xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision f4f7d9d6f327da0f7d23fce3deda9a2f062f9a8e)
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;
401   PetscBool              use_potr = PETSC_FALSE, use_sytr = PETSC_FALSE;
402   PetscErrorCode         ierr;
403 
404   PetscFunctionBegin;
405   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
406   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
407 
408 #if defined(PETSC_USE_COMPLEX)
409   sub_schurs->is_hermitian = PETSC_FALSE; /* Hermitian Cholesky is not supported by PETSc and external packages */
410 #else
411   sub_schurs->is_hermitian = PETSC_TRUE;
412 #endif
413   sub_schurs->is_posdef    = PETSC_TRUE;
414   if (benign_trick) sub_schurs->is_posdef = PETSC_FALSE;
415   ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)sub_schurs->l2gmap),sub_schurs->prefix,"BDDC sub_schurs options","PC");CHKERRQ(ierr);
416   ierr = PetscOptionsBool("-sub_schurs_hermitian","Hermitian problem",NULL,sub_schurs->is_hermitian,&sub_schurs->is_hermitian,NULL);CHKERRQ(ierr);
417   ierr = PetscOptionsBool("-sub_schurs_posdef","Positive definite problem",NULL,sub_schurs->is_posdef,&sub_schurs->is_posdef,NULL);CHKERRQ(ierr);
418   ierr = PetscOptionsEnd();CHKERRQ(ierr);
419 
420   /* convert matrix if needed */
421   if (Ain) {
422     PetscBool isseqaij;
423     ierr = PetscObjectTypeCompare((PetscObject)Ain,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
424     if (isseqaij) {
425       ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
426       sub_schurs->A = Ain;
427     } else {
428       ierr = MatConvert(Ain,MATSEQAIJ,MAT_INITIAL_MATRIX,&sub_schurs->A);CHKERRQ(ierr);
429     }
430   }
431 
432   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
433   sub_schurs->S = Sin;
434   if (sub_schurs->schur_explicit) {
435     sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
436   }
437 
438   /* preliminary checks */
439   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");
440 
441   /* restrict work on active processes */
442   color = 0;
443   if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
444   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
445   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
446   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
447   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
448   ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
449   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
450   if (!sub_schurs->n_subs) {
451     ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
452     PetscFunctionReturn(0);
453   }
454   /* ierr = PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);CHKERRQ(ierr); */
455 
456   /* get Schur complement matrices */
457   if (!sub_schurs->schur_explicit) {
458     Mat       tA_IB,tA_BI,tA_BB;
459     PetscBool isseqsbaij;
460     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
461     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);CHKERRQ(ierr);
462     if (isseqsbaij) {
463       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
464       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
465       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
466     } else {
467       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
468       A_BB = tA_BB;
469       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
470       A_IB = tA_IB;
471       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
472       A_BI = tA_BI;
473     }
474   } else {
475     A_II = NULL;
476     A_IB = NULL;
477     A_BI = NULL;
478     A_BB = NULL;
479   }
480   S_all = NULL;
481 
482   /* determine interior problems */
483   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
484   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
485     PetscBT                touched;
486     const PetscInt*        idx_B;
487     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
488 
489     if (!xadj) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
490     /* get sizes */
491     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
492     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
493 
494     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
495     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
496     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
497 
498     /* all boundary dofs must be skipped when adding layers */
499     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
500     for (j=0;j<n_B;j++) {
501       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
502     }
503     ierr = PetscMemcpy(local_numbering,idx_B,n_B*sizeof(PetscInt));CHKERRQ(ierr);
504     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
505 
506     /* add prescribed number of layers of dofs */
507     n_local_dofs = n_B;
508     n_prev_added = n_B;
509     for (layer=0;layer<nlayers;layer++) {
510       PetscInt n_added;
511       if (n_local_dofs == n_I+n_B) break;
512       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);
513       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
514       n_prev_added = n_added;
515       n_local_dofs += n_added;
516       if (!n_added) break;
517     }
518     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
519 
520     /* IS for I layer dofs in original numbering */
521     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);
522     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
523     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
524     /* IS for I layer dofs in I numbering */
525     if (!sub_schurs->schur_explicit) {
526       ISLocalToGlobalMapping ItoNmap;
527       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
528       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
529       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
530 
531       /* II block */
532       ierr = MatCreateSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
533     }
534   } else {
535     PetscInt n_I;
536 
537     /* IS for I dofs in original numbering */
538     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
539     is_I_layer = sub_schurs->is_I;
540 
541     /* IS for I dofs in I numbering (strided 1) */
542     if (!sub_schurs->schur_explicit) {
543       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
544       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
545 
546       /* II block is the same */
547       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
548       AE_II = A_II;
549     }
550   }
551 
552   /* Get info on subset sizes and sum of all subsets sizes */
553   max_subset_size = 0;
554   local_size = 0;
555   for (i=0;i<sub_schurs->n_subs;i++) {
556     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
557     max_subset_size = PetscMax(subset_size,max_subset_size);
558     local_size += subset_size;
559   }
560 
561   /* Work arrays for local indices */
562   extra = 0;
563   ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
564   if (sub_schurs->schur_explicit && is_I_layer) {
565     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
566   }
567   ierr = PetscMalloc1(n_B+extra,&all_local_idx_N);CHKERRQ(ierr);
568   if (extra) {
569     const PetscInt *idxs;
570     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
571     ierr = PetscMemcpy(all_local_idx_N,idxs,extra*sizeof(PetscInt));CHKERRQ(ierr);
572     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
573   }
574   ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
575   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum1);CHKERRQ(ierr);
576   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
577 
578   /* Get local indices in local numbering */
579   local_size = 0;
580   for (i=0;i<sub_schurs->n_subs;i++) {
581     PetscInt j;
582     const    PetscInt *idxs;
583 
584     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
585     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
586     /* start (smallest in global ordering) and multiplicity */
587     auxnum1[i] = idxs[0];
588     auxnum2[i] = subset_size;
589     /* subset indices in local numbering */
590     ierr = PetscMemcpy(all_local_idx_N+local_size+extra,idxs,subset_size*sizeof(PetscInt));CHKERRQ(ierr);
591     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
592     for (j=0;j<subset_size;j++) nnz[local_size+j] = subset_size;
593     local_size += subset_size;
594   }
595 
596   /* allocate extra workspace needed only for GETRI or SYTRF */
597   use_potr = PETSC_TRUE;
598   if (local_size && !benign_trick && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) {
599     PetscScalar  lwork,dummyscalar = 0.;
600     PetscBLASInt dummyint = 0;
601 
602     use_potr = PETSC_FALSE;
603     use_sytr = sub_schurs->is_hermitian;
604     B_lwork = -1;
605     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
606     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
607     if (use_sytr) {
608       PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
609       if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYTRF Lapack routine %d",(int)B_ierr);
610     } else {
611       PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
612       if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
613     }
614     ierr = PetscFPTrapPop();CHKERRQ(ierr);
615     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
616     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
617   } else {
618     Bwork = NULL;
619     pivots = NULL;
620   }
621 
622   /* prepare parallel matrices for summing up properly schurs on subsets */
623   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);CHKERRQ(ierr);
624   ierr = ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);CHKERRQ(ierr);
625   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
626   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);CHKERRQ(ierr);
627   ierr = ISRenumber(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);CHKERRQ(ierr);
628   ierr = ISDestroy(&all_subsets);CHKERRQ(ierr);
629   ierr = ISDestroy(&all_subsets_mult);CHKERRQ(ierr);
630   ierr = ISGetLocalSize(all_subsets_n,&i);CHKERRQ(ierr);
631   if (i != local_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",i,local_size);
632   ierr = ISLocalToGlobalMappingCreateIS(all_subsets_n,&l2gmap_subsets);CHKERRQ(ierr);
633   ierr = MatCreateIS(comm_n,1,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size,l2gmap_subsets,NULL,&work_mat);CHKERRQ(ierr);
634   ierr = ISLocalToGlobalMappingDestroy(&l2gmap_subsets);CHKERRQ(ierr);
635   ierr = MatCreate(PetscObjectComm((PetscObject)work_mat),&global_schur_subsets);CHKERRQ(ierr);
636   ierr = MatSetSizes(global_schur_subsets,PETSC_DECIDE,PETSC_DECIDE,global_size,global_size);CHKERRQ(ierr);
637   ierr = MatSetType(global_schur_subsets,MATMPIAIJ);CHKERRQ(ierr);
638 
639   /* subset indices in local boundary numbering */
640   if (!sub_schurs->is_Ej_all) {
641     PetscInt *all_local_idx_B;
642 
643     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
644     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
645     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);
646     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
647   }
648 
649   if (change) {
650     ISLocalToGlobalMapping BtoS;
651     IS                     change_primal_B;
652     IS                     change_primal_all;
653 
654     if (sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
655     if (sub_schurs->change) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
656     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change_primal_sub);CHKERRQ(ierr);
657     for (i=0;i<sub_schurs->n_subs;i++) {
658       ISLocalToGlobalMapping NtoS;
659       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);CHKERRQ(ierr);
660       ierr = ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
661       ierr = ISLocalToGlobalMappingDestroy(&NtoS);CHKERRQ(ierr);
662     }
663     ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);CHKERRQ(ierr);
664     ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);CHKERRQ(ierr);
665     ierr = ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);CHKERRQ(ierr);
666     ierr = ISLocalToGlobalMappingDestroy(&BtoS);CHKERRQ(ierr);
667     ierr = ISDestroy(&change_primal_B);CHKERRQ(ierr);
668     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change);CHKERRQ(ierr);
669     for (i=0;i<sub_schurs->n_subs;i++) {
670       Mat change_sub;
671 
672       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
673       ierr = KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);CHKERRQ(ierr);
674       ierr = KSPSetType(sub_schurs->change[i],KSPPREONLY);CHKERRQ(ierr);
675       if (!sub_schurs->change_with_qr) {
676         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
677       } else {
678         Mat change_subt;
679         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);CHKERRQ(ierr);
680         ierr = MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
681         ierr = MatDestroy(&change_subt);CHKERRQ(ierr);
682       }
683       ierr = KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);CHKERRQ(ierr);
684       ierr = MatDestroy(&change_sub);CHKERRQ(ierr);
685       ierr = KSPSetOptionsPrefix(sub_schurs->change[i],sub_schurs->prefix);CHKERRQ(ierr);
686       ierr = KSPAppendOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");CHKERRQ(ierr);
687     }
688     ierr = ISDestroy(&change_primal_all);CHKERRQ(ierr);
689   }
690 
691   /* Local matrix of all local Schur on subsets (transposed) */
692   if (!sub_schurs->S_Ej_all) {
693     ierr = MatCreate(PETSC_COMM_SELF,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
694     ierr = MatSetSizes(sub_schurs->S_Ej_all,PETSC_DECIDE,PETSC_DECIDE,local_size,local_size);CHKERRQ(ierr);
695     ierr = MatSetType(sub_schurs->S_Ej_all,MATAIJ);CHKERRQ(ierr);
696     ierr = MatSeqAIJSetPreallocation(sub_schurs->S_Ej_all,0,nnz);CHKERRQ(ierr);
697   }
698 
699   /* Compute Schur complements explicitly */
700   F = NULL;
701   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 */
702     Mat         S_Ej_expl;
703     PetscScalar *work;
704     PetscInt    j,*dummy_idx;
705     PetscBool   Sdense;
706 
707     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
708     local_size = 0;
709     for (i=0;i<sub_schurs->n_subs;i++) {
710       IS  is_subset_B;
711       Mat AE_EE,AE_IE,AE_EI,S_Ej;
712 
713       /* subsets in original and boundary numbering */
714       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
715       /* EE block */
716       ierr = MatCreateSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
717       /* IE block */
718       ierr = MatCreateSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
719       /* EI block */
720       if (sub_schurs->is_hermitian) {
721         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
722       } else {
723         ierr = MatCreateSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
724       }
725       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
726       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
727       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
728       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
729       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
730       if (AE_II == A_II) { /* we can reuse the same ksp */
731         KSP ksp;
732         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
733         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
734       } else { /* build new ksp object which inherits ksp and pc types from the original one */
735         KSP       origksp,schurksp;
736         PC        origpc,schurpc;
737         KSPType   ksp_type;
738         PetscInt  n_internal;
739         PetscBool ispcnone;
740 
741         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
742         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
743         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
744         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
745         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
746         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
747         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
748         if (!ispcnone) {
749           PCType pc_type;
750           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
751           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
752         } else {
753           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
754         }
755         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
756         if (n_internal) { /* UMFPACK gives error with 0 sized problems */
757           MatSolverType solver = NULL;
758           ierr = PCFactorGetMatSolverType(origpc,(MatSolverType*)&solver);CHKERRQ(ierr);
759           if (solver) {
760             ierr = PCFactorSetMatSolverType(schurpc,solver);CHKERRQ(ierr);
761           }
762         }
763         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
764       }
765       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
766       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
767       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_hermitian,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
768       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
769       if (Sdense) {
770         for (j=0;j<subset_size;j++) {
771           dummy_idx[j]=local_size+j;
772         }
773         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
774       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
775       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
776       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
777       local_size += subset_size;
778     }
779     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
780     /* free */
781     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
782     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
783     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
784   } else {
785     Mat         A,cs_AIB_mat = NULL,benign_AIIm1_ones_mat = NULL;
786     Vec         Dall = NULL;
787     IS          is_A_all,*is_p_r = NULL;
788     PetscScalar *work,*S_data,*schur_factor,infty = PETSC_MAX_REAL;
789     PetscInt    n,n_I,*dummy_idx,size_schur,size_active_schur,cum,cum2;
790     PetscBool   economic,solver_S,S_lower_triangular = PETSC_FALSE;
791     PetscBool   schur_has_vertices,factor_workaround;
792     char        solver[256];
793 
794     /* get sizes */
795     n_I = 0;
796     if (is_I_layer) {
797       ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
798     }
799     economic = PETSC_FALSE;
800     ierr = ISGetLocalSize(sub_schurs->is_I,&cum);CHKERRQ(ierr);
801     if (cum != n_I) economic = PETSC_TRUE;
802     ierr = MatGetLocalSize(sub_schurs->A,&n,NULL);CHKERRQ(ierr);
803     size_active_schur = local_size;
804 
805     /* import scaling vector (wrong formulation if we have 3D edges) */
806     if (scaling && compute_Stilda) {
807       const PetscScalar *array;
808       PetscScalar       *array2;
809       const PetscInt    *idxs;
810       PetscInt          i;
811 
812       ierr = ISGetIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
813       ierr = VecCreateSeq(PETSC_COMM_SELF,size_active_schur,&Dall);CHKERRQ(ierr);
814       ierr = VecGetArrayRead(scaling,&array);CHKERRQ(ierr);
815       ierr = VecGetArray(Dall,&array2);CHKERRQ(ierr);
816       for (i=0;i<size_active_schur;i++) array2[i] = array[idxs[i]];
817       ierr = VecRestoreArray(Dall,&array2);CHKERRQ(ierr);
818       ierr = VecRestoreArrayRead(scaling,&array);CHKERRQ(ierr);
819       ierr = ISRestoreIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
820       deluxe = PETSC_FALSE;
821     }
822 
823     /* size active schurs does not count any dirichlet or vertex dof on the interface */
824     factor_workaround = PETSC_FALSE;
825     schur_has_vertices = PETSC_FALSE;
826     cum = n_I+size_active_schur;
827     if (sub_schurs->is_dir) {
828       const PetscInt* idxs;
829       PetscInt        n_dir;
830 
831       ierr = ISGetLocalSize(sub_schurs->is_dir,&n_dir);CHKERRQ(ierr);
832       ierr = ISGetIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
833       ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_dir*sizeof(PetscInt));CHKERRQ(ierr);
834       ierr = ISRestoreIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
835       cum += n_dir;
836       factor_workaround = PETSC_TRUE;
837     }
838     /* include the primal vertices in the Schur complement */
839     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
840       PetscInt n_v;
841 
842       ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
843       if (n_v) {
844         const PetscInt* idxs;
845 
846         ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
847         ierr = PetscMemcpy(all_local_idx_N+cum,idxs,n_v*sizeof(PetscInt));CHKERRQ(ierr);
848         ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
849         cum += n_v;
850         factor_workaround = PETSC_TRUE;
851         schur_has_vertices = PETSC_TRUE;
852       }
853     }
854     size_schur = cum - n_I;
855     ierr = ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);CHKERRQ(ierr);
856     if (cum == n) {
857       ierr = ISSetPermutation(is_A_all);CHKERRQ(ierr);
858       ierr = MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
859     } else {
860       ierr = MatCreateSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
861     }
862     ierr = MatSetOptionsPrefix(A,sub_schurs->prefix);CHKERRQ(ierr);
863     ierr = MatAppendOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
864 
865     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
866        n^2 instead of n^1.5 or something. This is a workaround */
867     if (benign_n) {
868       Vec                    v;
869       ISLocalToGlobalMapping N_to_reor;
870       IS                     is_p0,is_p0_p;
871       PetscScalar            *cs_AIB,*AIIm1_data;
872       PetscInt               sizeA;
873 
874       ierr = ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);CHKERRQ(ierr);
875       ierr = ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
876       ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);CHKERRQ(ierr);
877       ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
878       ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
879       ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
880       ierr = MatCreateSeqDense(PETSC_COMM_SELF,sizeA,benign_n,NULL,&benign_AIIm1_ones_mat);CHKERRQ(ierr);
881       ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,benign_n,NULL,&cs_AIB_mat);CHKERRQ(ierr);
882       ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
883       ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
884       ierr = PetscMalloc1(benign_n,&is_p_r);CHKERRQ(ierr);
885       /* compute colsum of A_IB restricted to pressures */
886       for (i=0;i<benign_n;i++) {
887         Vec            benign_AIIm1_ones;
888         PetscScalar    *array;
889         const PetscInt *idxs;
890         PetscInt       j,nz;
891 
892         ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);CHKERRQ(ierr);
893         ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
894         ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
895         for (j=0;j<nz;j++) AIIm1_data[idxs[j]+sizeA*i] = 1.;
896         ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
897         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
898         ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
899         ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
900         ierr = VecGetArray(v,&array);CHKERRQ(ierr);
901         for (j=0;j<size_schur;j++) {
902 #if defined(PETSC_USE_COMPLEX)
903           cs_AIB[i*size_schur + j] = (PetscRealPart(array[j+n_I])/nz + PETSC_i*(PetscImaginaryPart(array[j+n_I])/nz));
904 #else
905           cs_AIB[i*size_schur + j] = array[j+n_I]/nz;
906 #endif
907         }
908         ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
909       }
910       ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
911       ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
912       ierr = VecDestroy(&v);CHKERRQ(ierr);
913       ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);CHKERRQ(ierr);
914       ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
915       ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
916       ierr = MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);CHKERRQ(ierr);
917       ierr = ISDestroy(&is_p0_p);CHKERRQ(ierr);
918       ierr = ISLocalToGlobalMappingDestroy(&N_to_reor);CHKERRQ(ierr);
919     }
920     ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_hermitian);CHKERRQ(ierr);
921     ierr = MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
922     ierr = MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
923 #if defined(PETSC_HAVE_MUMPS)
924     ierr = PetscStrcpy(solver,MATSOLVERMUMPS);CHKERRQ(ierr);
925 #else
926     ierr = PetscStrcpy(solver,MATSOLVERMKL_PARDISO);CHKERRQ(ierr);
927 #endif
928     ierr = PetscOptionsGetString(NULL,((PetscObject)A)->prefix,"-mat_solver_type",solver,256,NULL);CHKERRQ(ierr);
929 
930     /* when using the benign subspace trick, the local Schur complements are SPD */
931     if (benign_trick) sub_schurs->is_posdef = PETSC_TRUE;
932 
933     if (n_I) {
934       IS is_schur;
935 
936       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
937         ierr = MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
938       } else {
939         ierr = MatGetFactor(A,solver,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
940       }
941       ierr = MatSetErrorIfFailure(A,PETSC_TRUE);CHKERRQ(ierr);
942 
943       /* subsets ordered last */
944       ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is_schur);CHKERRQ(ierr);
945       ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
946       ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
947 
948       /* factorization step */
949       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
950         ierr = MatCholeskyFactorSymbolic(F,A,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,19,2);CHKERRQ(ierr);
953 #endif
954         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
955         S_lower_triangular = PETSC_TRUE;
956       } else {
957         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
958 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
959         ierr = MatMumpsSetIcntl(F,19,3);CHKERRQ(ierr);
960 #endif
961         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
962       }
963       ierr = MatViewFromOptions(F,(PetscObject)A,"-mat_factor_view");CHKERRQ(ierr);
964 
965       /* get explicit Schur Complement computed during numeric factorization */
966       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
967       ierr = MatSetOption(S_all,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
968       ierr = MatSetOption(S_all,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
969 
970       /* we can reuse the solvers if we are not using the economic version */
971       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
972       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
973       if (!sub_schurs->is_posdef && factor_workaround && compute_Stilda && size_active_schur)
974         reuse_solvers = factor_workaround = PETSC_FALSE;
975 
976       solver_S = PETSC_TRUE;
977 
978       /* update the Schur complement with the change of basis on the pressures */
979       if (benign_n) {
980         PetscScalar *S_data,*cs_AIB,*AIIm1_data;
981         Vec         v;
982         PetscInt    sizeA;
983 
984         ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
985         ierr = MatCreateVecs(A,&v,NULL);CHKERRQ(ierr);
986         ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
987 #if defined(PETSC_HAVE_MUMPS)
988         ierr = MatMumpsSetIcntl(F,26,0);CHKERRQ(ierr);
989 #endif
990 #if defined(PETSC_HAVE_MKL_PARDISO)
991         ierr = MatMkl_PardisoSetCntl(F,70,1);CHKERRQ(ierr);
992 #endif
993         ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
994         ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
995         for (i=0;i<benign_n;i++) {
996           Vec            benign_AIIm1_ones;
997           PetscScalar    *array,sum = 0.,one = 1.;
998           const PetscInt *idxs;
999           PetscInt       j,nz;
1000           PetscBLASInt   B_k,B_n;
1001 
1002           ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,sizeA,AIIm1_data+sizeA*i,&benign_AIIm1_ones);CHKERRQ(ierr);
1003           ierr = VecCopy(benign_AIIm1_ones,v);CHKERRQ(ierr);
1004           ierr = MatSolve(F,v,benign_AIIm1_ones);CHKERRQ(ierr);
1005           ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
1006           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1007           /* p0 dof (eliminated) is excluded from the sum */
1008           for (j=0;j<nz-1;j++) sum -= AIIm1_data[idxs[j]+sizeA*i];
1009           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1010           ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
1011           ierr = VecGetArray(v,&array);CHKERRQ(ierr);
1012           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
1013           /* cs_AIB already scaled by 1./nz */
1014           B_k = 1;
1015           ierr = PetscBLASIntCast(size_schur,&B_n);CHKERRQ(ierr);
1016           PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
1017           sum  = 1.;
1018           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));
1019           ierr = VecRestoreArray(v,&array);CHKERRQ(ierr);
1020           /* set p0 entry of AIIm1_ones to zero */
1021           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1022           for (j=0;j<benign_n;j++) AIIm1_data[idxs[nz-1]+sizeA*j] = 0.;
1023           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1024           ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
1025         }
1026         if (!S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1027           PetscInt k,j;
1028           for (k=0;k<size_schur;k++) {
1029             for (j=k;j<size_schur;j++) {
1030               S_data[j*size_schur+k] = PetscConj(S_data[k*size_schur+j]);
1031             }
1032           }
1033         }
1034 
1035         /* restore defaults */
1036 #if defined(PETSC_HAVE_MUMPS)
1037         ierr = MatMumpsSetIcntl(F,26,-1);CHKERRQ(ierr);
1038 #endif
1039 #if defined(PETSC_HAVE_MKL_PARDISO)
1040         ierr = MatMkl_PardisoSetCntl(F,70,0);CHKERRQ(ierr);
1041 #endif
1042         ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1043         ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1044         ierr = VecDestroy(&v);CHKERRQ(ierr);
1045         ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1046       }
1047       if (!reuse_solvers) {
1048         for (i=0;i<benign_n;i++) {
1049           ierr = ISDestroy(&is_p_r[i]);CHKERRQ(ierr);
1050         }
1051         ierr = PetscFree(is_p_r);CHKERRQ(ierr);
1052         ierr = MatDestroy(&cs_AIB_mat);CHKERRQ(ierr);
1053         ierr = MatDestroy(&benign_AIIm1_ones_mat);CHKERRQ(ierr);
1054       }
1055     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1056       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
1057       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1058       factor_workaround = PETSC_FALSE;
1059       solver_S = PETSC_FALSE;
1060     }
1061 
1062     if (reuse_solvers) {
1063       Mat                A_II,Afake;
1064       Vec                vec1_B;
1065       PCBDDCReuseSolvers msolv_ctx;
1066       PetscInt           n_R;
1067 
1068       if (sub_schurs->reuse_solver) {
1069         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1070       } else {
1071         ierr = PetscNew(&sub_schurs->reuse_solver);CHKERRQ(ierr);
1072       }
1073       msolv_ctx = sub_schurs->reuse_solver;
1074       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1075       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
1076       msolv_ctx->F = F;
1077       ierr = MatCreateVecs(F,&msolv_ctx->sol,NULL);CHKERRQ(ierr);
1078       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1079       {
1080         PetscScalar *array;
1081         PetscInt    n;
1082 
1083         ierr = VecGetLocalSize(msolv_ctx->sol,&n);CHKERRQ(ierr);
1084         ierr = VecGetArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1085         ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);CHKERRQ(ierr);
1086         ierr = VecRestoreArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1087       }
1088       msolv_ctx->has_vertices = schur_has_vertices;
1089 
1090       /* interior solver */
1091       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);CHKERRQ(ierr);
1092       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
1093       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
1094       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
1095       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);CHKERRQ(ierr);
1096       ierr = PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);CHKERRQ(ierr);
1097 
1098       /* correction solver */
1099       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->correction_solver);CHKERRQ(ierr);
1100       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
1101       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
1102       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);CHKERRQ(ierr);
1103       ierr = PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);CHKERRQ(ierr);
1104 
1105       /* scatter and vecs for Schur complement solver */
1106       ierr = MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);CHKERRQ(ierr);
1107       ierr = MatCreateVecs(sub_schurs->S,&vec1_B,NULL);CHKERRQ(ierr);
1108       if (!schur_has_vertices) {
1109         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1110         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1111         ierr = PetscObjectReference((PetscObject)is_A_all);CHKERRQ(ierr);
1112         msolv_ctx->is_R = is_A_all;
1113       } else {
1114         IS              is_B_all;
1115         const PetscInt* idxs;
1116         PetscInt        dual,n_v,n;
1117 
1118         ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
1119         dual = size_schur - n_v;
1120         ierr = ISGetLocalSize(is_A_all,&n);CHKERRQ(ierr);
1121         ierr = ISGetIndices(is_A_all,&idxs);CHKERRQ(ierr);
1122         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);CHKERRQ(ierr);
1123         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1124         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1125         ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);CHKERRQ(ierr);
1126         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1127         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1128         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);CHKERRQ(ierr);
1129         ierr = ISRestoreIndices(is_A_all,&idxs);CHKERRQ(ierr);
1130       }
1131       ierr = ISGetLocalSize(msolv_ctx->is_R,&n_R);CHKERRQ(ierr);
1132       ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,n_R,n_R,0,NULL,&Afake);CHKERRQ(ierr);
1133       ierr = MatAssemblyBegin(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1134       ierr = MatAssemblyEnd(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1135       ierr = PCSetOperators(msolv_ctx->correction_solver,Afake,Afake);CHKERRQ(ierr);
1136       ierr = MatDestroy(&Afake);CHKERRQ(ierr);
1137       ierr = VecDestroy(&vec1_B);CHKERRQ(ierr);
1138 
1139       /* communicate benign info to solver context */
1140       if (benign_n) {
1141         PetscScalar *array;
1142 
1143         msolv_ctx->benign_n = benign_n;
1144         msolv_ctx->benign_zerodiag_subs = is_p_r;
1145         ierr = PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);CHKERRQ(ierr);
1146         msolv_ctx->benign_csAIB = cs_AIB_mat;
1147         ierr = MatCreateVecs(cs_AIB_mat,&msolv_ctx->benign_corr_work,NULL);CHKERRQ(ierr);
1148         ierr = VecGetArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1149         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array,&msolv_ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
1150         ierr = VecRestoreArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1151         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1152       }
1153     } else {
1154       if (sub_schurs->reuse_solver) {
1155         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1156       }
1157       ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1158     }
1159     ierr = MatDestroy(&A);CHKERRQ(ierr);
1160     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
1161 
1162     /* Work arrays */
1163     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
1164 
1165     /* matrices for deluxe scaling and adaptive selection */
1166     if (compute_Stilda) {
1167       if (!sub_schurs->sum_S_Ej_tilda_all) {
1168         ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_SHARE_NONZERO_PATTERN,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1169       }
1170       if (!sub_schurs->sum_S_Ej_inv_all && deluxe) {
1171         ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_SHARE_NONZERO_PATTERN,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1172       }
1173     }
1174 
1175     /* S_Ej_all */
1176     cum = cum2 = 0;
1177     ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1178     for (i=0;i<sub_schurs->n_subs;i++) {
1179       PetscInt j;
1180 
1181       /* get S_E */
1182       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1183       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1184         PetscInt k;
1185         for (k=0;k<subset_size;k++) {
1186           for (j=k;j<subset_size;j++) {
1187             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1188             work[j*subset_size+k] = PetscConj(S_data[cum2+k*size_schur+j]);
1189           }
1190         }
1191       } else { /* just copy to workspace */
1192         PetscInt k;
1193         for (k=0;k<subset_size;k++) {
1194           for (j=0;j<subset_size;j++) {
1195             work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1196           }
1197         }
1198       }
1199       /* insert S_E values */
1200       for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1201       if (sub_schurs->change) {
1202         Mat change_sub,SEj,T;
1203 
1204         /* change basis */
1205         ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1206         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1207         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1208           Mat T2;
1209           ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1210           ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1211           ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1212           ierr = MatDestroy(&T2);CHKERRQ(ierr);
1213         } else {
1214           ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1215         }
1216         ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1217         ierr = MatDestroy(&T);CHKERRQ(ierr);
1218         ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1.0,NULL,NULL);CHKERRQ(ierr);
1219         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1220       }
1221       if (deluxe) {
1222         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1223         /* if adaptivity is requested, invert S_E blocks */
1224         if (compute_Stilda) {
1225           PetscInt k;
1226 
1227           ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1228           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1229           if (use_potr) {
1230             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,work,&B_N,&B_ierr));
1231             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1232             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,work,&B_N,&B_ierr));
1233             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1234             for (k=0;k<subset_size;k++) {
1235               for (j=k;j<subset_size;j++) {
1236                 work[j*subset_size+k] = work[k*subset_size+j];
1237               }
1238             }
1239           } else if (use_sytr) {
1240             PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1241             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRF Lapack routine %d",(int)B_ierr);
1242             PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&B_N,work,&B_N,pivots,Bwork,&B_ierr));
1243             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRI Lapack routine %d",(int)B_ierr);
1244             for (k=0;k<subset_size;k++) {
1245               for (j=k;j<subset_size;j++) {
1246                 work[j*subset_size+k] = work[k*subset_size+j];
1247               }
1248             }
1249           } else {
1250             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,work,&B_N,pivots,&B_ierr));
1251             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1252             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,work,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1253             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1254           }
1255           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1256           ierr = MatSetValues(sub_schurs->sum_S_Ej_inv_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1257         }
1258       } else if (compute_Stilda) { /* not using deluxe */
1259         Mat         SEj;
1260         Vec         D;
1261         PetscScalar *array;
1262 
1263         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1264         ierr = VecGetArray(Dall,&array);CHKERRQ(ierr);
1265         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,array+cum,&D);CHKERRQ(ierr);
1266         ierr = VecRestoreArray(Dall,&array);CHKERRQ(ierr);
1267         ierr = VecShift(D,-1.);CHKERRQ(ierr);
1268         ierr = MatDiagonalScale(SEj,D,D);CHKERRQ(ierr);
1269         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1270         ierr = VecDestroy(&D);CHKERRQ(ierr);
1271         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1272       }
1273       cum += subset_size;
1274       cum2 += subset_size*(size_schur + 1);
1275     }
1276     ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1277 
1278     if (solver_S) {
1279       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1280     }
1281 
1282     schur_factor = NULL;
1283     if (compute_Stilda && size_active_schur) {
1284 
1285       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1286         PetscInt j;
1287         for (j=0;j<size_schur;j++) dummy_idx[j] = j;
1288         ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,size_schur,dummy_idx,size_schur,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1289       } else {
1290         Mat S_all_inv=NULL;
1291         if (solver_S) {
1292           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1293              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 */
1294           if (factor_workaround) {/* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1295             PetscScalar *data;
1296             PetscInt     nd = 0;
1297 
1298             if (!use_potr) {
1299               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1300             }
1301             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1302             ierr = MatDenseGetArray(S_all_inv,&data);CHKERRQ(ierr);
1303             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1304               ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1305             }
1306 
1307             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
1308             if (schur_has_vertices) {
1309               Mat          M;
1310               PetscScalar *tdata;
1311               PetscInt     nv = 0, news;
1312 
1313               ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
1314               news = size_active_schur + nv;
1315               ierr = PetscCalloc1(news*news,&tdata);CHKERRQ(ierr);
1316               for (i=0;i<size_active_schur;i++) {
1317                 ierr = PetscMemcpy(tdata+i*(news+1),data+i*(size_schur+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1318                 ierr = PetscMemcpy(tdata+i*(news+1)+size_active_schur-i,data+i*size_schur+size_active_schur+nd,nv*sizeof(PetscScalar));CHKERRQ(ierr);
1319               }
1320               for (i=0;i<nv;i++) {
1321                 PetscInt k = i+size_active_schur;
1322                 ierr = PetscMemcpy(tdata+k*(news+1),data+(k+nd)*(size_schur+1),(nv-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1323               }
1324 
1325               ierr = MatCreateSeqDense(PETSC_COMM_SELF,news,news,tdata,&M);CHKERRQ(ierr);
1326               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1327               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1328               /* save the factors */
1329               cum = 0;
1330               ierr = PetscMalloc1((size_active_schur*(size_active_schur +1))/2+nd,&schur_factor);CHKERRQ(ierr);
1331               for (i=0;i<size_active_schur;i++) {
1332                 ierr = PetscMemcpy(schur_factor+cum,tdata+i*(news+1),(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1333                 cum += size_active_schur - i;
1334               }
1335               for (i=0;i<nd;i++) schur_factor[cum+i] = PetscSqrtReal(PetscRealPart(data[(i+size_active_schur)*(size_schur+1)]));
1336               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1337               /* move back just the active dofs to the Schur complement */
1338               for (i=0;i<size_active_schur;i++) {
1339                 ierr = PetscMemcpy(data+i*size_schur,tdata+i*news,size_active_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1340               }
1341               ierr = PetscFree(tdata);CHKERRQ(ierr);
1342               ierr = MatDestroy(&M);CHKERRQ(ierr);
1343             } else { /* we can factorize and invert just the activedofs */
1344               Mat         M;
1345               PetscScalar *aux;
1346 
1347               ierr = PetscMalloc1(nd,&aux);CHKERRQ(ierr);
1348               for (i=0;i<nd;i++) aux[i] = 1.0/data[(i+size_active_schur)*(size_schur+1)];
1349               ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_active_schur,size_active_schur,data,&M);CHKERRQ(ierr);
1350               ierr = MatSeqDenseSetLDA(M,size_schur);CHKERRQ(ierr);
1351               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1352               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1353               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1354               ierr = MatDestroy(&M);CHKERRQ(ierr);
1355               ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,nd,data+size_active_schur*size_schur,&M);CHKERRQ(ierr);
1356               ierr = MatZeroEntries(M);CHKERRQ(ierr);
1357               ierr = MatDestroy(&M);CHKERRQ(ierr);
1358               ierr = MatCreateSeqDense(PETSC_COMM_SELF,nd,size_schur,data+size_active_schur,&M);CHKERRQ(ierr);
1359               ierr = MatSeqDenseSetLDA(M,size_schur);CHKERRQ(ierr);
1360               ierr = MatZeroEntries(M);CHKERRQ(ierr);
1361               ierr = MatDestroy(&M);CHKERRQ(ierr);
1362               for (i=0;i<nd;i++) data[(i+size_active_schur)*(size_schur+1)] = aux[i];
1363               ierr = PetscFree(aux);CHKERRQ(ierr);
1364             }
1365             ierr = MatDenseRestoreArray(S_all_inv,&data);CHKERRQ(ierr);
1366           } else { /* use MatFactor calls to invert S */
1367             ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
1368             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1369           }
1370         } else { /* we need to invert explicitly since we are not using MatFactor for S */
1371           ierr = PetscObjectReference((PetscObject)S_all);CHKERRQ(ierr);
1372           S_all_inv = S_all;
1373           ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1374           ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1375           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1376           if (use_potr) {
1377             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
1378             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1379             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
1380             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1381           } else if (use_sytr) {
1382             PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1383             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRF Lapack routine %d",(int)B_ierr);
1384             PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&B_N,S_data,&B_N,pivots,Bwork,&B_ierr));
1385             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRI Lapack routine %d",(int)B_ierr);
1386           } else {
1387             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
1388             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1389             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1390             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1391           }
1392           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1393           ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1394         }
1395         /* S_Ej_tilda_all */
1396         cum = cum2 = 0;
1397         ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1398         for (i=0;i<sub_schurs->n_subs;i++) {
1399           PetscInt j;
1400 
1401           ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1402           /* get (St^-1)_E */
1403           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1404              will be properly accessed later during adaptive selection */
1405           if (S_lower_triangular) {
1406             PetscInt k;
1407             if (sub_schurs->change) {
1408               for (k=0;k<subset_size;k++) {
1409                 for (j=k;j<subset_size;j++) {
1410                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1411                   work[j*subset_size+k] = work[k*subset_size+j];
1412                 }
1413               }
1414             } else {
1415               for (k=0;k<subset_size;k++) {
1416                 for (j=k;j<subset_size;j++) {
1417                   work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1418                 }
1419               }
1420             }
1421           } else {
1422             PetscInt k;
1423             for (k=0;k<subset_size;k++) {
1424               for (j=0;j<subset_size;j++) {
1425                 work[k*subset_size+j] = S_data[cum2+k*size_schur+j];
1426               }
1427             }
1428           }
1429           if (sub_schurs->change) {
1430             Mat change_sub,SEj,T;
1431 
1432             /* change basis */
1433             ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1434             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1435             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1436               Mat T2;
1437               ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1438               ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1439               ierr = MatDestroy(&T2);CHKERRQ(ierr);
1440               ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1441             } else {
1442               ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1443             }
1444             ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1445             ierr = MatDestroy(&T);CHKERRQ(ierr);
1446             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
1447             ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1./PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
1448             ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1449           }
1450           for (j=0;j<subset_size;j++) dummy_idx[j] = cum+j;
1451           ierr = MatSetValues(sub_schurs->sum_S_Ej_tilda_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
1452           cum += subset_size;
1453           cum2 += subset_size*(size_schur + 1);
1454         }
1455         ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1456         if (solver_S) {
1457           if (schur_has_vertices) {
1458             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1459           } else {
1460             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_INVERTED);CHKERRQ(ierr);
1461           }
1462         }
1463         ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
1464       }
1465 
1466       /* move back factors if needed */
1467       if (schur_has_vertices) {
1468         Mat      S_tmp;
1469         PetscInt nd = 0;
1470 
1471         if (!solver_S) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
1472         ierr = MatFactorGetSchurComplement(F,&S_tmp,NULL);CHKERRQ(ierr);
1473         if (use_potr) {
1474           PetscScalar *data;
1475 
1476           ierr = MatDenseGetArray(S_tmp,&data);CHKERRQ(ierr);
1477           ierr = PetscMemzero(data,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1478 
1479           if (S_lower_triangular) {
1480             cum = 0;
1481             for (i=0;i<size_active_schur;i++) {
1482               ierr = PetscMemcpy(data+i*(size_schur+1),schur_factor+cum,(size_active_schur-i)*sizeof(PetscScalar));CHKERRQ(ierr);
1483               cum += size_active_schur-i;
1484 	    }
1485           } else {
1486             ierr = PetscMemcpy(data,schur_factor,size_schur*size_schur*sizeof(PetscScalar));CHKERRQ(ierr);
1487           }
1488           if (sub_schurs->is_dir) {
1489             ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1490 	    for (i=0;i<nd;i++) {
1491 	      data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
1492 	    }
1493           }
1494           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1495              set the diagonal entry of the Schur factor to a very large value */
1496           for (i=size_active_schur+nd;i<size_schur;i++) {
1497             data[i*(size_schur+1)] = infty;
1498           }
1499           ierr = MatDenseRestoreArray(S_tmp,&data);CHKERRQ(ierr);
1500         } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1501         ierr = MatFactorRestoreSchurComplement(F,&S_tmp,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1502       }
1503     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
1504       PetscScalar *data;
1505       PetscInt    nd = 0;
1506 
1507       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1508         ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1509       }
1510       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1511       ierr = MatDenseGetArray(S_all,&data);CHKERRQ(ierr);
1512       for (i=0;i<size_active_schur;i++) {
1513         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1514       }
1515       for (i=size_active_schur+nd;i<size_schur;i++) {
1516         ierr = PetscMemzero(data+i*size_schur+size_active_schur,(size_schur-size_active_schur)*sizeof(PetscScalar));CHKERRQ(ierr);
1517         data[i*(size_schur+1)] = infty;
1518       }
1519       ierr = MatDenseRestoreArray(S_all,&data);CHKERRQ(ierr);
1520       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1521     }
1522     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
1523     ierr = PetscFree(schur_factor);CHKERRQ(ierr);
1524     ierr = VecDestroy(&Dall);CHKERRQ(ierr);
1525   }
1526   ierr = PetscFree(nnz);CHKERRQ(ierr);
1527   ierr = MatDestroy(&F);CHKERRQ(ierr);
1528   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1529   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
1530   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1531   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1532   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1533   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1534   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1535   if (compute_Stilda) {
1536     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1537     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1538     if (deluxe) {
1539       ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1540       ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1541     }
1542   }
1543 
1544   /* Global matrix of all assembled Schur on subsets */
1545   ierr = MatISSetLocalMat(work_mat,sub_schurs->S_Ej_all);CHKERRQ(ierr);
1546   ierr = MatISSetMPIXAIJPreallocation_Private(work_mat,global_schur_subsets,PETSC_TRUE);CHKERRQ(ierr);
1547   ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1548 
1549   /* Get local part of (\sum_j S_Ej) */
1550   ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_INITIAL_MATRIX,&submats);CHKERRQ(ierr);
1551   if (!sub_schurs->sum_S_Ej_all) {
1552     ierr = MatDuplicate(submats[0],MAT_COPY_VALUES,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1553   } else {
1554     ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1555   }
1556 
1557   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1558   if (compute_Stilda) {
1559     ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1560     ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1561     ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1562     ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_tilda_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1563     if (deluxe) {
1564       ierr = MatISSetLocalMat(work_mat,sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1565       ierr = MatISGetMPIXAIJ(work_mat,MAT_REUSE_MATRIX,&global_schur_subsets);CHKERRQ(ierr);
1566       ierr = MatCreateSubMatrices(global_schur_subsets,1,&all_subsets_n,&all_subsets_n,MAT_REUSE_MATRIX,&submats);CHKERRQ(ierr);
1567       ierr = MatCopy(submats[0],sub_schurs->sum_S_Ej_inv_all,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1568     } else {
1569       PetscScalar *array;
1570       PetscInt    cum;
1571 
1572       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1573       cum = 0;
1574       for (i=0;i<sub_schurs->n_subs;i++) {
1575         ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1576         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1577         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1578         if (use_potr) {
1579           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
1580           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1581           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
1582           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1583         } else if (use_sytr) {
1584           PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1585           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRF Lapack routine %d",(int)B_ierr);
1586           PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&B_N,array+cum,&B_N,pivots,Bwork,&B_ierr));
1587           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRI Lapack routine %d",(int)B_ierr);
1588         } else {
1589           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
1590           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1591           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1592           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1593         }
1594         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1595         cum += subset_size*subset_size;
1596       }
1597       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1598       ierr = PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1599       ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1600       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1601     }
1602   }
1603   ierr = MatDestroySubMatrices(1,&submats);CHKERRQ(ierr);
1604 
1605   /* free workspace */
1606   ierr = PetscFree(submats);CHKERRQ(ierr);
1607   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
1608   ierr = MatDestroy(&global_schur_subsets);CHKERRQ(ierr);
1609   ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
1610   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
1611   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
1612   PetscFunctionReturn(0);
1613 }
1614 
1615 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc)
1616 {
1617   IS              *faces,*edges,*all_cc,vertices;
1618   PetscInt        i,n_faces,n_edges,n_all_cc;
1619   PetscBool       is_sorted;
1620   PetscErrorCode  ierr;
1621 
1622   PetscFunctionBegin;
1623   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
1624   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
1625   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
1626   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
1627 
1628   /* reset any previous data */
1629   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
1630 
1631   /* get index sets for faces and edges (already sorted by global ordering) */
1632   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1633   n_all_cc = n_faces+n_edges;
1634   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
1635   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
1636   for (i=0;i<n_faces;i++) {
1637     if (copycc) {
1638       ierr = ISDuplicate(faces[i],&all_cc[i]);CHKERRQ(ierr);
1639     } else {
1640       ierr = PetscObjectReference((PetscObject)faces[i]);CHKERRQ(ierr);
1641       all_cc[i] = faces[i];
1642     }
1643   }
1644   for (i=0;i<n_edges;i++) {
1645     if (copycc) {
1646       ierr = ISDuplicate(edges[i],&all_cc[n_faces+i]);CHKERRQ(ierr);
1647     } else {
1648       ierr = PetscObjectReference((PetscObject)edges[i]);CHKERRQ(ierr);
1649       all_cc[n_faces+i] = edges[i];
1650     }
1651     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
1652   }
1653   ierr = PetscObjectReference((PetscObject)vertices);CHKERRQ(ierr);
1654   sub_schurs->is_vertices = vertices;
1655   ierr = PCBDDCGraphRestoreCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1656   sub_schurs->is_dir = NULL;
1657   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
1658 
1659   /* Determine if MatFactor can be used */
1660   sub_schurs->schur_explicit = PETSC_FALSE;
1661 #if defined(PETSC_HAVE_MUMPS)
1662   sub_schurs->schur_explicit = PETSC_TRUE;
1663 #endif
1664 #if defined(PETSC_HAVE_MKL_PARDISO)
1665   sub_schurs->schur_explicit = PETSC_TRUE;
1666 #endif
1667 
1668   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
1669   sub_schurs->is_I = is_I;
1670   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
1671   sub_schurs->is_B = is_B;
1672   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
1673   sub_schurs->l2gmap = graph->l2gmap;
1674   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
1675   sub_schurs->BtoNmap = BtoNmap;
1676   sub_schurs->n_subs = n_all_cc;
1677   sub_schurs->is_subs = all_cc;
1678   if (!sub_schurs->schur_explicit) { /* sort by local ordering if we are not using MatFactor */
1679     for (i=0;i<sub_schurs->n_subs;i++) {
1680       ierr = ISSort(sub_schurs->is_subs[i]);CHKERRQ(ierr);
1681     }
1682   }
1683   sub_schurs->S_Ej_all = NULL;
1684   sub_schurs->sum_S_Ej_all = NULL;
1685   sub_schurs->sum_S_Ej_inv_all = NULL;
1686   sub_schurs->sum_S_Ej_tilda_all = NULL;
1687   sub_schurs->is_Ej_all = NULL;
1688   PetscFunctionReturn(0);
1689 }
1690 
1691 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1692 {
1693   PCBDDCSubSchurs schurs_ctx;
1694   PetscErrorCode  ierr;
1695 
1696   PetscFunctionBegin;
1697   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
1698   schurs_ctx->n_subs = 0;
1699   *sub_schurs = schurs_ctx;
1700   PetscFunctionReturn(0);
1701 }
1702 
1703 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1704 {
1705   PetscInt       i;
1706   PetscErrorCode ierr;
1707 
1708   PetscFunctionBegin;
1709   if (!sub_schurs) PetscFunctionReturn(0);
1710   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1711   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1712   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1713   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1714   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1715   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1716   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1717   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1718   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1719   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1720   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1721   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1722   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1723   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1724   for (i=0;i<sub_schurs->n_subs;i++) {
1725     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
1726   }
1727   if (sub_schurs->n_subs) {
1728     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
1729   }
1730   if (sub_schurs->reuse_solver) {
1731     ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1732   }
1733   ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1734   if (sub_schurs->change) {
1735     for (i=0;i<sub_schurs->n_subs;i++) {
1736       ierr = KSPDestroy(&sub_schurs->change[i]);CHKERRQ(ierr);
1737       ierr = ISDestroy(&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
1738     }
1739   }
1740   ierr = PetscFree(sub_schurs->change);CHKERRQ(ierr);
1741   ierr = PetscFree(sub_schurs->change_primal_sub);CHKERRQ(ierr);
1742   sub_schurs->n_subs = 0;
1743   PetscFunctionReturn(0);
1744 }
1745 
1746 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs* sub_schurs)
1747 {
1748   PetscErrorCode ierr;
1749 
1750   PetscFunctionBegin;
1751   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
1752   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
1753   PetscFunctionReturn(0);
1754 }
1755 
1756 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
1757 {
1758   PetscInt       i,j,n;
1759   PetscErrorCode ierr;
1760 
1761   PetscFunctionBegin;
1762   n = 0;
1763   for (i=-n_prev;i<0;i++) {
1764     PetscInt start_dof = queue_tip[i];
1765     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
1766       PetscInt dof = adjncy[j];
1767       if (!PetscBTLookup(touched,dof)) {
1768         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
1769         queue_tip[n] = dof;
1770         n++;
1771       }
1772     }
1773   }
1774   *n_added = n;
1775   PetscFunctionReturn(0);
1776 }
1777