xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 242a89d7bc99e0df0def19a239560d5d7580ecf3)
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   PetscScalar       *temp_basis,*correlation_mat;
300 #endif
301   /* change of basis */
302   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
303   PetscBool         boolforchange,*change_basis,*touched;
304   /* auxiliary stuff */
305   PetscInt          *nnz,*is_indices,*local_to_B;
306   /* some quantities */
307   PetscInt          n_vertices,total_primal_vertices;
308   PetscInt          size_of_constraint,max_size_of_constraint,max_constraints,temp_constraints;
309 
310 
311   PetscFunctionBegin;
312   /* Get index sets for faces, edges and vertices from graph */
313   get_faces = PETSC_TRUE;
314   get_edges = PETSC_TRUE;
315   get_vertices = PETSC_TRUE;
316   if (pcbddc->vertices_flag) {
317     get_faces = PETSC_FALSE;
318     get_edges = PETSC_FALSE;
319   }
320   if (pcbddc->constraints_flag) {
321     get_vertices = PETSC_FALSE;
322   }
323   if (pcbddc->faces_flag) {
324     get_edges = PETSC_FALSE;
325   }
326   if (pcbddc->edges_flag) {
327     get_faces = PETSC_FALSE;
328   }
329   /* default */
330   if (!get_faces && !get_edges && !get_vertices) {
331     get_vertices = PETSC_TRUE;
332   }
333   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
334   /* print some info */
335   if (pcbddc->dbg_flag) {
336     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
337     i = 0;
338     if (ISForVertices) {
339       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
340     }
341     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
342     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
343     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
344     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
345   }
346   /* check if near null space is attached to global mat */
347   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
348   if (nearnullsp) {
349     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
350   } else { /* if near null space is not provided BDDC uses constants by default */
351     nnsp_size = 0;
352     nnsp_has_cnst = PETSC_TRUE;
353   }
354   /* get max number of constraints on a single cc */
355   max_constraints = nnsp_size;
356   if (nnsp_has_cnst) max_constraints++;
357 
358   /*
359        Evaluate maximum storage size needed by the procedure
360        - temp_indices will contain start index of each constraint stored as follows
361        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
362        - 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
363        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
364                                                                                                                                                          */
365   total_counts = n_ISForFaces+n_ISForEdges;
366   total_counts *= max_constraints;
367   n_vertices = 0;
368   if (ISForVertices) {
369     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
370   }
371   total_counts += n_vertices;
372   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
373   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
374   total_counts = 0;
375   max_size_of_constraint = 0;
376   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
377     if (i<n_ISForEdges) {
378       used_IS = &ISForEdges[i];
379     } else {
380       used_IS = &ISForFaces[i-n_ISForEdges];
381     }
382     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
383     total_counts += j;
384     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
385   }
386   total_counts *= max_constraints;
387   total_counts += n_vertices;
388   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
389   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
390   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
391   /* local to boundary numbering */
392   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
393   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
394   for (i=0;i<pcis->n;i++) local_to_B[i]=-1;
395   for (i=0;i<pcis->n_B;i++) local_to_B[is_indices[i]]=i;
396   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
397   /* get local part of global near null space vectors */
398   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
399   for (k=0;k<nnsp_size;k++) {
400     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
401     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
402     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
403   }
404 
405   /* whether or not to skip lapack calls */
406   skip_lapack = PETSC_TRUE;
407   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
408 
409   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
410   if (!pcbddc->use_nnsp_true && !skip_lapack) {
411     PetscScalar temp_work;
412 #if defined(PETSC_MISSING_LAPACK_GESVD)
413     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
414     ierr = PetscMalloc(max_constraints*max_constraints*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
415     ierr = PetscMalloc(max_constraints*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
416     ierr = PetscMalloc(max_size_of_constraint*max_constraints*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
417 #if defined(PETSC_USE_COMPLEX)
418     ierr = PetscMalloc(3*max_constraints*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
419 #endif
420     /* now we evaluate the optimal workspace using query with lwork=-1 */
421     ierr = PetscBLASIntCast(max_constraints,&Bt);CHKERRQ(ierr);
422     lwork = -1;
423     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
424 #if !defined(PETSC_USE_COMPLEX)
425     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,&lierr));
426 #else
427     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,rwork,&lierr));
428 #endif
429     ierr = PetscFPTrapPop();CHKERRQ(ierr);
430     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
431 #else /* on missing GESVD */
432     /* SVD */
433     PetscInt max_n,min_n;
434     max_n = max_size_of_constraint;
435     min_n = max_constraints;
436     if (max_size_of_constraint < max_constraints) {
437       min_n = max_size_of_constraint;
438       max_n = max_constraints;
439     }
440     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
441 #if defined(PETSC_USE_COMPLEX)
442     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
443 #endif
444     /* now we evaluate the optimal workspace using query with lwork=-1 */
445     lwork = -1;
446     ierr = PetscBLASIntCast(max_n,&Bs);CHKERRQ(ierr);
447     ierr = PetscBLASIntCast(min_n,&Bt);CHKERRQ(ierr);
448     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
449 #if !defined(PETSC_USE_COMPLEX)
450     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,work,&Bt,work,&Bt,&temp_work,&lwork,&lierr));
451 #else
452     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,work,&Bt,work,&Bt,&temp_work,&lwork,rwork,&lierr));
453 #endif
454     ierr = PetscFPTrapPop();CHKERRQ(ierr);
455     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
456 #endif /* on missing GESVD */
457     /* Allocate optimal workspace */
458     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
459     ierr = PetscMalloc((PetscInt)lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
460   }
461   /* Now we can loop on constraining sets */
462   total_counts = 0;
463   temp_indices[0] = 0;
464   /* vertices */
465   if (ISForVertices) {
466     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
467     if (nnsp_has_cnst) { /* consider all vertices */
468       for (i=0;i<n_vertices;i++) {
469         temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
470         temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
471         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
472         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
473         change_basis[total_counts]=PETSC_FALSE;
474         total_counts++;
475       }
476     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
477       PetscBool used_vertex;
478       for (i=0;i<n_vertices;i++) {
479         used_vertex = PETSC_FALSE;
480         k = 0;
481         while (!used_vertex && k<nnsp_size) {
482           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
483           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
484             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
485             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
486             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
487             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
488             change_basis[total_counts]=PETSC_FALSE;
489             total_counts++;
490             used_vertex = PETSC_TRUE;
491           }
492           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
493           k++;
494         }
495       }
496     }
497     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
498     n_vertices = total_counts;
499   }
500 
501   /* edges and faces */
502   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
503     if (i<n_ISForEdges) {
504       used_IS = &ISForEdges[i];
505       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
506     } else {
507       used_IS = &ISForFaces[i-n_ISForEdges];
508       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
509     }
510     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
511     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
512     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
513     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
514     /* change of basis should not be performed on local periodic nodes */
515     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
516     if (nnsp_has_cnst) {
517       PetscScalar quad_value;
518       temp_constraints++;
519       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
520       for (j=0;j<size_of_constraint;j++) {
521         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
522         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
523         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
524       }
525       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
526       change_basis[total_counts]=boolforchange;
527       total_counts++;
528     }
529     for (k=0;k<nnsp_size;k++) {
530       PetscReal real_value;
531       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
532       for (j=0;j<size_of_constraint;j++) {
533         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
534         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
535         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
536       }
537       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
538       /* check if array is null on the connected component */
539       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
540       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone));
541       if (real_value > 0.0) { /* keep indices and values */
542         temp_constraints++;
543         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
544         change_basis[total_counts]=boolforchange;
545         total_counts++;
546       }
547     }
548     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
549     /* perform SVD on the constraints if use_nnsp_true has not be requested by the user */
550     if (!pcbddc->use_nnsp_true) {
551       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
552 
553       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
554       ierr = PetscBLASIntCast(temp_constraints,&Bt);CHKERRQ(ierr);
555 #if defined(PETSC_MISSING_LAPACK_GESVD)
556       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
557          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
558          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
559             the constraints basis will differ (by a complex factor with absolute value equal to 1)
560             from that computed using LAPACKgesvd
561          -> This is due to a different computation of eigenvectors in LAPACKheev
562          -> The quality of the POD-computed basis will be the same */
563       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
564       /* Store upper triangular part of correlation matrix */
565       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
566       for (j=0;j<temp_constraints;j++) {
567         for (k=0;k<j+1;k++) {
568           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));
569         }
570       }
571 #if !defined(PETSC_USE_COMPLEX)
572       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,&lierr));
573 #else
574       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,rwork,&lierr));
575 #endif
576       ierr = PetscFPTrapPop();CHKERRQ(ierr);
577       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
578       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
579       j=0;
580       while (j < temp_constraints && singular_vals[j] < tol) j++;
581       total_counts=total_counts-j;
582       if (j<temp_constraints) {
583         PetscInt ii;
584         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
585         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
586         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));
587         ierr = PetscFPTrapPop();CHKERRQ(ierr);
588         /* scale and copy POD basis into used quadrature memory */
589         for (k=0;k<temp_constraints-j;k++) {
590           for (ii=0;ii<size_of_constraint;ii++) {
591             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];
592           }
593         }
594       }
595 #else  /* on missing GESVD */
596       PetscInt min_n = temp_constraints;
597       if (min_n > size_of_constraint) min_n = size_of_constraint;
598       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
599 #if !defined(PETSC_USE_COMPLEX)
600       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,work,&Bt,work,&Bt,work,&lwork,&lierr));
601 #else
602       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,work,&Bt,work,&Bt,work,&lwork,rwork,&lierr));
603 #endif
604       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
605       ierr = PetscFPTrapPop();CHKERRQ(ierr);
606       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
607       j = 0;
608       while (j < min_n && singular_vals[min_n-j-1] < tol) j++;
609       total_counts = total_counts-temp_constraints+min_n-j;
610 #endif /* on missing GESVD */
611     }
612   }
613   /* free index sets of faces, edges and vertices */
614   for (i=0;i<n_ISForFaces;i++) {
615     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
616   }
617   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
618   for (i=0;i<n_ISForEdges;i++) {
619     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
620   }
621   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
622   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
623 
624   /* free workspace */
625   if (!pcbddc->use_nnsp_true && !skip_lapack) {
626     ierr = PetscFree(work);CHKERRQ(ierr);
627 #if defined(PETSC_USE_COMPLEX)
628     ierr = PetscFree(rwork);CHKERRQ(ierr);
629 #endif
630     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
631 #if defined(PETSC_MISSING_LAPACK_GESVD)
632     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
633     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
634 #endif
635   }
636   for (k=0;k<nnsp_size;k++) {
637     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
638   }
639   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
640 
641   /* set quantities in pcbddc data structure */
642   /* n_vertices defines the number of subdomain corners in the primal space */
643   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
644   pcbddc->local_primal_size = total_counts;
645   pcbddc->n_vertices = n_vertices;
646   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
647 
648   /* Create constraint matrix */
649   /* The constraint matrix is used to compute the l2g map of primal dofs */
650   /* so we need to set it up properly either with or without change of basis */
651   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
652   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
653   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
654   /* array to compute a local numbering of constraints : vertices first then constraints */
655   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
656   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
657   /* 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 */
658   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_minloc);CHKERRQ(ierr);
659   /* auxiliary stuff for basis change */
660   ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&global_indices);CHKERRQ(ierr);
661   ierr = PetscMalloc(pcis->n_B*sizeof(PetscBool),&touched);CHKERRQ(ierr);
662   ierr = PetscMemzero(touched,pcis->n_B*sizeof(PetscBool));CHKERRQ(ierr);
663 
664   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
665   total_primal_vertices=0;
666   for (i=0;i<pcbddc->local_primal_size;i++) {
667     size_of_constraint=temp_indices[i+1]-temp_indices[i];
668     if (size_of_constraint == 1) {
669       touched[temp_indices_to_constraint_B[temp_indices[i]]]=PETSC_TRUE;
670       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
671       aux_primal_minloc[total_primal_vertices]=0;
672       total_primal_vertices++;
673     } else if (change_basis[i]) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
674       PetscInt min_loc,min_index;
675       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
676       /* find first untouched local node */
677       k = 0;
678       while (touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) k++;
679       min_index = global_indices[k];
680       min_loc = k;
681       /* search the minimum among global nodes already untouched on the cc */
682       for (k=1;k<size_of_constraint;k++) {
683         /* there can be more than one constraint on a single connected component */
684         if (min_index > global_indices[k] && !touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) {
685           min_index = global_indices[k];
686           min_loc = k;
687         }
688       }
689       touched[temp_indices_to_constraint_B[temp_indices[i]+min_loc]] = PETSC_TRUE;
690       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
691       aux_primal_minloc[total_primal_vertices]=min_loc;
692       total_primal_vertices++;
693     }
694   }
695   /* free workspace */
696   ierr = PetscFree(global_indices);CHKERRQ(ierr);
697   ierr = PetscFree(touched);CHKERRQ(ierr);
698   /* permute indices in order to have a sorted set of vertices */
699   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);
700 
701   /* nonzero structure of constraint matrix */
702   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
703   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
704   j=total_primal_vertices;
705   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
706     if (!change_basis[i]) {
707       nnz[j]=temp_indices[i+1]-temp_indices[i];
708       j++;
709     }
710   }
711   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
712   ierr = PetscFree(nnz);CHKERRQ(ierr);
713   /* set values in constraint matrix */
714   for (i=0;i<total_primal_vertices;i++) {
715     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
716   }
717   total_counts = total_primal_vertices;
718   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
719     if (!change_basis[i]) {
720       size_of_constraint=temp_indices[i+1]-temp_indices[i];
721       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);
722       total_counts++;
723     }
724   }
725   /* assembling */
726   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
727   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
728   /*
729   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
730   */
731   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
732   if (pcbddc->use_change_of_basis) {
733     PetscBool qr_needed = PETSC_FALSE;
734     /* change of basis acts on local interfaces -> dimension is n_B x n_B */
735     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
736     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
737     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
738     /* work arrays */
739     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
740     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
741     /* nonzeros per row */
742     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
743       if (change_basis[i]) {
744         qr_needed = PETSC_TRUE;
745         size_of_constraint = temp_indices[i+1]-temp_indices[i];
746         for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
747       }
748     }
749     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
750     ierr = PetscFree(nnz);CHKERRQ(ierr);
751     /* Set initial identity in the matrix */
752     for (i=0;i<pcis->n_B;i++) {
753       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
754     }
755 
756     /* Now we loop on the constraints which need a change of basis */
757     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
758     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1) */
759     /* Change of basis matrix T computed via QR decomposition of constraints */
760     if (qr_needed) {
761       /* dual and primal dofs on a single cc */
762       PetscInt     dual_dofs,primal_dofs;
763       /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
764       PetscInt     primal_counter;
765       /* working stuff for GEQRF */
766       PetscScalar  *qr_basis,*qr_tau,*qr_work,lqr_work_t;
767       PetscBLASInt lqr_work;
768       /* working stuff for UNGQR */
769       PetscScalar  *gqr_work,lgqr_work_t;
770       PetscBLASInt lgqr_work;
771       /* working stuff for TRTRS */
772       PetscScalar  *trs_rhs;
773       /* pointers for values insertion into change of basis matrix */
774       PetscInt     *start_rows,*start_cols;
775       PetscScalar  *start_vals;
776       /* working stuff for values insertion */
777       PetscBool    *is_primal;
778 
779       /* space to store Q */
780       ierr = PetscMalloc((max_size_of_constraint)*(max_size_of_constraint)*sizeof(PetscScalar),&qr_basis);CHKERRQ(ierr);
781       /* first we issue queries for optimal work */
782       ierr = PetscBLASIntCast(max_size_of_constraint,&Bs);CHKERRQ(ierr);
783       ierr = PetscBLASIntCast(max_constraints,&Bt);CHKERRQ(ierr);
784       lqr_work = -1;
785       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Bs,&Bt,qr_basis,&Bs,qr_tau,&lqr_work_t,&lqr_work,&lierr));
786       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
787       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
788       ierr = PetscMalloc((PetscInt)PetscRealPart(lqr_work_t)*sizeof(*qr_work),&qr_work);CHKERRQ(ierr);
789       lgqr_work = -1;
790       if (Bt>Bs) Bt=Bs; /* adjust Bt just for computing optimal work */
791       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Bs,&Bs,&Bt,qr_basis,&Bs,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
792       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
793       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
794       ierr = PetscMalloc((PetscInt)PetscRealPart(lgqr_work_t)*sizeof(*gqr_work),&gqr_work);CHKERRQ(ierr);
795       /* array to store scaling factors for reflectors */
796       ierr = PetscMalloc(max_constraints*sizeof(*qr_tau),&qr_tau);CHKERRQ(ierr);
797       /* array to store rhs and solution of triangular solver */
798       ierr = PetscMalloc(max_constraints*max_constraints*sizeof(*trs_rhs),&trs_rhs);CHKERRQ(ierr);
799       /* array to store whether a node is primal or not */
800       ierr = PetscMalloc(pcis->n_B*sizeof(*is_primal),&is_primal);CHKERRQ(ierr);
801       ierr = PetscMemzero(is_primal,pcis->n_B*sizeof(*is_primal));CHKERRQ(ierr);
802       for (i=0;i<total_primal_vertices;i++) is_primal[local_to_B[aux_primal_numbering[i]]] = PETSC_TRUE;
803 
804       /* allocating workspace for check */
805       if (pcbddc->dbg_flag) {
806         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
807         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
808         ierr = PetscMalloc(max_size_of_constraint*(max_constraints+max_size_of_constraint)*sizeof(*work),&work);CHKERRQ(ierr);
809       }
810 
811       /* loop on constraints and see whether or not they need a change of basis */
812       /* -> using implicit ordering contained in temp_indices data */
813       total_counts = pcbddc->n_vertices;
814       primal_counter = total_counts;
815       while (total_counts<pcbddc->local_primal_size) {
816         primal_dofs = 1;
817         if (change_basis[total_counts]) {
818           /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
819           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]]) {
820             primal_dofs++;
821           }
822           /* get constraint info */
823           size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
824           dual_dofs = size_of_constraint-primal_dofs;
825           /* get BLAS dims */
826           ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
827           ierr = PetscBLASIntCast(primal_dofs,&Bt);CHKERRQ(ierr);
828 
829           /* copy quadrature constraints for change of basis check */
830           if (pcbddc->dbg_flag) {
831             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);
832             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
833           }
834 
835           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
836           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
837 
838           /* compute QR decomposition of constraints */
839           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
840           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Bs,&Bt,qr_basis,&Bs,qr_tau,qr_work,&lqr_work,&lierr));
841           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
842           ierr = PetscFPTrapPop();CHKERRQ(ierr);
843 
844           /* explictly compute R^-T */
845           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
846           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
847           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
848           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Bt,&Bt,qr_basis,&Bs,trs_rhs,&Bt,&lierr));
849           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
850           ierr = PetscFPTrapPop();CHKERRQ(ierr);
851 
852           /* explcitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
853           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
854           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Bs,&Bs,&Bt,qr_basis,&Bs,qr_tau,gqr_work,&lgqr_work,&lierr));
855           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
856           ierr = PetscFPTrapPop();CHKERRQ(ierr);
857 
858           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
859              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
860              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
861           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
862           PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Bs,&Bt,&Bt,&one,qr_basis,&Bs,trs_rhs,&Bt,&zero,&temp_quadrature_constraint[temp_indices[total_counts]],&Bs));
863           ierr = PetscFPTrapPop();CHKERRQ(ierr);
864           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
865 
866           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
867           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
868           /* insert cols for primal dofs */
869           for (j=0;j<primal_dofs;j++) {
870             start_vals = &qr_basis[j*size_of_constraint];
871             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
872             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
873           }
874           /* insert cols for dual dofs */
875           for (j=0,k=0;j<dual_dofs;k++) {
876             if (!is_primal[temp_indices_to_constraint_B[temp_indices[total_counts]+k]]) {
877               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
878               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
879               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
880               j++;
881             }
882           }
883 
884           /* check change of basis */
885           if (pcbddc->dbg_flag) {
886             PetscInt   ii,jj;
887             PetscBool valid_qr=PETSC_TRUE;
888             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
889             PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&Bt,&Bs,&Bs,&one,work,&Bs,qr_basis,&Bs,&zero,&work[size_of_constraint*primal_dofs],&Bt));
890             ierr = PetscFPTrapPop();CHKERRQ(ierr);
891             for (jj=0;jj<size_of_constraint;jj++) {
892               for (ii=0;ii<primal_dofs;ii++) {
893                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
894                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
895               }
896             }
897             if (!valid_qr) {
898               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
899               for (jj=0;jj<size_of_constraint;jj++) {
900                 for (ii=0;ii<primal_dofs;ii++) {
901                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
902                     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]));
903                   }
904                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
905                     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]));
906                   }
907                 }
908               }
909             } else {
910               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
911             }
912           }
913           /* increment primal counter */
914           primal_counter += primal_dofs;
915         } else {
916           if (pcbddc->dbg_flag) {
917             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);
918           }
919         }
920         /* increment constraint counter total_counts */
921         total_counts += primal_dofs;
922       }
923       if (pcbddc->dbg_flag) {
924         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
925         ierr = PetscFree(work);CHKERRQ(ierr);
926       }
927       /* free workspace */
928       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
929       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
930       ierr = PetscFree(qr_work);CHKERRQ(ierr);
931       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
932       ierr = PetscFree(is_primal);CHKERRQ(ierr);
933       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
934     }
935     /* assembling */
936     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
937     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
938     /*
939     ierr = MatView(pcbddc->ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
940     */
941   }
942   /* free workspace no longer needed */
943   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
944   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
945   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
946   ierr = PetscFree(change_basis);CHKERRQ(ierr);
947   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
948   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
949   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
950   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
951   PetscFunctionReturn(0);
952 }
953 
954 #undef __FUNCT__
955 #define __FUNCT__ "PCBDDCAnalyzeInterface"
956 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
957 {
958   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
959   PC_IS       *pcis = (PC_IS*)pc->data;
960   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
961   PetscInt    bs,ierr,i,vertex_size;
962   PetscViewer viewer=pcbddc->dbg_viewer;
963 
964   PetscFunctionBegin;
965   /* Init local Graph struct */
966   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
967 
968   /* Check validity of the csr graph passed in by the user */
969   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
970     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
971   }
972   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
973   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
974     Mat mat_adj;
975     const PetscInt *xadj,*adjncy;
976     PetscBool flg_row=PETSC_TRUE;
977 
978     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
979     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
980     if (!flg_row) {
981       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
982     }
983     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
984     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
985     if (!flg_row) {
986       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
987     }
988     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
989   }
990 
991   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
992   vertex_size = 1;
993   if (!pcbddc->n_ISForDofs) {
994     IS *custom_ISForDofs;
995 
996     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
997     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
998     for (i=0;i<bs;i++) {
999       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1000     }
1001     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1002     /* remove my references to IS objects */
1003     for (i=0;i<bs;i++) {
1004       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1005     }
1006     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1007   } else { /* mat block size as vertex size (used for elasticity) */
1008     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1009   }
1010 
1011   /* Setup of Graph */
1012   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1013 
1014   /* Graph's connected components analysis */
1015   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1016 
1017   /* print some info to stdout */
1018   if (pcbddc->dbg_flag) {
1019     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1020   }
1021   PetscFunctionReturn(0);
1022 }
1023 
1024 #undef __FUNCT__
1025 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1026 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1027 {
1028   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1029   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1030   PetscErrorCode ierr;
1031 
1032   PetscFunctionBegin;
1033   n = 0;
1034   vertices = 0;
1035   if (pcbddc->ConstraintMatrix) {
1036     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1037     for (i=0;i<local_primal_size;i++) {
1038       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1039       if (size_of_constraint == 1) n++;
1040       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1041     }
1042     ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1043     n = 0;
1044     for (i=0;i<local_primal_size;i++) {
1045       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1046       if (size_of_constraint == 1) {
1047         vertices[n++]=row_cmat_indices[0];
1048       }
1049       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1050     }
1051   }
1052   *n_vertices = n;
1053   *vertices_idx = vertices;
1054   PetscFunctionReturn(0);
1055 }
1056 
1057 #undef __FUNCT__
1058 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
1059 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
1060 {
1061   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1062   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
1063   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
1064   PetscBool      *touched;
1065   PetscErrorCode ierr;
1066 
1067   PetscFunctionBegin;
1068   n = 0;
1069   constraints_index = 0;
1070   if (pcbddc->ConstraintMatrix) {
1071     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
1072     max_size_of_constraint = 0;
1073     for (i=0;i<local_primal_size;i++) {
1074       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1075       if (size_of_constraint > 1) {
1076         n++;
1077       }
1078       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
1079       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1080     }
1081     ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
1082     ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
1083     ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1084     ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
1085     n = 0;
1086     for (i=0;i<local_primal_size;i++) {
1087       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1088       if (size_of_constraint > 1) {
1089         ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
1090         min_index = row_cmat_global_indices[0];
1091         min_loc = 0;
1092         for (j=1;j<size_of_constraint;j++) {
1093           /* there can be more than one constraint on a single connected component */
1094           if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
1095             min_index = row_cmat_global_indices[j];
1096             min_loc = j;
1097           }
1098         }
1099         touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
1100         constraints_index[n++] = row_cmat_indices[min_loc];
1101       }
1102       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1103     }
1104   }
1105   ierr = PetscFree(touched);CHKERRQ(ierr);
1106   ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
1107   *n_constraints = n;
1108   *constraints_idx = constraints_index;
1109   PetscFunctionReturn(0);
1110 }
1111 
1112 /* the next two functions has been adapted from pcis.c */
1113 #undef __FUNCT__
1114 #define __FUNCT__ "PCBDDCApplySchur"
1115 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1116 {
1117   PetscErrorCode ierr;
1118   PC_IS          *pcis = (PC_IS*)(pc->data);
1119 
1120   PetscFunctionBegin;
1121   if (!vec2_B) { vec2_B = v; }
1122   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1123   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
1124   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1125   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
1126   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 #undef __FUNCT__
1131 #define __FUNCT__ "PCBDDCApplySchurTranspose"
1132 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1133 {
1134   PetscErrorCode ierr;
1135   PC_IS          *pcis = (PC_IS*)(pc->data);
1136 
1137   PetscFunctionBegin;
1138   if (!vec2_B) { vec2_B = v; }
1139   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1140   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
1141   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1142   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
1143   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1144   PetscFunctionReturn(0);
1145 }
1146 
1147 #undef __FUNCT__
1148 #define __FUNCT__ "PCBDDCSubsetNumbering"
1149 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[])
1150 {
1151   Vec            local_vec,global_vec;
1152   IS             seqis,paris;
1153   VecScatter     scatter_ctx;
1154   PetscScalar    *array;
1155   PetscInt       *temp_global_dofs;
1156   PetscScalar    globalsum;
1157   PetscInt       i,j,s;
1158   PetscInt       nlocals,first_index,old_index,max_local;
1159   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
1160   PetscMPIInt    *dof_sizes,*dof_displs;
1161   PetscBool      first_found;
1162   PetscErrorCode ierr;
1163 
1164   PetscFunctionBegin;
1165   /* mpi buffers */
1166   MPI_Comm_size(comm,&size_prec_comm);
1167   MPI_Comm_rank(comm,&rank_prec_comm);
1168   j = ( !rank_prec_comm ? size_prec_comm : 0);
1169   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1170   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1171   /* get maximum size of subset */
1172   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
1173   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
1174   max_local = 0;
1175   if (n_local_dofs) {
1176     max_local = temp_global_dofs[0];
1177     for (i=1;i<n_local_dofs;i++) {
1178       if (max_local < temp_global_dofs[i] ) {
1179         max_local = temp_global_dofs[i];
1180       }
1181     }
1182   }
1183   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
1184   max_global++;
1185   max_local = 0;
1186   if (n_local_dofs) {
1187     max_local = local_dofs[0];
1188     for (i=1;i<n_local_dofs;i++) {
1189       if (max_local < local_dofs[i] ) {
1190         max_local = local_dofs[i];
1191       }
1192     }
1193   }
1194   max_local++;
1195   /* allocate workspace */
1196   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
1197   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
1198   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
1199   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
1200   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
1201   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
1202   /* create scatter */
1203   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
1204   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
1205   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
1206   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
1207   ierr = ISDestroy(&paris);CHKERRQ(ierr);
1208   /* init array */
1209   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1210   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1211   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1212   if (local_dofs_mult) {
1213     for (i=0;i<n_local_dofs;i++) {
1214       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
1215     }
1216   } else {
1217     for (i=0;i<n_local_dofs;i++) {
1218       array[local_dofs[i]]=1.0;
1219     }
1220   }
1221   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1222   /* scatter into global vec and get total number of global dofs */
1223   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1224   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1225   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
1226   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
1227   /* Fill global_vec with cumulative function for global numbering */
1228   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
1229   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
1230   nlocals = 0;
1231   first_index = -1;
1232   first_found = PETSC_FALSE;
1233   for (i=0;i<s;i++) {
1234     if (!first_found && PetscRealPart(array[i]) > 0.0) {
1235       first_found = PETSC_TRUE;
1236       first_index = i;
1237     }
1238     nlocals += (PetscInt)PetscRealPart(array[i]);
1239   }
1240   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1241   if (!rank_prec_comm) {
1242     dof_displs[0]=0;
1243     for (i=1;i<size_prec_comm;i++) {
1244       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1245     }
1246   }
1247   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1248   if (first_found) {
1249     array[first_index] += (PetscScalar)nlocals;
1250     old_index = first_index;
1251     for (i=first_index+1;i<s;i++) {
1252       if (PetscRealPart(array[i]) > 0.0) {
1253         array[i] += array[old_index];
1254         old_index = i;
1255       }
1256     }
1257   }
1258   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
1259   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1260   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1261   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1262   /* get global ordering of local dofs */
1263   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1264   if (local_dofs_mult) {
1265     for (i=0;i<n_local_dofs;i++) {
1266       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
1267     }
1268   } else {
1269     for (i=0;i<n_local_dofs;i++) {
1270       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
1271     }
1272   }
1273   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1274   /* free workspace */
1275   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1276   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1277   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1278   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1279   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1280   /* return pointer to global ordering of local dofs */
1281   *global_numbering_subset = temp_global_dofs;
1282   PetscFunctionReturn(0);
1283 }
1284