xref: /petsc/src/ksp/pc/impls/bddc/bddcschurs.c (revision c4762a1b19cd2af06abeed90e8f9d34fb975dd94)
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,(void **)&ctx);CHKERRQ(ierr);
125   if (full) {
126 #if defined(PETSC_HAVE_MUMPS)
127     ierr = MatMumpsSetIcntl(ctx->F,26,-1);CHKERRQ(ierr);
128 #endif
129 #if defined(PETSC_HAVE_MKL_PARDISO)
130     ierr = MatMkl_PardisoSetCntl(ctx->F,70,0);CHKERRQ(ierr);
131 #endif
132     copy = ctx->has_vertices;
133   } else { /* interior solver */
134 #if defined(PETSC_HAVE_MUMPS)
135     ierr = MatMumpsSetIcntl(ctx->F,26,0);CHKERRQ(ierr);
136 #endif
137 #if defined(PETSC_HAVE_MKL_PARDISO)
138     ierr = MatMkl_PardisoSetCntl(ctx->F,70,1);CHKERRQ(ierr);
139 #endif
140     copy = PETSC_TRUE;
141   }
142   /* copy rhs into factored matrix workspace */
143   if (copy) {
144     PetscInt    n;
145     PetscScalar *array,*array_solver;
146 
147     ierr = VecGetLocalSize(rhs,&n);CHKERRQ(ierr);
148     ierr = VecGetArrayRead(rhs,(const PetscScalar**)&array);CHKERRQ(ierr);
149     ierr = VecGetArray(ctx->rhs,&array_solver);CHKERRQ(ierr);
150     ierr = 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,(void **)&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);CHKERRQ(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 
423   PetscFunctionBegin;
424   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
425   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
426   if (Ain) {
427     ierr = PetscObjectReference((PetscObject)Ain);CHKERRQ(ierr);
428     sub_schurs->A = Ain;
429   }
430 
431   ierr = PetscObjectReference((PetscObject)Sin);CHKERRQ(ierr);
432   sub_schurs->S = Sin;
433   if (sub_schurs->schur_explicit) {
434     sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
435   }
436 
437   /* preliminary checks */
438   if (!sub_schurs->schur_explicit && compute_Stilda) SETERRQ(PetscObjectComm((PetscObject)sub_schurs->l2gmap),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS and/or MKL_PARDISO");
439 
440   if (benign_trick) sub_schurs->is_posdef = PETSC_FALSE;
441 
442   /* debug (MATLAB) */
443   if (sub_schurs->debug) {
444     PetscMPIInt size,rank;
445     PetscInt    nr,*print_schurs_ranks,print_schurs = PETSC_FALSE;
446     PetscBool   flg;
447 
448     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&size);CHKERRQ(ierr);
449     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(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 
471   /* restrict work on active processes */
472   if (sub_schurs->restrict_comm) {
473     PetscSubcomm subcomm;
474     PetscMPIInt  color,rank;
475 
476     color = 0;
477     if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
478     ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);CHKERRQ(ierr);
479     ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);CHKERRQ(ierr);
480     ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
481     ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
482     ierr = PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);CHKERRQ(ierr);
483     ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
484     if (!sub_schurs->n_subs) {
485       ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
486       PetscFunctionReturn(0);
487     }
488   } else {
489     ierr = PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);CHKERRQ(ierr);
490   }
491 
492   /* get Schur complement matrices */
493   if (!sub_schurs->schur_explicit) {
494     Mat       tA_IB,tA_BI,tA_BB;
495     PetscBool isseqsbaij;
496     ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);CHKERRQ(ierr);
497     ierr = PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);CHKERRQ(ierr);
498     if (isseqsbaij) {
499       ierr = MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
500       ierr = MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
501       ierr = MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
502     } else {
503       ierr = PetscObjectReference((PetscObject)tA_BB);CHKERRQ(ierr);
504       A_BB = tA_BB;
505       ierr = PetscObjectReference((PetscObject)tA_IB);CHKERRQ(ierr);
506       A_IB = tA_IB;
507       ierr = PetscObjectReference((PetscObject)tA_BI);CHKERRQ(ierr);
508       A_BI = tA_BI;
509     }
510   } else {
511     A_II = NULL;
512     A_IB = NULL;
513     A_BI = NULL;
514     A_BB = NULL;
515   }
516   S_all = NULL;
517 
518   /* determine interior problems */
519   ierr = ISGetLocalSize(sub_schurs->is_I,&i);CHKERRQ(ierr);
520   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
521     PetscBT                touched;
522     const PetscInt*        idx_B;
523     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;
524 
525     if (!xadj) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot request layering without adjacency");
526     /* get sizes */
527     ierr = ISGetLocalSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
528     ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
529 
530     ierr = PetscMalloc1(n_I+n_B,&local_numbering);CHKERRQ(ierr);
531     ierr = PetscBTCreate(n_I+n_B,&touched);CHKERRQ(ierr);
532     ierr = PetscBTMemzero(n_I+n_B,touched);CHKERRQ(ierr);
533 
534     /* all boundary dofs must be skipped when adding layers */
535     ierr = ISGetIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
536     for (j=0;j<n_B;j++) {
537       ierr = PetscBTSet(touched,idx_B[j]);CHKERRQ(ierr);
538     }
539     ierr = PetscArraycpy(local_numbering,idx_B,n_B);CHKERRQ(ierr);
540     ierr = ISRestoreIndices(sub_schurs->is_B,&idx_B);CHKERRQ(ierr);
541 
542     /* add prescribed number of layers of dofs */
543     n_local_dofs = n_B;
544     n_prev_added = n_B;
545     for (layer=0;layer<nlayers;layer++) {
546       PetscInt n_added;
547       if (n_local_dofs == n_I+n_B) break;
548       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);
549       ierr = PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);CHKERRQ(ierr);
550       n_prev_added = n_added;
551       n_local_dofs += n_added;
552       if (!n_added) break;
553     }
554     ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
555 
556     /* IS for I layer dofs in original numbering */
557     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);
558     ierr = PetscFree(local_numbering);CHKERRQ(ierr);
559     ierr = ISSort(is_I_layer);CHKERRQ(ierr);
560     /* IS for I layer dofs in I numbering */
561     if (!sub_schurs->schur_explicit) {
562       ISLocalToGlobalMapping ItoNmap;
563       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);CHKERRQ(ierr);
564       ierr = ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);CHKERRQ(ierr);
565       ierr = ISLocalToGlobalMappingDestroy(&ItoNmap);CHKERRQ(ierr);
566 
567       /* II block */
568       ierr = MatCreateSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);CHKERRQ(ierr);
569     }
570   } else {
571     PetscInt n_I;
572 
573     /* IS for I dofs in original numbering */
574     ierr = PetscObjectReference((PetscObject)sub_schurs->is_I);CHKERRQ(ierr);
575     is_I_layer = sub_schurs->is_I;
576 
577     /* IS for I dofs in I numbering (strided 1) */
578     if (!sub_schurs->schur_explicit) {
579       ierr = ISGetSize(sub_schurs->is_I,&n_I);CHKERRQ(ierr);
580       ierr = ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);CHKERRQ(ierr);
581 
582       /* II block is the same */
583       ierr = PetscObjectReference((PetscObject)A_II);CHKERRQ(ierr);
584       AE_II = A_II;
585     }
586   }
587 
588   /* Get info on subset sizes and sum of all subsets sizes */
589   max_subset_size = 0;
590   local_size = 0;
591   for (i=0;i<sub_schurs->n_subs;i++) {
592     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
593     max_subset_size = PetscMax(subset_size,max_subset_size);
594     local_size += subset_size;
595   }
596 
597   /* Work arrays for local indices */
598   extra = 0;
599   ierr = ISGetLocalSize(sub_schurs->is_B,&n_B);CHKERRQ(ierr);
600   if (sub_schurs->schur_explicit && is_I_layer) {
601     ierr = ISGetLocalSize(is_I_layer,&extra);CHKERRQ(ierr);
602   }
603   ierr = PetscMalloc1(n_B+extra,&all_local_idx_N);CHKERRQ(ierr);
604   if (extra) {
605     const PetscInt *idxs;
606     ierr = ISGetIndices(is_I_layer,&idxs);CHKERRQ(ierr);
607     ierr = PetscArraycpy(all_local_idx_N,idxs,extra);CHKERRQ(ierr);
608     ierr = ISRestoreIndices(is_I_layer,&idxs);CHKERRQ(ierr);
609   }
610   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum1);CHKERRQ(ierr);
611   ierr = PetscMalloc1(sub_schurs->n_subs,&auxnum2);CHKERRQ(ierr);
612 
613   /* Get local indices in local numbering */
614   local_size = 0;
615   local_stash_size = 0;
616   for (i=0;i<sub_schurs->n_subs;i++) {
617     const PetscInt *idxs;
618 
619     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
620     ierr = ISGetIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
621     /* start (smallest in global ordering) and multiplicity */
622     auxnum1[i] = idxs[0];
623     auxnum2[i] = subset_size*subset_size;
624     /* subset indices in local numbering */
625     ierr = PetscArraycpy(all_local_idx_N+local_size+extra,idxs,subset_size);CHKERRQ(ierr);
626     ierr = ISRestoreIndices(sub_schurs->is_subs[i],&idxs);CHKERRQ(ierr);
627     local_size += subset_size;
628     local_stash_size += subset_size*subset_size;
629   }
630 
631   /* allocate extra workspace needed only for GETRI or SYTRF */
632   use_potr = use_sytr = PETSC_FALSE;
633   if (benign_trick || (sub_schurs->is_hermitian && sub_schurs->is_posdef)) {
634     use_potr = PETSC_TRUE;
635   } else if (sub_schurs->is_symmetric) {
636     use_sytr = PETSC_TRUE;
637   }
638   if (local_size && !use_potr) {
639     PetscScalar  lwork,dummyscalar = 0.;
640     PetscBLASInt dummyint = 0;
641 
642     B_lwork = -1;
643     ierr = PetscBLASIntCast(local_size,&B_N);CHKERRQ(ierr);
644     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
645     if (use_sytr) {
646       PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
647       if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYTRF Lapack routine %d",(int)B_ierr);
648     } else {
649       PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
650       if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GETRI Lapack routine %d",(int)B_ierr);
651     }
652     ierr = PetscFPTrapPop();CHKERRQ(ierr);
653     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);CHKERRQ(ierr);
654     ierr = PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);CHKERRQ(ierr);
655   } else {
656     Bwork = NULL;
657     pivots = NULL;
658   }
659 
660   /* prepare data for summing up properly schurs on subsets */
661   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);CHKERRQ(ierr);
662   ierr = ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);CHKERRQ(ierr);
663   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
664   ierr = ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);CHKERRQ(ierr);
665   ierr = ISRenumber(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);CHKERRQ(ierr);
666   ierr = ISDestroy(&all_subsets);CHKERRQ(ierr);
667   ierr = ISDestroy(&all_subsets_mult);CHKERRQ(ierr);
668   ierr = ISGetLocalSize(all_subsets_n,&i);CHKERRQ(ierr);
669   if (i != local_stash_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid size of new subset! %D != %D",i,local_stash_size);
670   ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,local_stash_size,NULL,&lstash);CHKERRQ(ierr);
671   ierr = VecCreateMPI(comm_n,PETSC_DECIDE,global_size,&gstash);CHKERRQ(ierr);
672   ierr = VecScatterCreate(lstash,NULL,gstash,all_subsets_n,&sstash);CHKERRQ(ierr);
673   ierr = ISDestroy(&all_subsets_n);CHKERRQ(ierr);
674 
675   /* subset indices in local boundary numbering */
676   if (!sub_schurs->is_Ej_all) {
677     PetscInt *all_local_idx_B;
678 
679     ierr = PetscMalloc1(local_size,&all_local_idx_B);CHKERRQ(ierr);
680     ierr = ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);CHKERRQ(ierr);
681     if (subset_size != local_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in sub_schurs serial (BtoNmap)! %D != %D",subset_size,local_size);
682     ierr = ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);CHKERRQ(ierr);
683   }
684 
685   if (change) {
686     ISLocalToGlobalMapping BtoS;
687     IS                     change_primal_B;
688     IS                     change_primal_all;
689 
690     if (sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
691     if (sub_schurs->change) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
692     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change_primal_sub);CHKERRQ(ierr);
693     for (i=0;i<sub_schurs->n_subs;i++) {
694       ISLocalToGlobalMapping NtoS;
695       ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);CHKERRQ(ierr);
696       ierr = ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
697       ierr = ISLocalToGlobalMappingDestroy(&NtoS);CHKERRQ(ierr);
698     }
699     ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);CHKERRQ(ierr);
700     ierr = ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);CHKERRQ(ierr);
701     ierr = ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);CHKERRQ(ierr);
702     ierr = ISLocalToGlobalMappingDestroy(&BtoS);CHKERRQ(ierr);
703     ierr = ISDestroy(&change_primal_B);CHKERRQ(ierr);
704     ierr = PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change);CHKERRQ(ierr);
705     for (i=0;i<sub_schurs->n_subs;i++) {
706       Mat change_sub;
707 
708       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
709       ierr = KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);CHKERRQ(ierr);
710       ierr = KSPSetType(sub_schurs->change[i],KSPPREONLY);CHKERRQ(ierr);
711       if (!sub_schurs->change_with_qr) {
712         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
713       } else {
714         Mat change_subt;
715         ierr = MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);CHKERRQ(ierr);
716         ierr = MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);CHKERRQ(ierr);
717         ierr = MatDestroy(&change_subt);CHKERRQ(ierr);
718       }
719       ierr = KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);CHKERRQ(ierr);
720       ierr = MatDestroy(&change_sub);CHKERRQ(ierr);
721       ierr = KSPSetOptionsPrefix(sub_schurs->change[i],sub_schurs->prefix);CHKERRQ(ierr);
722       ierr = KSPAppendOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");CHKERRQ(ierr);
723     }
724     ierr = ISDestroy(&change_primal_all);CHKERRQ(ierr);
725   }
726 
727   /* Local matrix of all local Schur on subsets (transposed) */
728   if (!sub_schurs->S_Ej_all) {
729     Mat         T;
730     PetscScalar *v;
731     PetscInt    *ii,*jj;
732     PetscInt    cum,i,j,k;
733 
734     /* MatSeqAIJSetPreallocation + MatSetValues is slow for these kind of matrices (may have large blocks)
735        Allocate properly a representative matrix and duplicate */
736     ierr  = PetscMalloc3(local_size+1,&ii,local_stash_size,&jj,local_stash_size,&v);CHKERRQ(ierr);
737     ii[0] = 0;
738     cum   = 0;
739     for (i=0;i<sub_schurs->n_subs;i++) {
740       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
741       for (j=0;j<subset_size;j++) {
742         const PetscInt row = cum+j;
743         PetscInt col = cum;
744 
745         ii[row+1] = ii[row] + subset_size;
746         for (k=ii[row];k<ii[row+1];k++) {
747           jj[k] = col;
748           col++;
749         }
750       }
751       cum += subset_size;
752     }
753     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,local_size,local_size,ii,jj,v,&T);CHKERRQ(ierr);
754     ierr = MatDuplicate(T,MAT_DO_NOT_COPY_VALUES,&sub_schurs->S_Ej_all);CHKERRQ(ierr);
755     ierr = MatDestroy(&T);CHKERRQ(ierr);
756     ierr = PetscFree3(ii,jj,v);CHKERRQ(ierr);
757   }
758   /* matrices for deluxe scaling and adaptive selection */
759   if (compute_Stilda) {
760     if (!sub_schurs->sum_S_Ej_tilda_all) {
761       ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
762     }
763     if (!sub_schurs->sum_S_Ej_inv_all && deluxe) {
764       ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
765     }
766   }
767 
768   /* Compute Schur complements explicitly */
769   F = NULL;
770   if (!sub_schurs->schur_explicit) {
771     /* this code branch is used when MatFactor with Schur complement support is not present or when explicitly requested;
772        it is not efficient, unless the economic version of the scaling is used */
773     Mat         S_Ej_expl;
774     PetscScalar *work;
775     PetscInt    j,*dummy_idx;
776     PetscBool   Sdense;
777 
778     ierr = PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
779     local_size = 0;
780     for (i=0;i<sub_schurs->n_subs;i++) {
781       IS  is_subset_B;
782       Mat AE_EE,AE_IE,AE_EI,S_Ej;
783 
784       /* subsets in original and boundary numbering */
785       ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);CHKERRQ(ierr);
786       /* EE block */
787       ierr = MatCreateSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);CHKERRQ(ierr);
788       /* IE block */
789       ierr = MatCreateSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);CHKERRQ(ierr);
790       /* EI block */
791       if (sub_schurs->is_symmetric) {
792         ierr = MatCreateTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
793       } else if (sub_schurs->is_hermitian) {
794         ierr = MatCreateHermitianTranspose(AE_IE,&AE_EI);CHKERRQ(ierr);
795       } else {
796         ierr = MatCreateSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);CHKERRQ(ierr);
797       }
798       ierr = ISDestroy(&is_subset_B);CHKERRQ(ierr);
799       ierr = MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);CHKERRQ(ierr);
800       ierr = MatDestroy(&AE_EE);CHKERRQ(ierr);
801       ierr = MatDestroy(&AE_IE);CHKERRQ(ierr);
802       ierr = MatDestroy(&AE_EI);CHKERRQ(ierr);
803       if (AE_II == A_II) { /* we can reuse the same ksp */
804         KSP ksp;
805         ierr = MatSchurComplementGetKSP(sub_schurs->S,&ksp);CHKERRQ(ierr);
806         ierr = MatSchurComplementSetKSP(S_Ej,ksp);CHKERRQ(ierr);
807       } else { /* build new ksp object which inherits ksp and pc types from the original one */
808         KSP       origksp,schurksp;
809         PC        origpc,schurpc;
810         KSPType   ksp_type;
811         PetscInt  n_internal;
812         PetscBool ispcnone;
813 
814         ierr = MatSchurComplementGetKSP(sub_schurs->S,&origksp);CHKERRQ(ierr);
815         ierr = MatSchurComplementGetKSP(S_Ej,&schurksp);CHKERRQ(ierr);
816         ierr = KSPGetType(origksp,&ksp_type);CHKERRQ(ierr);
817         ierr = KSPSetType(schurksp,ksp_type);CHKERRQ(ierr);
818         ierr = KSPGetPC(schurksp,&schurpc);CHKERRQ(ierr);
819         ierr = KSPGetPC(origksp,&origpc);CHKERRQ(ierr);
820         ierr = PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);CHKERRQ(ierr);
821         if (!ispcnone) {
822           PCType pc_type;
823           ierr = PCGetType(origpc,&pc_type);CHKERRQ(ierr);
824           ierr = PCSetType(schurpc,pc_type);CHKERRQ(ierr);
825         } else {
826           ierr = PCSetType(schurpc,PCLU);CHKERRQ(ierr);
827         }
828         ierr = ISGetSize(is_I,&n_internal);CHKERRQ(ierr);
829         if (!n_internal) { /* UMFPACK gives error with 0 sized problems */
830           MatSolverType solver = NULL;
831           ierr = PCFactorGetMatSolverType(origpc,(MatSolverType*)&solver);CHKERRQ(ierr);
832           if (solver) {
833             ierr = PCFactorSetMatSolverType(schurpc,solver);CHKERRQ(ierr);
834           }
835         }
836         ierr = KSPSetUp(schurksp);CHKERRQ(ierr);
837       }
838       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
839       ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);CHKERRQ(ierr);
840       ierr = PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_symmetric,MAT_REUSE_MATRIX,&S_Ej_expl);CHKERRQ(ierr);
841       ierr = PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);CHKERRQ(ierr);
842       if (Sdense) {
843         for (j=0;j<subset_size;j++) {
844           dummy_idx[j]=local_size+j;
845         }
846         ierr = MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);CHKERRQ(ierr);
847       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
848       ierr = MatDestroy(&S_Ej);CHKERRQ(ierr);
849       ierr = MatDestroy(&S_Ej_expl);CHKERRQ(ierr);
850       local_size += subset_size;
851     }
852     ierr = PetscFree2(dummy_idx,work);CHKERRQ(ierr);
853     /* free */
854     ierr = ISDestroy(&is_I);CHKERRQ(ierr);
855     ierr = MatDestroy(&AE_II);CHKERRQ(ierr);
856     ierr = PetscFree(all_local_idx_N);CHKERRQ(ierr);
857   } else {
858     Mat               A,cs_AIB_mat = NULL,benign_AIIm1_ones_mat = NULL;
859     Vec               Dall = NULL;
860     IS                is_A_all,*is_p_r = NULL;
861     MatType           Stype;
862     PetscScalar       *work,*S_data,*schur_factor,infty = PETSC_MAX_REAL;
863     PetscScalar       *SEj_arr = NULL,*SEjinv_arr = NULL;
864     const PetscScalar *rS_data;
865     PetscInt          n,n_I,size_schur,size_active_schur,cum,cum2;
866     PetscBool         economic,solver_S,S_lower_triangular = PETSC_FALSE;
867     PetscBool         schur_has_vertices,factor_workaround;
868     PetscBool         use_cholesky;
869 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
870     PetscBool         oldpin;
871 #endif
872 
873     /* get sizes */
874     n_I = 0;
875     if (is_I_layer) {
876       ierr = ISGetLocalSize(is_I_layer,&n_I);CHKERRQ(ierr);
877     }
878     economic = PETSC_FALSE;
879     ierr = ISGetLocalSize(sub_schurs->is_I,&cum);CHKERRQ(ierr);
880     if (cum != n_I) economic = PETSC_TRUE;
881     ierr = MatGetLocalSize(sub_schurs->A,&n,NULL);CHKERRQ(ierr);
882     size_active_schur = local_size;
883 
884     /* import scaling vector (wrong formulation if we have 3D edges) */
885     if (scaling && compute_Stilda) {
886       const PetscScalar *array;
887       PetscScalar       *array2;
888       const PetscInt    *idxs;
889       PetscInt          i;
890 
891       ierr = ISGetIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
892       ierr = VecCreateSeq(PETSC_COMM_SELF,size_active_schur,&Dall);CHKERRQ(ierr);
893       ierr = VecGetArrayRead(scaling,&array);CHKERRQ(ierr);
894       ierr = VecGetArray(Dall,&array2);CHKERRQ(ierr);
895       for (i=0;i<size_active_schur;i++) array2[i] = array[idxs[i]];
896       ierr = VecRestoreArray(Dall,&array2);CHKERRQ(ierr);
897       ierr = VecRestoreArrayRead(scaling,&array);CHKERRQ(ierr);
898       ierr = ISRestoreIndices(sub_schurs->is_Ej_all,&idxs);CHKERRQ(ierr);
899       deluxe = PETSC_FALSE;
900     }
901 
902     /* size active schurs does not count any dirichlet or vertex dof on the interface */
903     factor_workaround = PETSC_FALSE;
904     schur_has_vertices = PETSC_FALSE;
905     cum = n_I+size_active_schur;
906     if (sub_schurs->is_dir) {
907       const PetscInt* idxs;
908       PetscInt        n_dir;
909 
910       ierr = ISGetLocalSize(sub_schurs->is_dir,&n_dir);CHKERRQ(ierr);
911       ierr = ISGetIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
912       ierr = PetscArraycpy(all_local_idx_N+cum,idxs,n_dir);CHKERRQ(ierr);
913       ierr = ISRestoreIndices(sub_schurs->is_dir,&idxs);CHKERRQ(ierr);
914       cum += n_dir;
915       factor_workaround = PETSC_TRUE;
916     }
917     /* include the primal vertices in the Schur complement */
918     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
919       PetscInt n_v;
920 
921       ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
922       if (n_v) {
923         const PetscInt* idxs;
924 
925         ierr = ISGetIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
926         ierr = PetscArraycpy(all_local_idx_N+cum,idxs,n_v);CHKERRQ(ierr);
927         ierr = ISRestoreIndices(sub_schurs->is_vertices,&idxs);CHKERRQ(ierr);
928         cum += n_v;
929         factor_workaround = PETSC_TRUE;
930         schur_has_vertices = PETSC_TRUE;
931       }
932     }
933     size_schur = cum - n_I;
934     ierr = ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);CHKERRQ(ierr);
935 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
936     oldpin = sub_schurs->A->boundtocpu;
937     ierr = MatBindToCPU(sub_schurs->A,PETSC_TRUE);CHKERRQ(ierr);
938 #endif
939     if (cum == n) {
940       ierr = ISSetPermutation(is_A_all);CHKERRQ(ierr);
941       ierr = MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);CHKERRQ(ierr);
942     } else {
943       ierr = MatCreateSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
944     }
945 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
946     ierr = MatBindToCPU(sub_schurs->A,oldpin);CHKERRQ(ierr);
947 #endif
948     ierr = MatSetOptionsPrefix(A,sub_schurs->prefix);CHKERRQ(ierr);
949     ierr = MatAppendOptionsPrefix(A,"sub_schurs_");CHKERRQ(ierr);
950 
951     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
952        this is a workaround */
953     if (benign_n) {
954       Vec                    v,benign_AIIm1_ones;
955       ISLocalToGlobalMapping N_to_reor;
956       IS                     is_p0,is_p0_p;
957       PetscScalar            *cs_AIB,*AIIm1_data;
958       PetscInt               sizeA;
959 
960       ierr = ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);CHKERRQ(ierr);
961       ierr = ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);CHKERRQ(ierr);
962       ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);CHKERRQ(ierr);
963       ierr = ISDestroy(&is_p0);CHKERRQ(ierr);
964       ierr = MatCreateVecs(A,&v,&benign_AIIm1_ones);CHKERRQ(ierr);
965       ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
966       ierr = MatCreateSeqDense(PETSC_COMM_SELF,sizeA,benign_n,NULL,&benign_AIIm1_ones_mat);CHKERRQ(ierr);
967       ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,benign_n,NULL,&cs_AIB_mat);CHKERRQ(ierr);
968       ierr = MatDenseGetArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
969       ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
970       ierr = PetscMalloc1(benign_n,&is_p_r);CHKERRQ(ierr);
971       /* compute colsum of A_IB restricted to pressures */
972       for (i=0;i<benign_n;i++) {
973         const PetscScalar *array;
974         const PetscInt    *idxs;
975         PetscInt          j,nz;
976 
977         ierr = ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);CHKERRQ(ierr);
978         ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
979         ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
980         for (j=0;j<nz;j++) AIIm1_data[idxs[j]+sizeA*i] = 1.;
981         ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
982         ierr = VecPlaceArray(benign_AIIm1_ones,AIIm1_data+sizeA*i);CHKERRQ(ierr);
983         ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
984         ierr = VecResetArray(benign_AIIm1_ones);CHKERRQ(ierr);
985         ierr = VecGetArrayRead(v,&array);CHKERRQ(ierr);
986         for (j=0;j<size_schur;j++) {
987 #if defined(PETSC_USE_COMPLEX)
988           cs_AIB[i*size_schur + j] = (PetscRealPart(array[j+n_I])/nz + PETSC_i*(PetscImaginaryPart(array[j+n_I])/nz));
989 #else
990           cs_AIB[i*size_schur + j] = array[j+n_I]/nz;
991 #endif
992         }
993         ierr = VecRestoreArrayRead(v,&array);CHKERRQ(ierr);
994       }
995       ierr = MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
996       ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
997       ierr = VecDestroy(&v);CHKERRQ(ierr);
998       ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
999       ierr = MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);CHKERRQ(ierr);
1000       ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1001       ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1002       ierr = MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);CHKERRQ(ierr);
1003       ierr = ISDestroy(&is_p0_p);CHKERRQ(ierr);
1004       ierr = ISLocalToGlobalMappingDestroy(&N_to_reor);CHKERRQ(ierr);
1005     }
1006     ierr = MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_symmetric);CHKERRQ(ierr);
1007     ierr = MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
1008     ierr = MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
1009 
1010     /* for complexes, symmetric and hermitian at the same time implies null imaginary part */
1011     use_cholesky = (PetscBool)((use_potr || use_sytr) && sub_schurs->is_hermitian && sub_schurs->is_symmetric);
1012 
1013     /* when using the benign subspace trick, the local Schur complements are SPD */
1014     if (benign_trick) sub_schurs->is_posdef = PETSC_TRUE;
1015 
1016     if (n_I) {
1017       IS        is_schur;
1018       char      stype[64];
1019       PetscBool gpu;
1020 
1021       if (use_cholesky) {
1022         ierr = MatGetFactor(A,sub_schurs->mat_solver_type,MAT_FACTOR_CHOLESKY,&F);CHKERRQ(ierr);
1023       } else {
1024         ierr = MatGetFactor(A,sub_schurs->mat_solver_type,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
1025       }
1026       ierr = MatSetErrorIfFailure(A,PETSC_TRUE);CHKERRQ(ierr);
1027 
1028       /* subsets ordered last */
1029       ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is_schur);CHKERRQ(ierr);
1030       ierr = MatFactorSetSchurIS(F,is_schur);CHKERRQ(ierr);
1031       ierr = ISDestroy(&is_schur);CHKERRQ(ierr);
1032 
1033       /* factorization step */
1034       if (use_cholesky) {
1035         ierr = MatCholeskyFactorSymbolic(F,A,NULL,NULL);CHKERRQ(ierr);
1036 #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
1037         ierr = MatMumpsSetIcntl(F,19,2);CHKERRQ(ierr);
1038 #endif
1039         ierr = MatCholeskyFactorNumeric(F,A,NULL);CHKERRQ(ierr);
1040         S_lower_triangular = PETSC_TRUE;
1041       } else {
1042         ierr = MatLUFactorSymbolic(F,A,NULL,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,19,3);CHKERRQ(ierr);
1045 #endif
1046         ierr = MatLUFactorNumeric(F,A,NULL);CHKERRQ(ierr);
1047       }
1048       ierr = MatViewFromOptions(F,(PetscObject)A,"-mat_factor_view");CHKERRQ(ierr);
1049 
1050       if (matl_dbg_viewer) {
1051         Mat S;
1052         IS  is;
1053 
1054         ierr = PetscObjectSetName((PetscObject)A,"A");CHKERRQ(ierr);
1055         ierr = MatView(A,matl_dbg_viewer);CHKERRQ(ierr);
1056         ierr = MatFactorCreateSchurComplement(F,&S,NULL);CHKERRQ(ierr);
1057         ierr = PetscObjectSetName((PetscObject)S,"S");CHKERRQ(ierr);
1058         ierr = MatView(S,matl_dbg_viewer);CHKERRQ(ierr);
1059         ierr = MatDestroy(&S);CHKERRQ(ierr);
1060         ierr = ISCreateStride(PETSC_COMM_SELF,n_I,0,1,&is);CHKERRQ(ierr);
1061         ierr = PetscObjectSetName((PetscObject)is,"I");CHKERRQ(ierr);
1062         ierr = ISView(is,matl_dbg_viewer);CHKERRQ(ierr);
1063         ierr = ISDestroy(&is);CHKERRQ(ierr);
1064         ierr = ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is);CHKERRQ(ierr);
1065         ierr = PetscObjectSetName((PetscObject)is,"B");CHKERRQ(ierr);
1066         ierr = ISView(is,matl_dbg_viewer);CHKERRQ(ierr);
1067         ierr = ISDestroy(&is);CHKERRQ(ierr);
1068         ierr = PetscObjectSetName((PetscObject)is_A_all,"IA");CHKERRQ(ierr);
1069         ierr = ISView(is_A_all,matl_dbg_viewer);CHKERRQ(ierr);
1070       }
1071 
1072       /* get explicit Schur Complement computed during numeric factorization */
1073       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1074       ierr = PetscStrncpy(stype,MATSEQDENSE,sizeof(stype));CHKERRQ(ierr);
1075       ierr = PetscObjectTypeCompareAny((PetscObject)A,&gpu,MATSEQAIJVIENNACL,MATSEQAIJCUSPARSE,"");CHKERRQ(ierr);
1076       if (gpu) {
1077         ierr = PetscStrncpy(stype,MATSEQDENSECUDA,sizeof(stype));CHKERRQ(ierr);
1078       }
1079       ierr = PetscOptionsGetString(NULL,sub_schurs->prefix,"-sub_schurs_schur_mat_type",stype,sizeof(stype),NULL);CHKERRQ(ierr);
1080       ierr = MatConvert(S_all,stype,MAT_INPLACE_MATRIX,&S_all);CHKERRQ(ierr);
1081       ierr = MatSetOption(S_all,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
1082       ierr = MatSetOption(S_all,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
1083       ierr = MatGetType(S_all,&Stype);CHKERRQ(ierr);
1084 
1085       /* we can reuse the solvers if we are not using the economic version */
1086       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
1087       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
1088       if (!sub_schurs->is_posdef && factor_workaround && compute_Stilda && size_active_schur)
1089         reuse_solvers = factor_workaround = PETSC_FALSE;
1090 
1091       solver_S = PETSC_TRUE;
1092 
1093       /* update the Schur complement with the change of basis on the pressures */
1094       if (benign_n) {
1095         const PetscScalar *cs_AIB;
1096         PetscScalar       *S_data,*AIIm1_data;
1097         Mat               S2 = NULL,S3 = NULL; /* dbg */
1098         PetscScalar       *S2_data,*S3_data; /* dbg */
1099         Vec               v,benign_AIIm1_ones;
1100         PetscInt          sizeA;
1101 
1102         ierr = MatDenseGetArray(S_all,&S_data);CHKERRQ(ierr);
1103         ierr = MatCreateVecs(A,&v,&benign_AIIm1_ones);CHKERRQ(ierr);
1104         ierr = VecGetSize(v,&sizeA);CHKERRQ(ierr);
1105 #if defined(PETSC_HAVE_MUMPS)
1106         ierr = MatMumpsSetIcntl(F,26,0);CHKERRQ(ierr);
1107 #endif
1108 #if defined(PETSC_HAVE_MKL_PARDISO)
1109         ierr = MatMkl_PardisoSetCntl(F,70,1);CHKERRQ(ierr);
1110 #endif
1111         ierr = MatDenseGetArrayRead(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1112         ierr = MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1113         if (matl_dbg_viewer) {
1114           ierr = MatDuplicate(S_all,MAT_DO_NOT_COPY_VALUES,&S2);CHKERRQ(ierr);
1115           ierr = MatDuplicate(S_all,MAT_DO_NOT_COPY_VALUES,&S3);CHKERRQ(ierr);
1116           ierr = MatDenseGetArray(S2,&S2_data);CHKERRQ(ierr);
1117           ierr = MatDenseGetArray(S3,&S3_data);CHKERRQ(ierr);
1118         }
1119         for (i=0;i<benign_n;i++) {
1120           PetscScalar    *array,sum = 0.,one = 1.,*sums;
1121           const PetscInt *idxs;
1122           PetscInt       k,j,nz;
1123           PetscBLASInt   B_k,B_n;
1124 
1125           ierr = PetscCalloc1(benign_n,&sums);CHKERRQ(ierr);
1126           ierr = VecPlaceArray(benign_AIIm1_ones,AIIm1_data+sizeA*i);CHKERRQ(ierr);
1127           ierr = VecCopy(benign_AIIm1_ones,v);CHKERRQ(ierr);
1128           ierr = MatSolve(F,v,benign_AIIm1_ones);CHKERRQ(ierr);
1129           ierr = MatMult(A,benign_AIIm1_ones,v);CHKERRQ(ierr);
1130           ierr = VecResetArray(benign_AIIm1_ones);CHKERRQ(ierr);
1131           /* p0 dofs (eliminated) are excluded from the sums */
1132           for (k=0;k<benign_n;k++) {
1133             ierr = ISGetLocalSize(is_p_r[k],&nz);CHKERRQ(ierr);
1134             ierr = ISGetIndices(is_p_r[k],&idxs);CHKERRQ(ierr);
1135             for (j=0;j<nz-1;j++) sums[k] -= AIIm1_data[idxs[j]+sizeA*i];
1136             ierr = ISRestoreIndices(is_p_r[k],&idxs);CHKERRQ(ierr);
1137           }
1138           ierr = VecGetArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
1139           if (matl_dbg_viewer) {
1140             Vec  vv;
1141             char name[16];
1142 
1143             ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array+n_I,&vv);CHKERRQ(ierr);
1144             ierr = PetscSNPrintf(name,sizeof(name),"Pvs%D",i);CHKERRQ(ierr);
1145             ierr = PetscObjectSetName((PetscObject)vv,name);CHKERRQ(ierr);
1146             ierr = VecView(vv,matl_dbg_viewer);CHKERRQ(ierr);
1147           }
1148           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
1149           /* cs_AIB already scaled by 1./nz */
1150           B_k = 1;
1151           for (k=0;k<benign_n;k++) {
1152             sum  = sums[k];
1153             ierr = PetscBLASIntCast(size_schur,&B_n);CHKERRQ(ierr);
1154 
1155             if (PetscAbsScalar(sum) == 0.0) continue;
1156             if (k == i) {
1157               PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
1158               if (matl_dbg_viewer) {
1159                 PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S3_data,&B_n));
1160               }
1161             } else { /* XXX Is it correct to use symmetric rank-2 update with half of the sum? */
1162               sum /= 2.0;
1163               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));
1164               if (matl_dbg_viewer) {
1165                 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));
1166               }
1167             }
1168           }
1169           sum  = 1.;
1170           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));
1171           if (matl_dbg_viewer) {
1172             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));
1173           }
1174           ierr = VecRestoreArrayRead(v,(const PetscScalar**)&array);CHKERRQ(ierr);
1175           /* set p0 entry of AIIm1_ones to zero */
1176           ierr = ISGetLocalSize(is_p_r[i],&nz);CHKERRQ(ierr);
1177           ierr = ISGetIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1178           for (j=0;j<benign_n;j++) AIIm1_data[idxs[nz-1]+sizeA*j] = 0.;
1179           ierr = ISRestoreIndices(is_p_r[i],&idxs);CHKERRQ(ierr);
1180           ierr = PetscFree(sums);CHKERRQ(ierr);
1181         }
1182         ierr = VecDestroy(&benign_AIIm1_ones);CHKERRQ(ierr);
1183         if (matl_dbg_viewer) {
1184           ierr = MatDenseRestoreArray(S2,&S2_data);CHKERRQ(ierr);
1185           ierr = MatDenseRestoreArray(S3,&S3_data);CHKERRQ(ierr);
1186         }
1187         if (!S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1188           PetscInt k,j;
1189           for (k=0;k<size_schur;k++) {
1190             for (j=k;j<size_schur;j++) {
1191               S_data[j*size_schur+k] = PetscConj(S_data[k*size_schur+j]);
1192             }
1193           }
1194         }
1195 
1196         /* restore defaults */
1197 #if defined(PETSC_HAVE_MUMPS)
1198         ierr = MatMumpsSetIcntl(F,26,-1);CHKERRQ(ierr);
1199 #endif
1200 #if defined(PETSC_HAVE_MKL_PARDISO)
1201         ierr = MatMkl_PardisoSetCntl(F,70,0);CHKERRQ(ierr);
1202 #endif
1203         ierr = MatDenseRestoreArrayRead(cs_AIB_mat,&cs_AIB);CHKERRQ(ierr);
1204         ierr = MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);CHKERRQ(ierr);
1205         ierr = VecDestroy(&v);CHKERRQ(ierr);
1206         ierr = MatDenseRestoreArray(S_all,&S_data);CHKERRQ(ierr);
1207         if (matl_dbg_viewer) {
1208           Mat S;
1209 
1210           ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1211           ierr = MatFactorCreateSchurComplement(F,&S,NULL);CHKERRQ(ierr);
1212           ierr = PetscObjectSetName((PetscObject)S,"Sb");CHKERRQ(ierr);
1213           ierr = MatView(S,matl_dbg_viewer);CHKERRQ(ierr);
1214           ierr = MatDestroy(&S);CHKERRQ(ierr);
1215           ierr = PetscObjectSetName((PetscObject)S2,"S2P");CHKERRQ(ierr);
1216           ierr = MatView(S2,matl_dbg_viewer);CHKERRQ(ierr);
1217           ierr = PetscObjectSetName((PetscObject)S3,"S3P");CHKERRQ(ierr);
1218           ierr = MatView(S3,matl_dbg_viewer);CHKERRQ(ierr);
1219           ierr = PetscObjectSetName((PetscObject)cs_AIB_mat,"cs");CHKERRQ(ierr);
1220           ierr = MatView(cs_AIB_mat,matl_dbg_viewer);CHKERRQ(ierr);
1221           ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1222         }
1223         ierr = MatDestroy(&S2);CHKERRQ(ierr);
1224         ierr = MatDestroy(&S3);CHKERRQ(ierr);
1225       }
1226       if (!reuse_solvers) {
1227         for (i=0;i<benign_n;i++) {
1228           ierr = ISDestroy(&is_p_r[i]);CHKERRQ(ierr);
1229         }
1230         ierr = PetscFree(is_p_r);CHKERRQ(ierr);
1231         ierr = MatDestroy(&cs_AIB_mat);CHKERRQ(ierr);
1232         ierr = MatDestroy(&benign_AIIm1_ones_mat);CHKERRQ(ierr);
1233       }
1234     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
1235       ierr = MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);CHKERRQ(ierr);
1236       ierr = MatGetType(S_all,&Stype);CHKERRQ(ierr);
1237       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
1238       factor_workaround = PETSC_FALSE;
1239       solver_S = PETSC_FALSE;
1240     }
1241 
1242     if (reuse_solvers) {
1243       Mat                A_II,Afake;
1244       Vec                vec1_B;
1245       PCBDDCReuseSolvers msolv_ctx;
1246       PetscInt           n_R;
1247 
1248       if (sub_schurs->reuse_solver) {
1249         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1250       } else {
1251         ierr = PetscNew(&sub_schurs->reuse_solver);CHKERRQ(ierr);
1252       }
1253       msolv_ctx = sub_schurs->reuse_solver;
1254       ierr = MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
1255       ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
1256       msolv_ctx->F = F;
1257       ierr = MatCreateVecs(F,&msolv_ctx->sol,NULL);CHKERRQ(ierr);
1258       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
1259       {
1260         PetscScalar *array;
1261         PetscInt    n;
1262 
1263         ierr = VecGetLocalSize(msolv_ctx->sol,&n);CHKERRQ(ierr);
1264         ierr = VecGetArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1265         ierr = VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);CHKERRQ(ierr);
1266         ierr = VecRestoreArray(msolv_ctx->sol,&array);CHKERRQ(ierr);
1267       }
1268       msolv_ctx->has_vertices = schur_has_vertices;
1269 
1270       /* interior solver */
1271       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);CHKERRQ(ierr);
1272       ierr = PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);CHKERRQ(ierr);
1273       ierr = PCSetType(msolv_ctx->interior_solver,PCSHELL);CHKERRQ(ierr);
1274       ierr = PCShellSetName(msolv_ctx->interior_solver,"Interior solver (w/o Schur factorization)");CHKERRQ(ierr);
1275       ierr = PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);CHKERRQ(ierr);
1276       ierr = PCShellSetView(msolv_ctx->interior_solver,PCBDDCReuseSolvers_View);CHKERRQ(ierr);
1277       ierr = PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);CHKERRQ(ierr);
1278       ierr = PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);CHKERRQ(ierr);
1279 
1280       /* correction solver */
1281       ierr = PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->correction_solver);CHKERRQ(ierr);
1282       ierr = PCSetType(msolv_ctx->correction_solver,PCSHELL);CHKERRQ(ierr);
1283       ierr = PCShellSetName(msolv_ctx->correction_solver,"Correction solver (with Schur factorization)");CHKERRQ(ierr);
1284       ierr = PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);CHKERRQ(ierr);
1285       ierr = PCShellSetView(msolv_ctx->interior_solver,PCBDDCReuseSolvers_View);CHKERRQ(ierr);
1286       ierr = PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);CHKERRQ(ierr);
1287       ierr = PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);CHKERRQ(ierr);
1288 
1289       /* scatter and vecs for Schur complement solver */
1290       ierr = MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);CHKERRQ(ierr);
1291       ierr = MatCreateVecs(sub_schurs->S,&vec1_B,NULL);CHKERRQ(ierr);
1292       if (!schur_has_vertices) {
1293         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1294         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1295         ierr = PetscObjectReference((PetscObject)is_A_all);CHKERRQ(ierr);
1296         msolv_ctx->is_R = is_A_all;
1297       } else {
1298         IS              is_B_all;
1299         const PetscInt* idxs;
1300         PetscInt        dual,n_v,n;
1301 
1302         ierr = ISGetLocalSize(sub_schurs->is_vertices,&n_v);CHKERRQ(ierr);
1303         dual = size_schur - n_v;
1304         ierr = ISGetLocalSize(is_A_all,&n);CHKERRQ(ierr);
1305         ierr = ISGetIndices(is_A_all,&idxs);CHKERRQ(ierr);
1306         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);CHKERRQ(ierr);
1307         ierr = ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);CHKERRQ(ierr);
1308         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1309         ierr = ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);CHKERRQ(ierr);
1310         ierr = VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);CHKERRQ(ierr);
1311         ierr = ISDestroy(&is_B_all);CHKERRQ(ierr);
1312         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);CHKERRQ(ierr);
1313         ierr = ISRestoreIndices(is_A_all,&idxs);CHKERRQ(ierr);
1314       }
1315       ierr = ISGetLocalSize(msolv_ctx->is_R,&n_R);CHKERRQ(ierr);
1316       ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,n_R,n_R,0,NULL,&Afake);CHKERRQ(ierr);
1317       ierr = MatAssemblyBegin(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1318       ierr = MatAssemblyEnd(Afake,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1319       ierr = PCSetOperators(msolv_ctx->correction_solver,Afake,Afake);CHKERRQ(ierr);
1320       ierr = MatDestroy(&Afake);CHKERRQ(ierr);
1321       ierr = VecDestroy(&vec1_B);CHKERRQ(ierr);
1322 
1323       /* communicate benign info to solver context */
1324       if (benign_n) {
1325         PetscScalar *array;
1326 
1327         msolv_ctx->benign_n = benign_n;
1328         msolv_ctx->benign_zerodiag_subs = is_p_r;
1329         ierr = PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);CHKERRQ(ierr);
1330         msolv_ctx->benign_csAIB = cs_AIB_mat;
1331         ierr = MatCreateVecs(cs_AIB_mat,&msolv_ctx->benign_corr_work,NULL);CHKERRQ(ierr);
1332         ierr = VecGetArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1333         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array,&msolv_ctx->benign_dummy_schur_vec);CHKERRQ(ierr);
1334         ierr = VecRestoreArray(msolv_ctx->benign_corr_work,&array);CHKERRQ(ierr);
1335         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
1336       }
1337     } else {
1338       if (sub_schurs->reuse_solver) {
1339         ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
1340       }
1341       ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
1342     }
1343     ierr = MatDestroy(&A);CHKERRQ(ierr);
1344     ierr = ISDestroy(&is_A_all);CHKERRQ(ierr);
1345 
1346     /* Work arrays */
1347     ierr = PetscMalloc1(max_subset_size*max_subset_size,&work);CHKERRQ(ierr);
1348 
1349     /* S_Ej_all */
1350     cum = cum2 = 0;
1351     ierr = MatDenseGetArrayRead(S_all,&rS_data);CHKERRQ(ierr);
1352     ierr = MatSeqAIJGetArray(sub_schurs->S_Ej_all,&SEj_arr);CHKERRQ(ierr);
1353     if (compute_Stilda) {
1354       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&SEjinv_arr);CHKERRQ(ierr);
1355     }
1356     for (i=0;i<sub_schurs->n_subs;i++) {
1357       PetscInt j;
1358 
1359       /* get S_E */
1360       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1361       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
1362         PetscInt k;
1363         for (k=0;k<subset_size;k++) {
1364           for (j=k;j<subset_size;j++) {
1365             work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1366             work[j*subset_size+k] = PetscConj(rS_data[cum2+k*size_schur+j]);
1367           }
1368         }
1369       } else { /* just copy to workspace */
1370         PetscInt k;
1371         for (k=0;k<subset_size;k++) {
1372           for (j=0;j<subset_size;j++) {
1373             work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1374           }
1375         }
1376       }
1377       /* insert S_E values */
1378       if (sub_schurs->change) {
1379         Mat change_sub,SEj,T;
1380 
1381         /* change basis */
1382         ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1383         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1384         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1385           Mat T2;
1386           ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1387           ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1388           ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1389           ierr = MatDestroy(&T2);CHKERRQ(ierr);
1390         } else {
1391           ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1392         }
1393         ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1394         ierr = MatDestroy(&T);CHKERRQ(ierr);
1395         ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1.0,NULL,NULL);CHKERRQ(ierr);
1396         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1397       }
1398       if (deluxe) {
1399         ierr = PetscArraycpy(SEj_arr,work,subset_size*subset_size);CHKERRQ(ierr);
1400         /* if adaptivity is requested, invert S_E blocks */
1401         if (compute_Stilda) {
1402           Mat               M;
1403           const PetscScalar *vals;
1404           PetscBool         isdense,isdensecuda;
1405 
1406           ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&M);CHKERRQ(ierr);
1407           ierr = MatSetOption(M,MAT_SPD,sub_schurs->is_posdef);CHKERRQ(ierr);
1408           ierr = MatSetOption(M,MAT_HERMITIAN,sub_schurs->is_hermitian);CHKERRQ(ierr);
1409           if (!PetscBTLookup(sub_schurs->is_edge,i)) {
1410             ierr = MatSetType(M,Stype);CHKERRQ(ierr);
1411           }
1412           ierr = PetscObjectTypeCompare((PetscObject)M,MATSEQDENSE,&isdense);CHKERRQ(ierr);
1413           ierr = PetscObjectTypeCompare((PetscObject)M,MATSEQDENSECUDA,&isdensecuda);CHKERRQ(ierr);
1414           if (use_cholesky) {
1415             ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1416           } else {
1417             ierr = MatLUFactor(M,NULL,NULL,NULL);CHKERRQ(ierr);
1418           }
1419           if (isdense) {
1420             ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1421 #if defined(PETSC_HAVE_CUDA)
1422           } else if (isdensecuda) {
1423             ierr = MatSeqDenseCUDAInvertFactors_Private(M);CHKERRQ(ierr);
1424 #endif
1425           } else SETERRQ1(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"Not implemented for type %s",Stype);
1426           ierr = MatDenseGetArrayRead(M,&vals);CHKERRQ(ierr);
1427           ierr = PetscArraycpy(SEjinv_arr,vals,subset_size*subset_size);CHKERRQ(ierr);
1428           ierr = MatDenseRestoreArrayRead(M,&vals);CHKERRQ(ierr);
1429           ierr = MatDestroy(&M);CHKERRQ(ierr);
1430         }
1431       } else if (compute_Stilda) { /* not using deluxe */
1432         Mat         SEj;
1433         Vec         D;
1434         PetscScalar *array;
1435 
1436         ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1437         ierr = VecGetArray(Dall,&array);CHKERRQ(ierr);
1438         ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,array+cum,&D);CHKERRQ(ierr);
1439         ierr = VecRestoreArray(Dall,&array);CHKERRQ(ierr);
1440         ierr = VecShift(D,-1.);CHKERRQ(ierr);
1441         ierr = MatDiagonalScale(SEj,D,D);CHKERRQ(ierr);
1442         ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1443         ierr = VecDestroy(&D);CHKERRQ(ierr);
1444         ierr = PetscArraycpy(SEj_arr,work,subset_size*subset_size);CHKERRQ(ierr);
1445       }
1446       cum += subset_size;
1447       cum2 += subset_size*(size_schur + 1);
1448       SEj_arr += subset_size*subset_size;
1449       if (SEjinv_arr) SEjinv_arr += subset_size*subset_size;
1450     }
1451     ierr = MatDenseRestoreArrayRead(S_all,&rS_data);CHKERRQ(ierr);
1452     ierr = MatSeqAIJRestoreArray(sub_schurs->S_Ej_all,&SEj_arr);CHKERRQ(ierr);
1453     if (compute_Stilda) {
1454       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&SEjinv_arr);CHKERRQ(ierr);
1455     }
1456     if (solver_S) {
1457       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1458     }
1459 
1460     /* may prevent from unneeded copies, since MUMPS or MKL_Pardiso always use CPU memory
1461        however, preliminary tests indicate using GPUs is still faster in the solve phase */
1462 #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
1463     if (reuse_solvers) {
1464       Mat                  St;
1465       MatFactorSchurStatus st;
1466       PetscBool            flg = PETSC_FALSE;
1467 
1468       ierr = PetscOptionsGetBool(NULL,sub_schurs->prefix,"-sub_schurs_schur_pin_to_cpu",&flg,NULL);CHKERRQ(ierr);
1469       ierr = MatFactorGetSchurComplement(F,&St,&st);CHKERRQ(ierr);
1470       ierr = MatBindToCPU(St,flg);CHKERRQ(ierr);
1471       ierr = MatFactorRestoreSchurComplement(F,&St,st);CHKERRQ(ierr);
1472     }
1473 #endif
1474 
1475     schur_factor = NULL;
1476     if (compute_Stilda && size_active_schur) {
1477 
1478       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&SEjinv_arr);CHKERRQ(ierr);
1479       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
1480         ierr = PetscArraycpy(SEjinv_arr,work,size_schur*size_schur);CHKERRQ(ierr);
1481       } else {
1482         Mat S_all_inv=NULL;
1483 
1484         if (solver_S) {
1485           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
1486              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 */
1487           if (factor_workaround) {/* invert without calling MatFactorInvertSchurComplement, since we are hacking */
1488             PetscScalar *data;
1489             PetscInt     nd = 0;
1490 
1491             if (!use_potr) {
1492               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1493             }
1494             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1495             ierr = MatDenseGetArray(S_all_inv,&data);CHKERRQ(ierr);
1496             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1497               ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1498             }
1499 
1500             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
1501             if (schur_has_vertices) {
1502               Mat          M;
1503               PetscScalar *tdata;
1504               PetscInt     nv = 0, news;
1505 
1506               ierr = ISGetLocalSize(sub_schurs->is_vertices,&nv);CHKERRQ(ierr);
1507               news = size_active_schur + nv;
1508               ierr = PetscCalloc1(news*news,&tdata);CHKERRQ(ierr);
1509               for (i=0;i<size_active_schur;i++) {
1510                 ierr = PetscArraycpy(tdata+i*(news+1),data+i*(size_schur+1),size_active_schur-i);CHKERRQ(ierr);
1511                 ierr = PetscArraycpy(tdata+i*(news+1)+size_active_schur-i,data+i*size_schur+size_active_schur+nd,nv);CHKERRQ(ierr);
1512               }
1513               for (i=0;i<nv;i++) {
1514                 PetscInt k = i+size_active_schur;
1515                 ierr = PetscArraycpy(tdata+k*(news+1),data+(k+nd)*(size_schur+1),nv-i);CHKERRQ(ierr);
1516               }
1517 
1518               ierr = MatCreateSeqDense(PETSC_COMM_SELF,news,news,tdata,&M);CHKERRQ(ierr);
1519               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1520               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1521               /* save the factors */
1522               cum = 0;
1523               ierr = PetscMalloc1((size_active_schur*(size_active_schur +1))/2+nd,&schur_factor);CHKERRQ(ierr);
1524               for (i=0;i<size_active_schur;i++) {
1525                 ierr = PetscArraycpy(schur_factor+cum,tdata+i*(news+1),size_active_schur-i);CHKERRQ(ierr);
1526                 cum += size_active_schur - i;
1527               }
1528               for (i=0;i<nd;i++) schur_factor[cum+i] = PetscSqrtReal(PetscRealPart(data[(i+size_active_schur)*(size_schur+1)]));
1529               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1530               /* move back just the active dofs to the Schur complement */
1531               for (i=0;i<size_active_schur;i++) {
1532                 ierr = PetscArraycpy(data+i*size_schur,tdata+i*news,size_active_schur);CHKERRQ(ierr);
1533               }
1534               ierr = PetscFree(tdata);CHKERRQ(ierr);
1535               ierr = MatDestroy(&M);CHKERRQ(ierr);
1536             } else { /* we can factorize and invert just the activedofs */
1537               Mat         M;
1538               PetscScalar *aux;
1539 
1540               ierr = PetscMalloc1(nd,&aux);CHKERRQ(ierr);
1541               for (i=0;i<nd;i++) aux[i] = 1.0/data[(i+size_active_schur)*(size_schur+1)];
1542               ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_active_schur,size_active_schur,data,&M);CHKERRQ(ierr);
1543               ierr = MatSeqDenseSetLDA(M,size_schur);CHKERRQ(ierr);
1544               ierr = MatSetOption(M,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
1545               ierr = MatCholeskyFactor(M,NULL,NULL);CHKERRQ(ierr);
1546               ierr = MatSeqDenseInvertFactors_Private(M);CHKERRQ(ierr);
1547               ierr = MatDestroy(&M);CHKERRQ(ierr);
1548               ierr = MatCreateSeqDense(PETSC_COMM_SELF,size_schur,nd,data+size_active_schur*size_schur,&M);CHKERRQ(ierr);
1549               ierr = MatZeroEntries(M);CHKERRQ(ierr);
1550               ierr = MatDestroy(&M);CHKERRQ(ierr);
1551               ierr = MatCreateSeqDense(PETSC_COMM_SELF,nd,size_schur,data+size_active_schur,&M);CHKERRQ(ierr);
1552               ierr = MatSeqDenseSetLDA(M,size_schur);CHKERRQ(ierr);
1553               ierr = MatZeroEntries(M);CHKERRQ(ierr);
1554               ierr = MatDestroy(&M);CHKERRQ(ierr);
1555               for (i=0;i<nd;i++) data[(i+size_active_schur)*(size_schur+1)] = aux[i];
1556               ierr = PetscFree(aux);CHKERRQ(ierr);
1557             }
1558             ierr = MatDenseRestoreArray(S_all_inv,&data);CHKERRQ(ierr);
1559           } else { /* use MatFactor calls to invert S */
1560             ierr = MatFactorInvertSchurComplement(F);CHKERRQ(ierr);
1561             ierr = MatFactorGetSchurComplement(F,&S_all_inv,NULL);CHKERRQ(ierr);
1562           }
1563         } else { /* we need to invert explicitly since we are not using MatFactor for S */
1564           ierr = PetscObjectReference((PetscObject)S_all);CHKERRQ(ierr);
1565           S_all_inv = S_all;
1566           ierr = MatDenseGetArray(S_all_inv,&S_data);CHKERRQ(ierr);
1567           ierr = PetscBLASIntCast(size_schur,&B_N);CHKERRQ(ierr);
1568           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1569           if (use_potr) {
1570             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
1571             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1572             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
1573             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1574           } else if (use_sytr) {
1575             PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1576             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRF Lapack routine %d",(int)B_ierr);
1577             PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&B_N,S_data,&B_N,pivots,Bwork,&B_ierr));
1578             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRI Lapack routine %d",(int)B_ierr);
1579           } else {
1580             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
1581             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1582             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1583             if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1584           }
1585           ierr = PetscLogFlops(1.0*size_schur*size_schur*size_schur);CHKERRQ(ierr);
1586           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1587           ierr = MatDenseRestoreArray(S_all_inv,&S_data);CHKERRQ(ierr);
1588         }
1589         /* S_Ej_tilda_all */
1590         cum = cum2 = 0;
1591         ierr = MatDenseGetArrayRead(S_all_inv,&rS_data);CHKERRQ(ierr);
1592         for (i=0;i<sub_schurs->n_subs;i++) {
1593           PetscInt j;
1594 
1595           ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1596           /* get (St^-1)_E */
1597           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
1598              will be properly accessed later during adaptive selection */
1599           if (S_lower_triangular) {
1600             PetscInt k;
1601             if (sub_schurs->change) {
1602               for (k=0;k<subset_size;k++) {
1603                 for (j=k;j<subset_size;j++) {
1604                   work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1605                   work[j*subset_size+k] = work[k*subset_size+j];
1606                 }
1607               }
1608             } else {
1609               for (k=0;k<subset_size;k++) {
1610                 for (j=k;j<subset_size;j++) {
1611                   work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1612                 }
1613               }
1614             }
1615           } else {
1616             PetscInt k;
1617             for (k=0;k<subset_size;k++) {
1618               for (j=0;j<subset_size;j++) {
1619                 work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
1620               }
1621             }
1622           }
1623           if (sub_schurs->change) {
1624             Mat change_sub,SEj,T;
1625 
1626             /* change basis */
1627             ierr = KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);CHKERRQ(ierr);
1628             ierr = MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);CHKERRQ(ierr);
1629             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
1630               Mat T2;
1631               ierr = MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);CHKERRQ(ierr);
1632               ierr = MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1633               ierr = MatDestroy(&T2);CHKERRQ(ierr);
1634               ierr = MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);CHKERRQ(ierr);
1635             } else {
1636               ierr = MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);CHKERRQ(ierr);
1637             }
1638             ierr = MatCopy(T,SEj,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
1639             ierr = MatDestroy(&T);CHKERRQ(ierr);
1640             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
1641             ierr = MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1./PETSC_SMALL,NULL,NULL);CHKERRQ(ierr);
1642             ierr = MatDestroy(&SEj);CHKERRQ(ierr);
1643           }
1644           ierr = PetscArraycpy(SEjinv_arr,work,subset_size*subset_size);CHKERRQ(ierr);
1645           cum += subset_size;
1646           cum2 += subset_size*(size_schur + 1);
1647           SEjinv_arr += subset_size*subset_size;
1648         }
1649         ierr = MatDenseRestoreArrayRead(S_all_inv,&rS_data);CHKERRQ(ierr);
1650         if (solver_S) {
1651           if (schur_has_vertices) {
1652             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1653           } else {
1654             ierr = MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_INVERTED);CHKERRQ(ierr);
1655           }
1656         }
1657         ierr = MatDestroy(&S_all_inv);CHKERRQ(ierr);
1658       }
1659       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&SEjinv_arr);CHKERRQ(ierr);
1660 
1661       /* move back factors if needed */
1662       if (schur_has_vertices) {
1663         Mat      S_tmp;
1664         PetscInt nd = 0;
1665 
1666         if (!solver_S) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
1667         ierr = MatFactorGetSchurComplement(F,&S_tmp,NULL);CHKERRQ(ierr);
1668         if (use_potr) {
1669           PetscScalar *data;
1670 
1671           ierr = MatDenseGetArray(S_tmp,&data);CHKERRQ(ierr);
1672           ierr = PetscArrayzero(data,size_schur*size_schur);CHKERRQ(ierr);
1673 
1674           if (S_lower_triangular) {
1675             cum = 0;
1676             for (i=0;i<size_active_schur;i++) {
1677               ierr = PetscArraycpy(data+i*(size_schur+1),schur_factor+cum,size_active_schur-i);CHKERRQ(ierr);
1678               cum += size_active_schur-i;
1679 	    }
1680           } else {
1681             ierr = PetscArraycpy(data,schur_factor,size_schur*size_schur);CHKERRQ(ierr);
1682           }
1683           if (sub_schurs->is_dir) {
1684             ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1685 	    for (i=0;i<nd;i++) {
1686 	      data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
1687 	    }
1688           }
1689           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
1690              set the diagonal entry of the Schur factor to a very large value */
1691           for (i=size_active_schur+nd;i<size_schur;i++) {
1692             data[i*(size_schur+1)] = infty;
1693           }
1694           ierr = MatDenseRestoreArray(S_tmp,&data);CHKERRQ(ierr);
1695         } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
1696         ierr = MatFactorRestoreSchurComplement(F,&S_tmp,MAT_FACTOR_SCHUR_FACTORED);CHKERRQ(ierr);
1697       }
1698     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
1699       PetscScalar *data;
1700       PetscInt    nd = 0;
1701 
1702       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
1703         ierr = ISGetLocalSize(sub_schurs->is_dir,&nd);CHKERRQ(ierr);
1704       }
1705       ierr = MatFactorGetSchurComplement(F,&S_all,NULL);CHKERRQ(ierr);
1706       ierr = MatDenseGetArray(S_all,&data);CHKERRQ(ierr);
1707       for (i=0;i<size_active_schur;i++) {
1708         ierr = PetscArrayzero(data+i*size_schur+size_active_schur,size_schur-size_active_schur);CHKERRQ(ierr);
1709       }
1710       for (i=size_active_schur+nd;i<size_schur;i++) {
1711         ierr = PetscArrayzero(data+i*size_schur+size_active_schur,size_schur-size_active_schur);CHKERRQ(ierr);
1712         data[i*(size_schur+1)] = infty;
1713       }
1714       ierr = MatDenseRestoreArray(S_all,&data);CHKERRQ(ierr);
1715       ierr = MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);CHKERRQ(ierr);
1716     }
1717     ierr = PetscFree(work);CHKERRQ(ierr);
1718     ierr = PetscFree(schur_factor);CHKERRQ(ierr);
1719     ierr = VecDestroy(&Dall);CHKERRQ(ierr);
1720   }
1721   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1722   ierr = MatDestroy(&S_all);CHKERRQ(ierr);
1723   ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
1724   ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
1725   ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
1726   ierr = MatDestroy(&F);CHKERRQ(ierr);
1727 
1728   ierr = PetscMalloc1(sub_schurs->n_subs,&nnz);CHKERRQ(ierr);
1729   for (i=0;i<sub_schurs->n_subs;i++) {
1730     ierr = ISGetLocalSize(sub_schurs->is_subs[i],&nnz[i]);CHKERRQ(ierr);
1731   }
1732   ierr = ISCreateGeneral(PETSC_COMM_SELF,sub_schurs->n_subs,nnz,PETSC_OWN_POINTER,&is_I_layer);CHKERRQ(ierr);
1733   ierr = MatSetVariableBlockSizes(sub_schurs->S_Ej_all,sub_schurs->n_subs,nnz);CHKERRQ(ierr);
1734   ierr = MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1735   ierr = MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1736   if (compute_Stilda) {
1737     ierr = MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_tilda_all,sub_schurs->n_subs,nnz);CHKERRQ(ierr);
1738     ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1739     ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1740     if (deluxe) {
1741       ierr = MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_inv_all,sub_schurs->n_subs,nnz);CHKERRQ(ierr);
1742       ierr = MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1743       ierr = MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1744     }
1745   }
1746   ierr = ISDestroy(&is_I_layer);CHKERRQ(ierr);
1747 
1748   /* Get local part of (\sum_j S_Ej) */
1749   if (!sub_schurs->sum_S_Ej_all) {
1750     ierr = MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1751   }
1752   ierr = VecSet(gstash,0.0);CHKERRQ(ierr);
1753   ierr = MatSeqAIJGetArray(sub_schurs->S_Ej_all,&stasharray);CHKERRQ(ierr);
1754   ierr = VecPlaceArray(lstash,stasharray);CHKERRQ(ierr);
1755   ierr = VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1756   ierr = VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1757   ierr = MatSeqAIJRestoreArray(sub_schurs->S_Ej_all,&stasharray);CHKERRQ(ierr);
1758   ierr = VecResetArray(lstash);CHKERRQ(ierr);
1759   ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all,&stasharray);CHKERRQ(ierr);
1760   ierr = VecPlaceArray(lstash,stasharray);CHKERRQ(ierr);
1761   ierr = VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1762   ierr = VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1763   ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all,&stasharray);CHKERRQ(ierr);
1764   ierr = VecResetArray(lstash);CHKERRQ(ierr);
1765 
1766   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
1767   if (compute_Stilda) {
1768     ierr = VecSet(gstash,0.0);CHKERRQ(ierr);
1769     ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&stasharray);CHKERRQ(ierr);
1770     ierr = VecPlaceArray(lstash,stasharray);CHKERRQ(ierr);
1771     ierr = VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1772     ierr = VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1773     ierr = VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1774     ierr = VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1775     ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&stasharray);CHKERRQ(ierr);
1776     ierr = VecResetArray(lstash);CHKERRQ(ierr);
1777     if (deluxe) {
1778       ierr = VecSet(gstash,0.0);CHKERRQ(ierr);
1779       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&stasharray);CHKERRQ(ierr);
1780       ierr = VecPlaceArray(lstash,stasharray);CHKERRQ(ierr);
1781       ierr = VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1782       ierr = VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1783       ierr = VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1784       ierr = VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1785       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&stasharray);CHKERRQ(ierr);
1786       ierr = VecResetArray(lstash);CHKERRQ(ierr);
1787     } else {
1788       PetscScalar *array;
1789       PetscInt    cum;
1790 
1791       ierr = MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1792       cum = 0;
1793       for (i=0;i<sub_schurs->n_subs;i++) {
1794         ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1795         ierr = PetscBLASIntCast(subset_size,&B_N);CHKERRQ(ierr);
1796         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1797         if (use_potr) {
1798           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
1799           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRF Lapack routine %d",(int)B_ierr);
1800           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
1801           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in POTRI Lapack routine %d",(int)B_ierr);
1802         } else if (use_sytr) {
1803           PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1804           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRF Lapack routine %d",(int)B_ierr);
1805           PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&B_N,array+cum,&B_N,pivots,Bwork,&B_ierr));
1806           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYTRI Lapack routine %d",(int)B_ierr);
1807         } else {
1808           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
1809           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRF Lapack routine %d",(int)B_ierr);
1810           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
1811           if (B_ierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GETRI Lapack routine %d",(int)B_ierr);
1812         }
1813         ierr = PetscLogFlops(1.0*subset_size*subset_size*subset_size);CHKERRQ(ierr);
1814         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1815         cum += subset_size*subset_size;
1816       }
1817       ierr = MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array);CHKERRQ(ierr);
1818       ierr = PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1819       ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1820       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
1821     }
1822   }
1823   ierr = VecDestroy(&lstash);CHKERRQ(ierr);
1824   ierr = VecDestroy(&gstash);CHKERRQ(ierr);
1825   ierr = VecScatterDestroy(&sstash);CHKERRQ(ierr);
1826 
1827   if (matl_dbg_viewer) {
1828     PetscInt cum;
1829 
1830     if (sub_schurs->S_Ej_all) {
1831       ierr = PetscObjectSetName((PetscObject)sub_schurs->S_Ej_all,"SE");CHKERRQ(ierr);
1832       ierr = MatView(sub_schurs->S_Ej_all,matl_dbg_viewer);CHKERRQ(ierr);
1833     }
1834     if (sub_schurs->sum_S_Ej_all) {
1835       ierr = PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_all,"SSE");CHKERRQ(ierr);
1836       ierr = MatView(sub_schurs->sum_S_Ej_all,matl_dbg_viewer);CHKERRQ(ierr);
1837     }
1838     if (sub_schurs->sum_S_Ej_inv_all) {
1839       ierr = PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_inv_all,"SSEm");CHKERRQ(ierr);
1840       ierr = MatView(sub_schurs->sum_S_Ej_inv_all,matl_dbg_viewer);CHKERRQ(ierr);
1841     }
1842     if (sub_schurs->sum_S_Ej_tilda_all) {
1843       ierr = PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_tilda_all,"SSEt");CHKERRQ(ierr);
1844       ierr = MatView(sub_schurs->sum_S_Ej_tilda_all,matl_dbg_viewer);CHKERRQ(ierr);
1845     }
1846     for (i=0,cum=0;i<sub_schurs->n_subs;i++) {
1847       IS   is;
1848       char name[16];
1849 
1850       ierr = PetscSNPrintf(name,sizeof(name),"IE%D",i);CHKERRQ(ierr);
1851       ierr = ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);CHKERRQ(ierr);
1852       ierr = ISCreateStride(PETSC_COMM_SELF,subset_size,cum,1,&is);CHKERRQ(ierr);
1853       ierr = PetscObjectSetName((PetscObject)is,name);CHKERRQ(ierr);
1854       ierr = ISView(is,matl_dbg_viewer);CHKERRQ(ierr);
1855       ierr = ISDestroy(&is);CHKERRQ(ierr);
1856       cum += subset_size;
1857     }
1858   }
1859 
1860   /* free workspace */
1861   ierr = PetscViewerDestroy(&matl_dbg_viewer);CHKERRQ(ierr);
1862   ierr = PetscFree2(Bwork,pivots);CHKERRQ(ierr);
1863   ierr = PetscCommDestroy(&comm_n);CHKERRQ(ierr);
1864   PetscFunctionReturn(0);
1865 }
1866 
1867 PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, const char* prefix, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc)
1868 {
1869   IS              *faces,*edges,*all_cc,vertices;
1870   PetscInt        i,n_faces,n_edges,n_all_cc;
1871   PetscBool       is_sorted,ispardiso,ismumps;
1872   PetscErrorCode  ierr;
1873 
1874   PetscFunctionBegin;
1875   ierr = ISSorted(is_I,&is_sorted);CHKERRQ(ierr);
1876   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_I),PETSC_ERR_PLIB,"IS for I dofs should be shorted");
1877   ierr = ISSorted(is_B,&is_sorted);CHKERRQ(ierr);
1878   if (!is_sorted) SETERRQ(PetscObjectComm((PetscObject)is_B),PETSC_ERR_PLIB,"IS for B dofs should be shorted");
1879 
1880   /* reset any previous data */
1881   ierr = PCBDDCSubSchursReset(sub_schurs);CHKERRQ(ierr);
1882 
1883   /* get index sets for faces and edges (already sorted by global ordering) */
1884   ierr = PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1885   n_all_cc = n_faces+n_edges;
1886   ierr = PetscBTCreate(n_all_cc,&sub_schurs->is_edge);CHKERRQ(ierr);
1887   ierr = PetscMalloc1(n_all_cc,&all_cc);CHKERRQ(ierr);
1888   for (i=0;i<n_faces;i++) {
1889     if (copycc) {
1890       ierr = ISDuplicate(faces[i],&all_cc[i]);CHKERRQ(ierr);
1891     } else {
1892       ierr = PetscObjectReference((PetscObject)faces[i]);CHKERRQ(ierr);
1893       all_cc[i] = faces[i];
1894     }
1895   }
1896   for (i=0;i<n_edges;i++) {
1897     if (copycc) {
1898       ierr = ISDuplicate(edges[i],&all_cc[n_faces+i]);CHKERRQ(ierr);
1899     } else {
1900       ierr = PetscObjectReference((PetscObject)edges[i]);CHKERRQ(ierr);
1901       all_cc[n_faces+i] = edges[i];
1902     }
1903     ierr = PetscBTSet(sub_schurs->is_edge,n_faces+i);CHKERRQ(ierr);
1904   }
1905   ierr = PetscObjectReference((PetscObject)vertices);CHKERRQ(ierr);
1906   sub_schurs->is_vertices = vertices;
1907   ierr = PCBDDCGraphRestoreCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);CHKERRQ(ierr);
1908   sub_schurs->is_dir = NULL;
1909   ierr = PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);CHKERRQ(ierr);
1910 
1911   /* Determine if MatFactor can be used */
1912   ierr = PetscStrallocpy(prefix,&sub_schurs->prefix);CHKERRQ(ierr);
1913 #if defined(PETSC_HAVE_MUMPS)
1914   ierr = PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERMUMPS,64);CHKERRQ(ierr);
1915 #elif defined(PETSC_HAVE_MKL_PARDISO)
1916   ierr = PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERMKL_PARDISO,64);CHKERRQ(ierr);
1917 #else
1918   ierr = PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERPETSC,64);CHKERRQ(ierr);
1919 #endif
1920 #if defined(PETSC_USE_COMPLEX)
1921   sub_schurs->is_hermitian  = PETSC_FALSE; /* Hermitian Cholesky is not supported by PETSc and external packages */
1922 #else
1923   sub_schurs->is_hermitian  = PETSC_TRUE;
1924 #endif
1925   sub_schurs->is_posdef     = PETSC_TRUE;
1926   sub_schurs->is_symmetric  = PETSC_TRUE;
1927   sub_schurs->debug         = PETSC_FALSE;
1928   sub_schurs->restrict_comm = PETSC_FALSE;
1929   ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)graph->l2gmap),sub_schurs->prefix,"BDDC sub_schurs options","PC");CHKERRQ(ierr);
1930   ierr = PetscOptionsString("-sub_schurs_mat_solver_type","Specific direct solver to use",NULL,sub_schurs->mat_solver_type,sub_schurs->mat_solver_type,64,NULL);CHKERRQ(ierr);
1931   ierr = PetscOptionsBool("-sub_schurs_symmetric","Symmetric problem",NULL,sub_schurs->is_symmetric,&sub_schurs->is_symmetric,NULL);CHKERRQ(ierr);
1932   ierr = PetscOptionsBool("-sub_schurs_hermitian","Hermitian problem",NULL,sub_schurs->is_hermitian,&sub_schurs->is_hermitian,NULL);CHKERRQ(ierr);
1933   ierr = PetscOptionsBool("-sub_schurs_posdef","Positive definite problem",NULL,sub_schurs->is_posdef,&sub_schurs->is_posdef,NULL);CHKERRQ(ierr);
1934   ierr = PetscOptionsBool("-sub_schurs_restrictcomm","Restrict communicator on active processes only",NULL,sub_schurs->restrict_comm,&sub_schurs->restrict_comm,NULL);CHKERRQ(ierr);
1935   ierr = PetscOptionsBool("-sub_schurs_debug","Debug output",NULL,sub_schurs->debug,&sub_schurs->debug,NULL);CHKERRQ(ierr);
1936   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1937   ierr = PetscStrcmp(sub_schurs->mat_solver_type,MATSOLVERMUMPS,&ismumps);CHKERRQ(ierr);
1938   ierr = PetscStrcmp(sub_schurs->mat_solver_type,MATSOLVERMKL_PARDISO,&ispardiso);CHKERRQ(ierr);
1939   sub_schurs->schur_explicit = (PetscBool)(ispardiso || ismumps);
1940 
1941   /* for reals, symmetric and hermitian are synonims */
1942 #if !defined(PETSC_USE_COMPLEX)
1943   sub_schurs->is_symmetric = (PetscBool)(sub_schurs->is_symmetric && sub_schurs->is_hermitian);
1944   sub_schurs->is_hermitian = sub_schurs->is_symmetric;
1945 #endif
1946 
1947   ierr = PetscObjectReference((PetscObject)is_I);CHKERRQ(ierr);
1948   sub_schurs->is_I = is_I;
1949   ierr = PetscObjectReference((PetscObject)is_B);CHKERRQ(ierr);
1950   sub_schurs->is_B = is_B;
1951   ierr = PetscObjectReference((PetscObject)graph->l2gmap);CHKERRQ(ierr);
1952   sub_schurs->l2gmap = graph->l2gmap;
1953   ierr = PetscObjectReference((PetscObject)BtoNmap);CHKERRQ(ierr);
1954   sub_schurs->BtoNmap = BtoNmap;
1955   sub_schurs->n_subs = n_all_cc;
1956   sub_schurs->is_subs = all_cc;
1957   sub_schurs->S_Ej_all = NULL;
1958   sub_schurs->sum_S_Ej_all = NULL;
1959   sub_schurs->sum_S_Ej_inv_all = NULL;
1960   sub_schurs->sum_S_Ej_tilda_all = NULL;
1961   sub_schurs->is_Ej_all = NULL;
1962   PetscFunctionReturn(0);
1963 }
1964 
1965 PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
1966 {
1967   PCBDDCSubSchurs schurs_ctx;
1968   PetscErrorCode  ierr;
1969 
1970   PetscFunctionBegin;
1971   ierr = PetscNew(&schurs_ctx);CHKERRQ(ierr);
1972   schurs_ctx->n_subs = 0;
1973   *sub_schurs = schurs_ctx;
1974   PetscFunctionReturn(0);
1975 }
1976 
1977 PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
1978 {
1979   PetscInt       i;
1980   PetscErrorCode ierr;
1981 
1982   PetscFunctionBegin;
1983   if (!sub_schurs) PetscFunctionReturn(0);
1984   ierr = PetscFree(sub_schurs->prefix);CHKERRQ(ierr);
1985   ierr = MatDestroy(&sub_schurs->A);CHKERRQ(ierr);
1986   ierr = MatDestroy(&sub_schurs->S);CHKERRQ(ierr);
1987   ierr = ISDestroy(&sub_schurs->is_I);CHKERRQ(ierr);
1988   ierr = ISDestroy(&sub_schurs->is_B);CHKERRQ(ierr);
1989   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);CHKERRQ(ierr);
1990   ierr = ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);CHKERRQ(ierr);
1991   ierr = MatDestroy(&sub_schurs->S_Ej_all);CHKERRQ(ierr);
1992   ierr = MatDestroy(&sub_schurs->sum_S_Ej_all);CHKERRQ(ierr);
1993   ierr = MatDestroy(&sub_schurs->sum_S_Ej_inv_all);CHKERRQ(ierr);
1994   ierr = MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);CHKERRQ(ierr);
1995   ierr = ISDestroy(&sub_schurs->is_Ej_all);CHKERRQ(ierr);
1996   ierr = ISDestroy(&sub_schurs->is_vertices);CHKERRQ(ierr);
1997   ierr = ISDestroy(&sub_schurs->is_dir);CHKERRQ(ierr);
1998   ierr = PetscBTDestroy(&sub_schurs->is_edge);CHKERRQ(ierr);
1999   for (i=0;i<sub_schurs->n_subs;i++) {
2000     ierr = ISDestroy(&sub_schurs->is_subs[i]);CHKERRQ(ierr);
2001   }
2002   if (sub_schurs->n_subs) {
2003     ierr = PetscFree(sub_schurs->is_subs);CHKERRQ(ierr);
2004   }
2005   if (sub_schurs->reuse_solver) {
2006     ierr = PCBDDCReuseSolversReset(sub_schurs->reuse_solver);CHKERRQ(ierr);
2007   }
2008   ierr = PetscFree(sub_schurs->reuse_solver);CHKERRQ(ierr);
2009   if (sub_schurs->change) {
2010     for (i=0;i<sub_schurs->n_subs;i++) {
2011       ierr = KSPDestroy(&sub_schurs->change[i]);CHKERRQ(ierr);
2012       ierr = ISDestroy(&sub_schurs->change_primal_sub[i]);CHKERRQ(ierr);
2013     }
2014   }
2015   ierr = PetscFree(sub_schurs->change);CHKERRQ(ierr);
2016   ierr = PetscFree(sub_schurs->change_primal_sub);CHKERRQ(ierr);
2017   sub_schurs->n_subs = 0;
2018   PetscFunctionReturn(0);
2019 }
2020 
2021 PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs* sub_schurs)
2022 {
2023   PetscErrorCode ierr;
2024 
2025   PetscFunctionBegin;
2026   ierr = PCBDDCSubSchursReset(*sub_schurs);CHKERRQ(ierr);
2027   ierr = PetscFree(*sub_schurs);CHKERRQ(ierr);
2028   PetscFunctionReturn(0);
2029 }
2030 
2031 PETSC_STATIC_INLINE PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
2032 {
2033   PetscInt       i,j,n;
2034   PetscErrorCode ierr;
2035 
2036   PetscFunctionBegin;
2037   n = 0;
2038   for (i=-n_prev;i<0;i++) {
2039     PetscInt start_dof = queue_tip[i];
2040     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
2041       PetscInt dof = adjncy[j];
2042       if (!PetscBTLookup(touched,dof)) {
2043         ierr = PetscBTSet(touched,dof);CHKERRQ(ierr);
2044         queue_tip[n] = dof;
2045         n++;
2046       }
2047     }
2048   }
2049   *n_added = n;
2050   PetscFunctionReturn(0);
2051 }
2052