xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 72b8c272419574d2ebd5d55592dbcb83cf34cd94)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <petscblaslapack.h>
4 
5 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt*,PetscInt,PetscBT,PetscInt*,PetscInt*,PetscInt*);
6 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat,PetscBool,MatReuse,Mat*);
7 static PetscErrorCode PCBDDCReuseSolvers_Interior(PC,Vec,Vec);
8 static PetscErrorCode PCBDDCReuseSolvers_Correction(PC,Vec,Vec);
9 
10 /* performs S = S + v^2 * a *v_1^T on the lower-triangular part, n the size of the matrix */
11 #undef __FUNCT__
12 #define __FUNCT__ "SparseRankOneUpdate"
13 PETSC_STATIC_INLINE PetscErrorCode SparseRankOneUpdate(PetscScalar *S,PetscInt n,PetscScalar a,PetscScalar *v1,PetscScalar *v2)
14 {
15   PetscInt i;
16 
17   PetscFunctionBegin;
18   for (i=0;i<n;i++) {
19     if (PetscUnlikely(PetscAbsScalar(v2[i]) > PETSC_SMALL)) {
20       PetscScalar  v2v = a*v2[i];
21       PetscBLASInt B_N = n-i,B_one = 1;
22       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&v2v,v1+i,&B_one,S+i*(n+1),&B_one));
23     }
24   }
25   PetscFunctionReturn(0);
26 }
27 
28 /* if v2 is not present, correction is done in-place */
29 #undef __FUNCT__
30 #define __FUNCT__ "PCBDDCReuseSolversChangeInterior"
31 PetscErrorCode PCBDDCReuseSolversChangeInterior(PCBDDCReuseSolvers ctx, Vec v, Vec v2, PetscBool sol)
32 {
33   PetscScalar    *array;
34   PetscScalar    *array2;
35   PetscErrorCode ierr;
36 
37   PetscFunctionBegin;
38   if (!ctx->benign_n) PetscFunctionReturn(0);
39   if (v2) {
40     PetscInt nl;
41 
42     ierr = VecGetArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
43     ierr = VecGetLocalSize(v2,&nl);CHKERRQ(ierr);
44     ierr = VecGetArray(v2,&array2);CHKERRQ(ierr);
45     ierr = PetscMemcpy(array2,array,nl*sizeof(PetscScalar));CHKERRQ(ierr);
46   } else {
47     ierr = VecGetArray(v,&array);CHKERRQ(ierr);
48     array2 = array;
49   }
50   if (!sol) { /* change rhs */
51     PetscInt n;
52     for (n=0;n<ctx->benign_n;n++) {
53       PetscScalar    sum = 0.;
54       const PetscInt *cols;
55       PetscInt       nz,i;
56 
57       ierr = ISGetLocalSize(ctx->benign_zerodiag_subs[n],&nz);CHKERRQ(ierr);
58       ierr = ISGetIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
59       for (i=0;i<nz-1;i++) sum += array[cols[i]];
60       sum = -sum/nz;
61       for (i=0;i<nz-1;i++) array2[cols[i]] += sum;
62       ctx->benign_save_vals[n] = array2[cols[nz-1]];
63       array2[cols[nz-1]] = sum;
64       ierr = ISRestoreIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
65     }
66   } else {
67     PetscInt n;
68     for (n=0;n<ctx->benign_n;n++) {
69       PetscScalar    sum = 0.;
70       const PetscInt *cols;
71       PetscInt       nz,i;
72       ierr = ISGetLocalSize(ctx->benign_zerodiag_subs[n],&nz);CHKERRQ(ierr);
73       ierr = ISGetIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
74       for (i=0;i<nz-1;i++) sum += array[cols[i]];
75       sum = -sum/nz;
76       for (i=0;i<nz-1;i++) array2[cols[i]] += sum;
77       array2[cols[nz-1]] = ctx->benign_save_vals[n];
78       ierr = ISRestoreIndices(ctx->benign_zerodiag_subs[n],&cols);CHKERRQ(ierr);
79     }
80   }
81   if (v2) {
82     ierr = VecRestoreArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
83     ierr = VecRestoreArray(v2,&array2);CHKERRQ(ierr);
84   } else {
85     ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
86   }
87   PetscFunctionReturn(0);
88 }
89 
90 #undef __FUNCT__
91 #define __FUNCT__ "PCBDDCReuseSolvers_Solve_Private"
92 static PetscErrorCode PCBDDCReuseSolvers_Solve_Private(PC pc, Vec rhs, Vec sol, PetscBool transpose, PetscBool full)
93 {
94   PCBDDCReuseSolvers ctx;
95   PetscBool          copy = PETSC_FALSE;
96   PetscErrorCode     ierr;
97 
98   PetscFunctionBegin;
99   ierr = PCShellGetContext(pc,(void **)&ctx);CHKERRQ(ierr);
100   if (full) {
101 #if defined(PETSC_HAVE_MUMPS)
102     ierr = MatMumpsSetIcntl(ctx->F,26,-1);CHKERRQ(ierr);
103 #endif
104     copy = ctx->has_vertices;
105   } else { /* interior solver */
106 #if defined(PETSC_HAVE_MUMPS)
107     ierr = MatMumpsSetIcntl(ctx->F,26,0);CHKERRQ(ierr);
108 #endif
109 #if defined(PETSC_HAVE_MKL_PARDISO)
110     ierr = MatMkl_PardisoSetCntl(ctx->F,70,1);CHKERRQ(ierr);
111 #endif
112     copy = PETSC_TRUE;
113   }
114   /* copy rhs into factored matrix workspace */
115   if (copy) {
116     PetscInt    n;
117     PetscScalar *array,*array_solver;
118 
119     ierr = VecGetLocalSize(rhs,&n);CHKERRQ(ierr);
120     ierr = VecGetArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
121     ierr = VecGetArray(ctx->rhs,&array_solver);CHKERRQ(ierr);
122     ierr = PetscMemcpy(array_solver,array,n*sizeof(PetscScalar));CHKERRQ(ierr);
123     ierr = VecRestoreArray(ctx->rhs,&array_solver);CHKERRQ(ierr);
124     ierr = VecRestoreArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
125 
126     ierr = PCBDDCReuseSolversChangeInterior(ctx,ctx->rhs,NULL,PETSC_FALSE);CHKERRQ(ierr);
127     if (transpose) {
128       ierr = MatSolveTranspose(ctx->F,ctx->rhs,ctx->sol);CHKERRQ(ierr);
129     } else {
130       ierr = MatSolve(ctx->F,ctx->rhs,ctx->sol);CHKERRQ(ierr);
131     }
132     ierr = PCBDDCReuseSolversChangeInterior(ctx,ctx->sol,NULL,PETSC_TRUE);CHKERRQ(ierr);
133 
134     /* get back data to caller worskpace */
135     ierr = VecGetArrayRead(ctx->sol,(const PetscScalar**)&array_solver);CHKERRQ(ierr);
136     ierr = VecGetArray(sol,&array);CHKERRQ(ierr);
137     ierr = PetscMemcpy(array,array_solver,n*sizeof(PetscScalar));CHKERRQ(ierr);
138     ierr = VecRestoreArray(sol,&array);CHKERRQ(ierr);
139     ierr = VecRestoreArrayRead(ctx->sol,(const PetscScalar**)&array_solver);CHKERRQ(ierr);
140   } else {
141     if (ctx->benign_n) {
142       ierr = PCBDDCReuseSolversChangeInterior(ctx,rhs,ctx->rhs,PETSC_FALSE);CHKERRQ(ierr);
143       if (transpose) {
144         ierr = MatSolveTranspose(ctx->F,ctx->rhs,sol);CHKERRQ(ierr);
145       } else {
146         ierr = MatSolve(ctx->F,ctx->rhs,sol);CHKERRQ(ierr);
147       }
148       ierr = PCBDDCReuseSolversChangeInterior(ctx,sol,NULL,PETSC_TRUE);CHKERRQ(ierr);
149     } else {
150       if (transpose) {
151         ierr = MatSolveTranspose(ctx->F,rhs,sol);CHKERRQ(ierr);
152       } else {
153         ierr = MatSolve(ctx->F,rhs,sol);CHKERRQ(ierr);
154       }
155     }
156   }
157 #if defined(PETSC_HAVE_MKL_PARDISO)
158   ierr = MatMkl_PardisoSetCntl(ctx->F,70,0);CHKERRQ(ierr);
159 #endif
160   PetscFunctionReturn(0);
161 }
162 
163 #undef __FUNCT__
164 #define __FUNCT__ "PCBDDCReuseSolvers_Correction"
165 static PetscErrorCode PCBDDCReuseSolvers_Correction(PC pc, Vec rhs, Vec sol)
166 {
167   PetscErrorCode   ierr;
168 
169   PetscFunctionBegin;
170   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
171   PetscFunctionReturn(0);
172 }
173 
174 #undef __FUNCT__
175 #define __FUNCT__ "PCBDDCReuseSolvers_CorrectionTranspose"
176 static PetscErrorCode PCBDDCReuseSolvers_CorrectionTranspose(PC pc, Vec rhs, Vec sol)
177 {
178   PetscErrorCode   ierr;
179 
180   PetscFunctionBegin;
181   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_TRUE,PETSC_TRUE);CHKERRQ(ierr);
182   PetscFunctionReturn(0);
183 }
184 
185 #undef __FUNCT__
186 #define __FUNCT__ "PCBDDCReuseSolvers_Interior"
187 static PetscErrorCode PCBDDCReuseSolvers_Interior(PC pc, Vec rhs, Vec sol)
188 {
189   PetscErrorCode   ierr;
190 
191   PetscFunctionBegin;
192   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_FALSE,PETSC_FALSE);CHKERRQ(ierr);
193   PetscFunctionReturn(0);
194 }
195 
196 #undef __FUNCT__
197 #define __FUNCT__ "PCBDDCReuseSolvers_InteriorTranspose"
198 static PetscErrorCode PCBDDCReuseSolvers_InteriorTranspose(PC pc, Vec rhs, Vec sol)
199 {
200   PetscErrorCode   ierr;
201 
202   PetscFunctionBegin;
203   ierr = PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
204   PetscFunctionReturn(0);
205 }
206 
207 #undef __FUNCT__
208 #define __FUNCT__ "PCBDDCReuseSolversReset"
209 static PetscErrorCode PCBDDCReuseSolversReset(PCBDDCReuseSolvers reuse)
210 {
211   PetscInt       i;
212   PetscErrorCode ierr;
213 
214   PetscFunctionBegin;
215   ierr = MatDestroy(&reuse->F);CHKERRQ(ierr);
216   ierr = VecDestroy(&reuse->sol);CHKERRQ(ierr);
217   ierr = VecDestroy(&reuse->rhs);CHKERRQ(ierr);
218   ierr = PCDestroy(&reuse->interior_solver);CHKERRQ(ierr);
219   ierr = PCDestroy(&reuse->correction_solver);CHKERRQ(ierr);
220   ierr = ISDestroy(&reuse->is_R);CHKERRQ(ierr);
221   ierr = ISDestroy(&reuse->is_B);CHKERRQ(ierr);
222   ierr = VecScatterDestroy(&reuse->correction_scatter_B);CHKERRQ(ierr);
223   ierr = VecDestroy(&reuse->sol_B);CHKERRQ(ierr);
224   ierr = VecDestroy(&reuse->rhs_B);CHKERRQ(ierr);
225   for (i=0;i<reuse->benign_n;i++) {
226     ierr = ISDestroy(&reuse->benign_zerodiag_subs[i]);CHKERRQ(ierr);
227   }
228   ierr = PetscFree(reuse->benign_zerodiag_subs);CHKERRQ(ierr);
229   ierr = PetscFree(reuse->benign_save_vals);CHKERRQ(ierr);
230   PetscFunctionReturn(0);
231 }
232 
233 #undef __FUNCT__
234 #define __FUNCT__ "PCBDDCComputeExplicitSchur"
235 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
236 {
237   Mat            B, C, D, Bd, Cd, AinvBd;
238   KSP            ksp;
239   PC             pc;
240   PetscBool      isLU, isILU, isCHOL, Bdense, Cdense;
241   PetscReal      fill = 2.0;
242   PetscInt       n_I;
243   PetscMPIInt    size;
244   PetscErrorCode ierr;
245 
246   PetscFunctionBegin;
247   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);CHKERRQ(ierr);
248   if (size != 1) {
249     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not for parallel matrices");
250   }
251   if (reuse == MAT_REUSE_MATRIX) {
252     PetscBool Sdense;
253 
254     ierr = PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense);CHKERRQ(ierr);
255     if (!Sdense) {
256       SETERRQ(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"S should be dense");
257     }
258   }
259   ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
260   ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
261   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
262   ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
263   ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
264   ierr = PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);CHKERRQ(ierr);
265   ierr = PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);CHKERRQ(ierr);
266   ierr = PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);CHKERRQ(ierr);
267   ierr = MatGetSize(B,&n_I,NULL);CHKERRQ(ierr);
268   if (n_I) {
269     if (!Bdense) {
270       ierr = MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
271     } else {
272       Bd = B;
273     }
274 
275     if (isLU || isILU || isCHOL) {
276       Mat fact;
277       ierr = KSPSetUp(ksp);CHKERRQ(ierr);
278       ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
279       ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
280       ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
281     } else {
282       PetscBool ex = PETSC_TRUE;
283 
284       if (ex) {
285         Mat Ainvd;
286 
287         ierr = PCComputeExplicitOperator(pc, &Ainvd);CHKERRQ(ierr);
288         ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
289         ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
290       } else {
291         Vec         sol,rhs;
292         PetscScalar *arrayrhs,*arraysol;
293         PetscInt    i,nrhs,n;
294 
295         ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
296         ierr = MatGetSize(Bd,&n,&nrhs);CHKERRQ(ierr);
297         ierr = MatDenseGetArray(Bd,&arrayrhs);CHKERRQ(ierr);
298         ierr = MatDenseGetArray(AinvBd,&arraysol);CHKERRQ(ierr);
299         ierr = KSPGetSolution(ksp,&sol);CHKERRQ(ierr);
300         ierr = KSPGetRhs(ksp,&rhs);CHKERRQ(ierr);
301         for (i=0;i<nrhs;i++) {
302           ierr = VecPlaceArray(rhs,arrayrhs+i*n);CHKERRQ(ierr);
303           ierr = VecPlaceArray(sol,arraysol+i*n);CHKERRQ(ierr);
304           ierr = KSPSolve(ksp,rhs,sol);CHKERRQ(ierr);
305           ierr = VecResetArray(rhs);CHKERRQ(ierr);
306           ierr = VecResetArray(sol);CHKERRQ(ierr);
307         }
308         ierr = MatDenseRestoreArray(Bd,&arrayrhs);CHKERRQ(ierr);
309         ierr = MatDenseRestoreArray(AinvBd,&arrayrhs);CHKERRQ(ierr);
310       }
311     }
312     if (!Bdense & !issym) {
313       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
314     }
315 
316     if (!issym) {
317       if (!Cdense) {
318         ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
319       } else {
320         Cd = C;
321       }
322       ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
323       if (!Cdense) {
324         ierr = MatDestroy(&Cd);CHKERRQ(ierr);
325       }
326     } else {
327       ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
328       if (!Bdense) {
329         ierr = MatDestroy(&Bd);CHKERRQ(ierr);
330       }
331     }
332     ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
333   }
334 
335   if (D) {
336     Mat       Dd;
337     PetscBool Ddense;
338 
339     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
340     if (!Ddense) {
341       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
342     } else {
343       Dd = D;
344     }
345     if (n_I) {
346       ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
347     } else {
348       if (reuse == MAT_INITIAL_MATRIX) {
349         ierr = MatDuplicate(Dd,MAT_COPY_VALUES,S);CHKERRQ(ierr);
350       } else {
351         ierr = MatCopy(Dd,*S,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
352       }
353     }
354     if (!Ddense) {
355       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
356     }
357   } else {
358     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
359   }
360   PetscFunctionReturn(0);
361 }
362 
363 #undef __FUNCT__
364 #define __FUNCT__ "PCBDDCSubSchursSetUp"
365 PetscErrorCode PCBDDCSubSchursSetUp(PCBDDCSubSchurs sub_schurs, Mat Ain, Mat Sin, PetscBool exact_schur, PetscInt xadj[], PetscInt adjncy[], PetscInt nlayers, PetscBool faster_deluxe, 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)
366 {
367   Mat                    F,A_II,A_IB,A_BI,A_BB,AE_II;
368   Mat                    S_all;
369   Mat                    global_schur_subsets,work_mat,*submats;
370   ISLocalToGlobalMapping l2gmap_subsets;
371   IS                     is_I,is_I_layer,*change_primal_sub;
372   IS                     all_subsets,all_subsets_mult,all_subsets_n;
373   PetscInt               *nnz,*all_local_idx_N;
374   PetscInt               *auxnum1,*auxnum2;
375   PetscInt               i,subset_size,max_subset_size;
376   PetscInt               n_B,extra,local_size,global_size;
377   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
378   PetscScalar            *Bwork;
379   PetscSubcomm           subcomm;
380   PetscMPIInt            color,rank;
381   MPI_Comm               comm_n;
382   PetscBool              use_getr = PETSC_FALSE;
383   PetscErrorCode         ierr;
384 
385   PetscFunctionBegin;
386   /* update info in sub_schurs */
387   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
388   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
389   sub_schurs->is_hermitian = PETSC_FALSE;
390   sub_schurs->is_posdef = PETSC_FALSE;
391   if (Ain) {
392     PetscBool isseqaij;
393     /* determine if we are dealing with hermitian positive definite problems */
394 #if !defined(PETSC_USE_COMPLEX)
395     if (Ain->symmetric_set) {
396       sub_schurs->is_hermitian = Ain->symmetric;
397     }
398 #else
399     if (Ain->hermitian_set) {
400       sub_schurs->is_hermitian = Ain->hermitian;
401     }
402 #endif
403     if (Ain->spd_set) {
404       sub_schurs->is_posdef = Ain->spd;
405     }
406 
407     /* check */
408     ierr = PetscObjectTypeCompare((PetscObject)Ain,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
409     if (compute_Stilda && (!Ain->hermitian_set || !Ain->spd_set)) { /* these are lazy checks, maybe I should throw an error if they are not set */
410       PetscInt lsize;
411 
412       ierr = MatGetSize(Ain,&lsize,NULL);CHKERRQ(ierr);
413       if (lsize) {
414         PetscScalar val;
415         PetscReal   norm;
416         Vec         vec1,vec2,vec3;
417 
418         ierr = MatCreateVecs(Ain,&vec1,&vec2);CHKERRQ(ierr);
419         ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
420         ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
421         ierr = MatMult(Ain,vec1,vec2);CHKERRQ(ierr);
422 #if !defined(PETSC_USE_COMPLEX)
423         ierr = MatMultTranspose(Ain,vec1,vec3);CHKERRQ(ierr);
424 #else
425         ierr = MatMultHermitianTranspose(Ain,vec1,vec3);CHKERRQ(ierr);
426 #endif
427         ierr = VecAXPY(vec3,-1.0,vec2);CHKERRQ(ierr);
428         ierr = VecNorm(vec3,NORM_INFINITY,&norm);CHKERRQ(ierr);
429         if (!Ain->hermitian_set) {
430           if (norm > PetscSqrtReal(PETSC_SMALL)) {
431             sub_schurs->is_hermitian = PETSC_FALSE;
432           } else {
433             sub_schurs->is_hermitian = PETSC_TRUE;
434           }
435         }
436         if (!Ain->spd_set && !benign_trick) {
437           ierr = VecDot(vec1,vec2,&val);CHKERRQ(ierr);
438           if (PetscRealPart(val) > 0. && PetscAbsReal(PetscImaginaryPart(val)) < PETSC_SMALL) sub_schurs->is_posdef = PETSC_TRUE;
439         }
440         ierr = VecDestroy(&vec1);CHKERRQ(ierr);
441         ierr = VecDestroy(&vec2);CHKERRQ(ierr);
442         ierr = VecDestroy(&vec3);CHKERRQ(ierr);
443       } else {
444         sub_schurs->is_hermitian = PETSC_TRUE;
445         sub_schurs->is_posdef = PETSC_TRUE;
446       }
447     }
448     if (isseqaij) {
449       ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
450       sub_schurs->A = Ain;
451     } else {
452       ierr = MatConvert(Ain,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
453     }
454   }
455 
456   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
457   sub_schurs->S = Sin;
458   if (sub_schurs->schur_explicit) {
459     sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
460   }
461 
462   /* preliminary checks */
463   if (!sub_schurs->schur_explicit && compute_Stilda) {
464     SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS and/or MKL_PARDISO");
465   }
466 
467   /* restrict work on active processes */
468   color = 0;
469   if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
470   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
471   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
472   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
473   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
474   ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
475   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
476   if (!sub_schurs->n_subs) {
477     ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
478     PetscFunctionReturn(0);
479   }
480   /* ierr = PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);CHKERRQ(ierr); */
481 
482   /* get Schur complement matrices */
483   if (!sub_schurs->schur_explicit) {
484     Mat       tA_IB,tA_BI,tA_BB;
485     PetscBool isseqsbaij;
486     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
487     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);CHKERRQ(ierr);
488     if (isseqsbaij) {
489       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
490       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
491       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
492     } else {
493       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
494       A_BB = tA_BB;
495       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
496       A_IB = tA_IB;
497       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
498       A_BI = tA_BI;
499     }
500   } else {
501     A_II = NULL;
502     A_IB = NULL;
503     A_BI = NULL;
504     A_BB = NULL;
505   }
506   S_all = NULL;
507 
508   /* determine interior problems */
509   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
510   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
511     PetscBT                touched;
512     const PetscInt*        idx_B;
513     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
514 
515     if (xadj == NULL || adjncy == NULL) {
516       SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
517     }
518     /* get sizes */
519     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
520     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
521 
522     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
523     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
524     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
525 
526     /* all boundary dofs must be skipped when adding layers */
527     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
528     for (j=0;j<n_B;j++) {
529       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
530     }
531     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
532     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
533 
534     /* add prescribed number of layers of dofs */
535     n_local_dofs = n_B;
536     n_prev_added = n_B;
537     for (layer=0;layer<nlayers;layer++) {
538       PetscInt n_added;
539       if (n_local_dofs == n_I+n_B) break;
540       if (n_local_dofs > n_I+n_B) {
541         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);
542       }
543       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
544       n_prev_added = n_added;
545       n_local_dofs += n_added;
546       if (!n_added) break;
547     }
548     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
549 
550     /* IS for I layer dofs in original numbering */
551     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);
552     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
553     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
554     /* IS for I layer dofs in I numbering */
555     if (!sub_schurs->schur_explicit) {
556       ISLocalToGlobalMapping ItoNmap;
557       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
558       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
559       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
560 
561       /* II block */
562       ierr = MatGetSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
563     }
564   } else {
565     PetscInt n_I;
566 
567     /* IS for I dofs in original numbering */
568     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
569     is_I_layer = sub_schurs->is_I;
570 
571     /* IS for I dofs in I numbering (strided 1) */
572     if (!sub_schurs->schur_explicit) {
573       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
574       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
575 
576       /* II block is the same */
577       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
578       AE_II = A_II;
579     }
580   }
581 
582   /* Get info on subset sizes and sum of all subsets sizes */
583   max_subset_size = 0;
584   local_size = 0;
585   for (i=0;i<sub_schurs->n_subs;i++) {
586     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
587     max_subset_size = PetscMax(subset_size,max_subset_size);
588     local_size += subset_size;
589   }
590 
591   /* Work arrays for local indices */
592   extra = 0;
593   ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
594   if (sub_schurs->schur_explicit && is_I_layer) {
595     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
596   }
597   ierr = PetscMalloc1(n_B+extra,&all_local_idx_N);CHKERRQ(ierr);
598   if (extra) {
599     const PetscInt *idxs;
600     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
601     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
602     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
603   }
604   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
605   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum1);CHKERRQ(ierr);
606   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
607 
608   /* Get local indices in local numbering */
609   local_size = 0;
610   for (i=0;i<sub_schurs->n_subs;i++) {
611     PetscInt j;
612     const    PetscInt *idxs;
613 
614     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
615     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
616     /* start (smallest in global ordering) and multiplicity */
617     auxnum1[i] = idxs[0];
618     auxnum2[i] = subset_size;
619     /* subset indices in local numbering */
620     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
621     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
622     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
623     local_size += subset_size;
624   }
625 
626   /* allocate extra workspace needed only for GETRI */
627   Bwork = NULL;
628   pivots = NULL;
629   if (local_size && !benign_trick && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
630     PetscScalar lwork;
631 
632     use_getr = PETSC_TRUE;
633     B_lwork = -1;
634     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
635     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
636     PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,Bwork,&B_N,pivots,&lwork,&B_lwork,&B_ierr));
637     ierr = PetscFPTrapPop();CHKERRQ(ierr);
638     if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
639     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
640     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
641   }
642 
643   /* prepare parallel matrices for summing up properly schurs on subsets */
644   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);CHKERRQ(ierr);
645   ierr = ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);CHKERRQ(ierr);
646   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
647   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);CHKERRQ(ierr);
648   ierr = PCBDDCSubsetNumbering(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);CHKERRQ(ierr);
649   ierr = ISDestroy(&all_subsets);CHKERRQ(ierr);
650   ierr = ISDestroy(&all_subsets_mult);CHKERRQ(ierr);
651   ierr = ISGetLocalSize(all_subsets_n,&i);CHKERRQ(ierr);
652   if (i != local_size) {
653     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %d != %d",i,local_size);
654   }
655   ierr = ISLocalToGlobalMappingCreateIS(all_subsets_n,&l2gmap_subsets);CHKERRQ(ierr);
656   ierr = MatCreateIS(comm_n,1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,NULL,&work_mat);CHKERRQ(ierr);
657   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
658   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
659   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
660   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
661 
662   /* subset indices in local boundary numbering */
663   if (!sub_schurs->is_Ej_all) {
664     PetscInt *all_local_idx_B;
665 
666     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
667     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
668     if (subset_size != local_size) {
669       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %d != %d\n",subset_size,local_size);
670     }
671     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
672   }
673 
674   change_primal_sub = NULL;
675   if (change) {
676     ISLocalToGlobalMapping BtoS;
677     IS                     change_primal_B;
678     IS                     change_primal_all;
679 
680     ierr = PetscMalloc1(sub_schurs->n_subs,&change_primal_sub);CHKERRQ(ierr);
681     for (i=0;i<sub_schurs->n_subs;i++) {
682       ISLocalToGlobalMapping NtoS;
683       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);CHKERRQ(ierr);
684       ierr = ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&change_primal_sub[i]);CHKERRQ(ierr);
685       ierr = ISLocalToGlobalMappingDestroy(&NtoS);CHKERRQ(ierr);
686     }
687     ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);CHKERRQ(ierr);
688     ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);CHKERRQ(ierr);
689     ierr = ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);CHKERRQ(ierr);
690     ierr = ISLocalToGlobalMappingDestroy(&BtoS);CHKERRQ(ierr);
691     ierr = ISDestroy(&change_primal_B);CHKERRQ(ierr);
692     if (!sub_schurs->change) {
693       ierr = PetscCalloc1(sub_schurs->n_subs,&sub_schurs->change);CHKERRQ(ierr);
694     }
695     for (i=0;i<sub_schurs->n_subs;i++) {
696       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
697       if (!sub_schurs->change[i]) {
698         Mat change_sub;
699 
700         ierr = KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);CHKERRQ(ierr);
701         ierr = KSPSetType(sub_schurs->change[i],KSPPREONLY);CHKERRQ(ierr);
702         if (!sub_schurs->change_with_qr) {
703           ierr = MatGetSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
704         } else {
705           Mat change_subt;
706           ierr = MatGetSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);CHKERRQ(ierr);
707           ierr = MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
708           ierr = MatDestroy(&change_subt);CHKERRQ(ierr);
709         }
710         ierr = KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);CHKERRQ(ierr);
711         ierr = MatDestroy(&change_sub);CHKERRQ(ierr);
712         ierr = KSPSetOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");CHKERRQ(ierr);
713       }
714     }
715     ierr = ISDestroy(&change_primal_all);CHKERRQ(ierr);
716   }
717 
718   /* Local matrix of all local Schur on subsets (transposed) */
719   if (!sub_schurs->S_Ej_all) {
720     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
721     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
722     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
723     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
724   }
725 
726   /* Compute Schur complements explicitly */
727   F = NULL;
728   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 */
729     Mat         S_Ej_expl;
730     PetscScalar *work;
731     PetscInt    j,*dummy_idx;
732     PetscBool   Sdense;
733 
734     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
735     local_size = 0;
736     for (i=0;i<sub_schurs->n_subs;i++) {
737       IS  is_subset_B;
738       Mat AE_EE,AE_IE,AE_EI,S_Ej;
739 
740       /* subsets in original and boundary numbering */
741       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
742       /* EE block */
743       ierr = MatGetSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
744       /* IE block */
745       ierr = MatGetSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
746       /* EI block */
747       if (sub_schurs->is_hermitian) {
748         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
749       } else {
750         ierr = MatGetSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
751       }
752       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
753       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
754       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
755       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
756       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
757       if (AE_II == A_II) { /* we can reuse the same ksp */
758         KSP ksp;
759         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
760         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
761       } else { /* build new ksp object which inherits ksp and pc types from the original one */
762         KSP       origksp,schurksp;
763         PC        origpc,schurpc;
764         KSPType   ksp_type;
765         PetscInt  n_internal;
766         PetscBool ispcnone;
767 
768         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
769         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
770         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
771         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
772         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
773         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
774         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
775         if (!ispcnone) {
776           PCType pc_type;
777           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
778           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
779         } else {
780           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
781         }
782         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
783         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
784           MatSolverPackage solver=NULL;
785           ierr = PCFactorGetMatSolverPackage(origpc,(const MatSolverPackage*)&solver);CHKERRQ(ierr);
786           if (solver) {
787             ierr = PCFactorSetMatSolverPackage(schurpc,solver);CHKERRQ(ierr);
788           }
789         }
790         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
791       }
792       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
793       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
794       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
795       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
796       if (Sdense) {
797         for (j=0;j<subset_size;j++) {
798           dummy_idx[j]=local_size+j;
799         }
800         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
801       } else {
802         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
803       }
804       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
805       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
806       local_size += subset_size;
807     }
808     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
809     /* free */
810     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
811     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
812     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
813   } else {
814     Mat         A;
815     Vec         *benign_AIIm1_ones = NULL;
816     IS          is_A_all,*is_p_r = NULL;
817     PetscScalar *work,*S_data,*schur_factor,*cs_AIB = NULL, infty = PETSC_MAX_REAL;
818     PetscInt    n,n_I,*dummy_idx,size_schur,size_active_schur,cum,cum2;
819     PetscBool   economic,solver_S,S_lower_triangular = PETSC_FALSE,factor_workaround;
820     char        solver[256];
821 
822     /* get sizes */
823     n_I = 0;
824     if (is_I_layer) {
825       ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
826     }
827     economic = PETSC_FALSE;
828     ierr = ISGetLocalSize(sub_schurs->is_I,&cum);CHKERRQ(ierr);
829     if (cum != n_I) economic = PETSC_TRUE;
830     ierr = MatGetLocalSize(sub_schurs->A,&n,NULL);CHKERRQ(ierr);
831 
832     /* size active schurs does not count any dirichlet or vertex dof on the interface */
833     size_active_schur = local_size;
834     cum = n_I+size_active_schur;
835     if (sub_schurs->is_dir) {
836       const PetscInt* idxs;
837       PetscInt        n_dir;
838 
839       ierr = ISGetLocalSize(sub_schurs->is_dir,&n_dir);CHKERRQ(ierr);
840       ierr = ISGetIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
841       ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_dir*sizeof(PetscInt));CHKERRQ(ierr);
842       ierr = ISRestoreIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
843       cum += n_dir;
844     }
845     factor_workaround = PETSC_FALSE;
846     /* include the primal vertices in the Schur complement */
847     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
848       PetscInt n_v;
849 
850       ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
851       if (n_v) {
852         const PetscInt* idxs;
853 
854         ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
855         ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_v*sizeof(PetscInt));CHKERRQ(ierr);
856         ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
857         cum += n_v;
858         factor_workaround = PETSC_TRUE;
859       }
860     }
861     size_schur = cum - n_I;
862     ierr = ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);CHKERRQ(ierr);
863     /* get working mat (TODO: factorize without actually permuting)  */
864     if (cum == n) {
865       ierr = ISSetPermutation(is_A_all);CHKERRQ(ierr);
866       ierr = MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
867     } else {
868       ierr = MatGetSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
869     }
870     ierr = MatSetOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
871 
872     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
873        n^2 instead of n^1.5 or something. This is a workaround */
874     if (benign_n) {
875       Vec                    v;
876       ISLocalToGlobalMapping N_to_reor;
877       IS                     is_p0,is_p0_p;
878 
879       ierr = ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);CHKERRQ(ierr);
880       ierr = ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
881       ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);CHKERRQ(ierr);
882       ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
883       ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
884       ierr = VecDuplicateVecs(v,benign_n,&benign_AIIm1_ones);CHKERRQ(ierr);
885       ierr = PetscMalloc1(size_schur*benign_n,&cs_AIB);CHKERRQ(ierr);
886       ierr = PetscMalloc1(benign_n,&is_p_r);CHKERRQ(ierr);
887       /* compute colsum of A_IB restricted to pressures */
888       for (i=0;i<benign_n;i++) {
889         PetscScalar    *array;
890         const PetscInt *idxs;
891         PetscInt       j,nz;
892 
893         ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);CHKERRQ(ierr);
894         ierr = VecGetArray(benign_AIIm1_ones[i],&array);CHKERRQ(ierr);
895         ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
896         ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
897         for (j=0;j<nz;j++) array[idxs[j]] = 1.;
898         ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
899         ierr = VecRestoreArray(benign_AIIm1_ones[i],&array);CHKERRQ(ierr);
900         ierr = MatMult(A,benign_AIIm1_ones[i],v);CHKERRQ(ierr);
901         ierr = VecGetArray(v,&array);CHKERRQ(ierr);
902         for (j=0;j<size_schur;j++) cs_AIB[i*size_schur + j] = array[j+n_I];
903         ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
904       }
905       ierr = VecDestroy(&v);CHKERRQ(ierr);
906       ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);CHKERRQ(ierr);
907       ierr = MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);CHKERRQ(ierr);
908       ierr = ISDestroy(&is_p0_p);CHKERRQ(ierr);
909       ierr = ISLocalToGlobalMappingDestroy(&N_to_reor);CHKERRQ(ierr);
910     }
911     ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_hermitian);CHKERRQ(ierr);
912     ierr = MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
913     ierr = MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
914 #if defined(PETSC_HAVE_MUMPS)
915     ierr = PetscStrcpy(solver,MATSOLVERMUMPS);CHKERRQ(ierr);
916 #else
917     ierr = PetscStrcpy(solver,MATSOLVERMKL_PARDISO);CHKERRQ(ierr);
918 #endif
919     ierr = PetscOptionsGetString("sub_schurs_","-mat_solver_package",solver,256,NULL);CHKERRQ(ierr);
920 
921     /* when using the benign subspace trick, the local Schur complements are SPD */
922     if (benign_trick) sub_schurs->is_posdef = PETSC_TRUE;
923 
924     if (n_I) { /* TODO add ordering from options */
925       IS is_schur;
926 
927       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
928         ierr = MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
929       } else {
930         ierr = MatGetFactor(A,solver,MAT_FACTOR_LU,&F);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         if (sub_schurs->is_posdef) {
944           ierr = MatFactorSetSchurComplementSolverType(F,1);CHKERRQ(ierr);
945         } else {
946           ierr = MatFactorSetSchurComplementSolverType(F,2);CHKERRQ(ierr);
947         }
948         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
949         S_lower_triangular = PETSC_TRUE;
950       } else {
951         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
952 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
953         ierr = MatMumpsSetIcntl(F,19,3);CHKERRQ(ierr);
954 #endif
955         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
956       }
957 
958       /* get explicit Schur Complement computed during numeric factorization */
959       ierr = MatFactorGetSchurComplement(F,&S_all);CHKERRQ(ierr);
960       /* we can reuse the solvers if we are not using the economic version */
961       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
962       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
963       solver_S = PETSC_TRUE;
964 
965       /* update the Schur complement with the change of basis on the pressures */
966       if (benign_n) {
967         PetscScalar *S_data;
968         Vec         v;
969 
970         ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
971         ierr = VecDuplicate(benign_AIIm1_ones[0],&v);CHKERRQ(ierr);
972 #if defined(PETSC_HAVE_MUMPS)
973         ierr = MatMumpsSetIcntl(F,26,0);CHKERRQ(ierr);
974 #endif
975 #if defined(PETSC_HAVE_MKL_PARDISO)
976         ierr = MatMkl_PardisoSetCntl(F,70,1);CHKERRQ(ierr);
977 #endif
978         for (i=0;i<benign_n;i++) {
979           PetscScalar    *array,sum = 0.;
980           const PetscInt *idxs;
981           PetscInt       j,nz;
982 
983           ierr = VecCopy(benign_AIIm1_ones[i],v);CHKERRQ(ierr);
984           ierr = MatSolve(F,v,benign_AIIm1_ones[i]);CHKERRQ(ierr);
985           ierr = VecGetArray(benign_AIIm1_ones[i],&array);CHKERRQ(ierr);
986           ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
987           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
988           for (j=0;j<nz;j++) sum += array[idxs[j]];
989           sum -= 1.; /* p0 dof (eliminated) is excluded from the sum */
990           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
991           ierr = VecRestoreArray(benign_AIIm1_ones[i],&array);CHKERRQ(ierr);
992           ierr = MatMult(A,benign_AIIm1_ones[i],v);CHKERRQ(ierr);
993           ierr = VecGetArray(v,&array);CHKERRQ(ierr);
994           /* perform sparse rank-1 updates on symmetric Schur */
995           sum  = -sum/(1.*nz*nz);
996           ierr = SparseRankOneUpdate(S_data,size_schur,sum,cs_AIB+i*size_schur,cs_AIB+i*size_schur);CHKERRQ(ierr);
997           sum  = 1./nz;
998           ierr = SparseRankOneUpdate(S_data,size_schur,sum,array+n_I,cs_AIB+i*size_schur);CHKERRQ(ierr);
999           ierr = SparseRankOneUpdate(S_data,size_schur,sum,cs_AIB+i*size_schur,array+n_I);CHKERRQ(ierr);
1000           ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
1001         }
1002         ierr = VecDestroy(&v);CHKERRQ(ierr);
1003         ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1004       }
1005       ierr = PetscFree(cs_AIB);CHKERRQ(ierr);
1006       ierr = VecDestroyVecs(benign_n,&benign_AIIm1_ones);CHKERRQ(ierr);
1007       if (!reuse_solvers) {
1008         for (i=0;i<benign_n;i++) {
1009           ierr = ISDestroy(&is_p_r[i]);CHKERRQ(ierr);
1010         }
1011         ierr = PetscFree(is_p_r);CHKERRQ(ierr);
1012       }
1013     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1014       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
1015       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1016       solver_S = PETSC_FALSE;
1017     }
1018 
1019     if (reuse_solvers) {
1020       Mat                A_II;
1021       Vec                vec1_B;
1022       PCBDDCReuseSolvers msolv_ctx;
1023 
1024       if (sub_schurs->reuse_solver) {
1025         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1026       } else {
1027         ierr = PetscNew(&sub_schurs->reuse_solver);CHKERRQ(ierr);
1028       }
1029       msolv_ctx = sub_schurs->reuse_solver;
1030       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1031       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
1032       msolv_ctx->F = F;
1033       ierr = MatCreateVecs(F,&msolv_ctx->sol,NULL);CHKERRQ(ierr);
1034       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1035       {
1036         PetscScalar *array;
1037         PetscInt    n;
1038 
1039         ierr = VecGetLocalSize(msolv_ctx->sol,&n);CHKERRQ(ierr);
1040         ierr = VecGetArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1041         ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);CHKERRQ(ierr);
1042         ierr = VecRestoreArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1043       }
1044       msolv_ctx->has_vertices = factor_workaround;
1045 
1046       /* interior solver */
1047       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);CHKERRQ(ierr);
1048       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
1049       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
1050       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
1051       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);CHKERRQ(ierr);
1052       ierr = PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);CHKERRQ(ierr);
1053 
1054       /* correction solver */
1055       ierr = PCCreate(PetscObjectComm((PetscObject)A),&msolv_ctx->correction_solver);CHKERRQ(ierr);
1056       ierr = PCSetOperators(msolv_ctx->correction_solver,A,A);CHKERRQ(ierr);
1057       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
1058       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
1059       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);CHKERRQ(ierr);
1060       ierr = PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);CHKERRQ(ierr);
1061 
1062       /* scatter and vecs for Schur complement solver */
1063       ierr = MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);CHKERRQ(ierr);
1064       ierr = MatCreateVecs(sub_schurs->S,&vec1_B,NULL);CHKERRQ(ierr);
1065       if (!factor_workaround) {
1066         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1067         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1068         ierr = PetscObjectReference((PetscObject)is_A_all);CHKERRQ(ierr);
1069         msolv_ctx->is_R = is_A_all;
1070       } else {
1071         IS              is_B_all;
1072         const PetscInt* idxs;
1073         PetscInt        dual,n_v,n;
1074 
1075         ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
1076         dual = size_schur - n_v;
1077         ierr = ISGetLocalSize(is_A_all,&n);CHKERRQ(ierr);
1078         ierr = ISGetIndices(is_A_all,&idxs);CHKERRQ(ierr);
1079         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);CHKERRQ(ierr);
1080         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1081         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1082         ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);CHKERRQ(ierr);
1083         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1084         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1085         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);CHKERRQ(ierr);
1086         ierr = ISRestoreIndices(is_A_all,&idxs);CHKERRQ(ierr);
1087       }
1088       ierr = VecDestroy(&vec1_B);CHKERRQ(ierr);
1089 
1090       /* communicate benign info to solver context */
1091       if (benign_n) {
1092         msolv_ctx->benign_n = benign_n;
1093         msolv_ctx->benign_zerodiag_subs = is_p_r;
1094         ierr = PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);CHKERRQ(ierr);
1095       }
1096     }
1097     ierr = MatDestroy(&A);CHKERRQ(ierr);
1098     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
1099 
1100     /* Work arrays */
1101     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
1102 
1103     /* matrices for adaptive selection */
1104     if (compute_Stilda) {
1105       if (!sub_schurs->sum_S_Ej_tilda_all) {
1106         ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1107         ierr = MatSetSizes(sub_schurs->sum_S_Ej_tilda_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
1108         ierr = MatSetType(sub_schurs->sum_S_Ej_tilda_all,MATAIJ);CHKERRQ(ierr);
1109         ierr = MatSeqAIJSetPreallocation(sub_schurs->sum_S_Ej_tilda_all,0,nnz);CHKERRQ(ierr);
1110       }
1111       if (!sub_schurs->sum_S_Ej_inv_all) {
1112         ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1113         ierr = MatSetSizes(sub_schurs->sum_S_Ej_inv_all,PETSC_DECIDE,PETSC_DECIDE,size_active_schur,size_active_schur);CHKERRQ(ierr);
1114         ierr = MatSetType(sub_schurs->sum_S_Ej_inv_all,MATAIJ);CHKERRQ(ierr);
1115         ierr = MatSeqAIJSetPreallocation(sub_schurs->sum_S_Ej_inv_all,0,nnz);CHKERRQ(ierr);
1116       }
1117     }
1118 
1119     /* S_Ej_all */
1120     cum = cum2 = 0;
1121     ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1122     for (i=0;i<sub_schurs->n_subs;i++) {
1123       PetscInt j;
1124 
1125       /* get S_E */
1126       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1127       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1128         PetscInt k;
1129         for (k=0;k<subset_size;k++) {
1130           for (j=k;j<subset_size;j++) {
1131             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1132             work[j*subset_size+k] = PetscConj(S_data[cum2+k*size_schur+j]);
1133           }
1134         }
1135       } else { /* just copy to workspace */
1136         PetscInt k;
1137         for (k=0;k<subset_size;k++) {
1138           for (j=0;j<subset_size;j++) {
1139             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1140           }
1141         }
1142       }
1143       /* insert S_E values */
1144       for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1145       if (change) {
1146         Mat change_sub,SEj;
1147 
1148         /* change basis */
1149         ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1150         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1151         { /* currently there's no support for PtAP with A dense */
1152           Mat T,T2,SEj2;
1153           ierr = MatConvert(SEj,MATSEQAIJ,MAT_INITIAL_MATRIX,&T);CHKERRQ(ierr);
1154           ierr = MatConvert(change_sub,MATSEQAIJ,MAT_INITIAL_MATRIX,&T2);CHKERRQ(ierr);
1155           ierr = MatPtAP(T,T2,MAT_INITIAL_MATRIX,1.0,&SEj2);CHKERRQ(ierr);
1156           ierr = MatDestroy(&T);CHKERRQ(ierr);
1157           ierr = MatDestroy(&T2);CHKERRQ(ierr);
1158           ierr = MatCopy(SEj2,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1159           ierr = MatDestroy(&SEj2);CHKERRQ(ierr);
1160         }
1161         { /* currently there's no support for ZeroRows with A dense */
1162           Mat T;
1163           ierr = MatConvert(SEj,MATSEQAIJ,MAT_INITIAL_MATRIX,&T);CHKERRQ(ierr);
1164           ierr = MatZeroRowsColumnsIS(T,change_primal_sub[i],1.,NULL,NULL);CHKERRQ(ierr);
1165           ierr = MatConvert(T,MATSEQDENSE,MAT_REUSE_MATRIX,&T);CHKERRQ(ierr);
1166           ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1167           ierr = MatDestroy(&T);CHKERRQ(ierr);
1168         }
1169         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1170       }
1171       ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1172 
1173       /* if adaptivity is requested, invert S_E blocks */
1174       if (compute_Stilda) {
1175         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1176         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1177         if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1178           PetscInt k;
1179           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,work,&B_N,&B_ierr));
1180           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1181           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,work,&B_N,&B_ierr));
1182           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1183           for (k=0;k<subset_size;k++) {
1184             for (j=k;j<subset_size;j++) {
1185               work[j*subset_size+k] = work[k*subset_size+j];
1186             }
1187           }
1188         } else {
1189           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,work,&B_N,pivots,&B_ierr));
1190           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1191           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1192           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1193         }
1194         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1195         ierr = MatSetValues(sub_schurs->sum_S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1196       }
1197       cum += subset_size;
1198       cum2 += subset_size*(size_schur + 1);
1199     }
1200     ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1201 
1202     if (solver_S) {
1203       ierr = MatFactorRestoreSchurComplement(F,&S_all);CHKERRQ(ierr);
1204     }
1205 
1206     schur_factor = NULL;
1207     if (compute_Stilda && size_active_schur) {
1208 
1209       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur) { /* we already computed the inverse */
1210         PetscInt j;
1211         for (j=0;j<size_schur;j++) dummy_idx[j] = j;
1212         ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,size_schur,dummy_idx,size_schur,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1213       } else {
1214         Mat S_all_inv=NULL;
1215         if (solver_S) { /* use MatFactor calls to invert S */
1216             /* let MatFactor factor the Schur complement */
1217           ierr = MatFactorFactorizeSchurComplement(F);CHKERRQ(ierr);
1218           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1219              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 */
1220           if (factor_workaround) {
1221             PetscScalar *data;
1222             PetscInt nd = 0;
1223 
1224             if (!sub_schurs->is_posdef) {
1225               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1226             }
1227             ierr = MatFactorGetSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1228             ierr = MatDenseGetArray(S_all_inv,&data);CHKERRQ(ierr);
1229             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1230               ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1231             }
1232             ierr = PetscMalloc1((size_active_schur*(size_active_schur+1))/2+nd,&schur_factor);CHKERRQ(ierr);
1233             cum = 0;
1234             for (i=0;i<size_active_schur;i++) {
1235               ierr = PetscMemcpy(schur_factor+cum,data+i*(size_schur+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1236               cum += size_active_schur-i;
1237             }
1238             for (i=0;i<nd;i++) schur_factor[cum+i] = data[(i+size_active_schur)*(size_schur+1)];
1239             /* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1240             ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1241             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1242             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,data,&B_N,&B_ierr));
1243             ierr = PetscFPTrapPop();CHKERRQ(ierr);
1244             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1245             ierr = MatDenseRestoreArray(S_all_inv,&data);CHKERRQ(ierr);
1246           } else {
1247             ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
1248             ierr = MatFactorGetSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1249           }
1250         } else { /* we need to invert explicitly since we are not using MatFactor for S */
1251           ierr = PetscObjectReference((PetscObject)S_all);CHKERRQ(ierr);
1252           S_all_inv = S_all;
1253           ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1254           ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1255           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1256           if (!use_getr) { /* TODO add sytrf/i for symmetric non hermitian */
1257             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
1258             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1259             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
1260             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1261           } else {
1262             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
1263             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1264             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1265             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1266           }
1267           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1268           ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1269         }
1270         /* S_Ej_tilda_all */
1271         cum = cum2 = 0;
1272         ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1273         for (i=0;i<sub_schurs->n_subs;i++) {
1274           PetscInt j;
1275 
1276           ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1277           /* get (St^-1)_E */
1278           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1279              will be properly accessed later during adaptive selection */
1280           if (S_lower_triangular) {
1281             PetscInt k;
1282             if (change) {
1283               for (k=0;k<subset_size;k++) {
1284                 for (j=k;j<subset_size;j++) {
1285                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1286                   work[j*subset_size+k] = work[k*subset_size+j];
1287                 }
1288               }
1289             } else {
1290               for (k=0;k<subset_size;k++) {
1291                 for (j=k;j<subset_size;j++) {
1292                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1293                 }
1294               }
1295             }
1296           } else {
1297             PetscInt k;
1298             for (k=0;k<subset_size;k++) {
1299               for (j=0;j<subset_size;j++) {
1300                 work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1301               }
1302             }
1303           }
1304           if (change) {
1305             Mat change_sub,SEj;
1306 
1307             /* change basis */
1308             ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1309             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1310             {
1311               Mat T,T2,SEj2;
1312               ierr = MatConvert(SEj,MATSEQAIJ,MAT_INITIAL_MATRIX,&T);CHKERRQ(ierr);
1313               ierr = MatConvert(change_sub,MATSEQAIJ,MAT_INITIAL_MATRIX,&T2);CHKERRQ(ierr);
1314               ierr = MatPtAP(T,T2,MAT_INITIAL_MATRIX,1.0,&SEj2);CHKERRQ(ierr);
1315               ierr = MatDestroy(&T);CHKERRQ(ierr);
1316               ierr = MatDestroy(&T2);CHKERRQ(ierr);
1317               ierr = MatCopy(SEj2,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1318               ierr = MatDestroy(&SEj2);CHKERRQ(ierr);
1319             }
1320             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
1321             {
1322               const PetscInt *idxs;
1323               PetscInt n,j;
1324               ierr = ISGetLocalSize(change_primal_sub[i],&n);CHKERRQ(ierr);
1325               ierr = ISGetIndices(change_primal_sub[i],&idxs);CHKERRQ(ierr);
1326               for (j=0;j<n;j++) {
1327                 PetscInt k;
1328                 for (k=0;k<subset_size;k++) {
1329                   work[k+idxs[j]*subset_size] = work[idxs[j]+k*subset_size] = 0.;
1330                 }
1331                 work[idxs[j] + idxs[j]*subset_size] = 1./PETSC_SMALL;
1332               }
1333               ierr = ISRestoreIndices(change_primal_sub[i],&idxs);CHKERRQ(ierr);
1334             }
1335             ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1336           }
1337           for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1338           ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1339           cum += subset_size;
1340           cum2 += subset_size*(size_schur + 1);
1341         }
1342         ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1343         if (solver_S) {
1344           ierr = MatFactorRestoreSchurComplement(F,&S_all_inv);CHKERRQ(ierr);
1345         }
1346         ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
1347       }
1348 
1349       /* move back factors to Schur data into F */
1350       if (factor_workaround) {
1351         Mat S_tmp;
1352         PetscInt nv,nd=0;
1353 
1354         if (!solver_S) {
1355           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
1356         }
1357         ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
1358         ierr = MatFactorGetSchurComplement(F,&S_tmp);CHKERRQ(ierr);
1359         if (sub_schurs->is_posdef) {
1360           PetscScalar *data;
1361 
1362           ierr = MatZeroEntries(S_tmp);CHKERRQ(ierr);
1363           ierr = MatDenseGetArray(S_tmp,&data);CHKERRQ(ierr);
1364 
1365           if (S_lower_triangular) {
1366             cum = 0;
1367             for (i=0;i<size_active_schur;i++) {
1368               ierr = PetscMemcpy(data+i*(size_schur+1),schur_factor+cum,(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1369               cum += size_active_schur-i;
1370 	    }
1371           } else {
1372             ierr = PetscMemcpy(data,schur_factor,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1373           }
1374           if (sub_schurs->is_dir) {
1375             ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1376 	    for (i=0;i<nd;i++) {
1377 	      data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
1378 	    }
1379           }
1380           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1381              set the diagonal entry of the Schur factor to a very large value */
1382           for (i=size_active_schur+nd;i<size_schur;i++) {
1383             data[i*(size_schur+1)] = infty;
1384           }
1385           ierr = MatDenseRestoreArray(S_tmp,&data);CHKERRQ(ierr);
1386         } else {
1387           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1388         }
1389         ierr = MatFactorRestoreSchurComplement(F,&S_tmp);CHKERRQ(ierr);
1390       }
1391     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
1392       PetscScalar *data;
1393       PetscInt    nd = 0;
1394 
1395       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1396         ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1397       }
1398       ierr = MatFactorGetSchurComplement(F,&S_all);CHKERRQ(ierr);
1399       ierr = MatDenseGetArray(S_all,&data);CHKERRQ(ierr);
1400       for (i=0;i<size_active_schur;i++) {
1401         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1402       }
1403       for (i=size_active_schur+nd;i<size_schur;i++) {
1404         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1405         data[i*(size_schur+1)] = infty;
1406       }
1407       ierr = MatDenseRestoreArray(S_all,&data);CHKERRQ(ierr);
1408       ierr = MatFactorRestoreSchurComplement(F,&S_all);CHKERRQ(ierr);
1409     }
1410     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
1411     ierr = PetscFree(schur_factor);CHKERRQ(ierr);
1412   }
1413   if (change_primal_sub) {
1414     for (i=0;i<sub_schurs->n_subs;i++) {
1415       ierr = ISDestroy(&change_primal_sub[i]);CHKERRQ(ierr);
1416     }
1417   }
1418   ierr = PetscFree(change_primal_sub);CHKERRQ(ierr);
1419   ierr = PetscFree(nnz);CHKERRQ(ierr);
1420   ierr = MatDestroy(&F);CHKERRQ(ierr);
1421   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1422   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
1423   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1424   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1425   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1426   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1427   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1428   if (compute_Stilda) {
1429     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1430     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1431     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1432     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1433   }
1434 
1435   /* Global matrix of all assembled Schur on subsets */
1436   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
1437   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
1438   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1439 
1440   /* Get local part of (\sum_j S_Ej) */
1441   if (!sub_schurs->sum_S_Ej_all) {
1442     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_INITIAL_MATRIX,&submats);CHKERRQ(ierr);
1443     sub_schurs->sum_S_Ej_all = submats[0];
1444   } else {
1445     ierr = PetscMalloc1(1,&submats);CHKERRQ(ierr);
1446     submats[0] = sub_schurs->sum_S_Ej_all;
1447     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1448   }
1449 
1450   /* Compute explicitly (\sum_j S_Ej)^-1 (faster scaling during PCApply, needs extra work when doing setup) */
1451 #if 0
1452   if (faster_deluxe) {
1453     Mat         tmpmat;
1454     PetscScalar *array;
1455     PetscInt    cum;
1456 
1457     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all,&array);CHKERRQ(ierr);
1458     cum = 0;
1459     for (i=0;i<sub_schurs->n_subs;i++) {
1460       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1461       ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1462       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1463       if (!use_getr) {
1464         PetscInt j,k;
1465 
1466         PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
1467         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1468         PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
1469         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1470         for (j=0;j<B_N;j++) {
1471           for (k=j+1;k<B_N;k++) {
1472             array[k*B_N+j+cum] = array[j*B_N+k+cum];
1473           }
1474         }
1475       } else {
1476         PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
1477         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1478         PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1479         if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1480       }
1481       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1482       cum += subset_size*subset_size;
1483     }
1484     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all,&array);CHKERRQ(ierr);
1485     ierr = MatMatMult(sub_schurs->S_Ej_all,sub_schurs->sum_S_Ej_all,MAT_INITIAL_MATRIX,1.0,&tmpmat);CHKERRQ(ierr);
1486     ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1487     ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1488     sub_schurs->S_Ej_all = tmpmat;
1489   }
1490 #endif
1491   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1492   if (compute_Stilda) {
1493     ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1494     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1495     submats[0] = sub_schurs->sum_S_Ej_tilda_all;
1496     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1497     ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1498     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1499     submats[0] = sub_schurs->sum_S_Ej_inv_all;
1500     ierr = MatGetSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1501   }
1502 
1503   /* free workspace */
1504   ierr = PetscFree(submats);CHKERRQ(ierr);
1505   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
1506   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
1507   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
1508   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
1509   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
1510   PetscFunctionReturn(0);
1511 }
1512 
1513 #undef __FUNCT__
1514 #define __FUNCT__ "PCBDDCSubSchursInit"
1515 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap)
1516 {
1517   IS              *faces,*edges,*all_cc,vertices;
1518   PetscInt        i,n_faces,n_edges,n_all_cc;
1519   PetscBool       is_sorted;
1520   PetscErrorCode  ierr;
1521 
1522   PetscFunctionBegin;
1523   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
1524   if (!is_sorted) {
1525     SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
1526   }
1527   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
1528   if (!is_sorted) {
1529     SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
1530   }
1531 
1532   /* reset any previous data */
1533   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
1534 
1535   /* get index sets for faces and edges (already sorted by global ordering) */
1536   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1537   n_all_cc = n_faces+n_edges;
1538   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
1539   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
1540   for (i=0;i<n_faces;i++) {
1541     all_cc[i] = faces[i];
1542   }
1543   for (i=0;i<n_edges;i++) {
1544     all_cc[n_faces+i] = edges[i];
1545     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
1546   }
1547   ierr = PetscFree(faces);CHKERRQ(ierr);
1548   ierr = PetscFree(edges);CHKERRQ(ierr);
1549   sub_schurs->is_dir = NULL;
1550   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
1551 
1552   /* Determine if MatFactor can be used */
1553   sub_schurs->schur_explicit = PETSC_FALSE;
1554 #if defined(PETSC_HAVE_MUMPS)
1555   sub_schurs->schur_explicit = PETSC_TRUE;
1556 #endif
1557 #if defined(PETSC_HAVE_MKL_PARDISO)
1558   sub_schurs->schur_explicit = PETSC_TRUE;
1559 #endif
1560 
1561   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
1562   sub_schurs->is_I = is_I;
1563   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
1564   sub_schurs->is_B = is_B;
1565   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
1566   sub_schurs->l2gmap = graph->l2gmap;
1567   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
1568   sub_schurs->BtoNmap = BtoNmap;
1569   sub_schurs->n_subs = n_all_cc;
1570   sub_schurs->is_subs = all_cc;
1571   if (!sub_schurs->schur_explicit) { /* sort by local ordering if we are not using MatFactor */
1572     for (i=0;i<sub_schurs->n_subs;i++) {
1573       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
1574     }
1575   }
1576   sub_schurs->is_vertices = vertices;
1577   sub_schurs->S_Ej_all = NULL;
1578   sub_schurs->sum_S_Ej_all = NULL;
1579   sub_schurs->sum_S_Ej_inv_all = NULL;
1580   sub_schurs->sum_S_Ej_tilda_all = NULL;
1581   sub_schurs->is_Ej_all = NULL;
1582   PetscFunctionReturn(0);
1583 }
1584 
1585 #undef __FUNCT__
1586 #define __FUNCT__ "PCBDDCSubSchursCreate"
1587 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1588 {
1589   PCBDDCSubSchurs schurs_ctx;
1590   PetscErrorCode  ierr;
1591 
1592   PetscFunctionBegin;
1593   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
1594   schurs_ctx->n_subs = 0;
1595   *sub_schurs = schurs_ctx;
1596   PetscFunctionReturn(0);
1597 }
1598 
1599 #undef __FUNCT__
1600 #define __FUNCT__ "PCBDDCSubSchursReset"
1601 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1602 {
1603   PetscInt       i;
1604   PetscErrorCode ierr;
1605 
1606   PetscFunctionBegin;
1607   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1608   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1609   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1610   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1611   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1612   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1613   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1614   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1615   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1616   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1617   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1618   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1619   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1620   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1621   for (i=0;i<sub_schurs->n_subs;i++) {
1622     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
1623   }
1624   if (sub_schurs->n_subs) {
1625     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1626   }
1627   if (sub_schurs->reuse_solver) {
1628     ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1629   }
1630   ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1631   if (sub_schurs->change) {
1632     for (i=0;i<sub_schurs->n_subs;i++) {
1633       ierr = KSPDestroy(&sub_schurs->change[i]);CHKERRQ(ierr);
1634     }
1635   }
1636   ierr = PetscFree(sub_schurs->change);CHKERRQ(ierr);
1637   sub_schurs->n_subs = 0;
1638   PetscFunctionReturn(0);
1639 }
1640 
1641 #undef __FUNCT__
1642 #define __FUNCT__ "PCBDDCAdjGetNextLayer_Private"
1643 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1644 {
1645   PetscInt       i,j,n;
1646   PetscErrorCode ierr;
1647 
1648   PetscFunctionBegin;
1649   n = 0;
1650   for (i=-n_prev;i<0;i++) {
1651     PetscInt start_dof = queue_tip[i];
1652     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1653       PetscInt dof = adjncy[j];
1654       if (!PetscBTLookup(touched,dof)) {
1655         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1656         queue_tip[n] = dof;
1657         n++;
1658       }
1659     }
1660   }
1661   *n_added = n;
1662   PetscFunctionReturn(0);
1663 }
1664