xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision b7d8b9f8d1200181c0d1a3244f3c8804b4e1de29)
1 #include "bddc.h"
2 #include "bddcprivate.h"
3 #include <petscblaslapack.h>
4 
5 #undef __FUNCT__
6 #define __FUNCT__ "PCBDDCResetCustomization"
7 PetscErrorCode PCBDDCResetCustomization(PC pc)
8 {
9   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
10   PetscInt       i;
11   PetscErrorCode ierr;
12 
13   PetscFunctionBegin;
14   ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
15   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
16   ierr = MatNullSpaceDestroy(&pcbddc->NullSpace);CHKERRQ(ierr);
17   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
18   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
19   for (i=0;i<pcbddc->n_ISForDofs;i++) {
20     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
21   }
22   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
23   PetscFunctionReturn(0);
24 }
25 
26 #undef __FUNCT__
27 #define __FUNCT__ "PCBDDCResetTopography"
28 PetscErrorCode PCBDDCResetTopography(PC pc)
29 {
30   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
31   PetscErrorCode ierr;
32 
33   PetscFunctionBegin;
34   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
35   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
36   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
37   PetscFunctionReturn(0);
38 }
39 
40 #undef __FUNCT__
41 #define __FUNCT__ "PCBDDCResetSolvers"
42 PetscErrorCode PCBDDCResetSolvers(PC pc)
43 {
44   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
45   PetscErrorCode ierr;
46 
47   PetscFunctionBegin;
48   ierr = VecDestroy(&pcbddc->temp_solution);CHKERRQ(ierr);
49   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
50   ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
51   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
52   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
53   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
54   ierr = MatDestroy(&pcbddc->coarse_mat);CHKERRQ(ierr);
55   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
56   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
57   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
58   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
59   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
60   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
61   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
62   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
63   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
64   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
65   ierr = VecDestroy(&pcbddc->vec4_D);CHKERRQ(ierr);
66   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
67   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
68   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
69   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
70   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
71   ierr = PetscFree(pcbddc->local_primal_indices);CHKERRQ(ierr);
72   ierr = PetscFree(pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
73   ierr = PetscFree(pcbddc->replicated_local_primal_values);CHKERRQ(ierr);
74   ierr = PetscFree(pcbddc->local_primal_displacements);CHKERRQ(ierr);
75   ierr = PetscFree(pcbddc->local_primal_sizes);CHKERRQ(ierr);
76   PetscFunctionReturn(0);
77 }
78 
79 #undef __FUNCT__
80 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
81 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
82 {
83   PetscErrorCode ierr;
84   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
85 
86   PetscFunctionBegin;
87   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
88   if (pcbddc->local_auxmat1) {
89     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
90     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
91   }
92   PetscFunctionReturn(0);
93 }
94 
95 #undef __FUNCT__
96 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
97 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
98 {
99   PetscErrorCode ierr;
100   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
101   PC_IS*            pcis = (PC_IS*)  (pc->data);
102   const PetscScalar zero = 0.0;
103 
104   PetscFunctionBegin;
105   /* Application of PHI^T (or PSI^T)  */
106   if (pcbddc->coarse_psi_B) {
107     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
108     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
109   } else {
110     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
111     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
112   }
113   /* Scatter data of coarse_rhs */
114   if (pcbddc->coarse_rhs) { ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr); }
115   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
116 
117   /* Local solution on R nodes */
118   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
119   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
120   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
121   if (pcbddc->inexact_prec_type) {
122     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
123     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
124   }
125   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
126   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
127   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
128   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
129   if (pcbddc->inexact_prec_type) {
130     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
131     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
132   }
133 
134   /* Coarse solution */
135   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
136   if (pcbddc->coarse_rhs) { /* TODO remove null space when doing multilevel */
137     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
138   }
139   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
140   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
141 
142   /* Sum contributions from two levels */
143   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
144   if (pcbddc->inexact_prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
145   PetscFunctionReturn(0);
146 }
147 
148 #undef __FUNCT__
149 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
150 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
151 {
152   PetscErrorCode ierr;
153   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
154 
155   PetscFunctionBegin;
156   switch (pcbddc->coarse_communications_type) {
157     case SCATTERS_BDDC:
158       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
159       break;
160     case GATHERS_BDDC:
161       break;
162   }
163   PetscFunctionReturn(0);
164 }
165 
166 #undef __FUNCT__
167 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
168 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
169 {
170   PetscErrorCode ierr;
171   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
172   PetscScalar*   array_to;
173   PetscScalar*   array_from;
174   MPI_Comm       comm;
175   PetscInt       i;
176 
177   PetscFunctionBegin;
178   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
179   switch (pcbddc->coarse_communications_type) {
180     case SCATTERS_BDDC:
181       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
182       break;
183     case GATHERS_BDDC:
184       if (vec_from) {
185         ierr = VecGetArray(vec_from,&array_from);CHKERRQ(ierr);
186       }
187       if (vec_to) {
188         ierr = VecGetArray(vec_to,&array_to);CHKERRQ(ierr);
189       }
190       switch(pcbddc->coarse_problem_type){
191         case SEQUENTIAL_BDDC:
192           if (smode == SCATTER_FORWARD) {
193             ierr = MPI_Gatherv(&array_from[0],pcbddc->local_primal_size,MPIU_SCALAR,&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,0,comm);CHKERRQ(ierr);
194             if (vec_to) {
195               if (imode == ADD_VALUES) {
196                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
197                   array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
198                 }
199               } else {
200                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
201                   array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
202                 }
203               }
204             }
205           } else {
206             if (vec_from) {
207               if (imode == ADD_VALUES) {
208                 MPI_Comm vec_from_comm;
209                 ierr = PetscObjectGetComm((PetscObject)(vec_from),&vec_from_comm);CHKERRQ(ierr);
210                 SETERRQ2(vec_from_comm,PETSC_ERR_SUP,"Unsupported insert mode ADD_VALUES for SCATTER_REVERSE in %s for case %d\n",__FUNCT__,pcbddc->coarse_problem_type);
211               }
212               for (i=0;i<pcbddc->replicated_primal_size;i++) {
213                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
214               }
215             }
216             ierr = MPI_Scatterv(&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,&array_to[0],pcbddc->local_primal_size,MPIU_SCALAR,0,comm);CHKERRQ(ierr);
217           }
218           break;
219         case REPLICATED_BDDC:
220           if (smode == SCATTER_FORWARD) {
221             ierr = MPI_Allgatherv(&array_from[0],pcbddc->local_primal_size,MPIU_SCALAR,&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,comm);CHKERRQ(ierr);
222             if (imode == ADD_VALUES) {
223               for (i=0;i<pcbddc->replicated_primal_size;i++) {
224                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
225               }
226             } else {
227               for (i=0;i<pcbddc->replicated_primal_size;i++) {
228                 array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
229               }
230             }
231           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
232             if (imode == ADD_VALUES) {
233               for (i=0;i<pcbddc->local_primal_size;i++) {
234                 array_to[i]+=array_from[pcbddc->local_primal_indices[i]];
235               }
236             } else {
237               for (i=0;i<pcbddc->local_primal_size;i++) {
238                 array_to[i]=array_from[pcbddc->local_primal_indices[i]];
239               }
240             }
241           }
242           break;
243         case MULTILEVEL_BDDC:
244           break;
245         case PARALLEL_BDDC:
246           break;
247       }
248       if (vec_from) {
249         ierr = VecRestoreArray(vec_from,&array_from);CHKERRQ(ierr);
250       }
251       if (vec_to) {
252         ierr = VecRestoreArray(vec_to,&array_to);CHKERRQ(ierr);
253       }
254       break;
255   }
256   PetscFunctionReturn(0);
257 }
258 
259 /* uncomment for testing purposes */
260 /* #define PETSC_MISSING_LAPACK_GESVD 1 */
261 #undef __FUNCT__
262 #define __FUNCT__ "PCBDDCConstraintsSetUp"
263 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
264 {
265   PetscErrorCode    ierr;
266   PC_IS*            pcis = (PC_IS*)(pc->data);
267   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
268   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
269   /* constraint and (optionally) change of basis matrix implemented as SeqAIJ */
270   MatType           impMatType=MATSEQAIJ;
271   /* one and zero */
272   PetscScalar       one=1.0,zero=0.0;
273   /* space to store constraints and their local indices */
274   PetscScalar       *temp_quadrature_constraint;
275   PetscInt          *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B;
276   /* iterators */
277   PetscInt          i,j,k,total_counts,temp_start_ptr;
278   /* stuff to store connected components stored in pcbddc->mat_graph */
279   IS                ISForVertices,*ISForFaces,*ISForEdges,*used_IS;
280   PetscInt          n_ISForFaces,n_ISForEdges;
281   PetscBool         get_faces,get_edges,get_vertices;
282   /* near null space stuff */
283   MatNullSpace      nearnullsp;
284   const Vec         *nearnullvecs;
285   Vec               *localnearnullsp;
286   PetscBool         nnsp_has_cnst;
287   PetscInt          nnsp_size;
288   PetscScalar       *array;
289   /* BLAS integers */
290   PetscBLASInt      Bs,Bt,lwork,lierr,Bone=1;
291   /* LAPACK working arrays for SVD or POD */
292   PetscBool         skip_lapack;
293   PetscScalar       *work;
294   PetscReal         *singular_vals;
295 #if defined(PETSC_USE_COMPLEX)
296   PetscReal         *rwork;
297 #endif
298 #if defined(PETSC_MISSING_LAPACK_GESVD)
299   PetscBLASInt      Blas_N,Blas_LDA;
300   PetscScalar       *temp_basis,*correlation_mat;
301 #else
302   PetscBLASInt      Blas_LDA;
303   PetscBLASInt      dummy_int_1=1,dummy_int_2=1;
304   PetscScalar       dummy_scalar_1=0.0,dummy_scalar_2=0.0;
305 #endif
306   /* change of basis */
307   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
308   PetscBool         boolforchange,*change_basis,*touched;
309   /* auxiliary stuff */
310   PetscInt          *nnz,*is_indices,*local_to_B;
311   /* some quantities */
312   PetscInt          n_vertices,total_primal_vertices;
313   PetscInt          size_of_constraint,max_size_of_constraint,max_constraints,temp_constraints;
314 
315 
316   PetscFunctionBegin;
317   /* Get index sets for faces, edges and vertices from graph */
318   get_faces = PETSC_TRUE;
319   get_edges = PETSC_TRUE;
320   get_vertices = PETSC_TRUE;
321   if (pcbddc->vertices_flag) {
322     get_faces = PETSC_FALSE;
323     get_edges = PETSC_FALSE;
324   }
325   if (pcbddc->constraints_flag) {
326     get_vertices = PETSC_FALSE;
327   }
328   if (pcbddc->faces_flag) {
329     get_edges = PETSC_FALSE;
330   }
331   if (pcbddc->edges_flag) {
332     get_faces = PETSC_FALSE;
333   }
334   /* default */
335   if (!get_faces && !get_edges && !get_vertices) {
336     get_vertices = PETSC_TRUE;
337   }
338   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
339   /* print some info */
340   if (pcbddc->dbg_flag) {
341     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
342     i = 0;
343     if (ISForVertices) {
344       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
345     }
346     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
347     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
348     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
349     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
350   }
351   /* check if near null space is attached to global mat */
352   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
353   if (nearnullsp) {
354     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
355   } else { /* if near null space is not provided BDDC uses constants by default */
356     nnsp_size = 0;
357     nnsp_has_cnst = PETSC_TRUE;
358   }
359   /* get max number of constraints on a single cc */
360   max_constraints = nnsp_size;
361   if (nnsp_has_cnst) max_constraints++;
362 
363   /*
364        Evaluate maximum storage size needed by the procedure
365        - temp_indices will contain start index of each constraint stored as follows
366        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
367        - temp_indices_to_constraint_B[temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in boundary numbering) on which the constraint acts
368        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
369                                                                                                                                                          */
370   total_counts = n_ISForFaces+n_ISForEdges;
371   total_counts *= max_constraints;
372   n_vertices = 0;
373   if (ISForVertices) {
374     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
375   }
376   total_counts += n_vertices;
377   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
378   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
379   total_counts = 0;
380   max_size_of_constraint = 0;
381   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
382     if (i<n_ISForEdges) {
383       used_IS = &ISForEdges[i];
384     } else {
385       used_IS = &ISForFaces[i-n_ISForEdges];
386     }
387     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
388     total_counts += j;
389     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
390   }
391   total_counts *= max_constraints;
392   total_counts += n_vertices;
393   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
394   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
395   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
396   /* local to boundary numbering */
397   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
398   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
399   for (i=0;i<pcis->n;i++) local_to_B[i]=-1;
400   for (i=0;i<pcis->n_B;i++) local_to_B[is_indices[i]]=i;
401   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
402   /* get local part of global near null space vectors */
403   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
404   for (k=0;k<nnsp_size;k++) {
405     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
406     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
407     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
408   }
409 
410   /* whether or not to skip lapack calls */
411   skip_lapack = PETSC_TRUE;
412   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
413 
414   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
415   if (!pcbddc->use_nnsp_true && !skip_lapack) {
416     PetscScalar temp_work;
417 #if defined(PETSC_MISSING_LAPACK_GESVD)
418     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
419     ierr = PetscMalloc(max_constraints*max_constraints*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
420     ierr = PetscMalloc(max_constraints*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
421     ierr = PetscMalloc(max_size_of_constraint*max_constraints*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
422 #if defined(PETSC_USE_COMPLEX)
423     ierr = PetscMalloc(3*max_constraints*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
424 #endif
425     /* now we evaluate the optimal workspace using query with lwork=-1 */
426     ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
427     ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
428     lwork = -1;
429     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
430 #if !defined(PETSC_USE_COMPLEX)
431     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
432 #else
433     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
434 #endif
435     ierr = PetscFPTrapPop();CHKERRQ(ierr);
436     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
437 #else /* on missing GESVD */
438     /* SVD */
439     PetscInt max_n,min_n;
440     max_n = max_size_of_constraint;
441     min_n = max_constraints;
442     if (max_size_of_constraint < max_constraints) {
443       min_n = max_size_of_constraint;
444       max_n = max_constraints;
445     }
446     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
447 #if defined(PETSC_USE_COMPLEX)
448     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
449 #endif
450     /* now we evaluate the optimal workspace using query with lwork=-1 */
451     lwork = -1;
452     ierr = PetscBLASIntCast(max_n,&Bs);CHKERRQ(ierr);
453     ierr = PetscBLASIntCast(min_n,&Bt);CHKERRQ(ierr);
454     ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
455     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
456 #if !defined(PETSC_USE_COMPLEX)
457     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Blas_LDA,singular_vals,&dummy_scalar_1,&dummy_int_1,&dummy_scalar_2,&dummy_int_2,&temp_work,&lwork,&lierr));
458 #else
459     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Blas_LDA,singular_vals,&dummy_scalar_1,&dummy_int_1,&dummy_scalar_2,&dummy_int_2,&temp_work,&lwork,rwork,&lierr));
460 #endif
461     ierr = PetscFPTrapPop();CHKERRQ(ierr);
462     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
463 #endif /* on missing GESVD */
464     /* Allocate optimal workspace */
465     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
466     ierr = PetscMalloc((PetscInt)lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
467   }
468   /* Now we can loop on constraining sets */
469   total_counts = 0;
470   temp_indices[0] = 0;
471   /* vertices */
472   if (ISForVertices) {
473     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
474     if (nnsp_has_cnst) { /* consider all vertices */
475       for (i=0;i<n_vertices;i++) {
476         temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
477         temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
478         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
479         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
480         change_basis[total_counts]=PETSC_FALSE;
481         total_counts++;
482       }
483     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
484       PetscBool used_vertex;
485       for (i=0;i<n_vertices;i++) {
486         used_vertex = PETSC_FALSE;
487         k = 0;
488         while (!used_vertex && k<nnsp_size) {
489           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
490           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
491             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
492             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
493             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
494             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
495             change_basis[total_counts]=PETSC_FALSE;
496             total_counts++;
497             used_vertex = PETSC_TRUE;
498           }
499           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
500           k++;
501         }
502       }
503     }
504     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
505     n_vertices = total_counts;
506   }
507 
508   /* edges and faces */
509   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
510     if (i<n_ISForEdges) {
511       used_IS = &ISForEdges[i];
512       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
513     } else {
514       used_IS = &ISForFaces[i-n_ISForEdges];
515       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
516     }
517     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
518     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
519     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
520     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
521     /* change of basis should not be performed on local periodic nodes */
522     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
523     if (nnsp_has_cnst) {
524       PetscScalar quad_value;
525       temp_constraints++;
526       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
527       for (j=0;j<size_of_constraint;j++) {
528         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
529         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
530         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
531       }
532       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
533       change_basis[total_counts]=boolforchange;
534       total_counts++;
535     }
536     for (k=0;k<nnsp_size;k++) {
537       PetscReal real_value;
538       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
539       for (j=0;j<size_of_constraint;j++) {
540         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
541         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
542         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
543       }
544       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
545       /* check if array is null on the connected component */
546       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
547       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone));
548       if (real_value > 0.0) { /* keep indices and values */
549         temp_constraints++;
550         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
551         change_basis[total_counts]=boolforchange;
552         total_counts++;
553       }
554     }
555     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
556     /* perform SVD on the constraints if use_nnsp_true has not be requested by the user */
557     if (!pcbddc->use_nnsp_true) {
558       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
559 
560       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
561       ierr = PetscBLASIntCast(temp_constraints,&Bt);CHKERRQ(ierr);
562 #if defined(PETSC_MISSING_LAPACK_GESVD)
563       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
564          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
565          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
566             the constraints basis will differ (by a complex factor with absolute value equal to 1)
567             from that computed using LAPACKgesvd
568          -> This is due to a different computation of eigenvectors in LAPACKheev
569          -> The quality of the POD-computed basis will be the same */
570       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
571       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
572       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
573       /* Store upper triangular part of correlation matrix */
574       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
575       for (j=0;j<temp_constraints;j++) {
576         for (k=0;k<j+1;k++) {
577           PetscStackCallBLAS("BLASdot",correlation_mat[j*temp_constraints+k]=BLASdot_(&Bs,&temp_quadrature_constraint[temp_indices[temp_start_ptr+k]],&Bone,&temp_quadrature_constraint[temp_indices[temp_start_ptr+j]],&Bone));
578         }
579       }
580 #if !defined(PETSC_USE_COMPLEX)
581       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
582 #else
583       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
584 #endif
585       ierr = PetscFPTrapPop();CHKERRQ(ierr);
586       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
587       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
588       j=0;
589       while (j < temp_constraints && singular_vals[j] < tol) j++;
590       total_counts=total_counts-j;
591       if (j<temp_constraints) {
592         PetscInt ii;
593         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
594         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
595         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Bs,&Bt,&Bt,&one,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,correlation_mat,&Bt,&zero,temp_basis,&Bs));
596         ierr = PetscFPTrapPop();CHKERRQ(ierr);
597         /* scale and copy POD basis into used quadrature memory */
598         for (k=0;k<temp_constraints-j;k++) {
599           for (ii=0;ii<size_of_constraint;ii++) {
600             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[temp_constraints-1-k]*temp_basis[(temp_constraints-1-k)*size_of_constraint+ii];
601           }
602         }
603       }
604 #else  /* on missing GESVD */
605       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
606       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
607 #if !defined(PETSC_USE_COMPLEX)
608       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Blas_LDA,singular_vals,&dummy_scalar_1,&dummy_int_1,&dummy_scalar_2,&dummy_int_2,work,&lwork,&lierr));
609 #else
610       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Blas_LDA,singular_vals,&dummy_scalar_1,&dummy_int_1,&dummy_scalar_2,&dummy_int_2,work,&lwork,rwork,&lierr));
611 #endif
612       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
613       ierr = PetscFPTrapPop();CHKERRQ(ierr);
614       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
615       PetscInt min_n = temp_constraints;
616       if (min_n > size_of_constraint) min_n = size_of_constraint;
617       j = 0;
618       while (j < min_n && singular_vals[min_n-j-1] < tol) j++;
619       total_counts = total_counts-temp_constraints+min_n-j;
620 #endif /* on missing GESVD */
621     }
622   }
623   /* free index sets of faces, edges and vertices */
624   for (i=0;i<n_ISForFaces;i++) {
625     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
626   }
627   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
628   for (i=0;i<n_ISForEdges;i++) {
629     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
630   }
631   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
632   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
633 
634   /* free workspace */
635   if (!pcbddc->use_nnsp_true && !skip_lapack) {
636     ierr = PetscFree(work);CHKERRQ(ierr);
637 #if defined(PETSC_USE_COMPLEX)
638     ierr = PetscFree(rwork);CHKERRQ(ierr);
639 #endif
640     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
641 #if defined(PETSC_MISSING_LAPACK_GESVD)
642     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
643     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
644 #endif
645   }
646   for (k=0;k<nnsp_size;k++) {
647     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
648   }
649   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
650 
651   /* set quantities in pcbddc data structure */
652   /* n_vertices defines the number of subdomain corners in the primal space */
653   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
654   pcbddc->local_primal_size = total_counts;
655   pcbddc->n_vertices = n_vertices;
656   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
657 
658   /* Create constraint matrix */
659   /* The constraint matrix is used to compute the l2g map of primal dofs */
660   /* so we need to set it up properly either with or without change of basis */
661   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
662   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
663   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
664   /* array to compute a local numbering of constraints : vertices first then constraints */
665   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
666   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
667   /* note: it should not be needed since IS for faces and edges are already sorted by global ordering when analyzing the graph but... just in case */
668   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_minloc);CHKERRQ(ierr);
669   /* auxiliary stuff for basis change */
670   ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&global_indices);CHKERRQ(ierr);
671   ierr = PetscMalloc(pcis->n_B*sizeof(PetscBool),&touched);CHKERRQ(ierr);
672   ierr = PetscMemzero(touched,pcis->n_B*sizeof(PetscBool));CHKERRQ(ierr);
673 
674   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
675   total_primal_vertices=0;
676   for (i=0;i<pcbddc->local_primal_size;i++) {
677     size_of_constraint=temp_indices[i+1]-temp_indices[i];
678     if (size_of_constraint == 1) {
679       touched[temp_indices_to_constraint_B[temp_indices[i]]]=PETSC_TRUE;
680       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
681       aux_primal_minloc[total_primal_vertices]=0;
682       total_primal_vertices++;
683     } else if (change_basis[i]) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
684       PetscInt min_loc,min_index;
685       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
686       /* find first untouched local node */
687       k = 0;
688       while (touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) k++;
689       min_index = global_indices[k];
690       min_loc = k;
691       /* search the minimum among global nodes already untouched on the cc */
692       for (k=1;k<size_of_constraint;k++) {
693         /* there can be more than one constraint on a single connected component */
694         if (min_index > global_indices[k] && !touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) {
695           min_index = global_indices[k];
696           min_loc = k;
697         }
698       }
699       touched[temp_indices_to_constraint_B[temp_indices[i]+min_loc]] = PETSC_TRUE;
700       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
701       aux_primal_minloc[total_primal_vertices]=min_loc;
702       total_primal_vertices++;
703     }
704   }
705   /* free workspace */
706   ierr = PetscFree(global_indices);CHKERRQ(ierr);
707   ierr = PetscFree(touched);CHKERRQ(ierr);
708   /* permute indices in order to have a sorted set of vertices */
709   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);
710 
711   /* nonzero structure of constraint matrix */
712   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
713   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
714   j=total_primal_vertices;
715   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
716     if (!change_basis[i]) {
717       nnz[j]=temp_indices[i+1]-temp_indices[i];
718       j++;
719     }
720   }
721   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
722   ierr = PetscFree(nnz);CHKERRQ(ierr);
723   /* set values in constraint matrix */
724   for (i=0;i<total_primal_vertices;i++) {
725     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
726   }
727   total_counts = total_primal_vertices;
728   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
729     if (!change_basis[i]) {
730       size_of_constraint=temp_indices[i+1]-temp_indices[i];
731       ierr = MatSetValues(pcbddc->ConstraintMatrix,1,&total_counts,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],&temp_quadrature_constraint[temp_indices[i]],INSERT_VALUES);CHKERRQ(ierr);
732       total_counts++;
733     }
734   }
735   /* assembling */
736   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
737   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
738   /*
739   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
740   */
741   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
742   if (pcbddc->use_change_of_basis) {
743     PetscBool qr_needed = PETSC_FALSE;
744     /* change of basis acts on local interfaces -> dimension is n_B x n_B */
745     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
746     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
747     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
748     /* work arrays */
749     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
750     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
751     /* nonzeros per row */
752     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
753       if (change_basis[i]) {
754         qr_needed = PETSC_TRUE;
755         size_of_constraint = temp_indices[i+1]-temp_indices[i];
756         for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
757       }
758     }
759     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
760     ierr = PetscFree(nnz);CHKERRQ(ierr);
761     /* Set initial identity in the matrix */
762     for (i=0;i<pcis->n_B;i++) {
763       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
764     }
765 
766     /* Now we loop on the constraints which need a change of basis */
767     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
768     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1) */
769     /* Change of basis matrix T computed via QR decomposition of constraints */
770     if (qr_needed) {
771       /* dual and primal dofs on a single cc */
772       PetscInt     dual_dofs,primal_dofs;
773       /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
774       PetscInt     primal_counter;
775       /* working stuff for GEQRF */
776       PetscScalar  *qr_basis,*qr_tau,*qr_work,lqr_work_t;
777       PetscBLASInt lqr_work;
778       /* working stuff for UNGQR */
779       PetscScalar  *gqr_work,lgqr_work_t;
780       PetscBLASInt lgqr_work;
781       /* working stuff for TRTRS */
782       PetscScalar  *trs_rhs;
783       /* pointers for values insertion into change of basis matrix */
784       PetscInt     *start_rows,*start_cols;
785       PetscScalar  *start_vals;
786       /* working stuff for values insertion */
787       PetscBool    *is_primal;
788 
789       /* space to store Q */
790       ierr = PetscMalloc((max_size_of_constraint)*(max_size_of_constraint)*sizeof(PetscScalar),&qr_basis);CHKERRQ(ierr);
791       /* first we issue queries for optimal work */
792       ierr = PetscBLASIntCast(max_size_of_constraint,&Bs);CHKERRQ(ierr);
793       ierr = PetscBLASIntCast(max_constraints,&Bt);CHKERRQ(ierr);
794       lqr_work = -1;
795       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Bs,&Bt,qr_basis,&Bs,qr_tau,&lqr_work_t,&lqr_work,&lierr));
796       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
797       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
798       ierr = PetscMalloc((PetscInt)PetscRealPart(lqr_work_t)*sizeof(*qr_work),&qr_work);CHKERRQ(ierr);
799       lgqr_work = -1;
800       if (Bt>Bs) Bt=Bs; /* adjust Bt just for computing optimal work */
801       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Bs,&Bs,&Bt,qr_basis,&Bs,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
802       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
803       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
804       ierr = PetscMalloc((PetscInt)PetscRealPart(lgqr_work_t)*sizeof(*gqr_work),&gqr_work);CHKERRQ(ierr);
805       /* array to store scaling factors for reflectors */
806       ierr = PetscMalloc(max_constraints*sizeof(*qr_tau),&qr_tau);CHKERRQ(ierr);
807       /* array to store rhs and solution of triangular solver */
808       ierr = PetscMalloc(max_constraints*max_constraints*sizeof(*trs_rhs),&trs_rhs);CHKERRQ(ierr);
809       /* array to store whether a node is primal or not */
810       ierr = PetscMalloc(pcis->n_B*sizeof(*is_primal),&is_primal);CHKERRQ(ierr);
811       ierr = PetscMemzero(is_primal,pcis->n_B*sizeof(*is_primal));CHKERRQ(ierr);
812       for (i=0;i<total_primal_vertices;i++) is_primal[local_to_B[aux_primal_numbering[i]]] = PETSC_TRUE;
813 
814       /* allocating workspace for check */
815       if (pcbddc->dbg_flag) {
816         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
817         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
818         ierr = PetscMalloc(max_size_of_constraint*(max_constraints+max_size_of_constraint)*sizeof(*work),&work);CHKERRQ(ierr);
819       }
820 
821       /* loop on constraints and see whether or not they need a change of basis */
822       /* -> using implicit ordering contained in temp_indices data */
823       total_counts = pcbddc->n_vertices;
824       primal_counter = total_counts;
825       while (total_counts<pcbddc->local_primal_size) {
826         primal_dofs = 1;
827         if (change_basis[total_counts]) {
828           /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
829           while (total_counts+primal_dofs < pcbddc->local_primal_size && temp_indices_to_constraint_B[temp_indices[total_counts]] == temp_indices_to_constraint_B[temp_indices[total_counts+primal_dofs]]) {
830             primal_dofs++;
831           }
832           /* get constraint info */
833           size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
834           dual_dofs = size_of_constraint-primal_dofs;
835           /* get BLAS dims */
836           ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
837           ierr = PetscBLASIntCast(primal_dofs,&Bt);CHKERRQ(ierr);
838 
839           /* copy quadrature constraints for change of basis check */
840           if (pcbddc->dbg_flag) {
841             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %d to %d need a change of basis (size %d)\n",total_counts,total_counts+primal_dofs,size_of_constraint);CHKERRQ(ierr);
842             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
843           }
844 
845           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
846           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
847 
848           /* compute QR decomposition of constraints */
849           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
850           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Bs,&Bt,qr_basis,&Bs,qr_tau,qr_work,&lqr_work,&lierr));
851           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
852           ierr = PetscFPTrapPop();CHKERRQ(ierr);
853 
854           /* explictly compute R^-T */
855           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
856           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
857           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
858           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Bt,&Bt,qr_basis,&Bs,trs_rhs,&Bt,&lierr));
859           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
860           ierr = PetscFPTrapPop();CHKERRQ(ierr);
861 
862           /* explcitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
863           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
864           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Bs,&Bs,&Bt,qr_basis,&Bs,qr_tau,gqr_work,&lgqr_work,&lierr));
865           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
866           ierr = PetscFPTrapPop();CHKERRQ(ierr);
867 
868           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
869              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
870              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
871           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
872           PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Bs,&Bt,&Bt,&one,qr_basis,&Bs,trs_rhs,&Bt,&zero,&temp_quadrature_constraint[temp_indices[total_counts]],&Bs));
873           ierr = PetscFPTrapPop();CHKERRQ(ierr);
874           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
875 
876           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
877           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
878           /* insert cols for primal dofs */
879           for (j=0;j<primal_dofs;j++) {
880             start_vals = &qr_basis[j*size_of_constraint];
881             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
882             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
883           }
884           /* insert cols for dual dofs */
885           for (j=0,k=0;j<dual_dofs;k++) {
886             if (!is_primal[temp_indices_to_constraint_B[temp_indices[total_counts]+k]]) {
887               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
888               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
889               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
890               j++;
891             }
892           }
893 
894           /* check change of basis */
895           if (pcbddc->dbg_flag) {
896             PetscInt   ii,jj;
897             PetscBool valid_qr=PETSC_TRUE;
898             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
899             PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&Bt,&Bs,&Bs,&one,work,&Bs,qr_basis,&Bs,&zero,&work[size_of_constraint*primal_dofs],&Bt));
900             ierr = PetscFPTrapPop();CHKERRQ(ierr);
901             for (jj=0;jj<size_of_constraint;jj++) {
902               for (ii=0;ii<primal_dofs;ii++) {
903                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
904                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
905               }
906             }
907             if (!valid_qr) {
908               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
909               for (jj=0;jj<size_of_constraint;jj++) {
910                 for (ii=0;ii<primal_dofs;ii++) {
911                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
912                     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %d is not orthogonal to constraint %d (%1.14e)!\n",jj,ii,PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
913                   }
914                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
915                     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %d is not unitary w.r.t constraint %d (%1.14e)!\n",jj,ii,PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
916                   }
917                 }
918               }
919             } else {
920               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
921             }
922           }
923           /* increment primal counter */
924           primal_counter += primal_dofs;
925         } else {
926           if (pcbddc->dbg_flag) {
927             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %d does not need a change of basis (size %d)\n",total_counts,temp_indices[total_counts+1]-temp_indices[total_counts]);CHKERRQ(ierr);
928           }
929         }
930         /* increment constraint counter total_counts */
931         total_counts += primal_dofs;
932       }
933       if (pcbddc->dbg_flag) {
934         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
935         ierr = PetscFree(work);CHKERRQ(ierr);
936       }
937       /* free workspace */
938       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
939       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
940       ierr = PetscFree(qr_work);CHKERRQ(ierr);
941       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
942       ierr = PetscFree(is_primal);CHKERRQ(ierr);
943       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
944     }
945     /* assembling */
946     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
947     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
948     /*
949     ierr = MatView(pcbddc->ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
950     */
951   }
952   /* free workspace no longer needed */
953   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
954   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
955   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
956   ierr = PetscFree(change_basis);CHKERRQ(ierr);
957   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
958   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
959   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
960   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
961   PetscFunctionReturn(0);
962 }
963 
964 #undef __FUNCT__
965 #define __FUNCT__ "PCBDDCAnalyzeInterface"
966 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
967 {
968   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
969   PC_IS       *pcis = (PC_IS*)pc->data;
970   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
971   PetscInt    bs,ierr,i,vertex_size;
972   PetscViewer viewer=pcbddc->dbg_viewer;
973 
974   PetscFunctionBegin;
975   /* Init local Graph struct */
976   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
977 
978   /* Check validity of the csr graph passed in by the user */
979   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
980     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
981   }
982   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
983   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
984     Mat mat_adj;
985     const PetscInt *xadj,*adjncy;
986     PetscBool flg_row=PETSC_TRUE;
987 
988     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
989     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
990     if (!flg_row) {
991       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
992     }
993     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
994     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
995     if (!flg_row) {
996       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
997     }
998     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
999   }
1000 
1001   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
1002   vertex_size = 1;
1003   if (!pcbddc->n_ISForDofs) {
1004     IS *custom_ISForDofs;
1005 
1006     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
1007     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
1008     for (i=0;i<bs;i++) {
1009       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1010     }
1011     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1012     /* remove my references to IS objects */
1013     for (i=0;i<bs;i++) {
1014       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1015     }
1016     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1017   } else { /* mat block size as vertex size (used for elasticity) */
1018     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1019   }
1020 
1021   /* Setup of Graph */
1022   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1023 
1024   /* Graph's connected components analysis */
1025   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1026 
1027   /* print some info to stdout */
1028   if (pcbddc->dbg_flag) {
1029     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1030   }
1031   PetscFunctionReturn(0);
1032 }
1033 
1034 #undef __FUNCT__
1035 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1036 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1037 {
1038   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1039   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1040   PetscErrorCode ierr;
1041 
1042   PetscFunctionBegin;
1043   n = 0;
1044   vertices = 0;
1045   if (pcbddc->ConstraintMatrix) {
1046     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1047     for (i=0;i<local_primal_size;i++) {
1048       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1049       if (size_of_constraint == 1) n++;
1050       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1051     }
1052     ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1053     n = 0;
1054     for (i=0;i<local_primal_size;i++) {
1055       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1056       if (size_of_constraint == 1) {
1057         vertices[n++]=row_cmat_indices[0];
1058       }
1059       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1060     }
1061   }
1062   *n_vertices = n;
1063   *vertices_idx = vertices;
1064   PetscFunctionReturn(0);
1065 }
1066 
1067 #undef __FUNCT__
1068 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
1069 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
1070 {
1071   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1072   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
1073   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
1074   PetscBool      *touched;
1075   PetscErrorCode ierr;
1076 
1077   PetscFunctionBegin;
1078   n = 0;
1079   constraints_index = 0;
1080   if (pcbddc->ConstraintMatrix) {
1081     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
1082     max_size_of_constraint = 0;
1083     for (i=0;i<local_primal_size;i++) {
1084       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1085       if (size_of_constraint > 1) {
1086         n++;
1087       }
1088       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
1089       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1090     }
1091     ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
1092     ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
1093     ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1094     ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
1095     n = 0;
1096     for (i=0;i<local_primal_size;i++) {
1097       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1098       if (size_of_constraint > 1) {
1099         ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
1100         min_index = row_cmat_global_indices[0];
1101         min_loc = 0;
1102         for (j=1;j<size_of_constraint;j++) {
1103           /* there can be more than one constraint on a single connected component */
1104           if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
1105             min_index = row_cmat_global_indices[j];
1106             min_loc = j;
1107           }
1108         }
1109         touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
1110         constraints_index[n++] = row_cmat_indices[min_loc];
1111       }
1112       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1113     }
1114   }
1115   ierr = PetscFree(touched);CHKERRQ(ierr);
1116   ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
1117   *n_constraints = n;
1118   *constraints_idx = constraints_index;
1119   PetscFunctionReturn(0);
1120 }
1121 
1122 /* the next two functions has been adapted from pcis.c */
1123 #undef __FUNCT__
1124 #define __FUNCT__ "PCBDDCApplySchur"
1125 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1126 {
1127   PetscErrorCode ierr;
1128   PC_IS          *pcis = (PC_IS*)(pc->data);
1129 
1130   PetscFunctionBegin;
1131   if (!vec2_B) { vec2_B = v; }
1132   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1133   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
1134   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1135   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
1136   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1137   PetscFunctionReturn(0);
1138 }
1139 
1140 #undef __FUNCT__
1141 #define __FUNCT__ "PCBDDCApplySchurTranspose"
1142 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1143 {
1144   PetscErrorCode ierr;
1145   PC_IS          *pcis = (PC_IS*)(pc->data);
1146 
1147   PetscFunctionBegin;
1148   if (!vec2_B) { vec2_B = v; }
1149   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1150   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
1151   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1152   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
1153   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1154   PetscFunctionReturn(0);
1155 }
1156 
1157 #undef __FUNCT__
1158 #define __FUNCT__ "PCBDDCSubsetNumbering"
1159 PetscErrorCode PCBDDCSubsetNumbering(MPI_Comm comm,ISLocalToGlobalMapping l2gmap, PetscInt n_local_dofs, PetscInt local_dofs[], PetscInt local_dofs_mult[], PetscInt* n_global_subset, PetscInt* global_numbering_subset[])
1160 {
1161   Vec            local_vec,global_vec;
1162   IS             seqis,paris;
1163   VecScatter     scatter_ctx;
1164   PetscScalar    *array;
1165   PetscInt       *temp_global_dofs;
1166   PetscScalar    globalsum;
1167   PetscInt       i,j,s;
1168   PetscInt       nlocals,first_index,old_index,max_local;
1169   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
1170   PetscMPIInt    *dof_sizes,*dof_displs;
1171   PetscBool      first_found;
1172   PetscErrorCode ierr;
1173 
1174   PetscFunctionBegin;
1175   /* mpi buffers */
1176   MPI_Comm_size(comm,&size_prec_comm);
1177   MPI_Comm_rank(comm,&rank_prec_comm);
1178   j = ( !rank_prec_comm ? size_prec_comm : 0);
1179   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1180   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1181   /* get maximum size of subset */
1182   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
1183   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
1184   max_local = 0;
1185   if (n_local_dofs) {
1186     max_local = temp_global_dofs[0];
1187     for (i=1;i<n_local_dofs;i++) {
1188       if (max_local < temp_global_dofs[i] ) {
1189         max_local = temp_global_dofs[i];
1190       }
1191     }
1192   }
1193   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
1194   max_global++;
1195   max_local = 0;
1196   if (n_local_dofs) {
1197     max_local = local_dofs[0];
1198     for (i=1;i<n_local_dofs;i++) {
1199       if (max_local < local_dofs[i] ) {
1200         max_local = local_dofs[i];
1201       }
1202     }
1203   }
1204   max_local++;
1205   /* allocate workspace */
1206   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
1207   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
1208   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
1209   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
1210   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
1211   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
1212   /* create scatter */
1213   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
1214   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
1215   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
1216   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
1217   ierr = ISDestroy(&paris);CHKERRQ(ierr);
1218   /* init array */
1219   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1220   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1221   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1222   if (local_dofs_mult) {
1223     for (i=0;i<n_local_dofs;i++) {
1224       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
1225     }
1226   } else {
1227     for (i=0;i<n_local_dofs;i++) {
1228       array[local_dofs[i]]=1.0;
1229     }
1230   }
1231   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1232   /* scatter into global vec and get total number of global dofs */
1233   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1234   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1235   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
1236   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
1237   /* Fill global_vec with cumulative function for global numbering */
1238   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
1239   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
1240   nlocals = 0;
1241   first_index = -1;
1242   first_found = PETSC_FALSE;
1243   for (i=0;i<s;i++) {
1244     if (!first_found && PetscRealPart(array[i]) > 0.0) {
1245       first_found = PETSC_TRUE;
1246       first_index = i;
1247     }
1248     nlocals += (PetscInt)PetscRealPart(array[i]);
1249   }
1250   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1251   if (!rank_prec_comm) {
1252     dof_displs[0]=0;
1253     for (i=1;i<size_prec_comm;i++) {
1254       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1255     }
1256   }
1257   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1258   if (first_found) {
1259     array[first_index] += (PetscScalar)nlocals;
1260     old_index = first_index;
1261     for (i=first_index+1;i<s;i++) {
1262       if (PetscRealPart(array[i]) > 0.0) {
1263         array[i] += array[old_index];
1264         old_index = i;
1265       }
1266     }
1267   }
1268   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
1269   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1270   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1271   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1272   /* get global ordering of local dofs */
1273   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1274   if (local_dofs_mult) {
1275     for (i=0;i<n_local_dofs;i++) {
1276       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
1277     }
1278   } else {
1279     for (i=0;i<n_local_dofs;i++) {
1280       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
1281     }
1282   }
1283   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1284   /* free workspace */
1285   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1286   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1287   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1288   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1289   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1290   /* return pointer to global ordering of local dofs */
1291   *global_numbering_subset = temp_global_dofs;
1292   PetscFunctionReturn(0);
1293 }
1294