xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision b0418fcf1b12943baba9236d58ccd85937632d39)
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 = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
51   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
52   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
53   ierr = MatDestroy(&pcbddc->coarse_mat);CHKERRQ(ierr);
54   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
55   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
56   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
57   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
58   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
59   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
60   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
61   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
62   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
63   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
64   ierr = VecDestroy(&pcbddc->vec4_D);CHKERRQ(ierr);
65   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
66   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
67   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
68   ierr = PetscFree(pcbddc->local_primal_indices);CHKERRQ(ierr);
69   ierr = PetscFree(pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
70   ierr = PetscFree(pcbddc->replicated_local_primal_values);CHKERRQ(ierr);
71   ierr = PetscFree(pcbddc->local_primal_displacements);CHKERRQ(ierr);
72   ierr = PetscFree(pcbddc->local_primal_sizes);CHKERRQ(ierr);
73   PetscFunctionReturn(0);
74 }
75 
76 #undef __FUNCT__
77 #define __FUNCT__ "PCBDDCCreateWorkVectors"
78 PetscErrorCode PCBDDCCreateWorkVectors(PC pc)
79 {
80   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
81   PC_IS          *pcis = (PC_IS*)pc->data;
82   VecType        impVecType;
83   PetscInt       n_vertices,n_constraints,local_primal_size,n_R;
84   PetscErrorCode ierr;
85 
86   PetscFunctionBegin;
87   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,NULL);CHKERRQ(ierr);
88   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&n_constraints,NULL);CHKERRQ(ierr);
89   local_primal_size = n_constraints+n_vertices;
90   n_R = pcis->n-n_vertices;
91   /* parallel work vectors used in presolve. TODO: move outside */
92   ierr = VecDuplicate(pcis->vec1_global,&pcbddc->original_rhs);CHKERRQ(ierr);
93   ierr = VecDuplicate(pcis->vec1_global,&pcbddc->temp_solution);CHKERRQ(ierr);
94   /* local work vectors */
95   ierr = VecGetType(pcis->vec1_N,&impVecType);CHKERRQ(ierr);
96   ierr = VecDuplicate(pcis->vec1_D,&pcbddc->vec4_D);CHKERRQ(ierr);
97   ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);CHKERRQ(ierr);
98   ierr = VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);CHKERRQ(ierr);
99   ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
100   ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
101   ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);CHKERRQ(ierr);
102   ierr = VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,local_primal_size);CHKERRQ(ierr);
103   ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
104   if (n_constraints) {
105     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);CHKERRQ(ierr);
106     ierr = VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);CHKERRQ(ierr);
107     ierr = VecSetType(pcbddc->vec1_C,impVecType);CHKERRQ(ierr);
108   }
109   PetscFunctionReturn(0);
110 }
111 
112 #undef __FUNCT__
113 #define __FUNCT__ "PCBDDCSetUpLocalMatrices"
114 PetscErrorCode PCBDDCSetUpLocalMatrices(PC pc)
115 {
116   PC_IS*            pcis = (PC_IS*)(pc->data);
117   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
118   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
119   /* manage repeated solves */
120   MatReuse          reuse;
121   MatStructure      matstruct;
122   PetscErrorCode    ierr;
123 
124   PetscFunctionBegin;
125   /* get mat flags */
126   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
127   reuse = MAT_INITIAL_MATRIX;
128   if (pc->setupcalled) {
129     /* when matstruct is SAME_PRECONDITIONER, we shouldn't be here */
130     if (matstruct == SAME_PRECONDITIONER) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
131     if (matstruct == SAME_NONZERO_PATTERN) {
132       reuse = MAT_REUSE_MATRIX;
133     } else {
134       reuse = MAT_INITIAL_MATRIX;
135     }
136   }
137   if (reuse == MAT_INITIAL_MATRIX) {
138     ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
139     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
140     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
141     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
142     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
143   }
144 
145   /* transform local matrices if needed */
146   if (pcbddc->use_change_of_basis) {
147     Mat         change_mat_all;
148     PetscScalar *row_cmat_values;
149     PetscInt    *row_cmat_indices;
150     PetscInt    *nnz,*is_indices,*temp_indices;
151     PetscInt    i,j,k,n_D,n_B;
152 
153     /* Get Non-overlapping dimensions */
154     n_B = pcis->n_B;
155     n_D = pcis->n-n_B;
156 
157     /* compute nonzero structure of change of basis on all local nodes */
158     ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
159     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
160     for (i=0;i<n_D;i++) nnz[is_indices[i]] = 1;
161     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
162     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
163     k=1;
164     for (i=0;i<n_B;i++) {
165       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
166       nnz[is_indices[i]]=j;
167       if (k < j) k = j;
168       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
169     }
170     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
171     /* assemble change of basis matrix on the whole set of local dofs */
172     ierr = PetscMalloc(k*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
173     ierr = MatCreate(PETSC_COMM_SELF,&change_mat_all);CHKERRQ(ierr);
174     ierr = MatSetSizes(change_mat_all,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
175     ierr = MatSetType(change_mat_all,MATSEQAIJ);CHKERRQ(ierr);
176     ierr = MatSeqAIJSetPreallocation(change_mat_all,0,nnz);CHKERRQ(ierr);
177     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
178     for (i=0;i<n_D;i++) {
179       ierr = MatSetValue(change_mat_all,is_indices[i],is_indices[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
180     }
181     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
182     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
183     for (i=0;i<n_B;i++) {
184       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
185       for (k=0; k<j; k++) temp_indices[k]=is_indices[row_cmat_indices[k]];
186       ierr = MatSetValues(change_mat_all,1,&is_indices[i],j,temp_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
187       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
188     }
189     ierr = MatAssemblyBegin(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
190     ierr = MatAssemblyEnd(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
191     /* TODO: HOW TO WORK WITH BAIJ? PtAP not provided */
192     ierr = MatGetBlockSize(matis->A,&i);CHKERRQ(ierr);
193     if (i==1) {
194       ierr = MatPtAP(matis->A,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
195     } else {
196       Mat work_mat;
197       ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
198       ierr = MatPtAP(work_mat,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
199       ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
200     }
201     ierr = MatDestroy(&change_mat_all);CHKERRQ(ierr);
202     ierr = PetscFree(nnz);CHKERRQ(ierr);
203     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
204   } else {
205     /* without change of basis, the local matrix is unchanged */
206     if (!pcbddc->local_mat) {
207       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
208       pcbddc->local_mat = matis->A;
209     }
210   }
211 
212   /* get submatrices */
213   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_I_local,reuse,&pcis->A_II);CHKERRQ(ierr);
214   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
215   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
216   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,reuse,&pcis->A_BB);CHKERRQ(ierr);
217   PetscFunctionReturn(0);
218 }
219 
220 #undef __FUNCT__
221 #define __FUNCT__ "PCBDDCSetUpLocalScatters"
222 PetscErrorCode PCBDDCSetUpLocalScatters(PC pc,IS* is_R_local_n)
223 {
224   PC_IS*         pcis = (PC_IS*)(pc->data);
225   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
226   IS             is_R_local,is_aux1,is_aux2;
227   PetscInt       *vertices,*aux_array1,*aux_array2,*is_indices,*idx_R_local;
228   PetscInt       n_vertices,n_constraints,i,j,n_R,n_D,n_B;
229   PetscBool      *array_bool;
230   PetscErrorCode ierr;
231 
232   PetscFunctionBegin;
233   /* Set Non-overlapping dimensions */
234   n_B = pcis->n_B; n_D = pcis->n - n_B;
235   /* get vertex indices from constraint matrix */
236   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,&vertices);CHKERRQ(ierr);
237   /* Set number of constraints */
238   n_constraints = pcbddc->local_primal_size-n_vertices;
239   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
240   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&array_bool);CHKERRQ(ierr);
241   for (i=0;i<pcis->n;i++) array_bool[i] = PETSC_TRUE;
242   for (i=0;i<n_vertices;i++) array_bool[vertices[i]] = PETSC_FALSE;
243   ierr = PetscMalloc((pcis->n-n_vertices)*sizeof(PetscInt),&idx_R_local);CHKERRQ(ierr);
244   for (i=0, n_R=0; i<pcis->n; i++) {
245     if (array_bool[i]) {
246       idx_R_local[n_R] = i;
247       n_R++;
248     }
249   }
250   ierr = PetscFree(vertices);CHKERRQ(ierr);
251   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_R,idx_R_local,PETSC_OWN_POINTER,&is_R_local);CHKERRQ(ierr);
252 
253   /* print some info if requested */
254   if (pcbddc->dbg_flag) {
255     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
256     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
257     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
258     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
259     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"r_size = %d, v_size = %d, constraints = %d, local_primal_size = %d\n",n_R,n_vertices,n_constraints,pcbddc->local_primal_size);CHKERRQ(ierr);
260     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
261     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
262   }
263 
264   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
265   ierr = PetscMalloc((pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
266   ierr = PetscMalloc((pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array2);CHKERRQ(ierr);
267   ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
268   for (i=0; i<n_D; i++) array_bool[is_indices[i]] = PETSC_FALSE;
269   ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
270   for (i=0, j=0; i<n_R; i++) {
271     if (array_bool[idx_R_local[i]]) {
272       aux_array1[j] = i;
273       j++;
274     }
275   }
276   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
277   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
278   for (i=0, j=0; i<n_B; i++) {
279     if (array_bool[is_indices[i]]) {
280       aux_array2[j] = i; j++;
281     }
282   }
283   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
284   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);CHKERRQ(ierr);
285   ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
286   ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
287   ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
288 
289   if (pcbddc->inexact_prec_type || pcbddc->dbg_flag ) {
290     ierr = PetscMalloc(n_D*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
291     for (i=0, j=0; i<n_R; i++) {
292       if (!array_bool[idx_R_local[i]]) {
293         aux_array1[j] = i;
294         j++;
295       }
296     }
297     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
298     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
299     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
300   }
301   ierr = PetscFree(array_bool);CHKERRQ(ierr);
302   *is_R_local_n = is_R_local;
303   PetscFunctionReturn(0);
304 }
305 
306 #undef __FUNCT__
307 #define __FUNCT__ "PCBDDCSetUseExactDirichlet"
308 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool use)
309 {
310   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
311 
312   PetscFunctionBegin;
313   pcbddc->use_exact_dirichlet=use;
314   PetscFunctionReturn(0);
315 }
316 
317 #undef __FUNCT__
318 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
319 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, IS is_I_local, IS is_R_local)
320 {
321   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
322   PC_IS          *pcis = (PC_IS*)pc->data;
323   PC             pc_temp;
324   Mat            A_RR;
325   Vec            vec1,vec2,vec3;
326   MatStructure   matstruct;
327   PetscScalar    m_one = -1.0;
328   PetscReal      value;
329   PetscInt       n_D,n_R,use_exact,use_exact_reduced;
330   PetscErrorCode ierr;
331 
332   PetscFunctionBegin;
333   /* Creating PC contexts for local Dirichlet and Neumann problems */
334   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
335 
336   /* DIRICHLET PROBLEM */
337   /* Matrix for Dirichlet problem is pcis->A_II */
338   ierr = ISGetSize(is_I_local,&n_D);CHKERRQ(ierr);
339   if (!pcbddc->ksp_D) { /* create object if not yet build */
340     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
341     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
342     /* default */
343     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
344     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
345     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
346     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
347     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
348   }
349   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,matstruct);CHKERRQ(ierr);
350   /* Allow user's customization */
351   ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
352   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
353   if (!n_D) {
354     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
355     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
356   }
357   /* Set Up KSP for Dirichlet problem of BDDC */
358   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
359   /* set ksp_D into pcis data */
360   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
361   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
362   pcis->ksp_D = pcbddc->ksp_D;
363 
364   /* NEUMANN PROBLEM */
365   /* Matrix for Neumann problem is A_RR -> we need to create it */
366   ierr = ISGetSize(is_R_local,&n_R);CHKERRQ(ierr);
367   ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
368   if (!pcbddc->ksp_R) { /* create object if not yet build */
369     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
370     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
371     /* default */
372     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
373     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
374     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
375     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
376     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
377   }
378   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,matstruct);CHKERRQ(ierr);
379   /* Allow user's customization */
380   ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
381   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
382   if (!n_R) {
383     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
384     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
385   }
386   /* Set Up KSP for Neumann problem of BDDC */
387   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
388 
389   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
390 
391   /* Dirichlet */
392   ierr = MatGetVecs(pcis->A_II,&vec1,&vec2);CHKERRQ(ierr);
393   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
394   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
395   ierr = MatMult(pcis->A_II,vec1,vec2);CHKERRQ(ierr);
396   ierr = KSPSolve(pcbddc->ksp_D,vec2,vec3);CHKERRQ(ierr);
397   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
398   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
399   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
400   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
401   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
402   /* need to be adapted? */
403   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
404   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
405   ierr = PCBDDCSetUseExactDirichlet(pc,(PetscBool)use_exact_reduced);CHKERRQ(ierr);
406   /* print info */
407   if (pcbddc->dbg_flag) {
408     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
409     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
410     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
411     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
412     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
413   }
414   if (n_D && pcbddc->NullSpace && !use_exact_reduced && !pcbddc->inexact_prec_type) {
415     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_I_local);CHKERRQ(ierr);
416   }
417 
418   /* Neumann */
419   ierr = MatGetVecs(A_RR,&vec1,&vec2);CHKERRQ(ierr);
420   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
421   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
422   ierr = MatMult(A_RR,vec1,vec2);CHKERRQ(ierr);
423   ierr = KSPSolve(pcbddc->ksp_R,vec2,vec3);CHKERRQ(ierr);
424   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
425   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
426   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
427   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
428   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
429   /* need to be adapted? */
430   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
431   if (PetscAbsReal(value) > 1.e-4) use_exact = 0;
432   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
433   /* print info */
434   if (pcbddc->dbg_flag) {
435     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
436     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
437   }
438   if (n_R && pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
439     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_R_local);CHKERRQ(ierr);
440   }
441 
442   /* free Neumann problem's matrix */
443   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
444   PetscFunctionReturn(0);
445 }
446 
447 #undef __FUNCT__
448 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
449 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
450 {
451   PetscErrorCode ierr;
452   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
453 
454   PetscFunctionBegin;
455   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
456   if (pcbddc->local_auxmat1) {
457     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
458     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
459   }
460   PetscFunctionReturn(0);
461 }
462 
463 #undef __FUNCT__
464 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
465 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
466 {
467   PetscErrorCode ierr;
468   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
469   PC_IS*            pcis = (PC_IS*)  (pc->data);
470   const PetscScalar zero = 0.0;
471 
472   PetscFunctionBegin;
473   /* Application of PHI^T (or PSI^T)  */
474   if (pcbddc->coarse_psi_B) {
475     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
476     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
477   } else {
478     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
479     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
480   }
481   /* Scatter data of coarse_rhs */
482   if (pcbddc->coarse_rhs) { ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr); }
483   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
484 
485   /* Local solution on R nodes */
486   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
487   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
488   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
489   if (pcbddc->inexact_prec_type) {
490     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
491     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
492   }
493   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
494   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
495   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
496   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
497   if (pcbddc->inexact_prec_type) {
498     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
499     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
500   }
501 
502   /* Coarse solution */
503   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
504   if (pcbddc->coarse_rhs) { /* TODO remove null space when doing multilevel */
505     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
506   }
507   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
508   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
509 
510   /* Sum contributions from two levels */
511   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
512   if (pcbddc->inexact_prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
513   PetscFunctionReturn(0);
514 }
515 
516 #undef __FUNCT__
517 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
518 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
519 {
520   PetscErrorCode ierr;
521   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
522 
523   PetscFunctionBegin;
524   switch (pcbddc->coarse_communications_type) {
525     case SCATTERS_BDDC:
526       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
527       break;
528     case GATHERS_BDDC:
529       break;
530   }
531   PetscFunctionReturn(0);
532 }
533 
534 #undef __FUNCT__
535 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
536 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
537 {
538   PetscErrorCode ierr;
539   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
540   PetscScalar*   array_to;
541   PetscScalar*   array_from;
542   MPI_Comm       comm;
543   PetscInt       i;
544 
545   PetscFunctionBegin;
546   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
547   switch (pcbddc->coarse_communications_type) {
548     case SCATTERS_BDDC:
549       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
550       break;
551     case GATHERS_BDDC:
552       if (vec_from) {
553         ierr = VecGetArray(vec_from,&array_from);CHKERRQ(ierr);
554       }
555       if (vec_to) {
556         ierr = VecGetArray(vec_to,&array_to);CHKERRQ(ierr);
557       }
558       switch(pcbddc->coarse_problem_type){
559         case SEQUENTIAL_BDDC:
560           if (smode == SCATTER_FORWARD) {
561             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);
562             if (vec_to) {
563               if (imode == ADD_VALUES) {
564                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
565                   array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
566                 }
567               } else {
568                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
569                   array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
570                 }
571               }
572             }
573           } else {
574             if (vec_from) {
575               if (imode == ADD_VALUES) {
576                 MPI_Comm vec_from_comm;
577                 ierr = PetscObjectGetComm((PetscObject)(vec_from),&vec_from_comm);CHKERRQ(ierr);
578                 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);
579               }
580               for (i=0;i<pcbddc->replicated_primal_size;i++) {
581                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
582               }
583             }
584             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);
585           }
586           break;
587         case REPLICATED_BDDC:
588           if (smode == SCATTER_FORWARD) {
589             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);
590             if (imode == ADD_VALUES) {
591               for (i=0;i<pcbddc->replicated_primal_size;i++) {
592                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
593               }
594             } else {
595               for (i=0;i<pcbddc->replicated_primal_size;i++) {
596                 array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
597               }
598             }
599           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
600             if (imode == ADD_VALUES) {
601               for (i=0;i<pcbddc->local_primal_size;i++) {
602                 array_to[i]+=array_from[pcbddc->local_primal_indices[i]];
603               }
604             } else {
605               for (i=0;i<pcbddc->local_primal_size;i++) {
606                 array_to[i]=array_from[pcbddc->local_primal_indices[i]];
607               }
608             }
609           }
610           break;
611         case MULTILEVEL_BDDC:
612           break;
613         case PARALLEL_BDDC:
614           break;
615       }
616       if (vec_from) {
617         ierr = VecRestoreArray(vec_from,&array_from);CHKERRQ(ierr);
618       }
619       if (vec_to) {
620         ierr = VecRestoreArray(vec_to,&array_to);CHKERRQ(ierr);
621       }
622       break;
623   }
624   PetscFunctionReturn(0);
625 }
626 
627 #undef __FUNCT__
628 #define __FUNCT__ "PCBDDCConstraintsSetUp"
629 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
630 {
631   PetscErrorCode ierr;
632   PC_IS*         pcis = (PC_IS*)(pc->data);
633   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
634   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
635   PetscInt       *nnz,*is_indices;
636   PetscScalar    *temp_quadrature_constraint;
637   PetscInt       *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B,*local_to_B;
638   PetscInt       local_primal_size,i,j,k,total_counts,max_size_of_constraint;
639   PetscInt       n_vertices,size_of_constraint;
640   PetscReal      real_value;
641   PetscBool      nnsp_has_cnst=PETSC_FALSE,use_nnsp_true=pcbddc->use_nnsp_true;
642   PetscInt       nnsp_size=0,nnsp_addone=0,temp_constraints,temp_start_ptr,n_ISForFaces,n_ISForEdges;
643   IS             *used_IS,ISForVertices,*ISForFaces,*ISForEdges;
644   MatType        impMatType=MATSEQAIJ;
645   PetscBLASInt   Bs,Bt,lwork,lierr;
646   PetscReal      tol=1.0e-8;
647   MatNullSpace   nearnullsp;
648   const Vec      *nearnullvecs;
649   Vec            *localnearnullsp;
650   PetscScalar    *work,*temp_basis,*array_vector,*correlation_mat;
651   PetscReal      *rwork,*singular_vals;
652   PetscBLASInt   Bone=1,*ipiv;
653   Vec            temp_vec;
654   Mat            temp_mat;
655   KSP            temp_ksp;
656   PC             temp_pc;
657   PetscInt       s,start_constraint,dual_dofs;
658   PetscBool      compute_submatrix,useksp=PETSC_FALSE;
659   PetscInt       *aux_primal_permutation,*aux_primal_numbering;
660   PetscBool      boolforchange,*change_basis;
661 /* some ugly conditional declarations */
662 #if defined(PETSC_MISSING_LAPACK_GESVD)
663   PetscScalar    one=1.0,zero=0.0;
664   PetscInt       ii;
665   PetscScalar    *singular_vectors;
666   PetscBLASInt   *iwork,*ifail;
667   PetscReal      dummy_real,abs_tol;
668   PetscBLASInt   eigs_found;
669 #endif
670   PetscBLASInt   dummy_int;
671   PetscScalar    dummy_scalar;
672   PetscBool      used_vertex,get_faces,get_edges,get_vertices;
673 
674   PetscFunctionBegin;
675   /* Get index sets for faces, edges and vertices from graph */
676   get_faces = PETSC_TRUE;
677   get_edges = PETSC_TRUE;
678   get_vertices = PETSC_TRUE;
679   if (pcbddc->vertices_flag) {
680     get_faces = PETSC_FALSE;
681     get_edges = PETSC_FALSE;
682   }
683   if (pcbddc->constraints_flag) {
684     get_vertices = PETSC_FALSE;
685   }
686   if (pcbddc->faces_flag) {
687     get_edges = PETSC_FALSE;
688   }
689   if (pcbddc->edges_flag) {
690     get_faces = PETSC_FALSE;
691   }
692   /* default */
693   if (!get_faces && !get_edges && !get_vertices) {
694     get_vertices = PETSC_TRUE;
695   }
696   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
697   if (pcbddc->dbg_flag) {
698     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
699     i = 0;
700     if (ISForVertices) {
701       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
702     }
703     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
704     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
705     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
706     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
707   }
708   /* check if near null space is attached to global mat */
709   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
710   if (nearnullsp) {
711     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
712   } else { /* if near null space is not provided it uses constants */
713     nnsp_has_cnst = PETSC_TRUE;
714     use_nnsp_true = PETSC_TRUE;
715   }
716   if (nnsp_has_cnst) {
717     nnsp_addone = 1;
718   }
719   /*
720        Evaluate maximum storage size needed by the procedure
721        - temp_indices will contain start index of each constraint stored as follows
722        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
723        - 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
724        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
725                                                                                                                                                          */
726   total_counts = n_ISForFaces+n_ISForEdges;
727   total_counts *= (nnsp_addone+nnsp_size);
728   n_vertices = 0;
729   if (ISForVertices) {
730     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
731   }
732   total_counts += n_vertices;
733   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
734   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
735   total_counts = 0;
736   max_size_of_constraint = 0;
737   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
738     if (i<n_ISForEdges) {
739       used_IS = &ISForEdges[i];
740     } else {
741       used_IS = &ISForFaces[i-n_ISForEdges];
742     }
743     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
744     total_counts += j;
745     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
746   }
747   total_counts *= (nnsp_addone+nnsp_size);
748   total_counts += n_vertices;
749   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
750   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
751   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
752   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
753   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
754   for (i=0;i<pcis->n;i++) {
755     local_to_B[i]=-1;
756   }
757   for (i=0;i<pcis->n_B;i++) {
758     local_to_B[is_indices[i]]=i;
759   }
760   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
761 
762   /* First we issue queries to allocate optimal workspace for LAPACKgesvd or LAPACKsyev/LAPACKheev */
763   rwork = 0;
764   work = 0;
765   singular_vals = 0;
766   temp_basis = 0;
767   correlation_mat = 0;
768   if (!pcbddc->use_nnsp_true) {
769     PetscScalar temp_work;
770 #if defined(PETSC_MISSING_LAPACK_GESVD)
771     /* POD */
772     PetscInt max_n;
773     max_n = nnsp_addone+nnsp_size;
774     /* using some techniques borrowed from Proper Orthogonal Decomposition */
775     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
776     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&singular_vectors);CHKERRQ(ierr);
777     ierr = PetscMalloc(max_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
778     ierr = PetscMalloc(max_size_of_constraint*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
779 #if defined(PETSC_USE_COMPLEX)
780     ierr = PetscMalloc(3*max_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
781 #endif
782     ierr = PetscMalloc(5*max_n*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
783     ierr = PetscMalloc(max_n*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
784     /* now we evaluate the optimal workspace using query with lwork=-1 */
785     ierr = PetscBLASIntCast(max_n,&Bt);CHKERRQ(ierr);
786     lwork=-1;
787     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
788 #if !defined(PETSC_USE_COMPLEX)
789     abs_tol=1.e-8;
790 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,&lierr); */
791     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));
792 #else
793 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,rwork,&lierr); */
794 /*  LAPACK call is missing here! TODO */
795     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
796 #endif
797     if ( lierr ) {
798       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEVX Lapack routine %d",(int)lierr);
799     }
800     ierr = PetscFPTrapPop();CHKERRQ(ierr);
801 #else /* on missing GESVD */
802     /* SVD */
803     PetscInt max_n,min_n;
804     max_n = max_size_of_constraint;
805     min_n = nnsp_addone+nnsp_size;
806     if (max_size_of_constraint < ( nnsp_addone+nnsp_size ) ) {
807       min_n = max_size_of_constraint;
808       max_n = nnsp_addone+nnsp_size;
809     }
810     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
811 #if defined(PETSC_USE_COMPLEX)
812     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
813 #endif
814     /* now we evaluate the optimal workspace using query with lwork=-1 */
815     lwork=-1;
816     ierr = PetscBLASIntCast(max_n,&Bs);CHKERRQ(ierr);
817     ierr = PetscBLASIntCast(min_n,&Bt);CHKERRQ(ierr);
818     dummy_int = Bs;
819     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
820 #if !defined(PETSC_USE_COMPLEX)
821     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));
822 #else
823     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));
824 #endif
825     if ( lierr ) {
826       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SVD Lapack routine %d",(int)lierr);
827     }
828     ierr = PetscFPTrapPop();CHKERRQ(ierr);
829 #endif
830     /* Allocate optimal workspace */
831     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
832     total_counts = (PetscInt)lwork;
833     ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&work);CHKERRQ(ierr);
834   }
835   /* get local part of global near null space vectors */
836   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
837   for (k=0;k<nnsp_size;k++) {
838     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
839     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
840     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
841   }
842   /* Now we can loop on constraining sets */
843   total_counts = 0;
844   temp_indices[0] = 0;
845   /* vertices */
846   if (ISForVertices) {
847     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
848     if (nnsp_has_cnst) { /* consider all vertices */
849       for (i=0;i<n_vertices;i++) {
850         temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
851         temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
852         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
853         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
854         change_basis[total_counts]=PETSC_FALSE;
855         total_counts++;
856       }
857     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
858       for (i=0;i<n_vertices;i++) {
859         used_vertex=PETSC_FALSE;
860         k=0;
861         while (!used_vertex && k<nnsp_size) {
862           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
863           if (PetscAbsScalar(array_vector[is_indices[i]])>0.0) {
864             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
865             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
866             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
867             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
868             change_basis[total_counts]=PETSC_FALSE;
869             total_counts++;
870             used_vertex=PETSC_TRUE;
871           }
872           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
873           k++;
874         }
875       }
876     }
877     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
878     n_vertices = total_counts;
879   }
880   /* edges and faces */
881   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
882     if (i<n_ISForEdges) {
883       used_IS = &ISForEdges[i];
884       boolforchange = pcbddc->use_change_of_basis;
885     } else {
886       used_IS = &ISForFaces[i-n_ISForEdges];
887       boolforchange = pcbddc->use_change_on_faces;
888     }
889     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
890     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
891     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
892     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
893     /* HACK: change of basis should not performed on local periodic nodes */
894     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) {
895       boolforchange = PETSC_FALSE;
896     }
897     if (nnsp_has_cnst) {
898       PetscScalar quad_value;
899       temp_constraints++;
900       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
901       for (j=0;j<size_of_constraint;j++) {
902         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
903         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
904         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
905       }
906       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
907       change_basis[total_counts]=boolforchange;
908       total_counts++;
909     }
910     for (k=0;k<nnsp_size;k++) {
911       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
912       for (j=0;j<size_of_constraint;j++) {
913         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
914         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
915         temp_quadrature_constraint[temp_indices[total_counts]+j]=array_vector[is_indices[j]];
916       }
917       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
918       real_value = 1.0;
919       if (use_nnsp_true) { /* check if array is null on the connected component in case use_nnsp_true has been requested */
920         ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
921         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone));
922       }
923       if (real_value > 0.0) { /* keep indices and values */
924         temp_constraints++;
925         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
926         change_basis[total_counts]=boolforchange;
927         total_counts++;
928       }
929     }
930     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
931     /* perform SVD on the constraint if use_nnsp_true has not be requested by the user */
932     if (!use_nnsp_true) {
933       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
934       ierr = PetscBLASIntCast(temp_constraints,&Bt);CHKERRQ(ierr);
935 
936 #if defined(PETSC_MISSING_LAPACK_GESVD)
937       ierr = PetscMemzero(correlation_mat,Bt*Bt*sizeof(PetscScalar));CHKERRQ(ierr);
938       /* Store upper triangular part of correlation matrix */
939       for (j=0;j<temp_constraints;j++) {
940         for (k=0;k<j+1;k++) {
941           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));
942 
943         }
944       }
945       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
946 #if !defined(PETSC_USE_COMPLEX)
947 /*      LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,&lierr); */
948       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));
949 #else
950 /*  LAPACK call is missing here! TODO */
951       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
952 #endif
953       if (lierr) {
954         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEVX Lapack routine %d",(int)lierr);
955       }
956       ierr = PetscFPTrapPop();CHKERRQ(ierr);
957       /* retain eigenvalues greater than tol: note that lapack SYEV gives eigs in ascending order */
958       j=0;
959       while (j < Bt && singular_vals[j] < tol) j++;
960       total_counts=total_counts-j;
961       if (j<temp_constraints) {
962         for (k=j;k<Bt;k++) {
963           singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
964         }
965         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
966         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));
967         ierr = PetscFPTrapPop();CHKERRQ(ierr);
968         /* copy POD basis into used quadrature memory */
969         for (k=0;k<Bt-j;k++) {
970           for (ii=0;ii<size_of_constraint;ii++) {
971             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[Bt-1-k]*temp_basis[(Bt-1-k)*size_of_constraint+ii];
972           }
973         }
974       }
975 
976 #else  /* on missing GESVD */
977       PetscInt min_n = temp_constraints;
978       if (min_n > size_of_constraint) min_n = size_of_constraint;
979       dummy_int = Bs;
980       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
981 #if !defined(PETSC_USE_COMPLEX)
982       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));
983 #else
984       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));
985 #endif
986       if (lierr) {
987         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD Lapack routine %d",(int)lierr);
988       }
989       ierr = PetscFPTrapPop();CHKERRQ(ierr);
990       /* retain eigenvalues greater than tol: note that lapack SVD gives eigs in descending order */
991       j = 0;
992       while (j < min_n && singular_vals[min_n-j-1] < tol) j++;
993       total_counts = total_counts-(PetscInt)Bt+(min_n-j);
994 #endif
995     }
996   }
997   /* free index sets of faces, edges and vertices */
998   for (i=0;i<n_ISForFaces;i++) {
999     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1000   }
1001   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1002   for (i=0;i<n_ISForEdges;i++) {
1003     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1004   }
1005   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1006   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1007 
1008   /* set quantities in pcbddc data structure */
1009   /* n_vertices defines the number of point primal dofs */
1010   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1011   local_primal_size = total_counts;
1012   pcbddc->n_vertices = n_vertices;
1013   pcbddc->n_constraints = total_counts-n_vertices;
1014   pcbddc->local_primal_size = local_primal_size;
1015 
1016   /* Create constraint matrix */
1017   /* The constraint matrix is used to compute the l2g map of primal dofs */
1018   /* so we need to set it up properly either with or without change of basis */
1019   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1020   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1021   ierr = MatSetSizes(pcbddc->ConstraintMatrix,local_primal_size,pcis->n,local_primal_size,pcis->n);CHKERRQ(ierr);
1022   /* compute a local numbering of constraints : vertices first then constraints */
1023   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
1024   ierr = VecGetArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
1025   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
1026   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_permutation);CHKERRQ(ierr);
1027   total_counts=0;
1028   /* find vertices: subdomain corners plus dofs with basis changed */
1029   for (i=0;i<local_primal_size;i++) {
1030     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1031     if (change_basis[i] || size_of_constraint == 1) {
1032       k=0;
1033       while(k < size_of_constraint && array_vector[temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1]] != 0.0) {
1034         k=k+1;
1035       }
1036       j=temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1];
1037       array_vector[j] = 1.0;
1038       aux_primal_numbering[total_counts]=j;
1039       aux_primal_permutation[total_counts]=total_counts;
1040       total_counts++;
1041     }
1042   }
1043   ierr = VecRestoreArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
1044   /* permute indices in order to have a sorted set of vertices */
1045   ierr = PetscSortIntWithPermutation(total_counts,aux_primal_numbering,aux_primal_permutation);
1046   /* nonzero structure */
1047   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1048   for (i=0;i<total_counts;i++) {
1049     nnz[i]=1;
1050   }
1051   j=total_counts;
1052   for (i=n_vertices;i<local_primal_size;i++) {
1053     if (!change_basis[i]) {
1054       nnz[j]=temp_indices[i+1]-temp_indices[i];
1055       j++;
1056     }
1057   }
1058   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1059   ierr = PetscFree(nnz);CHKERRQ(ierr);
1060   /* set values in constraint matrix */
1061   for (i=0;i<total_counts;i++) {
1062     j = aux_primal_permutation[i];
1063     k = aux_primal_numbering[j];
1064     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,k,1.0,INSERT_VALUES);CHKERRQ(ierr);
1065   }
1066   for (i=n_vertices;i<local_primal_size;i++) {
1067     if (!change_basis[i]) {
1068       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1069       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);
1070       total_counts++;
1071     }
1072   }
1073   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
1074   ierr = PetscFree(aux_primal_permutation);CHKERRQ(ierr);
1075   /* assembling */
1076   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1077   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1078 
1079   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1080   if (pcbddc->use_change_of_basis) {
1081     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1082     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1083     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1084     /* work arrays */
1085     /* we need to reuse these arrays, so we free them */
1086     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1087     ierr = PetscFree(work);CHKERRQ(ierr);
1088     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1089     ierr = PetscMalloc((nnsp_addone+nnsp_size)*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
1090     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscScalar),&work);CHKERRQ(ierr);
1091     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscBLASInt),&ipiv);CHKERRQ(ierr);
1092     for (i=0;i<pcis->n_B;i++) {
1093       nnz[i]=1;
1094     }
1095     /* Overestimated nonzeros per row */
1096     k=1;
1097     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
1098       if (change_basis[i]) {
1099         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1100         if (k < size_of_constraint) {
1101           k = size_of_constraint;
1102         }
1103         for (j=0;j<size_of_constraint;j++) {
1104           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1105         }
1106       }
1107     }
1108     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1109     ierr = PetscFree(nnz);CHKERRQ(ierr);
1110     /* Temporary array to store indices */
1111     ierr = PetscMalloc(k*sizeof(PetscInt),&is_indices);CHKERRQ(ierr);
1112     /* Set initial identity in the matrix */
1113     for (i=0;i<pcis->n_B;i++) {
1114       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1115     }
1116     /* Now we loop on the constraints which need a change of basis */
1117     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
1118     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (6.2.1) */
1119     temp_constraints = 0;
1120     if (pcbddc->n_vertices < local_primal_size) {
1121       temp_start_ptr = temp_indices_to_constraint_B[temp_indices[pcbddc->n_vertices]];
1122     }
1123     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
1124       if (change_basis[i]) {
1125         compute_submatrix = PETSC_FALSE;
1126         useksp = PETSC_FALSE;
1127         if (temp_start_ptr == temp_indices_to_constraint_B[temp_indices[i]]) {
1128           temp_constraints++;
1129           if (i == local_primal_size -1 ||  temp_start_ptr != temp_indices_to_constraint_B[temp_indices[i+1]]) {
1130             compute_submatrix = PETSC_TRUE;
1131           }
1132         }
1133         if (compute_submatrix) {
1134           if (temp_constraints > 1 || pcbddc->use_nnsp_true) {
1135             useksp = PETSC_TRUE;
1136           }
1137           size_of_constraint = temp_indices[i+1]-temp_indices[i];
1138           if (useksp) { /* experimental TODO: reuse KSP and MAT instead of creating them each time */
1139             ierr = MatCreate(PETSC_COMM_SELF,&temp_mat);CHKERRQ(ierr);
1140             ierr = MatSetType(temp_mat,impMatType);CHKERRQ(ierr);
1141             ierr = MatSetSizes(temp_mat,size_of_constraint,size_of_constraint,size_of_constraint,size_of_constraint);CHKERRQ(ierr);
1142             ierr = MatSeqAIJSetPreallocation(temp_mat,size_of_constraint,NULL);CHKERRQ(ierr);
1143           }
1144           /* First _size_of_constraint-temp_constraints_ columns */
1145           dual_dofs = size_of_constraint-temp_constraints;
1146           start_constraint = i+1-temp_constraints;
1147           for (s=0;s<dual_dofs;s++) {
1148             is_indices[0] = s;
1149             for (j=0;j<temp_constraints;j++) {
1150               for (k=0;k<temp_constraints;k++) {
1151                 temp_basis[j*temp_constraints+k]=temp_quadrature_constraint[temp_indices[start_constraint+k]+s+j+1];
1152               }
1153               work[j]=-temp_quadrature_constraint[temp_indices[start_constraint+j]+s];
1154               is_indices[j+1]=s+j+1;
1155             }
1156             Bt = temp_constraints;
1157             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1158             PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&Bt,&Bone,temp_basis,&Bt,ipiv,work,&Bt,&lierr));
1159             if ( lierr ) {
1160               SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESV Lapack routine %d",(int)lierr);
1161             }
1162             ierr = PetscFPTrapPop();CHKERRQ(ierr);
1163             j = temp_indices_to_constraint_B[temp_indices[start_constraint]+s];
1164             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,temp_constraints,&temp_indices_to_constraint_B[temp_indices[start_constraint]+s+1],1,&j,work,INSERT_VALUES);CHKERRQ(ierr);
1165             if (useksp) {
1166               /* temp mat with transposed rows and columns */
1167               ierr = MatSetValues(temp_mat,1,&s,temp_constraints,&is_indices[1],work,INSERT_VALUES);CHKERRQ(ierr);
1168               ierr = MatSetValue(temp_mat,is_indices[0],is_indices[0],1.0,INSERT_VALUES);CHKERRQ(ierr);
1169             }
1170           }
1171           if (useksp) {
1172             /* last rows of temp_mat */
1173             for (j=0;j<size_of_constraint;j++) {
1174               is_indices[j] = j;
1175             }
1176             for (s=0;s<temp_constraints;s++) {
1177               k = s + dual_dofs;
1178               ierr = MatSetValues(temp_mat,1,&k,size_of_constraint,is_indices,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
1179             }
1180             ierr = MatAssemblyBegin(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1181             ierr = MatAssemblyEnd(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1182             ierr = MatGetVecs(temp_mat,&temp_vec,NULL);CHKERRQ(ierr);
1183             ierr = KSPCreate(PETSC_COMM_SELF,&temp_ksp);CHKERRQ(ierr);
1184             ierr = KSPSetOperators(temp_ksp,temp_mat,temp_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
1185             ierr = KSPSetType(temp_ksp,KSPPREONLY);CHKERRQ(ierr);
1186             ierr = KSPGetPC(temp_ksp,&temp_pc);CHKERRQ(ierr);
1187             ierr = PCSetType(temp_pc,PCLU);CHKERRQ(ierr);
1188             ierr = KSPSetUp(temp_ksp);CHKERRQ(ierr);
1189             for (s=0;s<temp_constraints;s++) {
1190               ierr = VecSet(temp_vec,0.0);CHKERRQ(ierr);
1191               ierr = VecSetValue(temp_vec,s+dual_dofs,1.0,INSERT_VALUES);CHKERRQ(ierr);
1192               ierr = VecAssemblyBegin(temp_vec);CHKERRQ(ierr);
1193               ierr = VecAssemblyEnd(temp_vec);CHKERRQ(ierr);
1194               ierr = KSPSolve(temp_ksp,temp_vec,temp_vec);CHKERRQ(ierr);
1195               ierr = VecGetArray(temp_vec,&array_vector);CHKERRQ(ierr);
1196               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
1197               /* last columns of change of basis matrix associated to new primal dofs */
1198               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);
1199               ierr = VecRestoreArray(temp_vec,&array_vector);CHKERRQ(ierr);
1200             }
1201             ierr = MatDestroy(&temp_mat);CHKERRQ(ierr);
1202             ierr = KSPDestroy(&temp_ksp);CHKERRQ(ierr);
1203             ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
1204           } else {
1205             /* last columns of change of basis matrix associated to new primal dofs */
1206             for (s=0;s<temp_constraints;s++) {
1207               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
1208               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);
1209             }
1210           }
1211           /* prepare for the next cycle */
1212           temp_constraints = 0;
1213           if (i != local_primal_size -1 ) {
1214             temp_start_ptr = temp_indices_to_constraint_B[temp_indices[i+1]];
1215           }
1216         }
1217       }
1218     }
1219     /* assembling */
1220     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1221     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1222     ierr = PetscFree(ipiv);CHKERRQ(ierr);
1223     ierr = PetscFree(is_indices);CHKERRQ(ierr);
1224   }
1225   /* free workspace no longer needed */
1226   ierr = PetscFree(rwork);CHKERRQ(ierr);
1227   ierr = PetscFree(work);CHKERRQ(ierr);
1228   ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1229   ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1230   ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1231   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
1232   ierr = PetscFree(change_basis);CHKERRQ(ierr);
1233   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
1234   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
1235   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
1236   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
1237 #if defined(PETSC_MISSING_LAPACK_GESVD)
1238   ierr = PetscFree(iwork);CHKERRQ(ierr);
1239   ierr = PetscFree(ifail);CHKERRQ(ierr);
1240   ierr = PetscFree(singular_vectors);CHKERRQ(ierr);
1241 #endif
1242   for (k=0;k<nnsp_size;k++) {
1243     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1244   }
1245   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1246   PetscFunctionReturn(0);
1247 }
1248 
1249 #undef __FUNCT__
1250 #define __FUNCT__ "PCBDDCAnalyzeInterface"
1251 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
1252 {
1253   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
1254   PC_IS       *pcis = (PC_IS*)pc->data;
1255   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
1256   PetscInt    bs,ierr,i,vertex_size;
1257   PetscViewer viewer=pcbddc->dbg_viewer;
1258 
1259   PetscFunctionBegin;
1260   /* Init local Graph struct */
1261   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
1262 
1263   /* Check validity of the csr graph passed in by the user */
1264   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
1265     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
1266   }
1267   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
1268   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
1269     Mat mat_adj;
1270     const PetscInt *xadj,*adjncy;
1271     PetscBool flg_row=PETSC_TRUE;
1272 
1273     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
1274     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1275     if (!flg_row) {
1276       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
1277     }
1278     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
1279     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1280     if (!flg_row) {
1281       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
1282     }
1283     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
1284   }
1285 
1286   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
1287   vertex_size = 1;
1288   if (!pcbddc->n_ISForDofs) {
1289     IS *custom_ISForDofs;
1290 
1291     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
1292     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
1293     for (i=0;i<bs;i++) {
1294       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1295     }
1296     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1297     /* remove my references to IS objects */
1298     for (i=0;i<bs;i++) {
1299       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1300     }
1301     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1302   } else { /* mat block size as vertex size (used for elasticity) */
1303     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1304   }
1305 
1306   /* Setup of Graph */
1307   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1308 
1309   /* Graph's connected components analysis */
1310   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1311 
1312   /* print some info to stdout */
1313   if (pcbddc->dbg_flag) {
1314     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1315   }
1316   PetscFunctionReturn(0);
1317 }
1318 
1319 #undef __FUNCT__
1320 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1321 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1322 {
1323   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1324   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1325   PetscErrorCode ierr;
1326 
1327   PetscFunctionBegin;
1328   n = 0;
1329   vertices = 0;
1330   if (pcbddc->ConstraintMatrix) {
1331     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1332     for (i=0;i<local_primal_size;i++) {
1333       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1334       if (size_of_constraint == 1) n++;
1335       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1336     }
1337     if (vertices_idx) {
1338       ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1339       n = 0;
1340       for (i=0;i<local_primal_size;i++) {
1341         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1342         if (size_of_constraint == 1) {
1343           vertices[n++]=row_cmat_indices[0];
1344         }
1345         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1346       }
1347     }
1348   }
1349   *n_vertices = n;
1350   if (vertices_idx) *vertices_idx = vertices;
1351   PetscFunctionReturn(0);
1352 }
1353 
1354 #undef __FUNCT__
1355 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
1356 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
1357 {
1358   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1359   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
1360   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
1361   PetscBool      *touched;
1362   PetscErrorCode ierr;
1363 
1364   PetscFunctionBegin;
1365   n = 0;
1366   constraints_index = 0;
1367   if (pcbddc->ConstraintMatrix) {
1368     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
1369     max_size_of_constraint = 0;
1370     for (i=0;i<local_primal_size;i++) {
1371       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1372       if (size_of_constraint > 1) {
1373         n++;
1374       }
1375       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
1376       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1377     }
1378     if (constraints_idx) {
1379       ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
1380       ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
1381       ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1382       ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
1383       n = 0;
1384       for (i=0;i<local_primal_size;i++) {
1385         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1386         if (size_of_constraint > 1) {
1387           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
1388           /* find first untouched local node */
1389           j = 0;
1390           while(touched[row_cmat_indices[j]]) j++;
1391           min_index = row_cmat_global_indices[j];
1392           min_loc = j;
1393           /* search the minimum among nodes not yet touched on the connected component
1394              since there can be more than one constraint on a single cc */
1395           for (j=1;j<size_of_constraint;j++) {
1396             if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
1397               min_index = row_cmat_global_indices[j];
1398               min_loc = j;
1399             }
1400           }
1401           touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
1402           constraints_index[n++] = row_cmat_indices[min_loc];
1403         }
1404         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1405       }
1406       ierr = PetscFree(touched);CHKERRQ(ierr);
1407       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
1408     }
1409   }
1410   *n_constraints = n;
1411   if (constraints_idx) *constraints_idx = constraints_index;
1412   PetscFunctionReturn(0);
1413 }
1414 
1415 /* the next two functions has been adapted from pcis.c */
1416 #undef __FUNCT__
1417 #define __FUNCT__ "PCBDDCApplySchur"
1418 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1419 {
1420   PetscErrorCode ierr;
1421   PC_IS          *pcis = (PC_IS*)(pc->data);
1422 
1423   PetscFunctionBegin;
1424   if (!vec2_B) { vec2_B = v; }
1425   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1426   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
1427   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1428   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
1429   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1430   PetscFunctionReturn(0);
1431 }
1432 
1433 #undef __FUNCT__
1434 #define __FUNCT__ "PCBDDCApplySchurTranspose"
1435 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1436 {
1437   PetscErrorCode ierr;
1438   PC_IS          *pcis = (PC_IS*)(pc->data);
1439 
1440   PetscFunctionBegin;
1441   if (!vec2_B) { vec2_B = v; }
1442   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1443   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
1444   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1445   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
1446   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1447   PetscFunctionReturn(0);
1448 }
1449 
1450 #undef __FUNCT__
1451 #define __FUNCT__ "PCBDDCSubsetNumbering"
1452 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[])
1453 {
1454   Vec            local_vec,global_vec;
1455   IS             seqis,paris;
1456   VecScatter     scatter_ctx;
1457   PetscScalar    *array;
1458   PetscInt       *temp_global_dofs;
1459   PetscScalar    globalsum;
1460   PetscInt       i,j,s;
1461   PetscInt       nlocals,first_index,old_index,max_local;
1462   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
1463   PetscMPIInt    *dof_sizes,*dof_displs;
1464   PetscBool      first_found;
1465   PetscErrorCode ierr;
1466 
1467   PetscFunctionBegin;
1468   /* mpi buffers */
1469   MPI_Comm_size(comm,&size_prec_comm);
1470   MPI_Comm_rank(comm,&rank_prec_comm);
1471   j = ( !rank_prec_comm ? size_prec_comm : 0);
1472   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1473   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1474   /* get maximum size of subset */
1475   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
1476   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
1477   max_local = 0;
1478   if (n_local_dofs) {
1479     max_local = temp_global_dofs[0];
1480     for (i=1;i<n_local_dofs;i++) {
1481       if (max_local < temp_global_dofs[i] ) {
1482         max_local = temp_global_dofs[i];
1483       }
1484     }
1485   }
1486   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
1487   max_global++;
1488   max_local = 0;
1489   if (n_local_dofs) {
1490     max_local = local_dofs[0];
1491     for (i=1;i<n_local_dofs;i++) {
1492       if (max_local < local_dofs[i] ) {
1493         max_local = local_dofs[i];
1494       }
1495     }
1496   }
1497   max_local++;
1498   /* allocate workspace */
1499   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
1500   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
1501   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
1502   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
1503   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
1504   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
1505   /* create scatter */
1506   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
1507   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
1508   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
1509   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
1510   ierr = ISDestroy(&paris);CHKERRQ(ierr);
1511   /* init array */
1512   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1513   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1514   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1515   if (local_dofs_mult) {
1516     for (i=0;i<n_local_dofs;i++) {
1517       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
1518     }
1519   } else {
1520     for (i=0;i<n_local_dofs;i++) {
1521       array[local_dofs[i]]=1.0;
1522     }
1523   }
1524   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1525   /* scatter into global vec and get total number of global dofs */
1526   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1527   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1528   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
1529   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
1530   /* Fill global_vec with cumulative function for global numbering */
1531   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
1532   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
1533   nlocals = 0;
1534   first_index = -1;
1535   first_found = PETSC_FALSE;
1536   for (i=0;i<s;i++) {
1537     if (!first_found && PetscRealPart(array[i]) > 0.0) {
1538       first_found = PETSC_TRUE;
1539       first_index = i;
1540     }
1541     nlocals += (PetscInt)PetscRealPart(array[i]);
1542   }
1543   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1544   if (!rank_prec_comm) {
1545     dof_displs[0]=0;
1546     for (i=1;i<size_prec_comm;i++) {
1547       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1548     }
1549   }
1550   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1551   if (first_found) {
1552     array[first_index] += (PetscScalar)nlocals;
1553     old_index = first_index;
1554     for (i=first_index+1;i<s;i++) {
1555       if (PetscRealPart(array[i]) > 0.0) {
1556         array[i] += array[old_index];
1557         old_index = i;
1558       }
1559     }
1560   }
1561   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
1562   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1563   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1564   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1565   /* get global ordering of local dofs */
1566   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1567   if (local_dofs_mult) {
1568     for (i=0;i<n_local_dofs;i++) {
1569       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
1570     }
1571   } else {
1572     for (i=0;i<n_local_dofs;i++) {
1573       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
1574     }
1575   }
1576   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1577   /* free workspace */
1578   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1579   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1580   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1581   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1582   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1583   /* return pointer to global ordering of local dofs */
1584   *global_numbering_subset = temp_global_dofs;
1585   PetscFunctionReturn(0);
1586 }
1587 
1588 #undef __FUNCT__
1589 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
1590 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
1591 {
1592   PetscInt       i,j;
1593   PetscScalar    *alphas;
1594   PetscErrorCode ierr;
1595 
1596   PetscFunctionBegin;
1597   /* this implements stabilized Gram-Schmidt */
1598   ierr = PetscMalloc(n*sizeof(PetscScalar),&alphas);CHKERRQ(ierr);
1599   for (i=0;i<n;i++) {
1600     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
1601     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
1602     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
1603   }
1604   ierr = PetscFree(alphas);CHKERRQ(ierr);
1605   PetscFunctionReturn(0);
1606 }
1607 
1608 
1609