xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision 7d5fd1e4d9337468ad3f05b65b7facdcd2dfd2a4)
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 = PetscArraycpy(array2,array,nl);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,&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 = PetscArraycpy(array_solver,array,n);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 = PetscArraycpy(array,array_solver,n);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 PCBDDCReuseSolvers_View(PC pc, PetscViewer viewer)
232 {
233   PCBDDCReuseSolvers ctx;
234   PetscBool          iascii;
235   PetscErrorCode     ierr;
236 
237   PetscFunctionBegin;
238   ierr = PCShellGetContext(pc,&ctx);CHKERRQ(ierr);
239   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
240   if (iascii) {
241     ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO);CHKERRQ(ierr);
242   }
243   ierr = MatView(ctx->F,viewer);CHKERRQ(ierr);
244   if (iascii) {
245     ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
246   }
247   PetscFunctionReturn(0);
248 }
249 
250 static PetscErrorCode PCBDDCReuseSolversReset(PCBDDCReuseSolvers reuse)
251 {
252   PetscInt       i;
253   PetscErrorCode ierr;
254 
255   PetscFunctionBegin;
256   ierr = MatDestroy(&reuse->F);CHKERRQ(ierr);
257   ierr = VecDestroy(&reuse->sol);CHKERRQ(ierr);
258   ierr = VecDestroy(&reuse->rhs);CHKERRQ(ierr);
259   ierr = PCDestroy(&reuse->interior_solver);CHKERRQ(ierr);
260   ierr = PCDestroy(&reuse->correction_solver);CHKERRQ(ierr);
261   ierr = ISDestroy(&reuse->is_R);CHKERRQ(ierr);
262   ierr = ISDestroy(&reuse->is_B);CHKERRQ(ierr);
263   ierr = VecScatterDestroy(&reuse->correction_scatter_B);CHKERRQ(ierr);
264   ierr = VecDestroy(&reuse->sol_B);CHKERRQ(ierr);
265   ierr = VecDestroy(&reuse->rhs_B);CHKERRQ(ierr);
266   for (i=0;i<reuse->benign_n;i++) {
267     ierr = ISDestroy(&reuse->benign_zerodiag_subs[i]);CHKERRQ(ierr);
268   }
269   ierr = PetscFree(reuse->benign_zerodiag_subs);CHKERRQ(ierr);
270   ierr = PetscFree(reuse->benign_save_vals);CHKERRQ(ierr);
271   ierr = MatDestroy(&reuse->benign_csAIB);CHKERRQ(ierr);
272   ierr = MatDestroy(&reuse->benign_AIIm1ones);CHKERRQ(ierr);
273   ierr = VecDestroy(&reuse->benign_corr_work);CHKERRQ(ierr);
274   ierr = VecDestroy(&reuse->benign_dummy_schur_vec);CHKERRQ(ierr);
275   PetscFunctionReturn(0);
276 }
277 
278 static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
279 {
280   Mat            B, C, D, Bd, Cd, AinvBd;
281   KSP            ksp;
282   PC             pc;
283   PetscBool      isLU, isILU, isCHOL, Bdense, Cdense;
284   PetscReal      fill = 2.0;
285   PetscInt       n_I;
286   PetscMPIInt    size;
287   PetscErrorCode ierr;
288 
289   PetscFunctionBegin;
290   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);CHKERRMPI(ierr);
291   if (size != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not for parallel matrices");
292   if (reuse == MAT_REUSE_MATRIX) {
293     PetscBool Sdense;
294 
295     ierr = PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense);CHKERRQ(ierr);
296     if (!Sdense) SETERRQ(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"S should dense");
297   }
298   ierr = MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);CHKERRQ(ierr);
299   ierr = MatSchurComplementGetKSP(M, &ksp);CHKERRQ(ierr);
300   ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
301   ierr = PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);CHKERRQ(ierr);
302   ierr = PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);CHKERRQ(ierr);
303   ierr = PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);CHKERRQ(ierr);
304   ierr = PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);CHKERRQ(ierr);
305   ierr = PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);CHKERRQ(ierr);
306   ierr = MatGetSize(B,&n_I,NULL);CHKERRQ(ierr);
307   if (n_I) {
308     if (!Bdense) {
309       ierr = MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);CHKERRQ(ierr);
310     } else {
311       Bd = B;
312     }
313 
314     if (isLU || isILU || isCHOL) {
315       Mat fact;
316       ierr = KSPSetUp(ksp);CHKERRQ(ierr);
317       ierr = PCFactorGetMatrix(pc, &fact);CHKERRQ(ierr);
318       ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
319       ierr = MatMatSolve(fact, Bd, AinvBd);CHKERRQ(ierr);
320     } else {
321       PetscBool ex = PETSC_TRUE;
322 
323       if (ex) {
324         Mat Ainvd;
325 
326         ierr = PCComputeOperator(pc, MATDENSE, &Ainvd);CHKERRQ(ierr);
327         ierr = MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);CHKERRQ(ierr);
328         ierr = MatDestroy(&Ainvd);CHKERRQ(ierr);
329       } else {
330         Vec         sol,rhs;
331         PetscScalar *arrayrhs,*arraysol;
332         PetscInt    i,nrhs,n;
333 
334         ierr = MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);CHKERRQ(ierr);
335         ierr = MatGetSize(Bd,&n,&nrhs);CHKERRQ(ierr);
336         ierr = MatDenseGetArray(Bd,&arrayrhs);CHKERRQ(ierr);
337         ierr = MatDenseGetArray(AinvBd,&arraysol);CHKERRQ(ierr);
338         ierr = KSPGetSolution(ksp,&sol);CHKERRQ(ierr);
339         ierr = KSPGetRhs(ksp,&rhs);CHKERRQ(ierr);
340         for (i=0;i<nrhs;i++) {
341           ierr = VecPlaceArray(rhs,arrayrhs+i*n);CHKERRQ(ierr);
342           ierr = VecPlaceArray(sol,arraysol+i*n);CHKERRQ(ierr);
343           ierr = KSPSolve(ksp,rhs,sol);CHKERRQ(ierr);
344           ierr = VecResetArray(rhs);CHKERRQ(ierr);
345           ierr = VecResetArray(sol);CHKERRQ(ierr);
346         }
347         ierr = MatDenseRestoreArray(Bd,&arrayrhs);CHKERRQ(ierr);
348         ierr = MatDenseRestoreArray(AinvBd,&arrayrhs);CHKERRQ(ierr);
349       }
350     }
351     if (!Bdense & !issym) {
352       ierr = MatDestroy(&Bd);CHKERRQ(ierr);
353     }
354 
355     if (!issym) {
356       if (!Cdense) {
357         ierr = MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);CHKERRQ(ierr);
358       } else {
359         Cd = C;
360       }
361       ierr = MatMatMult(Cd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
362       if (!Cdense) {
363         ierr = MatDestroy(&Cd);CHKERRQ(ierr);
364       }
365     } else {
366       ierr = MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);CHKERRQ(ierr);
367       if (!Bdense) {
368         ierr = MatDestroy(&Bd);CHKERRQ(ierr);
369       }
370     }
371     ierr = MatDestroy(&AinvBd);CHKERRQ(ierr);
372   }
373 
374   if (D) {
375     Mat       Dd;
376     PetscBool Ddense;
377 
378     ierr = PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);CHKERRQ(ierr);
379     if (!Ddense) {
380       ierr = MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);CHKERRQ(ierr);
381     } else {
382       Dd = D;
383     }
384     if (n_I) {
385       ierr = MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
386     } else {
387       if (reuse == MAT_INITIAL_MATRIX) {
388         ierr = MatDuplicate(Dd,MAT_COPY_VALUES,S);CHKERRQ(ierr);
389       } else {
390         ierr = MatCopy(Dd,*S,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
391       }
392     }
393     if (!Ddense) {
394       ierr = MatDestroy(&Dd);CHKERRQ(ierr);
395     }
396   } else {
397     ierr = MatScale(*S,-1.0);CHKERRQ(ierr);
398   }
399   PetscFunctionReturn(0);
400 }
401 
402 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)
403 {
404   Mat                    F,A_II,A_IB,A_BI,A_BB,AE_II;
405   Mat                    S_all;
406   Vec                    gstash,lstash;
407   VecScatter             sstash;
408   IS                     is_I,is_I_layer;
409   IS                     all_subsets,all_subsets_mult,all_subsets_n;
410   PetscScalar            *stasharray,*Bwork;
411   PetscInt               *nnz,*all_local_idx_N;
412   PetscInt               *auxnum1,*auxnum2;
413   PetscInt               i,subset_size,max_subset_size;
414   PetscInt               n_B,extra,local_size,global_size;
415   PetscInt               local_stash_size;
416   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
417   MPI_Comm               comm_n;
418   PetscBool              deluxe = PETSC_TRUE;
419   PetscBool              use_potr = PETSC_FALSE, use_sytr = PETSC_FALSE;
420   PetscViewer            matl_dbg_viewer = NULL;
421   PetscErrorCode         ierr;
422   PetscBool              flg;
423 
424   PetscFunctionBegin;
425   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
426   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
427   if (Ain) {
428     ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
429     sub_schurs->A = Ain;
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   if (benign_trick) sub_schurs->is_posdef = PETSC_FALSE;
442 
443   /* debug (MATLAB) */
444   if (sub_schurs->debug) {
445     PetscMPIInt size,rank;
446     PetscInt    nr,*print_schurs_ranks,print_schurs = PETSC_FALSE;
447 
448     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&size);CHKERRMPI(ierr);
449     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRMPI(ierr);
450     nr   = size;
451     ierr = PetscMalloc1(nr,&print_schurs_ranks);CHKERRQ(ierr);
452     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)sub_schurs->l2gmap),sub_schurs->prefix,"BDDC sub_schurs options","PC");CHKERRQ(ierr);
453     ierr = PetscOptionsIntArray("-sub_schurs_debug_ranks","Ranks to debug (all if the option is not used)",NULL,print_schurs_ranks,&nr,&flg);CHKERRQ(ierr);
454     if (!flg) print_schurs = PETSC_TRUE;
455     else {
456       print_schurs = PETSC_FALSE;
457       for (i=0;i<nr;i++) if (print_schurs_ranks[i] == (PetscInt)rank) { print_schurs = PETSC_TRUE; break; }
458     }
459     ierr = PetscOptionsEnd();CHKERRQ(ierr);
460     ierr = PetscFree(print_schurs_ranks);CHKERRQ(ierr);
461     if (print_schurs) {
462       char filename[256];
463 
464       ierr = PetscSNPrintf(filename,sizeof(filename),"sub_schurs_Schur_r%d.m",PetscGlobalRank);CHKERRQ(ierr);
465       ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&matl_dbg_viewer);CHKERRQ(ierr);
466       ierr = PetscViewerPushFormat(matl_dbg_viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
467     }
468   }
469 
470   /* restrict work on active processes */
471   if (sub_schurs->restrict_comm) {
472     PetscSubcomm subcomm;
473     PetscMPIInt  color,rank;
474 
475     color = 0;
476     if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
477     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRMPI(ierr);
478     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
479     ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
480     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
481     ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
482     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
483     if (!sub_schurs->n_subs) {
484       ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
485       PetscFunctionReturn(0);
486     }
487   } else {
488     ierr = PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);CHKERRQ(ierr);
489   }
490 
491   /* get Schur complement matrices */
492   if (!sub_schurs->schur_explicit) {
493     Mat       tA_IB,tA_BI,tA_BB;
494     PetscBool isseqsbaij;
495     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
496     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);CHKERRQ(ierr);
497     if (isseqsbaij) {
498       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
499       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
500       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
501     } else {
502       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
503       A_BB = tA_BB;
504       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
505       A_IB = tA_IB;
506       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
507       A_BI = tA_BI;
508     }
509   } else {
510     A_II = NULL;
511     A_IB = NULL;
512     A_BI = NULL;
513     A_BB = NULL;
514   }
515   S_all = NULL;
516 
517   /* determine interior problems */
518   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
519   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
520     PetscBT                touched;
521     const PetscInt*        idx_B;
522     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
523 
524     if (!xadj) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
525     /* get sizes */
526     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
527     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
528 
529     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
530     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
531     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
532 
533     /* all boundary dofs must be skipped when adding layers */
534     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
535     for (j=0;j<n_B;j++) {
536       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
537     }
538     ierr = PetscArraycpy(local_numbering,idx_B,n_B);CHKERRQ(ierr);
539     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
540 
541     /* add prescribed number of layers of dofs */
542     n_local_dofs = n_B;
543     n_prev_added = n_B;
544     for (layer=0;layer<nlayers;layer++) {
545       PetscInt n_added;
546       if (n_local_dofs == n_I+n_B) break;
547       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);
548       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
549       n_prev_added = n_added;
550       n_local_dofs += n_added;
551       if (!n_added) break;
552     }
553     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
554 
555     /* IS for I layer dofs in original numbering */
556     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);
557     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
558     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
559     /* IS for I layer dofs in I numbering */
560     if (!sub_schurs->schur_explicit) {
561       ISLocalToGlobalMapping ItoNmap;
562       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
563       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
564       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
565 
566       /* II block */
567       ierr = MatCreateSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
568     }
569   } else {
570     PetscInt n_I;
571 
572     /* IS for I dofs in original numbering */
573     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
574     is_I_layer = sub_schurs->is_I;
575 
576     /* IS for I dofs in I numbering (strided 1) */
577     if (!sub_schurs->schur_explicit) {
578       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
579       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
580 
581       /* II block is the same */
582       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
583       AE_II = A_II;
584     }
585   }
586 
587   /* Get info on subset sizes and sum of all subsets sizes */
588   max_subset_size = 0;
589   local_size = 0;
590   for (i=0;i<sub_schurs->n_subs;i++) {
591     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
592     max_subset_size = PetscMax(subset_size,max_subset_size);
593     local_size += subset_size;
594   }
595 
596   /* Work arrays for local indices */
597   extra = 0;
598   ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
599   if (sub_schurs->schur_explicit && is_I_layer) {
600     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
601   }
602   ierr = PetscMalloc1(n_B+extra,&all_local_idx_N);CHKERRQ(ierr);
603   if (extra) {
604     const PetscInt *idxs;
605     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
606     ierr = PetscArraycpy(all_local_idx_N,idxs,extra);CHKERRQ(ierr);
607     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
608   }
609   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum1);CHKERRQ(ierr);
610   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
611 
612   /* Get local indices in local numbering */
613   local_size = 0;
614   local_stash_size = 0;
615   for (i=0;i<sub_schurs->n_subs;i++) {
616     const PetscInt *idxs;
617 
618     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
619     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
620     /* start (smallest in global ordering) and multiplicity */
621     auxnum1[i] = idxs[0];
622     auxnum2[i] = subset_size*subset_size;
623     /* subset indices in local numbering */
624     ierr = PetscArraycpy(all_local_idx_N+local_size+extra,idxs,subset_size);CHKERRQ(ierr);
625     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
626     local_size += subset_size;
627     local_stash_size += subset_size*subset_size;
628   }
629 
630   /* allocate extra workspace needed only for GETRI or SYTRF */
631   use_potr = use_sytr = PETSC_FALSE;
632   if (benign_trick || (sub_schurs->is_hermitian && sub_schurs->is_posdef)) {
633     use_potr = PETSC_TRUE;
634   } else if (sub_schurs->is_symmetric) {
635     use_sytr = PETSC_TRUE;
636   }
637   if (local_size && !use_potr) {
638     PetscScalar  lwork,dummyscalar = 0.;
639     PetscBLASInt dummyint = 0;
640 
641     B_lwork = -1;
642     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
643     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
644     if (use_sytr) {
645       PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
646       if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYTRF Lapack routine %d",(int)B_ierr);
647     } else {
648       PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
649       if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
650     }
651     ierr = PetscFPTrapPop();CHKERRQ(ierr);
652     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
653     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
654   } else {
655     Bwork = NULL;
656     pivots = NULL;
657   }
658 
659   /* prepare data for summing up properly schurs on subsets */
660   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);CHKERRQ(ierr);
661   ierr = ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);CHKERRQ(ierr);
662   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
663   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);CHKERRQ(ierr);
664   ierr = ISRenumber(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);CHKERRQ(ierr);
665   ierr = ISDestroy(&all_subsets);CHKERRQ(ierr);
666   ierr = ISDestroy(&all_subsets_mult);CHKERRQ(ierr);
667   ierr = ISGetLocalSize(all_subsets_n,&i);CHKERRQ(ierr);
668   if (i != local_stash_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",i,local_stash_size);
669   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,local_stash_size,NULL,&lstash);CHKERRQ(ierr);
670   ierr = VecCreateMPI(comm_n,PETSC_DECIDE,global_size,&gstash);CHKERRQ(ierr);
671   ierr = VecScatterCreate(lstash,NULL,gstash,all_subsets_n,&sstash);CHKERRQ(ierr);
672   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
673 
674   /* subset indices in local boundary numbering */
675   if (!sub_schurs->is_Ej_all) {
676     PetscInt *all_local_idx_B;
677 
678     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
679     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
680     if (subset_size != local_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %D != %D",subset_size,local_size);
681     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
682   }
683 
684   if (change) {
685     ISLocalToGlobalMapping BtoS;
686     IS                     change_primal_B;
687     IS                     change_primal_all;
688 
689     if (sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
690     if (sub_schurs->change) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
691     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change_primal_sub);CHKERRQ(ierr);
692     for (i=0;i<sub_schurs->n_subs;i++) {
693       ISLocalToGlobalMapping NtoS;
694       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);CHKERRQ(ierr);
695       ierr = ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
696       ierr = ISLocalToGlobalMappingDestroy(&NtoS);CHKERRQ(ierr);
697     }
698     ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);CHKERRQ(ierr);
699     ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);CHKERRQ(ierr);
700     ierr = ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);CHKERRQ(ierr);
701     ierr = ISLocalToGlobalMappingDestroy(&BtoS);CHKERRQ(ierr);
702     ierr = ISDestroy(&change_primal_B);CHKERRQ(ierr);
703     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change);CHKERRQ(ierr);
704     for (i=0;i<sub_schurs->n_subs;i++) {
705       Mat change_sub;
706 
707       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
708       ierr = KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);CHKERRQ(ierr);
709       ierr = KSPSetType(sub_schurs->change[i],KSPPREONLY);CHKERRQ(ierr);
710       if (!sub_schurs->change_with_qr) {
711         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
712       } else {
713         Mat change_subt;
714         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);CHKERRQ(ierr);
715         ierr = MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
716         ierr = MatDestroy(&change_subt);CHKERRQ(ierr);
717       }
718       ierr = KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);CHKERRQ(ierr);
719       ierr = MatDestroy(&change_sub);CHKERRQ(ierr);
720       ierr = KSPSetOptionsPrefix(sub_schurs->change[i],sub_schurs->prefix);CHKERRQ(ierr);
721       ierr = KSPAppendOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");CHKERRQ(ierr);
722     }
723     ierr = ISDestroy(&change_primal_all);CHKERRQ(ierr);
724   }
725 
726   /* Local matrix of all local Schur on subsets (transposed) */
727   if (!sub_schurs->S_Ej_all) {
728     Mat         T;
729     PetscScalar *v;
730     PetscInt    *ii,*jj;
731     PetscInt    cum,i,j,k;
732 
733     /* MatSeqAIJSetPreallocation + MatSetValues is slow for these kind of matrices (may have large blocks)
734        Allocate properly a representative matrix and duplicate */
735     ierr  = PetscMalloc3(local_size+1,&ii,local_stash_size,&jj,local_stash_size,&v);CHKERRQ(ierr);
736     ii[0] = 0;
737     cum   = 0;
738     for (i=0;i<sub_schurs->n_subs;i++) {
739       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
740       for (j=0;j<subset_size;j++) {
741         const PetscInt row = cum+j;
742         PetscInt col = cum;
743 
744         ii[row+1] = ii[row] + subset_size;
745         for (k=ii[row];k<ii[row+1];k++) {
746           jj[k] = col;
747           col++;
748         }
749       }
750       cum += subset_size;
751     }
752     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,local_size,local_size,ii,jj,v,&T);CHKERRQ(ierr);
753     ierr = MatDuplicate(T,MAT_DO_NOT_COPY_VALUES,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
754     ierr = MatDestroy(&T);CHKERRQ(ierr);
755     ierr = PetscFree3(ii,jj,v);CHKERRQ(ierr);
756   }
757   /* matrices for deluxe scaling and adaptive selection */
758   if (compute_Stilda) {
759     if (!sub_schurs->sum_S_Ej_tilda_all) {
760       ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
761     }
762     if (!sub_schurs->sum_S_Ej_inv_all && deluxe) {
763       ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
764     }
765   }
766 
767   /* Compute Schur complements explicitly */
768   F = NULL;
769   if (!sub_schurs->schur_explicit) {
770     /* this code branch is used when MatFactor with Schur complement support is not present or when explicitly requested;
771        it is not efficient, unless the economic version of the scaling is used */
772     Mat         S_Ej_expl;
773     PetscScalar *work;
774     PetscInt    j,*dummy_idx;
775     PetscBool   Sdense;
776 
777     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
778     local_size = 0;
779     for (i=0;i<sub_schurs->n_subs;i++) {
780       IS  is_subset_B;
781       Mat AE_EE,AE_IE,AE_EI,S_Ej;
782 
783       /* subsets in original and boundary numbering */
784       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
785       /* EE block */
786       ierr = MatCreateSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
787       /* IE block */
788       ierr = MatCreateSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
789       /* EI block */
790       if (sub_schurs->is_symmetric) {
791         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
792       } else if (sub_schurs->is_hermitian) {
793         ierr = MatCreateHermitianTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
794       } else {
795         ierr = MatCreateSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
796       }
797       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
798       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
799       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
800       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
801       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
802       if (AE_II == A_II) { /* we can reuse the same ksp */
803         KSP ksp;
804         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
805         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
806       } else { /* build new ksp object which inherits ksp and pc types from the original one */
807         KSP       origksp,schurksp;
808         PC        origpc,schurpc;
809         KSPType   ksp_type;
810         PetscInt  n_internal;
811         PetscBool ispcnone;
812 
813         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
814         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
815         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
816         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
817         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
818         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
819         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
820         if (!ispcnone) {
821           PCType pc_type;
822           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
823           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
824         } else {
825           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
826         }
827         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
828         if (!n_internal) { /* UMFPACK gives error with 0 sized problems */
829           MatSolverType solver = NULL;
830           ierr = PCFactorGetMatSolverType(origpc,(MatSolverType*)&solver);CHKERRQ(ierr);
831           if (solver) {
832             ierr = PCFactorSetMatSolverType(schurpc,solver);CHKERRQ(ierr);
833           }
834         }
835         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
836       }
837       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
838       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
839       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_symmetric,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
840       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
841       if (Sdense) {
842         for (j=0;j<subset_size;j++) {
843           dummy_idx[j]=local_size+j;
844         }
845         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
846       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
847       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
848       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
849       local_size += subset_size;
850     }
851     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
852     /* free */
853     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
854     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
855     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
856   } else {
857     Mat               A,cs_AIB_mat = NULL,benign_AIIm1_ones_mat = NULL;
858     Vec               Dall = NULL;
859     IS                is_A_all,*is_p_r = NULL;
860     MatType           Stype;
861     PetscScalar       *work,*S_data,*schur_factor,infty = PETSC_MAX_REAL;
862     PetscScalar       *SEj_arr = NULL,*SEjinv_arr = NULL;
863     const PetscScalar *rS_data;
864     PetscInt          n,n_I,size_schur,size_active_schur,cum,cum2;
865     PetscBool         economic,solver_S,S_lower_triangular = PETSC_FALSE;
866     PetscBool         schur_has_vertices,factor_workaround;
867     PetscBool         use_cholesky;
868 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
869     PetscBool         oldpin;
870 #endif
871 
872     /* get sizes */
873     n_I = 0;
874     if (is_I_layer) {
875       ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
876     }
877     economic = PETSC_FALSE;
878     ierr = ISGetLocalSize(sub_schurs->is_I,&cum);CHKERRQ(ierr);
879     if (cum != n_I) economic = PETSC_TRUE;
880     ierr = MatGetLocalSize(sub_schurs->A,&n,NULL);CHKERRQ(ierr);
881     size_active_schur = local_size;
882 
883     /* import scaling vector (wrong formulation if we have 3D edges) */
884     if (scaling && compute_Stilda) {
885       const PetscScalar *array;
886       PetscScalar       *array2;
887       const PetscInt    *idxs;
888       PetscInt          i;
889 
890       ierr = ISGetIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
891       ierr = VecCreateSeq(PETSC_COMM_SELF,size_active_schur,&Dall);CHKERRQ(ierr);
892       ierr = VecGetArrayRead(scaling,&array);CHKERRQ(ierr);
893       ierr = VecGetArray(Dall,&array2);CHKERRQ(ierr);
894       for (i=0;i<size_active_schur;i++) array2[i] = array[idxs[i]];
895       ierr = VecRestoreArray(Dall,&array2);CHKERRQ(ierr);
896       ierr = VecRestoreArrayRead(scaling,&array);CHKERRQ(ierr);
897       ierr = ISRestoreIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
898       deluxe = PETSC_FALSE;
899     }
900 
901     /* size active schurs does not count any dirichlet or vertex dof on the interface */
902     factor_workaround = PETSC_FALSE;
903     schur_has_vertices = PETSC_FALSE;
904     cum = n_I+size_active_schur;
905     if (sub_schurs->is_dir) {
906       const PetscInt* idxs;
907       PetscInt        n_dir;
908 
909       ierr = ISGetLocalSize(sub_schurs->is_dir,&n_dir);CHKERRQ(ierr);
910       ierr = ISGetIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
911       ierr = PetscArraycpy(all_local_idx_N+cum,idxs,n_dir);CHKERRQ(ierr);
912       ierr = ISRestoreIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
913       cum += n_dir;
914       factor_workaround = PETSC_TRUE;
915     }
916     /* include the primal vertices in the Schur complement */
917     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
918       PetscInt n_v;
919 
920       ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
921       if (n_v) {
922         const PetscInt* idxs;
923 
924         ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
925         ierr = PetscArraycpy(all_local_idx_N+cum,idxs,n_v);CHKERRQ(ierr);
926         ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
927         cum += n_v;
928         factor_workaround = PETSC_TRUE;
929         schur_has_vertices = PETSC_TRUE;
930       }
931     }
932     size_schur = cum - n_I;
933     ierr = ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);CHKERRQ(ierr);
934 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
935     oldpin = sub_schurs->A->boundtocpu;
936     ierr = MatBindToCPU(sub_schurs->A,PETSC_TRUE);CHKERRQ(ierr);
937 #endif
938     if (cum == n) {
939       ierr = ISSetPermutation(is_A_all);CHKERRQ(ierr);
940       ierr = MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
941     } else {
942       ierr = MatCreateSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
943     }
944 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
945     ierr = MatBindToCPU(sub_schurs->A,oldpin);CHKERRQ(ierr);
946 #endif
947     ierr = MatSetOptionsPrefix(A,sub_schurs->prefix);CHKERRQ(ierr);
948     ierr = MatAppendOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
949 
950     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
951        this is a workaround */
952     if (benign_n) {
953       Vec                    v,benign_AIIm1_ones;
954       ISLocalToGlobalMapping N_to_reor;
955       IS                     is_p0,is_p0_p;
956       PetscScalar            *cs_AIB,*AIIm1_data;
957       PetscInt               sizeA;
958 
959       ierr = ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);CHKERRQ(ierr);
960       ierr = ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
961       ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);CHKERRQ(ierr);
962       ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
963       ierr = MatCreateVecs(A,&v,&benign_AIIm1_ones);CHKERRQ(ierr);
964       ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
965       ierr = MatCreateSeqDense(PETSC_COMM_SELF,sizeA,benign_n,NULL,&benign_AIIm1_ones_mat);CHKERRQ(ierr);
966       ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,benign_n,NULL,&cs_AIB_mat);CHKERRQ(ierr);
967       ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
968       ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
969       ierr = PetscMalloc1(benign_n,&is_p_r);CHKERRQ(ierr);
970       /* compute colsum of A_IB restricted to pressures */
971       for (i=0;i<benign_n;i++) {
972         const PetscScalar *array;
973         const PetscInt    *idxs;
974         PetscInt          j,nz;
975 
976         ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);CHKERRQ(ierr);
977         ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
978         ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
979         for (j=0;j<nz;j++) AIIm1_data[idxs[j]+sizeA*i] = 1.;
980         ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
981         ierr = VecPlaceArray(benign_AIIm1_ones,AIIm1_data+sizeA*i);CHKERRQ(ierr);
982         ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
983         ierr = VecResetArray(benign_AIIm1_ones);CHKERRQ(ierr);
984         ierr = VecGetArrayRead(v,&array);CHKERRQ(ierr);
985         for (j=0;j<size_schur;j++) {
986 #if defined(PETSC_USE_COMPLEX)
987           cs_AIB[i*size_schur + j] = (PetscRealPart(array[j+n_I])/nz + PETSC_i*(PetscImaginaryPart(array[j+n_I])/nz));
988 #else
989           cs_AIB[i*size_schur + j] = array[j+n_I]/nz;
990 #endif
991         }
992         ierr = VecRestoreArrayRead(v,&array);CHKERRQ(ierr);
993       }
994       ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
995       ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
996       ierr = VecDestroy(&v);CHKERRQ(ierr);
997       ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
998       ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);CHKERRQ(ierr);
999       ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1000       ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1001       ierr = MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);CHKERRQ(ierr);
1002       ierr = ISDestroy(&is_p0_p);CHKERRQ(ierr);
1003       ierr = ISLocalToGlobalMappingDestroy(&N_to_reor);CHKERRQ(ierr);
1004     }
1005     ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_symmetric);CHKERRQ(ierr);
1006     ierr = MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
1007     ierr = MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
1008 
1009     /* for complexes, symmetric and hermitian at the same time implies null imaginary part */
1010     use_cholesky = (PetscBool)((use_potr || use_sytr) && sub_schurs->is_hermitian && sub_schurs->is_symmetric);
1011 
1012     /* when using the benign subspace trick, the local Schur complements are SPD */
1013     /* MKL_PARDISO does not handle well the computation of a Schur complement from a symmetric indefinite factorization
1014        Use LU and adapt pivoting perturbation (still, solution is not as accurate as with using MUMPS) */
1015     if (benign_trick) {
1016       sub_schurs->is_posdef = PETSC_TRUE;
1017       ierr = PetscStrcmp(sub_schurs->mat_solver_type,MATSOLVERMKL_PARDISO,&flg);CHKERRQ(ierr);
1018       if (flg) use_cholesky = PETSC_FALSE;
1019     }
1020 
1021     if (n_I) {
1022       IS        is_schur;
1023       char      stype[64];
1024       PetscBool gpu = PETSC_FALSE;
1025 
1026       if (use_cholesky) {
1027         ierr = MatGetFactor(A,sub_schurs->mat_solver_type,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
1028       } else {
1029         ierr = MatGetFactor(A,sub_schurs->mat_solver_type,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
1030       }
1031       ierr = MatSetErrorIfFailure(A,PETSC_TRUE);CHKERRQ(ierr);
1032 #if defined(PETSC_HAVE_MKL_PARDISO)
1033       if (benign_trick) { ierr = MatMkl_PardisoSetCntl(F,10,10);CHKERRQ(ierr); }
1034 #endif
1035       /* subsets ordered last */
1036       ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is_schur);CHKERRQ(ierr);
1037       ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
1038       ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
1039 
1040       /* factorization step */
1041       if (use_cholesky) {
1042         ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
1043 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
1044         ierr = MatMumpsSetIcntl(F,19,2);CHKERRQ(ierr);
1045 #endif
1046         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
1047         S_lower_triangular = PETSC_TRUE;
1048       } else {
1049         ierr = MatLUFactorSymbolic(F,A,NULL,NULL,NULL);CHKERRQ(ierr);
1050 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
1051         ierr = MatMumpsSetIcntl(F,19,3);CHKERRQ(ierr);
1052 #endif
1053         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
1054       }
1055       ierr = MatViewFromOptions(F,(PetscObject)A,"-mat_factor_view");CHKERRQ(ierr);
1056 
1057       if (matl_dbg_viewer) {
1058         Mat S;
1059         IS  is;
1060 
1061         ierr = PetscObjectSetName((PetscObject)A,"A");CHKERRQ(ierr);
1062         ierr = MatView(A,matl_dbg_viewer);CHKERRQ(ierr);
1063         ierr = MatFactorCreateSchurComplement(F,&S,NULL);CHKERRQ(ierr);
1064         ierr = PetscObjectSetName((PetscObject)S,"S");CHKERRQ(ierr);
1065         ierr = MatView(S,matl_dbg_viewer);CHKERRQ(ierr);
1066         ierr = MatDestroy(&S);CHKERRQ(ierr);
1067         ierr = ISCreateStride(PETSC_COMM_SELF,n_I,0,1,&is);CHKERRQ(ierr);
1068         ierr = PetscObjectSetName((PetscObject)is,"I");CHKERRQ(ierr);
1069         ierr = ISView(is,matl_dbg_viewer);CHKERRQ(ierr);
1070         ierr = ISDestroy(&is);CHKERRQ(ierr);
1071         ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is);CHKERRQ(ierr);
1072         ierr = PetscObjectSetName((PetscObject)is,"B");CHKERRQ(ierr);
1073         ierr = ISView(is,matl_dbg_viewer);CHKERRQ(ierr);
1074         ierr = ISDestroy(&is);CHKERRQ(ierr);
1075         ierr = PetscObjectSetName((PetscObject)is_A_all,"IA");CHKERRQ(ierr);
1076         ierr = ISView(is_A_all,matl_dbg_viewer);CHKERRQ(ierr);
1077       }
1078 
1079       /* get explicit Schur Complement computed during numeric factorization */
1080       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1081       ierr = PetscStrncpy(stype,MATSEQDENSE,sizeof(stype));CHKERRQ(ierr);
1082 #if defined(PETSC_HAVE_CUDA)
1083       ierr = PetscObjectTypeCompareAny((PetscObject)A,&gpu,MATSEQAIJVIENNACL,MATSEQAIJCUSPARSE,"");CHKERRQ(ierr);
1084 #endif
1085       if (gpu) {
1086         ierr = PetscStrncpy(stype,MATSEQDENSECUDA,sizeof(stype));CHKERRQ(ierr);
1087       }
1088       ierr = PetscOptionsGetString(NULL,sub_schurs->prefix,"-sub_schurs_schur_mat_type",stype,sizeof(stype),NULL);CHKERRQ(ierr);
1089       ierr = MatConvert(S_all,stype,MAT_INPLACE_MATRIX,&S_all);CHKERRQ(ierr);
1090       ierr = MatSetOption(S_all,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
1091       ierr = MatSetOption(S_all,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
1092       ierr = MatGetType(S_all,&Stype);CHKERRQ(ierr);
1093 
1094       /* we can reuse the solvers if we are not using the economic version */
1095       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
1096       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
1097       if (!sub_schurs->is_posdef && factor_workaround && compute_Stilda && size_active_schur)
1098         reuse_solvers = factor_workaround = PETSC_FALSE;
1099 
1100       solver_S = PETSC_TRUE;
1101 
1102       /* update the Schur complement with the change of basis on the pressures */
1103       if (benign_n) {
1104         const PetscScalar *cs_AIB;
1105         PetscScalar       *S_data,*AIIm1_data;
1106         Mat               S2 = NULL,S3 = NULL; /* dbg */
1107         PetscScalar       *S2_data,*S3_data; /* dbg */
1108         Vec               v,benign_AIIm1_ones;
1109         PetscInt          sizeA;
1110 
1111         ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1112         ierr = MatCreateVecs(A,&v,&benign_AIIm1_ones);CHKERRQ(ierr);
1113         ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
1114 #if defined(PETSC_HAVE_MUMPS)
1115         ierr = MatMumpsSetIcntl(F,26,0);CHKERRQ(ierr);
1116 #endif
1117 #if defined(PETSC_HAVE_MKL_PARDISO)
1118         ierr = MatMkl_PardisoSetCntl(F,70,1);CHKERRQ(ierr);
1119 #endif
1120         ierr = MatDenseGetArrayRead(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1121         ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1122         if (matl_dbg_viewer) {
1123           ierr = MatDuplicate(S_all,MAT_DO_NOT_COPY_VALUES,&S2);CHKERRQ(ierr);
1124           ierr = MatDuplicate(S_all,MAT_DO_NOT_COPY_VALUES,&S3);CHKERRQ(ierr);
1125           ierr = MatDenseGetArray(S2,&S2_data);CHKERRQ(ierr);
1126           ierr = MatDenseGetArray(S3,&S3_data);CHKERRQ(ierr);
1127         }
1128         for (i=0;i<benign_n;i++) {
1129           PetscScalar    *array,sum = 0.,one = 1.,*sums;
1130           const PetscInt *idxs;
1131           PetscInt       k,j,nz;
1132           PetscBLASInt   B_k,B_n;
1133 
1134           ierr = PetscCalloc1(benign_n,&sums);CHKERRQ(ierr);
1135           ierr = VecPlaceArray(benign_AIIm1_ones,AIIm1_data+sizeA*i);CHKERRQ(ierr);
1136           ierr = VecCopy(benign_AIIm1_ones,v);CHKERRQ(ierr);
1137           ierr = MatSolve(F,v,benign_AIIm1_ones);CHKERRQ(ierr);
1138           ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
1139           ierr = VecResetArray(benign_AIIm1_ones);CHKERRQ(ierr);
1140           /* p0 dofs (eliminated) are excluded from the sums */
1141           for (k=0;k<benign_n;k++) {
1142             ierr = ISGetLocalSize(is_p_r[k],&nz);CHKERRQ(ierr);
1143             ierr = ISGetIndices(is_p_r[k],&idxs);CHKERRQ(ierr);
1144             for (j=0;j<nz-1;j++) sums[k] -= AIIm1_data[idxs[j]+sizeA*i];
1145             ierr = ISRestoreIndices(is_p_r[k],&idxs);CHKERRQ(ierr);
1146           }
1147           ierr = VecGetArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
1148           if (matl_dbg_viewer) {
1149             Vec  vv;
1150             char name[16];
1151 
1152             ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array+n_I,&vv);CHKERRQ(ierr);
1153             ierr = PetscSNPrintf(name,sizeof(name),"Pvs%D",i);CHKERRQ(ierr);
1154             ierr = PetscObjectSetName((PetscObject)vv,name);CHKERRQ(ierr);
1155             ierr = VecView(vv,matl_dbg_viewer);CHKERRQ(ierr);
1156           }
1157           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
1158           /* cs_AIB already scaled by 1./nz */
1159           B_k = 1;
1160           for (k=0;k<benign_n;k++) {
1161             sum  = sums[k];
1162             ierr = PetscBLASIntCast(size_schur,&B_n);CHKERRQ(ierr);
1163 
1164             if (PetscAbsScalar(sum) == 0.0) continue;
1165             if (k == i) {
1166               PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
1167               if (matl_dbg_viewer) {
1168                 PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S3_data,&B_n));
1169               }
1170             } else { /* XXX Is it correct to use symmetric rank-2 update with half of the sum? */
1171               sum /= 2.0;
1172               PetscStackCallBLAS("BLASsyr2k",BLASsyr2k_("L","N",&B_n,&B_k,&sum,cs_AIB+k*size_schur,&B_n,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
1173               if (matl_dbg_viewer) {
1174                 PetscStackCallBLAS("BLASsyr2k",BLASsyr2k_("L","N",&B_n,&B_k,&sum,cs_AIB+k*size_schur,&B_n,cs_AIB+i*size_schur,&B_n,&one,S3_data,&B_n));
1175               }
1176             }
1177           }
1178           sum  = 1.;
1179           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));
1180           if (matl_dbg_viewer) {
1181             PetscStackCallBLAS("BLASsyr2k",BLASsyr2k_("L","N",&B_n,&B_k,&sum,array+n_I,&B_n,cs_AIB+i*size_schur,&B_n,&one,S2_data,&B_n));
1182           }
1183           ierr = VecRestoreArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
1184           /* set p0 entry of AIIm1_ones to zero */
1185           ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
1186           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1187           for (j=0;j<benign_n;j++) AIIm1_data[idxs[nz-1]+sizeA*j] = 0.;
1188           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1189           ierr = PetscFree(sums);CHKERRQ(ierr);
1190         }
1191         ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
1192         if (matl_dbg_viewer) {
1193           ierr = MatDenseRestoreArray(S2,&S2_data);CHKERRQ(ierr);
1194           ierr = MatDenseRestoreArray(S3,&S3_data);CHKERRQ(ierr);
1195         }
1196         if (!S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1197           PetscInt k,j;
1198           for (k=0;k<size_schur;k++) {
1199             for (j=k;j<size_schur;j++) {
1200               S_data[j*size_schur+k] = PetscConj(S_data[k*size_schur+j]);
1201             }
1202           }
1203         }
1204 
1205         /* restore defaults */
1206 #if defined(PETSC_HAVE_MUMPS)
1207         ierr = MatMumpsSetIcntl(F,26,-1);CHKERRQ(ierr);
1208 #endif
1209 #if defined(PETSC_HAVE_MKL_PARDISO)
1210         ierr = MatMkl_PardisoSetCntl(F,70,0);CHKERRQ(ierr);
1211 #endif
1212         ierr = MatDenseRestoreArrayRead(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1213         ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1214         ierr = VecDestroy(&v);CHKERRQ(ierr);
1215         ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1216         if (matl_dbg_viewer) {
1217           Mat S;
1218 
1219           ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1220           ierr = MatFactorCreateSchurComplement(F,&S,NULL);CHKERRQ(ierr);
1221           ierr = PetscObjectSetName((PetscObject)S,"Sb");CHKERRQ(ierr);
1222           ierr = MatView(S,matl_dbg_viewer);CHKERRQ(ierr);
1223           ierr = MatDestroy(&S);CHKERRQ(ierr);
1224           ierr = PetscObjectSetName((PetscObject)S2,"S2P");CHKERRQ(ierr);
1225           ierr = MatView(S2,matl_dbg_viewer);CHKERRQ(ierr);
1226           ierr = PetscObjectSetName((PetscObject)S3,"S3P");CHKERRQ(ierr);
1227           ierr = MatView(S3,matl_dbg_viewer);CHKERRQ(ierr);
1228           ierr = PetscObjectSetName((PetscObject)cs_AIB_mat,"cs");CHKERRQ(ierr);
1229           ierr = MatView(cs_AIB_mat,matl_dbg_viewer);CHKERRQ(ierr);
1230           ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1231         }
1232         ierr = MatDestroy(&S2);CHKERRQ(ierr);
1233         ierr = MatDestroy(&S3);CHKERRQ(ierr);
1234       }
1235       if (!reuse_solvers) {
1236         for (i=0;i<benign_n;i++) {
1237           ierr = ISDestroy(&is_p_r[i]);CHKERRQ(ierr);
1238         }
1239         ierr = PetscFree(is_p_r);CHKERRQ(ierr);
1240         ierr = MatDestroy(&cs_AIB_mat);CHKERRQ(ierr);
1241         ierr = MatDestroy(&benign_AIIm1_ones_mat);CHKERRQ(ierr);
1242       }
1243     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1244       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
1245       ierr = MatGetType(S_all,&Stype);CHKERRQ(ierr);
1246       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1247       factor_workaround = PETSC_FALSE;
1248       solver_S = PETSC_FALSE;
1249     }
1250 
1251     if (reuse_solvers) {
1252       Mat                A_II,Afake;
1253       Vec                vec1_B;
1254       PCBDDCReuseSolvers msolv_ctx;
1255       PetscInt           n_R;
1256 
1257       if (sub_schurs->reuse_solver) {
1258         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1259       } else {
1260         ierr = PetscNew(&sub_schurs->reuse_solver);CHKERRQ(ierr);
1261       }
1262       msolv_ctx = sub_schurs->reuse_solver;
1263       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1264       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
1265       msolv_ctx->F = F;
1266       ierr = MatCreateVecs(F,&msolv_ctx->sol,NULL);CHKERRQ(ierr);
1267       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1268       {
1269         PetscScalar *array;
1270         PetscInt    n;
1271 
1272         ierr = VecGetLocalSize(msolv_ctx->sol,&n);CHKERRQ(ierr);
1273         ierr = VecGetArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1274         ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);CHKERRQ(ierr);
1275         ierr = VecRestoreArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1276       }
1277       msolv_ctx->has_vertices = schur_has_vertices;
1278 
1279       /* interior solver */
1280       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);CHKERRQ(ierr);
1281       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
1282       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
1283       ierr = PCShellSetName(msolv_ctx->interior_solver,"Interior solver (w/o Schur factorization)");CHKERRQ(ierr);
1284       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
1285       ierr = PCShellSetView(msolv_ctx->interior_solver,PCBDDCReuseSolvers_View);CHKERRQ(ierr);
1286       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);CHKERRQ(ierr);
1287       ierr = PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);CHKERRQ(ierr);
1288 
1289       /* correction solver */
1290       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->correction_solver);CHKERRQ(ierr);
1291       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
1292       ierr = PCShellSetName(msolv_ctx->correction_solver,"Correction solver (with Schur factorization)");CHKERRQ(ierr);
1293       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
1294       ierr = PCShellSetView(msolv_ctx->interior_solver,PCBDDCReuseSolvers_View);CHKERRQ(ierr);
1295       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);CHKERRQ(ierr);
1296       ierr = PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);CHKERRQ(ierr);
1297 
1298       /* scatter and vecs for Schur complement solver */
1299       ierr = MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);CHKERRQ(ierr);
1300       ierr = MatCreateVecs(sub_schurs->S,&vec1_B,NULL);CHKERRQ(ierr);
1301       if (!schur_has_vertices) {
1302         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1303         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1304         ierr = PetscObjectReference((PetscObject)is_A_all);CHKERRQ(ierr);
1305         msolv_ctx->is_R = is_A_all;
1306       } else {
1307         IS              is_B_all;
1308         const PetscInt* idxs;
1309         PetscInt        dual,n_v,n;
1310 
1311         ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
1312         dual = size_schur - n_v;
1313         ierr = ISGetLocalSize(is_A_all,&n);CHKERRQ(ierr);
1314         ierr = ISGetIndices(is_A_all,&idxs);CHKERRQ(ierr);
1315         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);CHKERRQ(ierr);
1316         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1317         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1318         ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);CHKERRQ(ierr);
1319         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1320         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1321         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);CHKERRQ(ierr);
1322         ierr = ISRestoreIndices(is_A_all,&idxs);CHKERRQ(ierr);
1323       }
1324       ierr = ISGetLocalSize(msolv_ctx->is_R,&n_R);CHKERRQ(ierr);
1325       ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,n_R,n_R,0,NULL,&Afake);CHKERRQ(ierr);
1326       ierr = MatAssemblyBegin(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1327       ierr = MatAssemblyEnd(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1328       ierr = PCSetOperators(msolv_ctx->correction_solver,Afake,Afake);CHKERRQ(ierr);
1329       ierr = MatDestroy(&Afake);CHKERRQ(ierr);
1330       ierr = VecDestroy(&vec1_B);CHKERRQ(ierr);
1331 
1332       /* communicate benign info to solver context */
1333       if (benign_n) {
1334         PetscScalar *array;
1335 
1336         msolv_ctx->benign_n = benign_n;
1337         msolv_ctx->benign_zerodiag_subs = is_p_r;
1338         ierr = PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);CHKERRQ(ierr);
1339         msolv_ctx->benign_csAIB = cs_AIB_mat;
1340         ierr = MatCreateVecs(cs_AIB_mat,&msolv_ctx->benign_corr_work,NULL);CHKERRQ(ierr);
1341         ierr = VecGetArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1342         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array,&msolv_ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
1343         ierr = VecRestoreArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1344         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1345       }
1346     } else {
1347       if (sub_schurs->reuse_solver) {
1348         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1349       }
1350       ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1351     }
1352     ierr = MatDestroy(&A);CHKERRQ(ierr);
1353     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
1354 
1355     /* Work arrays */
1356     ierr = PetscMalloc1(max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
1357 
1358     /* S_Ej_all */
1359     cum = cum2 = 0;
1360     ierr = MatDenseGetArrayRead(S_all,&rS_data);CHKERRQ(ierr);
1361     ierr = MatSeqAIJGetArray(sub_schurs->S_Ej_all,&SEj_arr);CHKERRQ(ierr);
1362     if (compute_Stilda) {
1363       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&SEjinv_arr);CHKERRQ(ierr);
1364     }
1365     for (i=0;i<sub_schurs->n_subs;i++) {
1366       PetscInt j;
1367 
1368       /* get S_E */
1369       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1370       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1371         PetscInt k;
1372         for (k=0;k<subset_size;k++) {
1373           for (j=k;j<subset_size;j++) {
1374             work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1375             work[j*subset_size+k] = PetscConj(rS_data[cum2+k*size_schur+j]);
1376           }
1377         }
1378       } else { /* just copy to workspace */
1379         PetscInt k;
1380         for (k=0;k<subset_size;k++) {
1381           for (j=0;j<subset_size;j++) {
1382             work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1383           }
1384         }
1385       }
1386       /* insert S_E values */
1387       if (sub_schurs->change) {
1388         Mat change_sub,SEj,T;
1389 
1390         /* change basis */
1391         ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1392         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1393         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1394           Mat T2;
1395           ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1396           ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1397           ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1398           ierr = MatDestroy(&T2);CHKERRQ(ierr);
1399         } else {
1400           ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1401         }
1402         ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1403         ierr = MatDestroy(&T);CHKERRQ(ierr);
1404         ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1.0,NULL,NULL);CHKERRQ(ierr);
1405         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1406       }
1407       if (deluxe) {
1408         ierr = PetscArraycpy(SEj_arr,work,subset_size*subset_size);CHKERRQ(ierr);
1409         /* if adaptivity is requested, invert S_E blocks */
1410         if (compute_Stilda) {
1411           Mat               M;
1412           const PetscScalar *vals;
1413           PetscBool         isdense,isdensecuda;
1414 
1415           ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&M);CHKERRQ(ierr);
1416           ierr = MatSetOption(M,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
1417           ierr = MatSetOption(M,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
1418           if (!PetscBTLookup(sub_schurs->is_edge,i)) {
1419             ierr = MatSetType(M,Stype);CHKERRQ(ierr);
1420           }
1421           ierr = PetscObjectTypeCompare((PetscObject)M,MATSEQDENSE,&isdense);CHKERRQ(ierr);
1422           ierr = PetscObjectTypeCompare((PetscObject)M,MATSEQDENSECUDA,&isdensecuda);CHKERRQ(ierr);
1423           if (use_cholesky) {
1424             ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1425           } else {
1426             ierr = MatLUFactor(M,NULL,NULL,NULL);CHKERRQ(ierr);
1427           }
1428           if (isdense) {
1429             ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1430 #if defined(PETSC_HAVE_CUDA)
1431           } else if (isdensecuda) {
1432             ierr = MatSeqDenseCUDAInvertFactors_Private(M);CHKERRQ(ierr);
1433 #endif
1434           } else SETERRQ1(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"Not implemented for type %s",Stype);
1435           ierr = MatDenseGetArrayRead(M,&vals);CHKERRQ(ierr);
1436           ierr = PetscArraycpy(SEjinv_arr,vals,subset_size*subset_size);CHKERRQ(ierr);
1437           ierr = MatDenseRestoreArrayRead(M,&vals);CHKERRQ(ierr);
1438           ierr = MatDestroy(&M);CHKERRQ(ierr);
1439         }
1440       } else if (compute_Stilda) { /* not using deluxe */
1441         Mat         SEj;
1442         Vec         D;
1443         PetscScalar *array;
1444 
1445         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1446         ierr = VecGetArray(Dall,&array);CHKERRQ(ierr);
1447         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,array+cum,&D);CHKERRQ(ierr);
1448         ierr = VecRestoreArray(Dall,&array);CHKERRQ(ierr);
1449         ierr = VecShift(D,-1.);CHKERRQ(ierr);
1450         ierr = MatDiagonalScale(SEj,D,D);CHKERRQ(ierr);
1451         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1452         ierr = VecDestroy(&D);CHKERRQ(ierr);
1453         ierr = PetscArraycpy(SEj_arr,work,subset_size*subset_size);CHKERRQ(ierr);
1454       }
1455       cum += subset_size;
1456       cum2 += subset_size*(size_schur + 1);
1457       SEj_arr += subset_size*subset_size;
1458       if (SEjinv_arr) SEjinv_arr += subset_size*subset_size;
1459     }
1460     ierr = MatDenseRestoreArrayRead(S_all,&rS_data);CHKERRQ(ierr);
1461     ierr = MatSeqAIJRestoreArray(sub_schurs->S_Ej_all,&SEj_arr);CHKERRQ(ierr);
1462     if (compute_Stilda) {
1463       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&SEjinv_arr);CHKERRQ(ierr);
1464     }
1465     if (solver_S) {
1466       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1467     }
1468 
1469     /* may prevent from unneeded copies, since MUMPS or MKL_Pardiso always use CPU memory
1470        however, preliminary tests indicate using GPUs is still faster in the solve phase */
1471 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
1472     if (reuse_solvers) {
1473       Mat                  St;
1474       MatFactorSchurStatus st;
1475 
1476       flg  = PETSC_FALSE;
1477       ierr = PetscOptionsGetBool(NULL,sub_schurs->prefix,"-sub_schurs_schur_pin_to_cpu",&flg,NULL);CHKERRQ(ierr);
1478       ierr = MatFactorGetSchurComplement(F,&St,&st);CHKERRQ(ierr);
1479       ierr = MatBindToCPU(St,flg);CHKERRQ(ierr);
1480       ierr = MatFactorRestoreSchurComplement(F,&St,st);CHKERRQ(ierr);
1481     }
1482 #endif
1483 
1484     schur_factor = NULL;
1485     if (compute_Stilda && size_active_schur) {
1486 
1487       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&SEjinv_arr);CHKERRQ(ierr);
1488       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1489         ierr = PetscArraycpy(SEjinv_arr,work,size_schur*size_schur);CHKERRQ(ierr);
1490       } else {
1491         Mat S_all_inv=NULL;
1492 
1493         if (solver_S) {
1494           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1495              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 */
1496           if (factor_workaround) {/* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1497             PetscScalar *data;
1498             PetscInt     nd = 0;
1499 
1500             if (!use_potr) {
1501               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1502             }
1503             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1504             ierr = MatDenseGetArray(S_all_inv,&data);CHKERRQ(ierr);
1505             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1506               ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1507             }
1508 
1509             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
1510             if (schur_has_vertices) {
1511               Mat          M;
1512               PetscScalar *tdata;
1513               PetscInt     nv = 0, news;
1514 
1515               ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
1516               news = size_active_schur + nv;
1517               ierr = PetscCalloc1(news*news,&tdata);CHKERRQ(ierr);
1518               for (i=0;i<size_active_schur;i++) {
1519                 ierr = PetscArraycpy(tdata+i*(news+1),data+i*(size_schur+1),size_active_schur-i);CHKERRQ(ierr);
1520                 ierr = PetscArraycpy(tdata+i*(news+1)+size_active_schur-i,data+i*size_schur+size_active_schur+nd,nv);CHKERRQ(ierr);
1521               }
1522               for (i=0;i<nv;i++) {
1523                 PetscInt k = i+size_active_schur;
1524                 ierr = PetscArraycpy(tdata+k*(news+1),data+(k+nd)*(size_schur+1),nv-i);CHKERRQ(ierr);
1525               }
1526 
1527               ierr = MatCreateSeqDense(PETSC_COMM_SELF,news,news,tdata,&M);CHKERRQ(ierr);
1528               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1529               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1530               /* save the factors */
1531               cum = 0;
1532               ierr = PetscMalloc1((size_active_schur*(size_active_schur +1))/2+nd,&schur_factor);CHKERRQ(ierr);
1533               for (i=0;i<size_active_schur;i++) {
1534                 ierr = PetscArraycpy(schur_factor+cum,tdata+i*(news+1),size_active_schur-i);CHKERRQ(ierr);
1535                 cum += size_active_schur - i;
1536               }
1537               for (i=0;i<nd;i++) schur_factor[cum+i] = PetscSqrtReal(PetscRealPart(data[(i+size_active_schur)*(size_schur+1)]));
1538               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1539               /* move back just the active dofs to the Schur complement */
1540               for (i=0;i<size_active_schur;i++) {
1541                 ierr = PetscArraycpy(data+i*size_schur,tdata+i*news,size_active_schur);CHKERRQ(ierr);
1542               }
1543               ierr = PetscFree(tdata);CHKERRQ(ierr);
1544               ierr = MatDestroy(&M);CHKERRQ(ierr);
1545             } else { /* we can factorize and invert just the activedofs */
1546               Mat         M;
1547               PetscScalar *aux;
1548 
1549               ierr = PetscMalloc1(nd,&aux);CHKERRQ(ierr);
1550               for (i=0;i<nd;i++) aux[i] = 1.0/data[(i+size_active_schur)*(size_schur+1)];
1551               ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_active_schur,size_active_schur,data,&M);CHKERRQ(ierr);
1552               ierr = MatDenseSetLDA(M,size_schur);CHKERRQ(ierr);
1553               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1554               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1555               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1556               ierr = MatDestroy(&M);CHKERRQ(ierr);
1557               ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,nd,data+size_active_schur*size_schur,&M);CHKERRQ(ierr);
1558               ierr = MatZeroEntries(M);CHKERRQ(ierr);
1559               ierr = MatDestroy(&M);CHKERRQ(ierr);
1560               ierr = MatCreateSeqDense(PETSC_COMM_SELF,nd,size_schur,data+size_active_schur,&M);CHKERRQ(ierr);
1561               ierr = MatDenseSetLDA(M,size_schur);CHKERRQ(ierr);
1562               ierr = MatZeroEntries(M);CHKERRQ(ierr);
1563               ierr = MatDestroy(&M);CHKERRQ(ierr);
1564               for (i=0;i<nd;i++) data[(i+size_active_schur)*(size_schur+1)] = aux[i];
1565               ierr = PetscFree(aux);CHKERRQ(ierr);
1566             }
1567             ierr = MatDenseRestoreArray(S_all_inv,&data);CHKERRQ(ierr);
1568           } else { /* use MatFactor calls to invert S */
1569             ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
1570             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1571           }
1572         } else { /* we need to invert explicitly since we are not using MatFactor for S */
1573           ierr = PetscObjectReference((PetscObject)S_all);CHKERRQ(ierr);
1574           S_all_inv = S_all;
1575           ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1576           ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1577           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1578           if (use_potr) {
1579             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&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,S_data,&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,S_data,&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,S_data,&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,S_data,&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,S_data,&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 = PetscLogFlops(1.0*size_schur*size_schur*size_schur);CHKERRQ(ierr);
1595           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1596           ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1597         }
1598         /* S_Ej_tilda_all */
1599         cum = cum2 = 0;
1600         ierr = MatDenseGetArrayRead(S_all_inv,&rS_data);CHKERRQ(ierr);
1601         for (i=0;i<sub_schurs->n_subs;i++) {
1602           PetscInt j;
1603 
1604           ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1605           /* get (St^-1)_E */
1606           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1607              will be properly accessed later during adaptive selection */
1608           if (S_lower_triangular) {
1609             PetscInt k;
1610             if (sub_schurs->change) {
1611               for (k=0;k<subset_size;k++) {
1612                 for (j=k;j<subset_size;j++) {
1613                   work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1614                   work[j*subset_size+k] = work[k*subset_size+j];
1615                 }
1616               }
1617             } else {
1618               for (k=0;k<subset_size;k++) {
1619                 for (j=k;j<subset_size;j++) {
1620                   work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1621                 }
1622               }
1623             }
1624           } else {
1625             PetscInt k;
1626             for (k=0;k<subset_size;k++) {
1627               for (j=0;j<subset_size;j++) {
1628                 work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1629               }
1630             }
1631           }
1632           if (sub_schurs->change) {
1633             Mat change_sub,SEj,T;
1634 
1635             /* change basis */
1636             ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1637             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1638             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1639               Mat T2;
1640               ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1641               ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1642               ierr = MatDestroy(&T2);CHKERRQ(ierr);
1643               ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1644             } else {
1645               ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1646             }
1647             ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1648             ierr = MatDestroy(&T);CHKERRQ(ierr);
1649             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
1650             ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1./PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
1651             ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1652           }
1653           ierr = PetscArraycpy(SEjinv_arr,work,subset_size*subset_size);CHKERRQ(ierr);
1654           cum += subset_size;
1655           cum2 += subset_size*(size_schur + 1);
1656           SEjinv_arr += subset_size*subset_size;
1657         }
1658         ierr = MatDenseRestoreArrayRead(S_all_inv,&rS_data);CHKERRQ(ierr);
1659         if (solver_S) {
1660           if (schur_has_vertices) {
1661             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1662           } else {
1663             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_INVERTED);CHKERRQ(ierr);
1664           }
1665         }
1666         ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
1667       }
1668       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&SEjinv_arr);CHKERRQ(ierr);
1669 
1670       /* move back factors if needed */
1671       if (schur_has_vertices) {
1672         Mat      S_tmp;
1673         PetscInt nd = 0;
1674 
1675         if (!solver_S) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
1676         ierr = MatFactorGetSchurComplement(F,&S_tmp,NULL);CHKERRQ(ierr);
1677         if (use_potr) {
1678           PetscScalar *data;
1679 
1680           ierr = MatDenseGetArray(S_tmp,&data);CHKERRQ(ierr);
1681           ierr = PetscArrayzero(data,size_schur*size_schur);CHKERRQ(ierr);
1682 
1683           if (S_lower_triangular) {
1684             cum = 0;
1685             for (i=0;i<size_active_schur;i++) {
1686               ierr = PetscArraycpy(data+i*(size_schur+1),schur_factor+cum,size_active_schur-i);CHKERRQ(ierr);
1687               cum += size_active_schur-i;
1688             }
1689           } else {
1690             ierr = PetscArraycpy(data,schur_factor,size_schur*size_schur);CHKERRQ(ierr);
1691           }
1692           if (sub_schurs->is_dir) {
1693             ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1694             for (i=0;i<nd;i++) {
1695               data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
1696             }
1697           }
1698           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1699              set the diagonal entry of the Schur factor to a very large value */
1700           for (i=size_active_schur+nd;i<size_schur;i++) {
1701             data[i*(size_schur+1)] = infty;
1702           }
1703           ierr = MatDenseRestoreArray(S_tmp,&data);CHKERRQ(ierr);
1704         } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1705         ierr = MatFactorRestoreSchurComplement(F,&S_tmp,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1706       }
1707     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
1708       PetscScalar *data;
1709       PetscInt    nd = 0;
1710 
1711       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1712         ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1713       }
1714       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1715       ierr = MatDenseGetArray(S_all,&data);CHKERRQ(ierr);
1716       for (i=0;i<size_active_schur;i++) {
1717         ierr = PetscArrayzero(data+i*size_schur+size_active_schur,size_schur-size_active_schur);CHKERRQ(ierr);
1718       }
1719       for (i=size_active_schur+nd;i<size_schur;i++) {
1720         ierr = PetscArrayzero(data+i*size_schur+size_active_schur,size_schur-size_active_schur);CHKERRQ(ierr);
1721         data[i*(size_schur+1)] = infty;
1722       }
1723       ierr = MatDenseRestoreArray(S_all,&data);CHKERRQ(ierr);
1724       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1725     }
1726     ierr = PetscFree(work);CHKERRQ(ierr);
1727     ierr = PetscFree(schur_factor);CHKERRQ(ierr);
1728     ierr = VecDestroy(&Dall);CHKERRQ(ierr);
1729   }
1730   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1731   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
1732   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1733   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1734   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1735   ierr = MatDestroy(&F);CHKERRQ(ierr);
1736 
1737   ierr = PetscMalloc1(sub_schurs->n_subs,&nnz);CHKERRQ(ierr);
1738   for (i=0;i<sub_schurs->n_subs;i++) {
1739     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&nnz[i]);CHKERRQ(ierr);
1740   }
1741   ierr = ISCreateGeneral(PETSC_COMM_SELF,sub_schurs->n_subs,nnz,PETSC_OWN_POINTER,&is_I_layer);CHKERRQ(ierr);
1742   ierr = MatSetVariableBlockSizes(sub_schurs->S_Ej_all,sub_schurs->n_subs,nnz);CHKERRQ(ierr);
1743   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1744   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1745   if (compute_Stilda) {
1746     ierr = MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_tilda_all,sub_schurs->n_subs,nnz);CHKERRQ(ierr);
1747     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1748     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1749     if (deluxe) {
1750       ierr = MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_inv_all,sub_schurs->n_subs,nnz);CHKERRQ(ierr);
1751       ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1752       ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1753     }
1754   }
1755   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1756 
1757   /* Get local part of (\sum_j S_Ej) */
1758   if (!sub_schurs->sum_S_Ej_all) {
1759     ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1760   }
1761   ierr = VecSet(gstash,0.0);CHKERRQ(ierr);
1762   ierr = MatSeqAIJGetArray(sub_schurs->S_Ej_all,&stasharray);CHKERRQ(ierr);
1763   ierr = VecPlaceArray(lstash,stasharray);CHKERRQ(ierr);
1764   ierr = VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1765   ierr = VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1766   ierr = MatSeqAIJRestoreArray(sub_schurs->S_Ej_all,&stasharray);CHKERRQ(ierr);
1767   ierr = VecResetArray(lstash);CHKERRQ(ierr);
1768   ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all,&stasharray);CHKERRQ(ierr);
1769   ierr = VecPlaceArray(lstash,stasharray);CHKERRQ(ierr);
1770   ierr = VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1771   ierr = VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1772   ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all,&stasharray);CHKERRQ(ierr);
1773   ierr = VecResetArray(lstash);CHKERRQ(ierr);
1774 
1775   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1776   if (compute_Stilda) {
1777     ierr = VecSet(gstash,0.0);CHKERRQ(ierr);
1778     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&stasharray);CHKERRQ(ierr);
1779     ierr = VecPlaceArray(lstash,stasharray);CHKERRQ(ierr);
1780     ierr = VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1781     ierr = VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1782     ierr = VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1783     ierr = VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1784     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&stasharray);CHKERRQ(ierr);
1785     ierr = VecResetArray(lstash);CHKERRQ(ierr);
1786     if (deluxe) {
1787       ierr = VecSet(gstash,0.0);CHKERRQ(ierr);
1788       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&stasharray);CHKERRQ(ierr);
1789       ierr = VecPlaceArray(lstash,stasharray);CHKERRQ(ierr);
1790       ierr = VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1791       ierr = VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1792       ierr = VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1793       ierr = VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1794       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&stasharray);CHKERRQ(ierr);
1795       ierr = VecResetArray(lstash);CHKERRQ(ierr);
1796     } else {
1797       PetscScalar *array;
1798       PetscInt    cum;
1799 
1800       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1801       cum = 0;
1802       for (i=0;i<sub_schurs->n_subs;i++) {
1803         ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1804         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1805         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1806         if (use_potr) {
1807           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
1808           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1809           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
1810           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1811         } else if (use_sytr) {
1812           PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1813           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRF Lapack routine %d",(int)B_ierr);
1814           PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&B_N,array+cum,&B_N,pivots,Bwork,&B_ierr));
1815           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRI Lapack routine %d",(int)B_ierr);
1816         } else {
1817           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
1818           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1819           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1820           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1821         }
1822         ierr = PetscLogFlops(1.0*subset_size*subset_size*subset_size);CHKERRQ(ierr);
1823         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1824         cum += subset_size*subset_size;
1825       }
1826       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1827       ierr = PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1828       ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1829       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1830     }
1831   }
1832   ierr = VecDestroy(&lstash);CHKERRQ(ierr);
1833   ierr = VecDestroy(&gstash);CHKERRQ(ierr);
1834   ierr = VecScatterDestroy(&sstash);CHKERRQ(ierr);
1835 
1836   if (matl_dbg_viewer) {
1837     PetscInt cum;
1838 
1839     if (sub_schurs->S_Ej_all) {
1840       ierr = PetscObjectSetName((PetscObject)sub_schurs->S_Ej_all,"SE");CHKERRQ(ierr);
1841       ierr = MatView(sub_schurs->S_Ej_all,matl_dbg_viewer);CHKERRQ(ierr);
1842     }
1843     if (sub_schurs->sum_S_Ej_all) {
1844       ierr = PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_all,"SSE");CHKERRQ(ierr);
1845       ierr = MatView(sub_schurs->sum_S_Ej_all,matl_dbg_viewer);CHKERRQ(ierr);
1846     }
1847     if (sub_schurs->sum_S_Ej_inv_all) {
1848       ierr = PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_inv_all,"SSEm");CHKERRQ(ierr);
1849       ierr = MatView(sub_schurs->sum_S_Ej_inv_all,matl_dbg_viewer);CHKERRQ(ierr);
1850     }
1851     if (sub_schurs->sum_S_Ej_tilda_all) {
1852       ierr = PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_tilda_all,"SSEt");CHKERRQ(ierr);
1853       ierr = MatView(sub_schurs->sum_S_Ej_tilda_all,matl_dbg_viewer);CHKERRQ(ierr);
1854     }
1855     for (i=0,cum=0;i<sub_schurs->n_subs;i++) {
1856       IS   is;
1857       char name[16];
1858 
1859       ierr = PetscSNPrintf(name,sizeof(name),"IE%D",i);CHKERRQ(ierr);
1860       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1861       ierr = ISCreateStride(PETSC_COMM_SELF,subset_size,cum,1,&is);CHKERRQ(ierr);
1862       ierr = PetscObjectSetName((PetscObject)is,name);CHKERRQ(ierr);
1863       ierr = ISView(is,matl_dbg_viewer);CHKERRQ(ierr);
1864       ierr = ISDestroy(&is);CHKERRQ(ierr);
1865       cum += subset_size;
1866     }
1867   }
1868 
1869   /* free workspace */
1870   ierr = PetscViewerDestroy(&matl_dbg_viewer);CHKERRQ(ierr);
1871   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
1872   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
1873   PetscFunctionReturn(0);
1874 }
1875 
1876 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, const char* prefix, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc)
1877 {
1878   IS              *faces,*edges,*all_cc,vertices;
1879   PetscInt        i,n_faces,n_edges,n_all_cc;
1880   PetscBool       is_sorted,ispardiso,ismumps;
1881   PetscErrorCode  ierr;
1882 
1883   PetscFunctionBegin;
1884   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
1885   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
1886   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
1887   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
1888 
1889   /* reset any previous data */
1890   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
1891 
1892   /* get index sets for faces and edges (already sorted by global ordering) */
1893   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1894   n_all_cc = n_faces+n_edges;
1895   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
1896   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
1897   for (i=0;i<n_faces;i++) {
1898     if (copycc) {
1899       ierr = ISDuplicate(faces[i],&all_cc[i]);CHKERRQ(ierr);
1900     } else {
1901       ierr = PetscObjectReference((PetscObject)faces[i]);CHKERRQ(ierr);
1902       all_cc[i] = faces[i];
1903     }
1904   }
1905   for (i=0;i<n_edges;i++) {
1906     if (copycc) {
1907       ierr = ISDuplicate(edges[i],&all_cc[n_faces+i]);CHKERRQ(ierr);
1908     } else {
1909       ierr = PetscObjectReference((PetscObject)edges[i]);CHKERRQ(ierr);
1910       all_cc[n_faces+i] = edges[i];
1911     }
1912     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
1913   }
1914   ierr = PetscObjectReference((PetscObject)vertices);CHKERRQ(ierr);
1915   sub_schurs->is_vertices = vertices;
1916   ierr = PCBDDCGraphRestoreCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1917   sub_schurs->is_dir = NULL;
1918   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
1919 
1920   /* Determine if MatFactor can be used */
1921   ierr = PetscStrallocpy(prefix,&sub_schurs->prefix);CHKERRQ(ierr);
1922 #if defined(PETSC_HAVE_MUMPS)
1923   ierr = PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERMUMPS,sizeof(sub_schurs->mat_solver_type));CHKERRQ(ierr);
1924 #elif defined(PETSC_HAVE_MKL_PARDISO)
1925   ierr = PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERMKL_PARDISO,sizeof(sub_schurs->mat_solver_type));CHKERRQ(ierr);
1926 #else
1927   ierr = PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERPETSC,sizeof(sub_schurs->mat_solver_type));CHKERRQ(ierr);
1928 #endif
1929 #if defined(PETSC_USE_COMPLEX)
1930   sub_schurs->is_hermitian  = PETSC_FALSE; /* Hermitian Cholesky is not supported by PETSc and external packages */
1931 #else
1932   sub_schurs->is_hermitian  = PETSC_TRUE;
1933 #endif
1934   sub_schurs->is_posdef     = PETSC_TRUE;
1935   sub_schurs->is_symmetric  = PETSC_TRUE;
1936   sub_schurs->debug         = PETSC_FALSE;
1937   sub_schurs->restrict_comm = PETSC_FALSE;
1938   ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)graph->l2gmap),sub_schurs->prefix,"BDDC sub_schurs options","PC");CHKERRQ(ierr);
1939   ierr = PetscOptionsString("-sub_schurs_mat_solver_type","Specific direct solver to use",NULL,sub_schurs->mat_solver_type,sub_schurs->mat_solver_type,sizeof(sub_schurs->mat_solver_type),NULL);CHKERRQ(ierr);
1940   ierr = PetscOptionsBool("-sub_schurs_symmetric","Symmetric problem",NULL,sub_schurs->is_symmetric,&sub_schurs->is_symmetric,NULL);CHKERRQ(ierr);
1941   ierr = PetscOptionsBool("-sub_schurs_hermitian","Hermitian problem",NULL,sub_schurs->is_hermitian,&sub_schurs->is_hermitian,NULL);CHKERRQ(ierr);
1942   ierr = PetscOptionsBool("-sub_schurs_posdef","Positive definite problem",NULL,sub_schurs->is_posdef,&sub_schurs->is_posdef,NULL);CHKERRQ(ierr);
1943   ierr = PetscOptionsBool("-sub_schurs_restrictcomm","Restrict communicator on active processes only",NULL,sub_schurs->restrict_comm,&sub_schurs->restrict_comm,NULL);CHKERRQ(ierr);
1944   ierr = PetscOptionsBool("-sub_schurs_debug","Debug output",NULL,sub_schurs->debug,&sub_schurs->debug,NULL);CHKERRQ(ierr);
1945   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1946   ierr = PetscStrcmp(sub_schurs->mat_solver_type,MATSOLVERMUMPS,&ismumps);CHKERRQ(ierr);
1947   ierr = PetscStrcmp(sub_schurs->mat_solver_type,MATSOLVERMKL_PARDISO,&ispardiso);CHKERRQ(ierr);
1948   sub_schurs->schur_explicit = (PetscBool)(ispardiso || ismumps);
1949 
1950   /* for reals, symmetric and hermitian are synonims */
1951 #if !defined(PETSC_USE_COMPLEX)
1952   sub_schurs->is_symmetric = (PetscBool)(sub_schurs->is_symmetric && sub_schurs->is_hermitian);
1953   sub_schurs->is_hermitian = sub_schurs->is_symmetric;
1954 #endif
1955 
1956   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
1957   sub_schurs->is_I = is_I;
1958   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
1959   sub_schurs->is_B = is_B;
1960   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
1961   sub_schurs->l2gmap = graph->l2gmap;
1962   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
1963   sub_schurs->BtoNmap = BtoNmap;
1964   sub_schurs->n_subs = n_all_cc;
1965   sub_schurs->is_subs = all_cc;
1966   sub_schurs->S_Ej_all = NULL;
1967   sub_schurs->sum_S_Ej_all = NULL;
1968   sub_schurs->sum_S_Ej_inv_all = NULL;
1969   sub_schurs->sum_S_Ej_tilda_all = NULL;
1970   sub_schurs->is_Ej_all = NULL;
1971   PetscFunctionReturn(0);
1972 }
1973 
1974 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1975 {
1976   PCBDDCSubSchurs schurs_ctx;
1977   PetscErrorCode  ierr;
1978 
1979   PetscFunctionBegin;
1980   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
1981   schurs_ctx->n_subs = 0;
1982   *sub_schurs = schurs_ctx;
1983   PetscFunctionReturn(0);
1984 }
1985 
1986 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1987 {
1988   PetscInt       i;
1989   PetscErrorCode ierr;
1990 
1991   PetscFunctionBegin;
1992   if (!sub_schurs) PetscFunctionReturn(0);
1993   ierr = PetscFree(sub_schurs->prefix);CHKERRQ(ierr);
1994   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1995   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1996   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1997   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1998   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1999   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
2000   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
2001   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
2002   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
2003   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
2004   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
2005   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
2006   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
2007   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
2008   for (i=0;i<sub_schurs->n_subs;i++) {
2009     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
2010   }
2011   if (sub_schurs->n_subs) {
2012     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
2013   }
2014   if (sub_schurs->reuse_solver) {
2015     ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
2016   }
2017   ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
2018   if (sub_schurs->change) {
2019     for (i=0;i<sub_schurs->n_subs;i++) {
2020       ierr = KSPDestroy(&sub_schurs->change[i]);CHKERRQ(ierr);
2021       ierr = ISDestroy(&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
2022     }
2023   }
2024   ierr = PetscFree(sub_schurs->change);CHKERRQ(ierr);
2025   ierr = PetscFree(sub_schurs->change_primal_sub);CHKERRQ(ierr);
2026   sub_schurs->n_subs = 0;
2027   PetscFunctionReturn(0);
2028 }
2029 
2030 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs* sub_schurs)
2031 {
2032   PetscErrorCode ierr;
2033 
2034   PetscFunctionBegin;
2035   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
2036   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
2037   PetscFunctionReturn(0);
2038 }
2039 
2040 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
2041 {
2042   PetscInt       i,j,n;
2043   PetscErrorCode ierr;
2044 
2045   PetscFunctionBegin;
2046   n = 0;
2047   for (i=-n_prev;i<0;i++) {
2048     PetscInt start_dof = queue_tip[i];
2049     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
2050       PetscInt dof = adjncy[j];
2051       if (!PetscBTLookup(touched,dof)) {
2052         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
2053         queue_tip[n] = dof;
2054         n++;
2055       }
2056     }
2057   }
2058   *n_added = n;
2059   PetscFunctionReturn(0);
2060 }
2061