xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 33bc96a4f4522c7e77c48419ee53fa1f761cd021)
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 = PetscFree(pcbddc->local_primal_indices);CHKERRQ(ierr);
70   ierr = PetscFree(pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
71   ierr = PetscFree(pcbddc->replicated_local_primal_values);CHKERRQ(ierr);
72   ierr = PetscFree(pcbddc->local_primal_displacements);CHKERRQ(ierr);
73   ierr = PetscFree(pcbddc->local_primal_sizes);CHKERRQ(ierr);
74   PetscFunctionReturn(0);
75 }
76 
77 #undef __FUNCT__
78 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
79 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
80 {
81   PetscErrorCode ierr;
82   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
83 
84   PetscFunctionBegin;
85   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
86   if (pcbddc->local_auxmat1) {
87     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
88     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
89   }
90   PetscFunctionReturn(0);
91 }
92 
93 #undef __FUNCT__
94 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
95 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
96 {
97   PetscErrorCode ierr;
98   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
99   PC_IS*            pcis = (PC_IS*)  (pc->data);
100   const PetscScalar zero = 0.0;
101 
102   PetscFunctionBegin;
103   /* Application of PHI^T (or PSI^T)  */
104   if (pcbddc->coarse_psi_B) {
105     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
106     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
107   } else {
108     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
109     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
110   }
111   /* Scatter data of coarse_rhs */
112   if (pcbddc->coarse_rhs) { ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr); }
113   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
114 
115   /* Local solution on R nodes */
116   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
117   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
118   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
119   if (pcbddc->inexact_prec_type) {
120     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
121     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
122   }
123   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
124   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
125   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
126   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
127   if (pcbddc->inexact_prec_type) {
128     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
129     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
130   }
131 
132   /* Coarse solution */
133   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
134   if (pcbddc->coarse_rhs) { /* TODO remove null space when doing multilevel */
135     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
136   }
137   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
138   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
139 
140   /* Sum contributions from two levels */
141   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
142   if (pcbddc->inexact_prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
143   PetscFunctionReturn(0);
144 }
145 
146 #undef __FUNCT__
147 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
148 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
149 {
150   PetscErrorCode ierr;
151   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
152 
153   PetscFunctionBegin;
154   switch (pcbddc->coarse_communications_type) {
155     case SCATTERS_BDDC:
156       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
157       break;
158     case GATHERS_BDDC:
159       break;
160   }
161   PetscFunctionReturn(0);
162 }
163 
164 #undef __FUNCT__
165 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
166 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
167 {
168   PetscErrorCode ierr;
169   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
170   PetscScalar*   array_to;
171   PetscScalar*   array_from;
172   MPI_Comm       comm;
173   PetscInt       i;
174 
175   PetscFunctionBegin;
176   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
177   switch (pcbddc->coarse_communications_type) {
178     case SCATTERS_BDDC:
179       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
180       break;
181     case GATHERS_BDDC:
182       if (vec_from) {
183         ierr = VecGetArray(vec_from,&array_from);CHKERRQ(ierr);
184       }
185       if (vec_to) {
186         ierr = VecGetArray(vec_to,&array_to);CHKERRQ(ierr);
187       }
188       switch(pcbddc->coarse_problem_type){
189         case SEQUENTIAL_BDDC:
190           if (smode == SCATTER_FORWARD) {
191             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);
192             if (vec_to) {
193               if (imode == ADD_VALUES) {
194                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
195                   array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
196                 }
197               } else {
198                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
199                   array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
200                 }
201               }
202             }
203           } else {
204             if (vec_from) {
205               if (imode == ADD_VALUES) {
206                 MPI_Comm vec_from_comm;
207                 ierr = PetscObjectGetComm((PetscObject)(vec_from),&vec_from_comm);CHKERRQ(ierr);
208                 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);
209               }
210               for (i=0;i<pcbddc->replicated_primal_size;i++) {
211                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
212               }
213             }
214             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);
215           }
216           break;
217         case REPLICATED_BDDC:
218           if (smode == SCATTER_FORWARD) {
219             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);
220             if (imode == ADD_VALUES) {
221               for (i=0;i<pcbddc->replicated_primal_size;i++) {
222                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
223               }
224             } else {
225               for (i=0;i<pcbddc->replicated_primal_size;i++) {
226                 array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
227               }
228             }
229           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
230             if (imode == ADD_VALUES) {
231               for (i=0;i<pcbddc->local_primal_size;i++) {
232                 array_to[i]+=array_from[pcbddc->local_primal_indices[i]];
233               }
234             } else {
235               for (i=0;i<pcbddc->local_primal_size;i++) {
236                 array_to[i]=array_from[pcbddc->local_primal_indices[i]];
237               }
238             }
239           }
240           break;
241         case MULTILEVEL_BDDC:
242           break;
243         case PARALLEL_BDDC:
244           break;
245       }
246       if (vec_from) {
247         ierr = VecRestoreArray(vec_from,&array_from);CHKERRQ(ierr);
248       }
249       if (vec_to) {
250         ierr = VecRestoreArray(vec_to,&array_to);CHKERRQ(ierr);
251       }
252       break;
253   }
254   PetscFunctionReturn(0);
255 }
256 
257 #undef __FUNCT__
258 #define __FUNCT__ "PCBDDCConstraintsSetUp"
259 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
260 {
261   PetscErrorCode ierr;
262   PC_IS*         pcis = (PC_IS*)(pc->data);
263   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
264   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
265   PetscInt       *nnz,*is_indices;
266   PetscScalar    *temp_quadrature_constraint;
267   PetscInt       *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B,*local_to_B;
268   PetscInt       local_primal_size,i,j,k,total_counts,max_size_of_constraint;
269   PetscInt       n_vertices,size_of_constraint;
270   PetscReal      real_value;
271   PetscBool      nnsp_has_cnst=PETSC_FALSE,use_nnsp_true=pcbddc->use_nnsp_true;
272   PetscInt       nnsp_size=0,nnsp_addone=0,temp_constraints,temp_start_ptr,n_ISForFaces,n_ISForEdges;
273   IS             *used_IS,ISForVertices,*ISForFaces,*ISForEdges;
274   MatType        impMatType=MATSEQAIJ;
275   PetscBLASInt   Bs,Bt,lwork,lierr;
276   PetscReal      tol=1.0e-8;
277   MatNullSpace   nearnullsp;
278   const Vec      *nearnullvecs;
279   Vec            *localnearnullsp;
280   PetscScalar    *work,*temp_basis,*array_vector,*correlation_mat;
281   PetscReal      *rwork,*singular_vals;
282   PetscBLASInt   Bone=1,*ipiv;
283   Vec            temp_vec;
284   Mat            temp_mat;
285   KSP            temp_ksp;
286   PC             temp_pc;
287   PetscInt       s,start_constraint,dual_dofs;
288   PetscBool      compute_submatrix,useksp=PETSC_FALSE;
289   PetscInt       *aux_primal_permutation,*aux_primal_numbering;
290   PetscBool      boolforchange,*change_basis;
291 /* some ugly conditional declarations */
292 #if defined(PETSC_MISSING_LAPACK_GESVD)
293   PetscScalar    one=1.0,zero=0.0;
294   PetscInt       ii;
295   PetscScalar    *singular_vectors;
296   PetscBLASInt   *iwork,*ifail;
297   PetscReal      dummy_real,abs_tol;
298   PetscBLASInt   eigs_found;
299 #endif
300   PetscBLASInt   dummy_int;
301   PetscScalar    dummy_scalar;
302   PetscBool      used_vertex,get_faces,get_edges,get_vertices;
303 
304   PetscFunctionBegin;
305   /* Get index sets for faces, edges and vertices from graph */
306   get_faces = PETSC_TRUE;
307   get_edges = PETSC_TRUE;
308   get_vertices = PETSC_TRUE;
309   if (pcbddc->vertices_flag) {
310     get_faces = PETSC_FALSE;
311     get_edges = PETSC_FALSE;
312   }
313   if (pcbddc->constraints_flag) {
314     get_vertices = PETSC_FALSE;
315   }
316   if (pcbddc->faces_flag) {
317     get_edges = PETSC_FALSE;
318   }
319   if (pcbddc->edges_flag) {
320     get_faces = PETSC_FALSE;
321   }
322   /* default */
323   if (!get_faces && !get_edges && !get_vertices) {
324     get_vertices = PETSC_TRUE;
325   }
326   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
327   if (pcbddc->dbg_flag) {
328     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
329     i = 0;
330     if (ISForVertices) {
331       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
332     }
333     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
334     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
335     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
336     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
337   }
338   /* check if near null space is attached to global mat */
339   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
340   if (nearnullsp) {
341     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
342   } else { /* if near null space is not provided it uses constants */
343     nnsp_has_cnst = PETSC_TRUE;
344     use_nnsp_true = PETSC_TRUE;
345   }
346   if (nnsp_has_cnst) {
347     nnsp_addone = 1;
348   }
349   /*
350        Evaluate maximum storage size needed by the procedure
351        - temp_indices will contain start index of each constraint stored as follows
352        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
353        - 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
354        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
355                                                                                                                                                          */
356   total_counts = n_ISForFaces+n_ISForEdges;
357   total_counts *= (nnsp_addone+nnsp_size);
358   n_vertices = 0;
359   if (ISForVertices) {
360     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
361   }
362   total_counts += n_vertices;
363   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
364   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
365   total_counts = 0;
366   max_size_of_constraint = 0;
367   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
368     if (i<n_ISForEdges) {
369       used_IS = &ISForEdges[i];
370     } else {
371       used_IS = &ISForFaces[i-n_ISForEdges];
372     }
373     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
374     total_counts += j;
375     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
376   }
377   total_counts *= (nnsp_addone+nnsp_size);
378   total_counts += n_vertices;
379   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
380   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
381   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
382   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
383   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
384   for (i=0;i<pcis->n;i++) {
385     local_to_B[i]=-1;
386   }
387   for (i=0;i<pcis->n_B;i++) {
388     local_to_B[is_indices[i]]=i;
389   }
390   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
391 
392   /* First we issue queries to allocate optimal workspace for LAPACKgesvd or LAPACKsyev/LAPACKheev */
393   rwork = 0;
394   work = 0;
395   singular_vals = 0;
396   temp_basis = 0;
397   correlation_mat = 0;
398   if (!pcbddc->use_nnsp_true) {
399     PetscScalar temp_work;
400 #if defined(PETSC_MISSING_LAPACK_GESVD)
401     /* POD */
402     PetscInt max_n;
403     max_n = nnsp_addone+nnsp_size;
404     /* using some techniques borrowed from Proper Orthogonal Decomposition */
405     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
406     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&singular_vectors);CHKERRQ(ierr);
407     ierr = PetscMalloc(max_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
408     ierr = PetscMalloc(max_size_of_constraint*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
409 #if defined(PETSC_USE_COMPLEX)
410     ierr = PetscMalloc(3*max_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
411 #endif
412     ierr = PetscMalloc(5*max_n*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
413     ierr = PetscMalloc(max_n*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
414     /* now we evaluate the optimal workspace using query with lwork=-1 */
415     ierr = PetscBLASIntCast(max_n,&Bt);CHKERRQ(ierr);
416     lwork=-1;
417     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
418 #if !defined(PETSC_USE_COMPLEX)
419     abs_tol=1.e-8;
420 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,&lierr); */
421     PetscStackCallBLAS("LAPACKsyevx",LAPACKsyevx_("V","A","U",&Bt,correlation_mat,&Bt,&dummy_real,&dummy_real,&dummy_int,&dummy_int,&abs_tol,&eigs_found,singular_vals,singular_vectors,&Bt,&temp_work,&lwork,iwork,ifail,&lierr));
422 #else
423 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,rwork,&lierr); */
424 /*  LAPACK call is missing here! TODO */
425     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
426 #endif
427     if ( lierr ) {
428       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEVX Lapack routine %d",(int)lierr);
429     }
430     ierr = PetscFPTrapPop();CHKERRQ(ierr);
431 #else /* on missing GESVD */
432     /* SVD */
433     PetscInt max_n,min_n;
434     max_n = max_size_of_constraint;
435     min_n = nnsp_addone+nnsp_size;
436     if (max_size_of_constraint < ( nnsp_addone+nnsp_size ) ) {
437       min_n = max_size_of_constraint;
438       max_n = nnsp_addone+nnsp_size;
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     dummy_int = Bs;
449     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
450 #if !defined(PETSC_USE_COMPLEX)
451     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,&lierr));
452 #else
453     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,rwork,&lierr));
454 #endif
455     if ( lierr ) {
456       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SVD Lapack routine %d",(int)lierr);
457     }
458     ierr = PetscFPTrapPop();CHKERRQ(ierr);
459 #endif
460     /* Allocate optimal workspace */
461     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
462     total_counts = (PetscInt)lwork;
463     ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&work);CHKERRQ(ierr);
464   }
465   /* get local part of global near null space vectors */
466   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
467   for (k=0;k<nnsp_size;k++) {
468     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
469     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
470     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
471   }
472   /* Now we can loop on constraining sets */
473   total_counts = 0;
474   temp_indices[0] = 0;
475   /* vertices */
476   if (ISForVertices) {
477     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
478     if (nnsp_has_cnst) { /* consider all vertices */
479       for (i=0;i<n_vertices;i++) {
480         temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
481         temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
482         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
483         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
484         change_basis[total_counts]=PETSC_FALSE;
485         total_counts++;
486       }
487     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
488       for (i=0;i<n_vertices;i++) {
489         used_vertex=PETSC_FALSE;
490         k=0;
491         while (!used_vertex && k<nnsp_size) {
492           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
493           if (PetscAbsScalar(array_vector[is_indices[i]])>0.0) {
494             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
495             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
496             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
497             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
498             change_basis[total_counts]=PETSC_FALSE;
499             total_counts++;
500             used_vertex=PETSC_TRUE;
501           }
502           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
503           k++;
504         }
505       }
506     }
507     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
508     n_vertices = total_counts;
509   }
510   /* edges and faces */
511   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
512     if (i<n_ISForEdges) {
513       used_IS = &ISForEdges[i];
514       boolforchange = pcbddc->use_change_of_basis;
515     } else {
516       used_IS = &ISForFaces[i-n_ISForEdges];
517       boolforchange = pcbddc->use_change_on_faces;
518     }
519     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
520     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
521     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
522     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
523     /* HACK: change of basis should not performed on local periodic nodes */
524     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) {
525       boolforchange = PETSC_FALSE;
526     }
527     if (nnsp_has_cnst) {
528       PetscScalar quad_value;
529       temp_constraints++;
530       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
531       for (j=0;j<size_of_constraint;j++) {
532         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
533         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
534         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
535       }
536       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
537       change_basis[total_counts]=boolforchange;
538       total_counts++;
539     }
540     for (k=0;k<nnsp_size;k++) {
541       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
542       for (j=0;j<size_of_constraint;j++) {
543         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
544         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
545         temp_quadrature_constraint[temp_indices[total_counts]+j]=array_vector[is_indices[j]];
546       }
547       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
548       real_value = 1.0;
549       if (use_nnsp_true) { /* check if array is null on the connected component in case use_nnsp_true has been requested */
550         ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
551         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone));
552       }
553       if (real_value > 0.0) { /* keep indices and values */
554         temp_constraints++;
555         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
556         change_basis[total_counts]=boolforchange;
557         total_counts++;
558       }
559     }
560     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
561     /* perform SVD on the constraint if use_nnsp_true has not be requested by the user */
562     if (!use_nnsp_true) {
563       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
564       ierr = PetscBLASIntCast(temp_constraints,&Bt);CHKERRQ(ierr);
565 
566 #if defined(PETSC_MISSING_LAPACK_GESVD)
567       ierr = PetscMemzero(correlation_mat,Bt*Bt*sizeof(PetscScalar));CHKERRQ(ierr);
568       /* Store upper triangular part of correlation matrix */
569       for (j=0;j<temp_constraints;j++) {
570         for (k=0;k<j+1;k++) {
571           PetscStackCallBLAS("BLASdot",correlation_mat[j*temp_constraints+k]=BLASdot_(&Bs,&temp_quadrature_constraint[temp_indices[temp_start_ptr+j]],&Bone,&temp_quadrature_constraint[temp_indices[temp_start_ptr+k]],&Bone));
572 
573         }
574       }
575       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
576 #if !defined(PETSC_USE_COMPLEX)
577 /*      LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,&lierr); */
578       PetscStackCallBLAS("LAPACKsyevx",LAPACKsyevx_("V","A","U",&Bt,correlation_mat,&Bt,&dummy_real,&dummy_real,&dummy_int,&dummy_int,&abs_tol,&eigs_found,singular_vals,singular_vectors,&Bt,work,&lwork,iwork,ifail,&lierr));
579 #else
580 /*  LAPACK call is missing here! TODO */
581       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
582 #endif
583       if (lierr) {
584         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEVX Lapack routine %d",(int)lierr);
585       }
586       ierr = PetscFPTrapPop();CHKERRQ(ierr);
587       /* retain eigenvalues greater than tol: note that lapack SYEV gives eigs in ascending order */
588       j=0;
589       while (j < Bt && singular_vals[j] < tol) j++;
590       total_counts=total_counts-j;
591       if (j<temp_constraints) {
592         for (k=j;k<Bt;k++) {
593           singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
594         }
595         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
596         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));
597         ierr = PetscFPTrapPop();CHKERRQ(ierr);
598         /* copy POD basis into used quadrature memory */
599         for (k=0;k<Bt-j;k++) {
600           for (ii=0;ii<size_of_constraint;ii++) {
601             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[Bt-1-k]*temp_basis[(Bt-1-k)*size_of_constraint+ii];
602           }
603         }
604       }
605 
606 #else  /* on missing GESVD */
607       PetscInt min_n = temp_constraints;
608       if (min_n > size_of_constraint) min_n = size_of_constraint;
609       dummy_int = Bs;
610       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
611 #if !defined(PETSC_USE_COMPLEX)
612       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,&lierr));
613 #else
614       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,rwork,&lierr));
615 #endif
616       if (lierr) {
617         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD Lapack routine %d",(int)lierr);
618       }
619       ierr = PetscFPTrapPop();CHKERRQ(ierr);
620       /* retain eigenvalues greater than tol: note that lapack SVD gives eigs in descending order */
621       j = 0;
622       while (j < min_n && singular_vals[min_n-j-1] < tol) j++;
623       total_counts = total_counts-(PetscInt)Bt+(min_n-j);
624 #endif
625     }
626   }
627   /* free index sets of faces, edges and vertices */
628   for (i=0;i<n_ISForFaces;i++) {
629     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
630   }
631   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
632   for (i=0;i<n_ISForEdges;i++) {
633     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
634   }
635   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
636   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
637 
638   /* set quantities in pcbddc data structure */
639   /* n_vertices defines the number of point primal dofs */
640   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
641   local_primal_size = total_counts;
642   pcbddc->n_vertices = n_vertices;
643   pcbddc->n_constraints = total_counts-n_vertices;
644   pcbddc->local_primal_size = local_primal_size;
645 
646   /* Create constraint matrix */
647   /* The constraint matrix is used to compute the l2g map of primal dofs */
648   /* so we need to set it up properly either with or without change of basis */
649   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
650   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
651   ierr = MatSetSizes(pcbddc->ConstraintMatrix,local_primal_size,pcis->n,local_primal_size,pcis->n);CHKERRQ(ierr);
652   /* compute a local numbering of constraints : vertices first then constraints */
653   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
654   ierr = VecGetArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
655   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
656   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_permutation);CHKERRQ(ierr);
657   total_counts=0;
658   /* find vertices: subdomain corners plus dofs with basis changed */
659   for (i=0;i<local_primal_size;i++) {
660     size_of_constraint=temp_indices[i+1]-temp_indices[i];
661     if (change_basis[i] || size_of_constraint == 1) {
662       k=0;
663       while(k < size_of_constraint && array_vector[temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1]] != 0.0) {
664         k=k+1;
665       }
666       j=temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1];
667       array_vector[j] = 1.0;
668       aux_primal_numbering[total_counts]=j;
669       aux_primal_permutation[total_counts]=total_counts;
670       total_counts++;
671     }
672   }
673   ierr = VecRestoreArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
674   /* permute indices in order to have a sorted set of vertices */
675   ierr = PetscSortIntWithPermutation(total_counts,aux_primal_numbering,aux_primal_permutation);
676   /* nonzero structure */
677   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
678   for (i=0;i<total_counts;i++) {
679     nnz[i]=1;
680   }
681   j=total_counts;
682   for (i=n_vertices;i<local_primal_size;i++) {
683     if (!change_basis[i]) {
684       nnz[j]=temp_indices[i+1]-temp_indices[i];
685       j++;
686     }
687   }
688   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
689   ierr = PetscFree(nnz);CHKERRQ(ierr);
690   /* set values in constraint matrix */
691   for (i=0;i<total_counts;i++) {
692     j = aux_primal_permutation[i];
693     k = aux_primal_numbering[j];
694     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,k,1.0,INSERT_VALUES);CHKERRQ(ierr);
695   }
696   for (i=n_vertices;i<local_primal_size;i++) {
697     if (!change_basis[i]) {
698       size_of_constraint=temp_indices[i+1]-temp_indices[i];
699       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);
700       total_counts++;
701     }
702   }
703   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
704   ierr = PetscFree(aux_primal_permutation);CHKERRQ(ierr);
705   /* assembling */
706   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
707   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
708 
709   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
710   if (pcbddc->use_change_of_basis) {
711     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
712     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
713     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
714     /* work arrays */
715     /* we need to reuse these arrays, so we free them */
716     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
717     ierr = PetscFree(work);CHKERRQ(ierr);
718     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
719     ierr = PetscMalloc((nnsp_addone+nnsp_size)*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
720     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscScalar),&work);CHKERRQ(ierr);
721     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscBLASInt),&ipiv);CHKERRQ(ierr);
722     for (i=0;i<pcis->n_B;i++) {
723       nnz[i]=1;
724     }
725     /* Overestimated nonzeros per row */
726     k=1;
727     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
728       if (change_basis[i]) {
729         size_of_constraint = temp_indices[i+1]-temp_indices[i];
730         if (k < size_of_constraint) {
731           k = size_of_constraint;
732         }
733         for (j=0;j<size_of_constraint;j++) {
734           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
735         }
736       }
737     }
738     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
739     ierr = PetscFree(nnz);CHKERRQ(ierr);
740     /* Temporary array to store indices */
741     ierr = PetscMalloc(k*sizeof(PetscInt),&is_indices);CHKERRQ(ierr);
742     /* Set initial identity in the matrix */
743     for (i=0;i<pcis->n_B;i++) {
744       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
745     }
746     /* Now we loop on the constraints which need a change of basis */
747     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
748     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (6.2.1) */
749     temp_constraints = 0;
750     if (pcbddc->n_vertices < local_primal_size) {
751       temp_start_ptr = temp_indices_to_constraint_B[temp_indices[pcbddc->n_vertices]];
752     }
753     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
754       if (change_basis[i]) {
755         compute_submatrix = PETSC_FALSE;
756         useksp = PETSC_FALSE;
757         if (temp_start_ptr == temp_indices_to_constraint_B[temp_indices[i]]) {
758           temp_constraints++;
759           if (i == local_primal_size -1 ||  temp_start_ptr != temp_indices_to_constraint_B[temp_indices[i+1]]) {
760             compute_submatrix = PETSC_TRUE;
761           }
762         }
763         if (compute_submatrix) {
764           if (temp_constraints > 1 || pcbddc->use_nnsp_true) {
765             useksp = PETSC_TRUE;
766           }
767           size_of_constraint = temp_indices[i+1]-temp_indices[i];
768           if (useksp) { /* experimental TODO: reuse KSP and MAT instead of creating them each time */
769             ierr = MatCreate(PETSC_COMM_SELF,&temp_mat);CHKERRQ(ierr);
770             ierr = MatSetType(temp_mat,impMatType);CHKERRQ(ierr);
771             ierr = MatSetSizes(temp_mat,size_of_constraint,size_of_constraint,size_of_constraint,size_of_constraint);CHKERRQ(ierr);
772             ierr = MatSeqAIJSetPreallocation(temp_mat,size_of_constraint,NULL);CHKERRQ(ierr);
773           }
774           /* First _size_of_constraint-temp_constraints_ columns */
775           dual_dofs = size_of_constraint-temp_constraints;
776           start_constraint = i+1-temp_constraints;
777           for (s=0;s<dual_dofs;s++) {
778             is_indices[0] = s;
779             for (j=0;j<temp_constraints;j++) {
780               for (k=0;k<temp_constraints;k++) {
781                 temp_basis[j*temp_constraints+k]=temp_quadrature_constraint[temp_indices[start_constraint+k]+s+j+1];
782               }
783               work[j]=-temp_quadrature_constraint[temp_indices[start_constraint+j]+s];
784               is_indices[j+1]=s+j+1;
785             }
786             Bt = temp_constraints;
787             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
788             PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&Bt,&Bone,temp_basis,&Bt,ipiv,work,&Bt,&lierr));
789             if ( lierr ) {
790               SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESV Lapack routine %d",(int)lierr);
791             }
792             ierr = PetscFPTrapPop();CHKERRQ(ierr);
793             j = temp_indices_to_constraint_B[temp_indices[start_constraint]+s];
794             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,temp_constraints,&temp_indices_to_constraint_B[temp_indices[start_constraint]+s+1],1,&j,work,INSERT_VALUES);CHKERRQ(ierr);
795             if (useksp) {
796               /* temp mat with transposed rows and columns */
797               ierr = MatSetValues(temp_mat,1,&s,temp_constraints,&is_indices[1],work,INSERT_VALUES);CHKERRQ(ierr);
798               ierr = MatSetValue(temp_mat,is_indices[0],is_indices[0],1.0,INSERT_VALUES);CHKERRQ(ierr);
799             }
800           }
801           if (useksp) {
802             /* last rows of temp_mat */
803             for (j=0;j<size_of_constraint;j++) {
804               is_indices[j] = j;
805             }
806             for (s=0;s<temp_constraints;s++) {
807               k = s + dual_dofs;
808               ierr = MatSetValues(temp_mat,1,&k,size_of_constraint,is_indices,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
809             }
810             ierr = MatAssemblyBegin(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
811             ierr = MatAssemblyEnd(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
812             ierr = MatGetVecs(temp_mat,&temp_vec,NULL);CHKERRQ(ierr);
813             ierr = KSPCreate(PETSC_COMM_SELF,&temp_ksp);CHKERRQ(ierr);
814             ierr = KSPSetOperators(temp_ksp,temp_mat,temp_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
815             ierr = KSPSetType(temp_ksp,KSPPREONLY);CHKERRQ(ierr);
816             ierr = KSPGetPC(temp_ksp,&temp_pc);CHKERRQ(ierr);
817             ierr = PCSetType(temp_pc,PCLU);CHKERRQ(ierr);
818             ierr = KSPSetUp(temp_ksp);CHKERRQ(ierr);
819             for (s=0;s<temp_constraints;s++) {
820               ierr = VecSet(temp_vec,0.0);CHKERRQ(ierr);
821               ierr = VecSetValue(temp_vec,s+dual_dofs,1.0,INSERT_VALUES);CHKERRQ(ierr);
822               ierr = VecAssemblyBegin(temp_vec);CHKERRQ(ierr);
823               ierr = VecAssemblyEnd(temp_vec);CHKERRQ(ierr);
824               ierr = KSPSolve(temp_ksp,temp_vec,temp_vec);CHKERRQ(ierr);
825               ierr = VecGetArray(temp_vec,&array_vector);CHKERRQ(ierr);
826               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
827               /* last columns of change of basis matrix associated to new primal dofs */
828               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,&temp_indices_to_constraint_B[temp_indices[start_constraint+s]],1,&j,array_vector,INSERT_VALUES);CHKERRQ(ierr);
829               ierr = VecRestoreArray(temp_vec,&array_vector);CHKERRQ(ierr);
830             }
831             ierr = MatDestroy(&temp_mat);CHKERRQ(ierr);
832             ierr = KSPDestroy(&temp_ksp);CHKERRQ(ierr);
833             ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
834           } else {
835             /* last columns of change of basis matrix associated to new primal dofs */
836             for (s=0;s<temp_constraints;s++) {
837               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
838               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,&temp_indices_to_constraint_B[temp_indices[start_constraint+s]],1,&j,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
839             }
840           }
841           /* prepare for the next cycle */
842           temp_constraints = 0;
843           if (i != local_primal_size -1 ) {
844             temp_start_ptr = temp_indices_to_constraint_B[temp_indices[i+1]];
845           }
846         }
847       }
848     }
849     /* assembling */
850     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
851     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
852     ierr = PetscFree(ipiv);CHKERRQ(ierr);
853     ierr = PetscFree(is_indices);CHKERRQ(ierr);
854   }
855   /* free workspace no longer needed */
856   ierr = PetscFree(rwork);CHKERRQ(ierr);
857   ierr = PetscFree(work);CHKERRQ(ierr);
858   ierr = PetscFree(temp_basis);CHKERRQ(ierr);
859   ierr = PetscFree(singular_vals);CHKERRQ(ierr);
860   ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
861   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
862   ierr = PetscFree(change_basis);CHKERRQ(ierr);
863   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
864   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
865   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
866   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
867 #if defined(PETSC_MISSING_LAPACK_GESVD)
868   ierr = PetscFree(iwork);CHKERRQ(ierr);
869   ierr = PetscFree(ifail);CHKERRQ(ierr);
870   ierr = PetscFree(singular_vectors);CHKERRQ(ierr);
871 #endif
872   for (k=0;k<nnsp_size;k++) {
873     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
874   }
875   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
876   PetscFunctionReturn(0);
877 }
878 
879 #undef __FUNCT__
880 #define __FUNCT__ "PCBDDCAnalyzeInterface"
881 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
882 {
883   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
884   PC_IS       *pcis = (PC_IS*)pc->data;
885   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
886   PetscInt    bs,ierr,i,vertex_size;
887   PetscViewer viewer=pcbddc->dbg_viewer;
888 
889   PetscFunctionBegin;
890   /* Init local Graph struct */
891   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
892 
893   /* Check validity of the csr graph passed in by the user */
894   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
895     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
896   }
897   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
898   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
899     Mat mat_adj;
900     const PetscInt *xadj,*adjncy;
901     PetscBool flg_row=PETSC_TRUE;
902 
903     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
904     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
905     if (!flg_row) {
906       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
907     }
908     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
909     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
910     if (!flg_row) {
911       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
912     }
913     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
914   }
915 
916   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
917   vertex_size = 1;
918   if (!pcbddc->n_ISForDofs) {
919     IS *custom_ISForDofs;
920 
921     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
922     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
923     for (i=0;i<bs;i++) {
924       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
925     }
926     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
927     /* remove my references to IS objects */
928     for (i=0;i<bs;i++) {
929       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
930     }
931     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
932   } else { /* mat block size as vertex size (used for elasticity) */
933     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
934   }
935 
936   /* Setup of Graph */
937   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
938 
939   /* Graph's connected components analysis */
940   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
941 
942   /* print some info to stdout */
943   if (pcbddc->dbg_flag) {
944     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
945   }
946   PetscFunctionReturn(0);
947 }
948 
949 #undef __FUNCT__
950 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
951 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
952 {
953   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
954   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
955   PetscErrorCode ierr;
956 
957   PetscFunctionBegin;
958   n = 0;
959   vertices = 0;
960   if (pcbddc->ConstraintMatrix) {
961     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
962     for (i=0;i<local_primal_size;i++) {
963       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
964       if (size_of_constraint == 1) n++;
965       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
966     }
967     ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
968     n = 0;
969     for (i=0;i<local_primal_size;i++) {
970       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
971       if (size_of_constraint == 1) {
972         vertices[n++]=row_cmat_indices[0];
973       }
974       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
975     }
976   }
977   *n_vertices = n;
978   *vertices_idx = vertices;
979   PetscFunctionReturn(0);
980 }
981 
982 #undef __FUNCT__
983 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
984 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
985 {
986   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
987   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
988   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
989   PetscBool      *touched;
990   PetscErrorCode ierr;
991 
992   PetscFunctionBegin;
993   n = 0;
994   constraints_index = 0;
995   if (pcbddc->ConstraintMatrix) {
996     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
997     max_size_of_constraint = 0;
998     for (i=0;i<local_primal_size;i++) {
999       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1000       if (size_of_constraint > 1) {
1001         n++;
1002       }
1003       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
1004       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1005     }
1006     ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
1007     ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
1008     ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1009     ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
1010     n = 0;
1011     for (i=0;i<local_primal_size;i++) {
1012       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1013       if (size_of_constraint > 1) {
1014         ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
1015         min_index = row_cmat_global_indices[0];
1016         min_loc = 0;
1017         for (j=1;j<size_of_constraint;j++) {
1018           /* there can be more than one constraint on a single connected component */
1019           if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
1020             min_index = row_cmat_global_indices[j];
1021             min_loc = j;
1022           }
1023         }
1024         touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
1025         constraints_index[n++] = row_cmat_indices[min_loc];
1026       }
1027       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1028     }
1029   }
1030   ierr = PetscFree(touched);CHKERRQ(ierr);
1031   ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
1032   *n_constraints = n;
1033   *constraints_idx = constraints_index;
1034   PetscFunctionReturn(0);
1035 }
1036 
1037 /* the next two functions has been adapted from pcis.c */
1038 #undef __FUNCT__
1039 #define __FUNCT__ "PCBDDCApplySchur"
1040 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1041 {
1042   PetscErrorCode ierr;
1043   PC_IS          *pcis = (PC_IS*)(pc->data);
1044 
1045   PetscFunctionBegin;
1046   if (!vec2_B) { vec2_B = v; }
1047   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1048   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
1049   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1050   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
1051   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1052   PetscFunctionReturn(0);
1053 }
1054 
1055 #undef __FUNCT__
1056 #define __FUNCT__ "PCBDDCApplySchurTranspose"
1057 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1058 {
1059   PetscErrorCode ierr;
1060   PC_IS          *pcis = (PC_IS*)(pc->data);
1061 
1062   PetscFunctionBegin;
1063   if (!vec2_B) { vec2_B = v; }
1064   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1065   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
1066   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1067   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
1068   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1069   PetscFunctionReturn(0);
1070 }
1071 
1072 #undef __FUNCT__
1073 #define __FUNCT__ "PCBDDCSubsetNumbering"
1074 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[])
1075 {
1076   Vec            local_vec,global_vec;
1077   IS             seqis,paris;
1078   VecScatter     scatter_ctx;
1079   PetscScalar    *array;
1080   PetscInt       *temp_global_dofs;
1081   PetscScalar    globalsum;
1082   PetscInt       i,j,s;
1083   PetscInt       nlocals,first_index,old_index,max_local;
1084   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
1085   PetscMPIInt    *dof_sizes,*dof_displs;
1086   PetscBool      first_found;
1087   PetscErrorCode ierr;
1088 
1089   PetscFunctionBegin;
1090   /* mpi buffers */
1091   MPI_Comm_size(comm,&size_prec_comm);
1092   MPI_Comm_rank(comm,&rank_prec_comm);
1093   j = ( !rank_prec_comm ? size_prec_comm : 0);
1094   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1095   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1096   /* get maximum size of subset */
1097   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
1098   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
1099   max_local = 0;
1100   if (n_local_dofs) {
1101     max_local = temp_global_dofs[0];
1102     for (i=1;i<n_local_dofs;i++) {
1103       if (max_local < temp_global_dofs[i] ) {
1104         max_local = temp_global_dofs[i];
1105       }
1106     }
1107   }
1108   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
1109   max_global++;
1110   max_local = 0;
1111   if (n_local_dofs) {
1112     max_local = local_dofs[0];
1113     for (i=1;i<n_local_dofs;i++) {
1114       if (max_local < local_dofs[i] ) {
1115         max_local = local_dofs[i];
1116       }
1117     }
1118   }
1119   max_local++;
1120   /* allocate workspace */
1121   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
1122   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
1123   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
1124   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
1125   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
1126   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
1127   /* create scatter */
1128   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
1129   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
1130   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
1131   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
1132   ierr = ISDestroy(&paris);CHKERRQ(ierr);
1133   /* init array */
1134   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1135   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1136   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1137   if (local_dofs_mult) {
1138     for (i=0;i<n_local_dofs;i++) {
1139       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
1140     }
1141   } else {
1142     for (i=0;i<n_local_dofs;i++) {
1143       array[local_dofs[i]]=1.0;
1144     }
1145   }
1146   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1147   /* scatter into global vec and get total number of global dofs */
1148   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1149   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1150   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
1151   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
1152   /* Fill global_vec with cumulative function for global numbering */
1153   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
1154   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
1155   nlocals = 0;
1156   first_index = -1;
1157   first_found = PETSC_FALSE;
1158   for (i=0;i<s;i++) {
1159     if (!first_found && PetscRealPart(array[i]) > 0.0) {
1160       first_found = PETSC_TRUE;
1161       first_index = i;
1162     }
1163     nlocals += (PetscInt)PetscRealPart(array[i]);
1164   }
1165   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1166   if (!rank_prec_comm) {
1167     dof_displs[0]=0;
1168     for (i=1;i<size_prec_comm;i++) {
1169       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1170     }
1171   }
1172   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1173   if (first_found) {
1174     array[first_index] += (PetscScalar)nlocals;
1175     old_index = first_index;
1176     for (i=first_index+1;i<s;i++) {
1177       if (PetscRealPart(array[i]) > 0.0) {
1178         array[i] += array[old_index];
1179         old_index = i;
1180       }
1181     }
1182   }
1183   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
1184   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1185   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1186   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1187   /* get global ordering of local dofs */
1188   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1189   if (local_dofs_mult) {
1190     for (i=0;i<n_local_dofs;i++) {
1191       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
1192     }
1193   } else {
1194     for (i=0;i<n_local_dofs;i++) {
1195       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
1196     }
1197   }
1198   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1199   /* free workspace */
1200   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1201   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1202   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1203   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1204   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1205   /* return pointer to global ordering of local dofs */
1206   *global_numbering_subset = temp_global_dofs;
1207   PetscFunctionReturn(0);
1208 }
1209