hermitian = PETSC_TRUE;
411 #endif
412   sub_schurs->is_posdef    = PETSC_TRUE;
413   if (benign_trick) sub_schurs->is_posdef = PETSC_FALSE;
414   ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)sub_schurs->l2gmap),sub_schurs->prefix,"BDDC sub_schurs options","PC");CHKERRQ(ierr);
415   ierr = PetscOptionsBool("-sub_schurs_hermitian","Hermitian problem",NULL,sub_schurs->is_hermitian,&sub_schurs->is_hermitian,NULL);CHKERRQ(ierr);
416   ierr = PetscOptionsBool("-sub_schurs_posdef","Positive definite problem",NULL,sub_schurs->is_posdef,&sub_schurs->is_posdef,NULL);CHKERRQ(ierr);
417   ierr = PetscOptionsEnd();CHKERRQ(ierr);
418 
419   /* convert matrix if needed */
420   if (Ain) {
421     PetscBool isseqaij;
422     ierr = PetscObjectTypeCompare((PetscObject)Ain,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
423     if (isseqaij) {
424       ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
425       sub_schurs->A = Ain;
426     } else {
427       ierr = MatConvert(Ain,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
428     }
429   }
430 
431   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
432   sub_schurs->S = Sin;
433   if (sub_schurs->schur_explicit) {
434     sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
435   }
436 
437   /* preliminary checks */
438   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");
439 
440   /* restrict work on active processes */
441   color = 0;
442   if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
443   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
444   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
445   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
446   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
447   ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
448   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
449   if (!sub_schurs->n_subs) {
450     ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
451     PetscFunctionReturn(0);
452   }
453   /* ierr = PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);CHKERRQ(ierr); */
454 
455   /* get Schur complement matrices */
456   if (!sub_schurs->schur_explicit) {
457     Mat       tA_IB,tA_BI,tA_BB;
458     PetscBool isseqsbaij;
459     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
460     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);CHKERRQ(ierr);
461     if (isseqsbaij) {
462       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
463       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
464       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
465     } else {
466       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
467       A_BB = tA_BB;
468       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
469       A_IB = tA_IB;
470       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
471       A_BI = tA_BI;
472     }
473   } else {
474     A_II = NULL;
475     A_IB = NULL;
476     A_BI = NULL;
477     A_BB = NULL;
478   }
479   S_all = NULL;
480 
481   /* determine interior problems */
482   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
483   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
484     PetscBT                touched;
485     const PetscInt*        idx_B;
486     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
487 
488     if (!xadj) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
489     /* get sizes */
490     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
491     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
492 
493     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
494     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
495     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
496 
497     /* all boundary dofs must be skipped when adding layers */
498     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
499     for (j=0;j<n_B;j++) {
500       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
501     }
502     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
503     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
504 
505     /* add prescribed number of layers of dofs */
506     n_local_dofs = n_B;
507     n_prev_added = n_B;
508     for (layer=0;layer<nlayers;layer++) {
509       PetscInt n_added;
510       if (n_local_dofs == n_I+n_B) break;
511       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);
512       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
513       n_prev_added = n_added;
514       n_local_dofs += n_added;
515       if (!n_added) break;
516     }
517     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
518 
519     /* IS for I layer dofs in original numbering */
520     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);
521     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
522     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
523     /* IS for I layer dofs in I numbering */
524     if (!sub_schurs->schur_explicit) {
525       ISLocalToGlobalMapping ItoNmap;
526       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
527       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
528       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
529 
530       /* II block */
531       ierr = MatCreateSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
532     }
533   } else {
534     PetscInt n_I;
535 
536     /* IS for I dofs in original numbering */
537     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
538     is_I_layer = sub_schurs->is_I;
539 
540     /* IS for I dofs in I numbering (strided 1) */
541     if (!sub_schurs->schur_explicit) {
542       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
543       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
544 
545       /* II block is the same */
546       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
547       AE_II = A_II;
548     }
549   }
550 
551   /* Get info on subset sizes and sum of all subsets sizes */
552   max_subset_size = 0;
553   local_size = 0;
554   for (i=0;i<sub_schurs->n_subs;i++) {
555     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
556     max_subset_size = PetscMax(subset_size,max_subset_size);
557     local_size += subset_size;
558   }
559 
560   /* Work arrays for local indices */
561   extra = 0;
562   ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
563   if (sub_schurs->schur_explicit && is_I_layer) {
564     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
565   }
566   ierr = PetscMalloc1(n_B+extra,&all_local_idx_N);CHKERRQ(ierr);
567   if (extra) {
568     const PetscInt *idxs;
569     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
570     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
571     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
572   }
573   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
574   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum1);CHKERRQ(ierr);
575   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
576 
577   /* Get local indices in local numbering */
578   local_size = 0;
579   for (i=0;i<sub_schurs->n_subs;i++) {
580     PetscInt j;
581     const    PetscInt *idxs;
582 
583     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
584     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
585     /* start (smallest in global ordering) and multiplicity */
586     auxnum1[i] = idxs[0];
587     auxnum2[i] = subset_size;
588     /* subset indices in local numbering */
589     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
590     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
591     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
592     local_size += subset_size;
593   }
594 
595   /* allocate extra workspace needed only for GETRI */
596   if (local_size && !benign_trick && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
597     PetscScalar  lwork,dummyscalar = 0.;
598     PetscBLASInt dummyint = 0;
599 
600     use_getr = PETSC_TRUE;
601     B_lwork = -1;
602     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
603     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
604     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
605     ierr = PetscFPTrapPop();CHKERRQ(ierr);
606     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
607     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
608     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
609   } else {
610     Bwork = NULL;
611     pivots = NULL;
612   }
613 
614   /* prepare parallel matrices for summing up properly schurs on subsets */
615   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);CHKERRQ(ierr);
616   ierr = ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);CHKERRQ(ierr);
617   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
618   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);CHKERRQ(ierr);
619   ierr = ISRenumber(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);CHKERRQ(ierr);
620   ierr = ISDestroy(&all_subsets);CHKERRQ(ierr);
621   ierr = ISDestroy(&all_subsets_mult);CHKERRQ(ierr);
622   ierr = ISGetLocalSize(all_subsets_n,&i);CHKERRQ(ierr);
623   if (i != local_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",i,local_size);
624   ierr = ISLocalToGlobalMappingCreateIS(all_subsets_n,&l2gmap_subsets);CHKERRQ(ierr);
625   ierr = MatCreateIS(comm_n,1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,NULL,&work_mat);CHKERRQ(ierr);
626   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
627   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
628   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
629   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
630 
631   /* subset indices in local boundary numbering */
632   if (!sub_schurs->is_Ej_all) {
633     PetscInt *all_local_idx_B;
634 
635     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
636     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
637     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);
638     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
639   }
640 
641   if (change) {
642     ISLocalToGlobalMapping BtoS;
643     IS                     change_primal_B;
644     IS                     change_primal_all;
645 
646     if (sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
647     if (sub_schurs->change) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
648     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change_primal_sub);CHKERRQ(ierr);
649     for (i=0;i<sub_schurs->n_subs;i++) {
650       ISLocalToGlobalMapping NtoS;
651       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);CHKERRQ(ierr);
652       ierr = ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
653       ierr = ISLocalToGlobalMappingDestroy(&NtoS);CHKERRQ(ierr);
654     }
655     ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);CHKERRQ(ierr);
656     ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);CHKERRQ(ierr);
657     ierr = ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);CHKERRQ(ierr);
658     ierr = ISLocalToGlobalMappingDestroy(&BtoS);CHKERRQ(ierr);
659     ierr = ISDestroy(&change_primal_B);CHKERRQ(ierr);
660     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change);CHKERRQ(ierr);
661     for (i=0;i<sub_schurs->n_subs;i++) {
662       Mat change_sub;
663 
664       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
665       ierr = KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);CHKERRQ(ierr);
666       ierr = KSPSetType(sub_schurs->change[i],KSPPREONLY);CHKERRQ(ierr);
667       if (!sub_schurs->change_with_qr) {
668         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
669       } else {
670         Mat change_subt;
671         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);CHKERRQ(ierr);
672         ierr = MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
673         ierr = MatDestroy(&change_subt);CHKERRQ(ierr);
674       }
675       ierr = KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);CHKERRQ(ierr);
676       ierr = MatDestroy(&change_sub);CHKERRQ(ierr);
677       ierr = KSPSetOptionsPrefix(sub_schurs->change[i],sub_schurs->prefix);CHKERRQ(ierr);
678       ierr = KSPAppendOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");CHKERRQ(ierr);
679     }
680     ierr = ISDestroy(&change_primal_all);CHKERRQ(ierr);
681   }
682 
683   /* Local matrix of all local Schur on subsets (transposed) */
684   if (!sub_schurs->S_Ej_all) {
685     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
686     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
687     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
688     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
689   }
690 
691   /* Compute Schur complements explicitly */
692   F = NULL;
693   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 */
694     Mat         S_Ej_expl;
695     PetscScalar *work;
696     PetscInt    j,*dummy_idx;
697     PetscBool   Sdense;
698 
699     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
700     local_size = 0;
701     for (i=0;i<sub_schurs->n_subs;i++) {
702       IS  is_subset_B;
703       Mat AE_EE,AE_IE,AE_EI,S_Ej;
704 
705       /* subsets in original and boundary numbering */
706       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
707       /* EE block */
708       ierr = MatCreateSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
709       /* IE block */
710       ierr = MatCreateSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
711       /* EI block */
712       if (sub_schurs->is_hermitian) {
713         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
714       } else {
715         ierr = MatCreateSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
716       }
717       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
718       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
719       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
720       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
721       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
722       if (AE_II == A_II) { /* we can reuse the same ksp */
723         KSP ksp;
724         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
725         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
726       } else { /* build new ksp object which inherits ksp and pc types from the original one */
727         KSP       origksp,schurksp;
728         PC        origpc,schurpc;
729         KSPType   ksp_type;
730         PetscInt  n_internal;
731         PetscBool ispcnone;
732 
733         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
734         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
735         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
736         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
737         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
738         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
739         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
740         if (!ispcnone) {
741           PCType pc_type;
742           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
743           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
744         } else {
745           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
746         }
747         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
748         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
749           MatSolverType solver = NULL;
750           ierr = PCFactorGetMatSolverType(origpc,(MatSolverType*)&solver);CHKERRQ(ierr);
751           if (solver) {
752             ierr = PCFactorSetMatSolverType(schurpc,solver);CHKERRQ(ierr);
753           }
754         }
755         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
756       }
757       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
758       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
759       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
760       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
761       if (Sdense) {
762         for (j=0;j<subset_size;j++) {
763           dummy_idx[j]=local_size+j;
764         }
765         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
766       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
767       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
768       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
769       local_size += subset_size;
770     }
771     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
772     /* free */
773     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
774     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
775     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
776   } else {
777     Mat         A,cs_AIB_mat = NULL,benign_AIIm1_ones_mat = NULL;
778     Vec         Dall = NULL;
779     IS          is_A_all,*is_p_r = NULL;
780     PetscScalar *work,*S_data,*schur_factor,infty = PETSC_MAX_REAL;
781     PetscInt    n,n_I,*dummy_idx,size_schur,size_active_schur,cum,cum2;
782     PetscBool   economic,solver_S,S_lower_triangular = PETSC_FALSE;
783     PetscBool   schur_has_vertices,factor_workaround;
784     char        solver[256];
785 
786     /* get sizes */
787     n_I = 0;
788     if (is_I_layer) {
789       ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
790     }
791     economic = PETSC_FALSE;
792     ierr = ISGetLocalSize(sub_schurs->is_I,&cum);CHKERRQ(ierr);
793     if (cum != n_I) economic = PETSC_TRUE;
794     ierr = MatGetLocalSize(sub_schurs->A,&n,NULL);CHKERRQ(ierr);
795     size_active_schur = local_size;
796 
797     /* import scaling vector (wrong formulation if we have 3D edges) */
798     if (scaling && compute_Stilda) {
799       const PetscScalar *array;
800       PetscScalar       *array2;
801       const PetscInt    *idxs;
802       PetscInt          i;
803 
804       ierr = ISGetIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
805       ierr = VecCreateSeq(PETSC_COMM_SELF,size_active_schur,&Dall);CHKERRQ(ierr);
806       ierr = VecGetArrayRead(scaling,&array);CHKERRQ(ierr);
807       ierr = VecGetArray(Dall,&array2);CHKERRQ(ierr);
808       for (i=0;i<size_active_schur;i++) array2[i] = array[idxs[i]];
809       ierr = VecRestoreArray(Dall,&array2);CHKERRQ(ierr);
810       ierr = VecRestoreArrayRead(scaling,&array);CHKERRQ(ierr);
811       ierr = ISRestoreIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
812       deluxe = PETSC_FALSE;
813     }
814 
815     /* size active schurs does not count any dirichlet or vertex dof on the interface */
816     factor_workaround = PETSC_FALSE;
817     schur_has_vertices = PETSC_FALSE;
818     cum = n_I+size_active_schur;
819     if (sub_schurs->is_dir) {
820       const PetscInt* idxs;
821       PetscInt        n_dir;
822 
823       ierr = ISGetLocalSize(sub_schurs->is_dir,&n_dir);CHKERRQ(ierr);
824       ierr = ISGetIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
825       ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_dir*sizeof(PetscInt));CHKERRQ(ierr);
826       ierr = ISRestoreIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
827       cum += n_dir;
828       factor_workaround = PETSC_TRUE;
829     }
830     /* include the primal vertices in the Schur complement */
831     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
832       PetscInt n_v;
833 
834       ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
835       if (n_v) {
836         const PetscInt* idxs;
837 
838         ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
839         ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_v*sizeof(PetscInt));CHKERRQ(ierr);
840         ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
841         cum += n_v;
842         factor_workaround = PETSC_TRUE;
843         schur_has_vertices = PETSC_TRUE;
844       }
845     }
846     size_schur = cum - n_I;
847     ierr = ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);CHKERRQ(ierr);
848     /* get working mat (TODO: factorize without actually permuting)  */
849     if (cum == n) {
850       ierr = ISSetPermutation(is_A_all);CHKERRQ(ierr);
851       ierr = MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
852     } else {
853       ierr = MatCreateSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
854     }
855     ierr = MatSetOptionsPrefix(A,sub_schurs->prefix);CHKERRQ(ierr);
856     ierr = MatAppendOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
857 
858     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
859        n^2 instead of n^1.5 or something. This is a workaround */
860     if (benign_n) {
861       Vec                    v;
862       ISLocalToGlobalMapping N_to_reor;
863       IS                     is_p0,is_p0_p;
864       PetscScalar            *cs_AIB,*AIIm1_data;
865       PetscInt               sizeA;
866 
867       ierr = ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);CHKERRQ(ierr);
868       ierr = ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
869       ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);CHKERRQ(ierr);
870       ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
871       ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
872       ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
873       ierr = MatCreateSeqDense(PETSC_COMM_SELF,sizeA,benign_n,NULL,&benign_AIIm1_ones_mat);CHKERRQ(ierr);
874       ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,benign_n,NULL,&cs_AIB_mat);CHKERRQ(ierr);
875       ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
876       ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
877       ierr = PetscMalloc1(benign_n,&is_p_r);CHKERRQ(ierr);
878       /* compute colsum of A_IB restricted to pressures */
879       for (i=0;i<benign_n;i++) {
880         Vec            benign_AIIm1_ones;
881         PetscScalar    *array;
882         const PetscInt *idxs;
883         PetscInt       j,nz;
884 
885         ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);CHKERRQ(ierr);
886         ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
887         ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
888         for (j=0;j<nz;j++) AIIm1_data[idxs[j]+sizeA*i] = 1.;
889         ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
890         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
891         ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
892         ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
893         ierr = VecGetArray(v,&array);CHKERRQ(ierr);
894         for (j=0;j<size_schur;j++) {
895 #if defined(PETSC_USE_COMPLEX)
896           cs_AIB[i*size_schur + j] = (PetscRealPart(array[j+n_I])/nz + PETSC_i*(PetscImaginaryPart(array[j+n_I])/nz));
897 #else
898           cs_AIB[i*size_schur + j] = array[j+n_I]/nz;
899 #endif
900         }
901         ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
902       }
903       ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
904       ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
905       ierr = VecDestroy(&v);CHKERRQ(ierr);
906       ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);CHKERRQ(ierr);
907       ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
908       ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
909       ierr = MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);CHKERRQ(ierr);
910       ierr = ISDestroy(&is_p0_p);CHKERRQ(ierr);
911       ierr = ISLocalToGlobalMappingDestroy(&N_to_reor);CHKERRQ(ierr);
912     }
913     ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_hermitian);CHKERRQ(ierr);
914     ierr = MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
915     ierr = MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
916 #if defined(PETSC_HAVE_MUMPS)
917     ierr = PetscStrcpy(solver,MATSOLVERMUMPS);CHKERRQ(ierr);
918 #else
919     ierr = PetscStrcpy(solver,MATSOLVERMKL_PARDISO);CHKERRQ(ierr);
920 #endif
921     ierr = PetscOptionsGetString(NULL,((PetscObject)A)->prefix,"-mat_solver_type",solver,256,NULL);CHKERRQ(ierr);
922 
923     /* when using the benign subspace trick, the local Schur complements are SPD */
924     if (benign_trick) sub_schurs->is_posdef = PETSC_TRUE;
925 
926     if (n_I) { /* TODO add ordering from options */
927       IS is_schur;
928 
929       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
930         ierr = MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
931       } else {
932         ierr = MatGetFactor(A,solver,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
933       }
934       ierr = MatSetErrorIfFailure(A,PETSC_TRUE);CHKERRQ(ierr);
935 
936       /* subsets ordered last */
937       ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is_schur);CHKERRQ(ierr);
938       ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
939       ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
940 
941       /* factorization step */
942       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
943         ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
944 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
945         ierr = MatMumpsSetIcntl(F,19,2);CHKERRQ(ierr);
946 #endif
947         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
948         S_lower_triangular = PETSC_TRUE;
949       } else {
950         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
951 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
952         ierr = MatMumpsSetIcntl(F,19,3);CHKERRQ(ierr);
953 #endif
954         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
955       }
956       ierr = MatViewFromOptions(F,(PetscObject)A,"-mat_factor_view");CHKERRQ(ierr);
957 
958       /* get explicit Schur Complement computed during numeric factorization */
959       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
960       ierr = MatSetOption(S_all,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
961       ierr = MatSetOption(S_all,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
962 
963       /* we can reuse the solvers if we are not using the economic version */
964       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
965       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
966       solver_S = PETSC_TRUE;
967 
968       /* update the Schur complement with the change of basis on the pressures */
969       if (benign_n) {
970         PetscScalar *S_data,*cs_AIB,*AIIm1_data;
971         Vec         v;
972         PetscInt    sizeA;
973 
974         ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
975         ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
976         ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
977 #if defined(PETSC_HAVE_MUMPS)
978         ierr = MatMumpsSetIcntl(F,26,0);CHKERRQ(ierr);
979 #endif
980 #if defined(PETSC_HAVE_MKL_PARDISO)
981         ierr = MatMkl_PardisoSetCntl(F,70,1);CHKERRQ(ierr);
982 #endif
983         ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
984         ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
985         for (i=0;i<benign_n;i++) {
986           Vec            benign_AIIm1_ones;
987           PetscScalar    *array,sum = 0.,one = 1.;
988           const PetscInt *idxs;
989           PetscInt       j,nz;
990           PetscBLASInt   B_k,B_n;
991 
992           ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
993           ierr = VecCopy(benign_AIIm1_ones,v);CHKERRQ(ierr);
994           ierr = MatSolve(F,v,benign_AIIm1_ones);CHKERRQ(ierr);
995           ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
996           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
997           /* p0 dof (eliminated) is excluded from the sum */
998           for (j=0;j<nz-1;j++) sum -= AIIm1_data[idxs[j]+sizeA*i];
999           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1000           ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
1001           ierr = VecGetArray(v,&array);CHKERRQ(ierr);
1002           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
1003           /* cs_AIB already scaled by 1./nz */
1004           B_k = 1;
1005           ierr = PetscBLASIntCast(size_schur,&B_n);CHKERRQ(ierr);
1006           PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
1007           sum  = 1.;
1008           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));
1009           ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
1010           /* set p0 entry of AIIm1_ones to zero */
1011           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1012           for (j=0;j<benign_n;j++) AIIm1_data[idxs[nz-1]+sizeA*j] = 0.;
1013           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1014           ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
1015         }
1016         if (!S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1017           PetscInt k,j;
1018           for (k=0;k<size_schur;k++) {
1019             for (j=k;j<size_schur;j++) {
1020               S_data[j*size_schur+k] = PetscConj(S_data[k*size_schur+j]);
1021             }
1022           }
1023         }
1024 
1025         /* restore defaults */
1026 #if defined(PETSC_HAVE_MUMPS)
1027         ierr = MatMumpsSetIcntl(F,26,-1);CHKERRQ(ierr);
1028 #endif
1029 #if defined(PETSC_HAVE_MKL_PARDISO)
1030         ierr = MatMkl_PardisoSetCntl(F,70,0);CHKERRQ(ierr);
1031 #endif
1032         ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1033         ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1034         ierr = VecDestroy(&v);CHKERRQ(ierr);
1035         ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1036       }
1037       if (!reuse_solvers) {
1038         for (i=0;i<benign_n;i++) {
1039           ierr = ISDestroy(&is_p_r[i]);CHKERRQ(ierr);
1040         }
1041         ierr = PetscFree(is_p_r);CHKERRQ(ierr);
1042         ierr = MatDestroy(&cs_AIB_mat);CHKERRQ(ierr);
1043         ierr = MatDestroy(&benign_AIIm1_ones_mat);CHKERRQ(ierr);
1044       }
1045     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1046       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
1047       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1048       factor_workaround = PETSC_FALSE;
1049       solver_S = PETSC_FALSE;
1050     }
1051 
1052     if (reuse_solvers) {
1053       Mat                A_II,Afake;
1054       Vec                vec1_B;
1055       PCBDDCReuseSolvers msolv_ctx;
1056       PetscInt           n_R;
1057 
1058       if (sub_schurs->reuse_solver) {
1059         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1060       } else {
1061         ierr = PetscNew(&sub_schurs->reuse_solver);CHKERRQ(ierr);
1062       }
1063       msolv_ctx = sub_schurs->reuse_solver;
1064       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1065       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
1066       msolv_ctx->F = F;
1067       ierr = MatCreateVecs(F,&msolv_ctx->sol,NULL);CHKERRQ(ierr);
1068       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1069       {
1070         PetscScalar *array;
1071         PetscInt    n;
1072 
1073         ierr = VecGetLocalSize(msolv_ctx->sol,&n);CHKERRQ(ierr);
1074         ierr = VecGetArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1075         ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);CHKERRQ(ierr);
1076         ierr = VecRestoreArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1077       }
1078       msolv_ctx->has_vertices = schur_has_vertices;
1079 
1080       /* interior solver */
1081       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);CHKERRQ(ierr);
1082       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
1083       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
1084       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
1085       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);CHKERRQ(ierr);
1086       ierr = PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);CHKERRQ(ierr);
1087 
1088       /* correction solver */
1089       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->correction_solver);CHKERRQ(ierr);
1090       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
1091       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
1092       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);CHKERRQ(ierr);
1093       ierr = PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);CHKERRQ(ierr);
1094 
1095       /* scatter and vecs for Schur complement solver */
1096       ierr = MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);CHKERRQ(ierr);
1097       ierr = MatCreateVecs(sub_schurs->S,&vec1_B,NULL);CHKERRQ(ierr);
1098       if (!schur_has_vertices) {
1099         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1100         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1101         ierr = PetscObjectReference((PetscObject)is_A_all);CHKERRQ(ierr);
1102         msolv_ctx->is_R = is_A_all;
1103       } else {
1104         IS              is_B_all;
1105         const PetscInt* idxs;
1106         PetscInt        dual,n_v,n;
1107 
1108         ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
1109         dual = size_schur - n_v;
1110         ierr = ISGetLocalSize(is_A_all,&n);CHKERRQ(ierr);
1111         ierr = ISGetIndices(is_A_all,&idxs);CHKERRQ(ierr);
1112         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);CHKERRQ(ierr);
1113         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1114         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1115         ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);CHKERRQ(ierr);
1116         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1117         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1118         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);CHKERRQ(ierr);
1119         ierr = ISRestoreIndices(is_A_all,&idxs);CHKERRQ(ierr);
1120       }
1121       ierr = ISGetLocalSize(msolv_ctx->is_R,&n_R);CHKERRQ(ierr);
1122       ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,n_R,n_R,0,NULL,&Afake);CHKERRQ(ierr);
1123       ierr = MatAssemblyBegin(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1124       ierr = MatAssemblyEnd(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1125       ierr = PCSetOperators(msolv_ctx->correction_solver,Afake,Afake);CHKERRQ(ierr);
1126       ierr = MatDestroy(&Afake);CHKERRQ(ierr);
1127       ierr = VecDestroy(&vec1_B);CHKERRQ(ierr);
1128 
1129       /* communicate benign info to solver context */
1130       if (benign_n) {
1131         PetscScalar *array;
1132 
1133         msolv_ctx->benign_n = benign_n;
1134         msolv_ctx->benign_zerodiag_subs = is_p_r;
1135         ierr = PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);CHKERRQ(ierr);
1136         msolv_ctx->benign_csAIB = cs_AIB_mat;
1137         ierr = MatCreateVecs(cs_AIB_mat,&msolv_ctx->benign_corr_work,NULL);CHKERRQ(ierr);
1138         ierr = VecGetArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1139         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array,&msolv_ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
1140         ierr = VecRestoreArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1141         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1142       }
1143     } else {
1144       if (sub_schurs->reuse_solver) {
1145         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1146       }
1147       ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1148     }
1149     ierr = MatDestroy(&A);CHKERRQ(ierr);
1150     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
1151 
1152     /* Work arrays */
1153     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
1154 
1155     /* matrices for deluxe scaling and adaptive selection */
1156     if (compute_Stilda) {
1157       if (!sub_schurs->sum_S_Ej_tilda_all) {
1158         ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_SHARE_NONZERO_PATTERN,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1159       }
1160       if (!sub_schurs->sum_S_Ej_inv_all && deluxe) {
1161         ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_SHARE_NONZERO_PATTERN,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1162       }
1163     }
1164 
1165     /* S_Ej_all */
1166     cum = cum2 = 0;
1167     ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1168     for (i=0;i<sub_schurs->n_subs;i++) {
1169       PetscInt j;
1170 
1171       /* get S_E */
1172       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1173       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1174         PetscInt k;
1175         for (k=0;k<subset_size;k++) {
1176           for (j=k;j<subset_size;j++) {
1177             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1178             work[j*subset_size+k] = PetscConj(S_data[cum2+k*size_schur+j]);
1179           }
1180         }
1181       } else { /* just copy to workspace */
1182         PetscInt k;
1183         for (k=0;k<subset_size;k++) {
1184           for (j=0;j<subset_size;j++) {
1185             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1186           }
1187         }
1188       }
1189       /* insert S_E values */
1190       for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1191       if (sub_schurs->change) {
1192         Mat            change_sub,SEj,T;
1193 
1194         /* change basis */
1195         ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1196         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1197         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1198           Mat T2;
1199           ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1200           ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1201           ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1202           ierr = MatDestroy(&T2);CHKERRQ(ierr);
1203         } else {
1204           ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1205         }
1206         ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1207         ierr = MatDestroy(&T);CHKERRQ(ierr);
1208         ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1.0,NULL,NULL);CHKERRQ(ierr);
1209         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1210       }
1211       if (deluxe) {
1212         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1213         /* if adaptivity is requested, invert S_E blocks */
1214         if (compute_Stilda) {
1215           ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1216           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1217           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1218             PetscInt k;
1219             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,work,&B_N,&B_ierr));
1220             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1221             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,work,&B_N,&B_ierr));
1222             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1223             for (k=0;k<subset_size;k++) {
1224               for (j=k;j<subset_size;j++) {
1225                 work[j*subset_size+k] = work[k*subset_size+j];
1226               }
1227             }
1228           } else {
1229             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,work,&B_N,pivots,&B_ierr));
1230             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1231             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1232             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1233           }
1234           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1235           ierr = MatSetValues(sub_schurs->sum_S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1236         }
1237       } else if (compute_Stilda) { /* not using deluxe */
1238         Mat         SEj;
1239         Vec         D;
1240         PetscScalar *array;
1241 
1242         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1243         ierr = VecGetArray(Dall,&array);CHKERRQ(ierr);
1244         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,array+cum,&D);CHKERRQ(ierr);
1245         ierr = VecRestoreArray(Dall,&array);CHKERRQ(ierr);
1246         ierr = VecShift(D,-1.);CHKERRQ(ierr);
1247         ierr = MatDiagonalScale(SEj,D,D);CHKERRQ(ierr);
1248         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1249         ierr = VecDestroy(&D);CHKERRQ(ierr);
1250         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1251       }
1252       cum += subset_size;
1253       cum2 += subset_size*(size_schur + 1);
1254     }
1255     ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1256 
1257     if (solver_S) {
1258       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1259     }
1260 
1261     schur_factor = NULL;
1262     if (compute_Stilda && size_active_schur) {
1263 
1264       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1265         PetscInt j;
1266         for (j=0;j<size_schur;j++) dummy_idx[j] = j;
1267         ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,size_schur,dummy_idx,size_schur,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1268       } else {
1269         Mat S_all_inv=NULL;
1270         if (solver_S) {
1271           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1272              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 */
1273           if (factor_workaround) {/* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1274             PetscScalar *data;
1275             PetscInt     nd = 0;
1276 
1277             if (!sub_schurs->is_posdef) {
1278               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1279             }
1280             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1281             ierr = MatDenseGetArray(S_all_inv,&data);CHKERRQ(ierr);
1282             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1283               ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1284             }
1285 
1286             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
1287             if (schur_has_vertices) {
1288               Mat          M;
1289               PetscScalar *tdata;
1290               PetscInt     nv = 0, news;
1291 
1292               ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
1293               news = size_active_schur + nv;
1294               ierr = PetscCalloc1(news*news,&tdata);CHKERRQ(ierr);
1295               for (i=0;i<size_active_schur;i++) {
1296                 ierr = PetscMemcpy(tdata+i*(news+1),data+i*(size_schur+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1297                 ierr = PetscMemcpy(tdata+i*(news+1)+size_active_schur-i,data+i*size_schur+size_active_schur+nd,nv*sizeof(PetscScalar));CHKERRQ(ierr);
1298               }
1299               for (i=0;i<nv;i++) {
1300                 PetscInt k = i+size_active_schur;
1301                 ierr = PetscMemcpy(tdata+k*(news+1),data+(k+nd)*(size_schur+1),(nv-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1302               }
1303 
1304               ierr = MatCreateSeqDense(PETSC_COMM_SELF,news,news,tdata,&M);CHKERRQ(ierr);
1305               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1306               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1307               /* save the factors */
1308               cum = 0;
1309               ierr = PetscMalloc1((size_active_schur*(size_active_schur +1))/2+nd,&schur_factor);CHKERRQ(ierr);
1310               for (i=0;i<size_active_schur;i++) {
1311                 ierr = PetscMemcpy(schur_factor+cum,tdata+i*(news+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1312                 cum += size_active_schur - i;
1313               }
1314               for (i=0;i<nd;i++) schur_factor[cum+i] = PetscSqrtReal(PetscRealPart(data[(i+size_active_schur)*(size_schur+1)]));
1315               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1316               /* move back just the active dofs to the Schur complement */
1317               for (i=0;i<size_active_schur;i++) {
1318                 ierr = PetscMemcpy(data+i*size_schur,tdata+i*news,size_active_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1319               }
1320               ierr = PetscFree(tdata);CHKERRQ(ierr);
1321               ierr = MatDestroy(&M);CHKERRQ(ierr);
1322             } else { /* we can factorize and invert just the activedofs */
1323               Mat M;
1324 
1325               ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_active_schur,size_active_schur,data,&M);CHKERRQ(ierr);
1326               ierr = MatSeqDenseSetLDA(M,size_schur);CHKERRQ(ierr);
1327               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1328               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1329               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1330               ierr = MatDestroy(&M);CHKERRQ(ierr);
1331               for (i=0;i<nd;i++) data[(i+size_active_schur)*(size_schur+1)] = 1.0/data[(i+size_active_schur)*(size_schur+1)];
1332             }
1333             ierr = MatDenseRestoreArray(S_all_inv,&data);CHKERRQ(ierr);
1334           } else { /* use MatFactor calls to invert S */
1335             ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
1336             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1337           }
1338         } else { /* we need to invert explicitly since we are not using MatFactor for S */
1339           ierr = PetscObjectReference((PetscObject)S_all);CHKERRQ(ierr);
1340           S_all_inv = S_all;
1341           ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1342           ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1343           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1344           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1345             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
1346             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1347             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
1348             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1349           } else {
1350             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
1351             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1352             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1353             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1354           }
1355           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1356           ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1357         }
1358         /* S_Ej_tilda_all */
1359         cum = cum2 = 0;
1360         ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1361         for (i=0;i<sub_schurs->n_subs;i++) {
1362           PetscInt j;
1363 
1364           ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1365           /* get (St^-1)_E */
1366           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1367              will be properly accessed later during adaptive selection */
1368           if (S_lower_triangular) {
1369             PetscInt k;
1370             if (sub_schurs->change) {
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                   work[j*subset_size+k] = work[k*subset_size+j];
1375                 }
1376               }
1377             } else {
1378               for (k=0;k<subset_size;k++) {
1379                 for (j=k;j<subset_size;j++) {
1380                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1381                 }
1382               }
1383             }
1384           } else {
1385             PetscInt k;
1386             for (k=0;k<subset_size;k++) {
1387               for (j=0;j<subset_size;j++) {
1388                 work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1389               }
1390             }
1391           }
1392           if (sub_schurs->change) {
1393             Mat change_sub,SEj,T;
1394 
1395             /* change basis */
1396             ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1397             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1398             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1399               Mat T2;
1400               ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1401               ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1402               ierr = MatDestroy(&T2);CHKERRQ(ierr);
1403               ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1404             } else {
1405               ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1406             }
1407             ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1408             ierr = MatDestroy(&T);CHKERRQ(ierr);
1409             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
1410             ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1./PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
1411             ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1412           }
1413           for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1414           ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1415           cum += subset_size;
1416           cum2 += subset_size*(size_schur + 1);
1417         }
1418         ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1419         if (solver_S) {
1420           if (schur_has_vertices) {
1421             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1422           } else {
1423             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_INVERTED);CHKERRQ(ierr);
1424           }
1425         }
1426         ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
1427       }
1428 
1429       /* move back factors if needed */
1430       if (schur_has_vertices) {
1431         Mat      S_tmp;
1432         PetscInt nd = 0;
1433 
1434         if (!solver_S) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
1435         ierr = MatFactorGetSchurComplement(F,&S_tmp,NULL);CHKERRQ(ierr);
1436         if (sub_schurs->is_posdef) {
1437           PetscScalar *data;
1438 
1439           ierr = MatDenseGetArray(S_tmp,&data);CHKERRQ(ierr);
1440           ierr = PetscMemzero(data,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1441 
1442           if (S_lower_triangular) {
1443             cum = 0;
1444             for (i=0;i<size_active_schur;i++) {
1445               ierr = PetscMemcpy(data+i*(size_schur+1),schur_factor+cum,(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1446               cum += size_active_schur-i;
1447 	    }
1448           } else {
1449             ierr = PetscMemcpy(data,schur_factor,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1450           }
1451           if (sub_schurs->is_dir) {
1452             ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1453 	    for (i=0;i<nd;i++) {
1454 	      data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
1455 	    }
1456           }
1457           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1458              set the diagonal entry of the Schur factor to a very large value */
1459           for (i=size_active_schur+nd;i<size_schur;i++) {
1460             data[i*(size_schur+1)] = infty;
1461           }
1462           ierr = MatDenseRestoreArray(S_tmp,&data);CHKERRQ(ierr);
1463         } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1464         ierr = MatFactorRestoreSchurComplement(F,&S_tmp,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1465       }
1466     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
1467       PetscScalar *data;
1468       PetscInt    nd = 0;
1469 
1470       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1471         ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1472       }
1473       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1474       ierr = MatDenseGetArray(S_all,&data);CHKERRQ(ierr);
1475       for (i=0;i<size_active_schur;i++) {
1476         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1477       }
1478       for (i=size_active_schur+nd;i<size_schur;i++) {
1479         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1480         data[i*(size_schur+1)] = infty;
1481       }
1482       ierr = MatDenseRestoreArray(S_all,&data);CHKERRQ(ierr);
1483       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1484     }
1485     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
1486     ierr = PetscFree(schur_factor);CHKERRQ(ierr);
1487     ierr = VecDestroy(&Dall);CHKERRQ(ierr);
1488   }
1489   ierr = PetscFree(nnz);CHKERRQ(ierr);
1490   ierr = MatDestroy(&F);CHKERRQ(ierr);
1491   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1492   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
1493   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1494   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1495   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1496   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1497   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1498   if (compute_Stilda) {
1499     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1500     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1501     if (deluxe) {
1502       ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1503       ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1504     }
1505   }
1506 
1507   /* Global matrix of all assembled Schur on subsets */
1508   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
1509   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
1510   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1511 
1512   /* Get local part of (\sum_j S_Ej) */
1513   ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_INITIAL_MATRIX,&submats);CHKERRQ(ierr);
1514   if (!sub_schurs->sum_S_Ej_all) {
1515     ierr = MatDuplicate(submats[0],MAT_COPY_VALUES,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1516   } else {
1517     ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1518   }
1519 
1520   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1521   if (compute_Stilda) {
1522     ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1523     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1524     ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1525     ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_tilda_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1526     if (deluxe) {
1527       ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1528       ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1529       ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1530       ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_inv_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1531     } else {
1532       PetscScalar *array;
1533       PetscInt    cum;
1534 
1535       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1536       cum = 0;
1537       for (i=0;i<sub_schurs->n_subs;i++) {
1538         ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1539         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1540         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1541         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
1542         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1543         PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
1544         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1545         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1546         cum += subset_size*subset_size;
1547       }
1548       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1549       ierr = PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1550       ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1551       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1552     }
1553   }
1554   ierr = MatDestroySubMatrices(1,&submats);CHKERRQ(ierr);
1555 
1556   /* free workspace */
1557   ierr = PetscFree(submats);CHKERRQ(ierr);
1558   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
1559   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
1560   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
1561   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
1562   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
1563   PetscFunctionReturn(0);
1564 }
1565 
1566 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc)
1567 {
1568   IS              *faces,*edges,*all_cc,vertices;
1569   PetscInt        i,n_faces,n_edges,n_all_cc;
1570   PetscBool       is_sorted;
1571   PetscErrorCode  ierr;
1572 
1573   PetscFunctionBegin;
1574   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
1575   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
1576   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
1577   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
1578 
1579   /* reset any previous data */
1580   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
1581 
1582   /* get index sets for faces and edges (already sorted by global ordering) */
1583   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1584   n_all_cc = n_faces+n_edges;
1585   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
1586   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
1587   for (i=0;i<n_faces;i++) {
1588     if (copycc) {
1589       ierr = ISDuplicate(faces[i],&all_cc[i]);CHKERRQ(ierr);
1590     } else {
1591       ierr = PetscObjectReference((PetscObject)faces[i]);CHKERRQ(ierr);
1592       all_cc[i] = faces[i];
1593     }
1594   }
1595   for (i=0;i<n_edges;i++) {
1596     if (copycc) {
1597       ierr = ISDuplicate(edges[i],&all_cc[n_faces+i]);CHKERRQ(ierr);
1598     } else {
1599       ierr = PetscObjectReference((PetscObject)edges[i]);CHKERRQ(ierr);
1600       all_cc[n_faces+i] = edges[i];
1601     }
1602     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
1603   }
1604   ierr = PetscObjectReference((PetscObject)vertices);CHKERRQ(ierr);
1605   sub_schurs->is_vertices = vertices;
1606   ierr = PCBDDCGraphRestoreCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1607   sub_schurs->is_dir = NULL;
1608   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
1609 
1610   /* Determine if MatFactor can be used */
1611   sub_schurs->schur_explicit = PETSC_FALSE;
1612 #if defined(PETSC_HAVE_MUMPS)
1613   sub_schurs->schur_explicit = PETSC_TRUE;
1614 #endif
1615 #if defined(PETSC_HAVE_MKL_PARDISO)
1616   sub_schurs->schur_explicit = PETSC_TRUE;
1617 #endif
1618 
1619   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
1620   sub_schurs->is_I = is_I;
1621   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
1622   sub_schurs->is_B = is_B;
1623   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
1624   sub_schurs->l2gmap = graph->l2gmap;
1625   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
1626   sub_schurs->BtoNmap = BtoNmap;
1627   sub_schurs->n_subs = n_all_cc;
1628   sub_schurs->is_subs = all_cc;
1629   if (!sub_schurs->schur_explicit) { /* sort by local ordering if we are not using MatFactor */
1630     for (i=0;i<sub_schurs->n_subs;i++) {
1631       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
1632     }
1633   }
1634   sub_schurs->S_Ej_all = NULL;
1635   sub_schurs->sum_S_Ej_all = NULL;
1636   sub_schurs->sum_S_Ej_inv_all = NULL;
1637   sub_schurs->sum_S_Ej_tilda_all = NULL;
1638   sub_schurs->is_Ej_all = NULL;
1639   PetscFunctionReturn(0);
1640 }
1641 
1642 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1643 {
1644   PCBDDCSubSchurs schurs_ctx;
1645   PetscErrorCode  ierr;
1646 
1647   PetscFunctionBegin;
1648   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
1649   schurs_ctx->n_subs = 0;
1650   *sub_schurs = schurs_ctx;
1651   PetscFunctionReturn(0);
1652 }
1653 
1654 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1655 {
1656   PetscInt       i;
1657   PetscErrorCode ierr;
1658 
1659   PetscFunctionBegin;
1660   if (!sub_schurs) PetscFunctionReturn(0);
1661   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1662   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1663   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1664   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1665   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1666   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1667   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1668   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1669   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1670   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1671   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1672   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1673   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1674   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1675   for (i=0;i<sub_schurs->n_subs;i++) {
1676     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
1677   }
1678   if (sub_schurs->n_subs) {
1679     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1680   }
1681   if (sub_schurs->reuse_solver) {
1682     ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1683   }
1684   ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1685   if (sub_schurs->change) {
1686     for (i=0;i<sub_schurs->n_subs;i++) {
1687       ierr = KSPDestroy(&sub_schurs->change[i]);CHKERRQ(ierr);
1688       ierr = ISDestroy(&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
1689     }
1690   }
1691   ierr = PetscFree(sub_schurs->change);CHKERRQ(ierr);
1692   ierr = PetscFree(sub_schurs->change_primal_sub);CHKERRQ(ierr);
1693   sub_schurs->n_subs = 0;
1694   PetscFunctionReturn(0);
1695 }
1696 
1697 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs* sub_schurs)
1698 {
1699   PetscErrorCode ierr;
1700 
1701   PetscFunctionBegin;
1702   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
1703   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
1704   PetscFunctionReturn(0);
1705 }
1706 
1707 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1708 {
1709   PetscInt       i,j,n;
1710   PetscErrorCode ierr;
1711 
1712   PetscFunctionBegin;
1713   n = 0;
1714   for (i=-n_prev;i<0;i++) {
1715     PetscInt start_dof = queue_tip[i];
1716     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1717       PetscInt dof = adjncy[j];
1718       if (!PetscBTLookup(touched,dof)) {
1719         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1720         queue_tip[n] = dof;
1721         n++;
1722       }
1723     }
1724   }
1725   *n_added = n;
1726   PetscFunctionReturn(0);
1727 }
1728