xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 6bfb181103e60beecc65f13fb5563f4dca53c470)
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 */
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(PETSC_COMM_SELF,&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   PetscFunctionReturn(0);
105 }
106 
107 #undef __FUNCT__
108 #define __FUNCT__ "PCBDDCSetUpLocalMatrices"
109 PetscErrorCode PCBDDCSetUpLocalMatrices(PC pc)
110 {
111   PC_IS*            pcis = (PC_IS*)(pc->data);
112   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
113   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
114   /* manage repeated solves */
115   MatReuse          reuse;
116   MatStructure      matstruct;
117   PetscErrorCode    ierr;
118 
119   PetscFunctionBegin;
120   /* get mat flags */
121   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
122   reuse = MAT_INITIAL_MATRIX;
123   if (pc->setupcalled) {
124     /* when matstruct is SAME_PRECONDITIONER, we shouldn't be here */
125     if (matstruct == SAME_PRECONDITIONER) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
126     if (matstruct == SAME_NONZERO_PATTERN) {
127       reuse = MAT_REUSE_MATRIX;
128     } else {
129       reuse = MAT_INITIAL_MATRIX;
130     }
131   }
132   if (reuse == MAT_INITIAL_MATRIX) {
133     ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
134     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
135     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
136     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
137     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
138   }
139 
140   /* transform local matrices if needed */
141   if (pcbddc->use_change_of_basis) {
142     Mat         change_mat_all;
143     PetscScalar *row_cmat_values;
144     PetscInt    *row_cmat_indices;
145     PetscInt    *nnz,*is_indices,*temp_indices;
146     PetscInt    i,j,k,n_D,n_B;
147 
148     /* Get Non-overlapping dimensions */
149     n_B = pcis->n_B;
150     n_D = pcis->n-n_B;
151 
152     /* compute nonzero structure of change of basis on all local nodes */
153     ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
154     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
155     for (i=0;i<n_D;i++) nnz[is_indices[i]] = 1;
156     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
157     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
158     k=1;
159     for (i=0;i<n_B;i++) {
160       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
161       nnz[is_indices[i]]=j;
162       if (k < j) k = j;
163       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
164     }
165     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
166     /* assemble change of basis matrix on the whole set of local dofs */
167     ierr = PetscMalloc(k*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
168     ierr = MatCreate(PETSC_COMM_SELF,&change_mat_all);CHKERRQ(ierr);
169     ierr = MatSetSizes(change_mat_all,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
170     ierr = MatSetType(change_mat_all,MATSEQAIJ);CHKERRQ(ierr);
171     ierr = MatSeqAIJSetPreallocation(change_mat_all,0,nnz);CHKERRQ(ierr);
172     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
173     for (i=0;i<n_D;i++) {
174       ierr = MatSetValue(change_mat_all,is_indices[i],is_indices[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
175     }
176     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
177     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
178     for (i=0;i<n_B;i++) {
179       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
180       for (k=0; k<j; k++) temp_indices[k]=is_indices[row_cmat_indices[k]];
181       ierr = MatSetValues(change_mat_all,1,&is_indices[i],j,temp_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
182       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
183     }
184     ierr = MatAssemblyBegin(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
185     ierr = MatAssemblyEnd(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
186     /* TODO: HOW TO WORK WITH BAIJ? PtAP not provided */
187     ierr = MatGetBlockSize(matis->A,&i);CHKERRQ(ierr);
188     if (i==1) {
189       ierr = MatPtAP(matis->A,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
190     } else {
191       Mat work_mat;
192       ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
193       ierr = MatPtAP(work_mat,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
194       ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
195     }
196     ierr = MatDestroy(&change_mat_all);CHKERRQ(ierr);
197     ierr = PetscFree(nnz);CHKERRQ(ierr);
198     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
199   } else {
200     /* without change of basis, the local matrix is unchanged */
201     if (!pcbddc->local_mat) {
202       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
203       pcbddc->local_mat = matis->A;
204     }
205   }
206 
207   /* get submatrices */
208   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_I_local,reuse,&pcis->A_II);CHKERRQ(ierr);
209   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
210   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
211   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,reuse,&pcis->A_BB);CHKERRQ(ierr);
212   PetscFunctionReturn(0);
213 }
214 
215 #undef __FUNCT__
216 #define __FUNCT__ "PCBDDCSetUpLocalScatters"
217 PetscErrorCode PCBDDCSetUpLocalScatters(PC pc,IS* is_R_local_n)
218 {
219   PC_IS*         pcis = (PC_IS*)(pc->data);
220   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
221   IS             is_R_local,is_aux1,is_aux2;
222   PetscInt       *vertices,*aux_array1,*aux_array2,*is_indices,*idx_R_local;
223   PetscInt       n_vertices,n_constraints,i,j,n_R,n_D,n_B;
224   PetscBool      *array_bool;
225   PetscErrorCode ierr;
226 
227   PetscFunctionBegin;
228   /* Set Non-overlapping dimensions */
229   n_B = pcis->n_B; n_D = pcis->n - n_B;
230   /* get vertex indices from constraint matrix */
231   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,&vertices);CHKERRQ(ierr);
232   /* Set number of constraints */
233   n_constraints = pcbddc->local_primal_size-n_vertices;
234   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
235   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&array_bool);CHKERRQ(ierr);
236   for (i=0;i<pcis->n;i++) array_bool[i] = PETSC_TRUE;
237   for (i=0;i<n_vertices;i++) array_bool[vertices[i]] = PETSC_FALSE;
238   ierr = PetscMalloc((pcis->n-n_vertices)*sizeof(PetscInt),&idx_R_local);CHKERRQ(ierr);
239   for (i=0, n_R=0; i<pcis->n; i++) {
240     if (array_bool[i]) {
241       idx_R_local[n_R] = i;
242       n_R++;
243     }
244   }
245   ierr = PetscFree(vertices);CHKERRQ(ierr);
246   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_R,idx_R_local,PETSC_OWN_POINTER,&is_R_local);CHKERRQ(ierr);
247 
248   /* print some info if requested */
249   if (pcbddc->dbg_flag) {
250     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
251     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
252     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
253     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
254     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);
255     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
256     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
257   }
258 
259   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
260   ierr = PetscMalloc((pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
261   ierr = PetscMalloc((pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array2);CHKERRQ(ierr);
262   ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
263   for (i=0; i<n_D; i++) array_bool[is_indices[i]] = PETSC_FALSE;
264   ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
265   for (i=0, j=0; i<n_R; i++) {
266     if (array_bool[idx_R_local[i]]) {
267       aux_array1[j] = i;
268       j++;
269     }
270   }
271   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
272   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
273   for (i=0, j=0; i<n_B; i++) {
274     if (array_bool[is_indices[i]]) {
275       aux_array2[j] = i; j++;
276     }
277   }
278   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
279   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);CHKERRQ(ierr);
280   ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
281   ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
282   ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
283 
284   if (pcbddc->inexact_prec_type || pcbddc->dbg_flag ) {
285     ierr = PetscMalloc(n_D*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
286     for (i=0, j=0; i<n_R; i++) {
287       if (!array_bool[idx_R_local[i]]) {
288         aux_array1[j] = i;
289         j++;
290       }
291     }
292     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
293     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
294     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
295   }
296   ierr = PetscFree(array_bool);CHKERRQ(ierr);
297   *is_R_local_n = is_R_local;
298   PetscFunctionReturn(0);
299 }
300 
301 #undef __FUNCT__
302 #define __FUNCT__ "PCBDDCSetUseExactDirichlet"
303 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool use)
304 {
305   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
306 
307   PetscFunctionBegin;
308   pcbddc->use_exact_dirichlet=use;
309   PetscFunctionReturn(0);
310 }
311 
312 #undef __FUNCT__
313 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
314 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, IS is_I_local, IS is_R_local)
315 {
316   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
317   PC_IS          *pcis = (PC_IS*)pc->data;
318   PC             pc_temp;
319   Mat            A_RR;
320   Vec            vec1,vec2,vec3;
321   MatStructure   matstruct;
322   PetscScalar    m_one = -1.0;
323   PetscReal      value;
324   PetscInt       n_D,n_R,use_exact,use_exact_reduced;
325   PetscErrorCode ierr;
326 
327   PetscFunctionBegin;
328   /* Creating PC contexts for local Dirichlet and Neumann problems */
329   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
330 
331   /* DIRICHLET PROBLEM */
332   /* Matrix for Dirichlet problem is pcis->A_II */
333   ierr = ISGetSize(is_I_local,&n_D);CHKERRQ(ierr);
334   if (!pcbddc->ksp_D) { /* create object if not yet build */
335     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
336     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
337     /* default */
338     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
339     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
340     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
341     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
342     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
343   }
344   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,matstruct);CHKERRQ(ierr);
345   /* Allow user's customization */
346   ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
347   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
348   if (!n_D) {
349     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
350     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
351   }
352   /* Set Up KSP for Dirichlet problem of BDDC */
353   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
354   /* set ksp_D into pcis data */
355   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
356   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
357   pcis->ksp_D = pcbddc->ksp_D;
358 
359   /* NEUMANN PROBLEM */
360   /* Matrix for Neumann problem is A_RR -> we need to create it */
361   ierr = ISGetSize(is_R_local,&n_R);CHKERRQ(ierr);
362   ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
363   if (!pcbddc->ksp_R) { /* create object if not yet build */
364     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
365     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
366     /* default */
367     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
368     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
369     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
370     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
371     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
372   }
373   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,matstruct);CHKERRQ(ierr);
374   /* Allow user's customization */
375   ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
376   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
377   if (!n_R) {
378     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
379     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
380   }
381   /* Set Up KSP for Neumann problem of BDDC */
382   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
383 
384   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
385 
386   /* Dirichlet */
387   ierr = MatGetVecs(pcis->A_II,&vec1,&vec2);CHKERRQ(ierr);
388   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
389   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
390   ierr = MatMult(pcis->A_II,vec1,vec2);CHKERRQ(ierr);
391   ierr = KSPSolve(pcbddc->ksp_D,vec2,vec3);CHKERRQ(ierr);
392   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
393   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
394   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
395   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
396   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
397   /* need to be adapted? */
398   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
399   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
400   ierr = PCBDDCSetUseExactDirichlet(pc,(PetscBool)use_exact_reduced);CHKERRQ(ierr);
401   /* print info */
402   if (pcbddc->dbg_flag) {
403     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
404     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
405     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
406     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
407     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
408   }
409   if (n_D && pcbddc->NullSpace && !use_exact_reduced && !pcbddc->inexact_prec_type) {
410     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_I_local);CHKERRQ(ierr);
411   }
412 
413   /* Neumann */
414   ierr = MatGetVecs(A_RR,&vec1,&vec2);CHKERRQ(ierr);
415   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
416   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
417   ierr = MatMult(A_RR,vec1,vec2);CHKERRQ(ierr);
418   ierr = KSPSolve(pcbddc->ksp_R,vec2,vec3);CHKERRQ(ierr);
419   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
420   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
421   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
422   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
423   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
424   /* need to be adapted? */
425   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
426   if (PetscAbsReal(value) > 1.e-4) use_exact = 0;
427   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
428   /* print info */
429   if (pcbddc->dbg_flag) {
430     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
431     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
432   }
433   if (n_R && pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
434     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_R_local);CHKERRQ(ierr);
435   }
436 
437   /* free Neumann problem's matrix */
438   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
439   PetscFunctionReturn(0);
440 }
441 
442 #undef __FUNCT__
443 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
444 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
445 {
446   PetscErrorCode ierr;
447   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
448 
449   PetscFunctionBegin;
450   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
451   if (pcbddc->local_auxmat1) {
452     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
453     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
454   }
455   PetscFunctionReturn(0);
456 }
457 
458 #undef __FUNCT__
459 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
460 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
461 {
462   PetscErrorCode ierr;
463   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
464   PC_IS*            pcis = (PC_IS*)  (pc->data);
465   const PetscScalar zero = 0.0;
466 
467   PetscFunctionBegin;
468   /* Application of PHI^T (or PSI^T)  */
469   if (pcbddc->coarse_psi_B) {
470     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
471     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
472   } else {
473     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
474     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
475   }
476   /* Scatter data of coarse_rhs */
477   if (pcbddc->coarse_rhs) { ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr); }
478   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
479 
480   /* Local solution on R nodes */
481   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
482   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
483   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
484   if (pcbddc->inexact_prec_type) {
485     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
486     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
487   }
488   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
489   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
490   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
491   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
492   if (pcbddc->inexact_prec_type) {
493     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
494     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
495   }
496 
497   /* Coarse solution */
498   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
499   if (pcbddc->coarse_rhs) { /* TODO remove null space when doing multilevel */
500     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
501   }
502   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
503   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
504 
505   /* Sum contributions from two levels */
506   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
507   if (pcbddc->inexact_prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
508   PetscFunctionReturn(0);
509 }
510 
511 #undef __FUNCT__
512 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
513 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
514 {
515   PetscErrorCode ierr;
516   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
517 
518   PetscFunctionBegin;
519   switch (pcbddc->coarse_communications_type) {
520     case SCATTERS_BDDC:
521       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
522       break;
523     case GATHERS_BDDC:
524       break;
525   }
526   PetscFunctionReturn(0);
527 }
528 
529 #undef __FUNCT__
530 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
531 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
532 {
533   PetscErrorCode ierr;
534   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
535   PetscScalar*   array_to;
536   PetscScalar*   array_from;
537   MPI_Comm       comm;
538   PetscInt       i;
539 
540   PetscFunctionBegin;
541   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
542   switch (pcbddc->coarse_communications_type) {
543     case SCATTERS_BDDC:
544       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
545       break;
546     case GATHERS_BDDC:
547       if (vec_from) {
548         ierr = VecGetArray(vec_from,&array_from);CHKERRQ(ierr);
549       }
550       if (vec_to) {
551         ierr = VecGetArray(vec_to,&array_to);CHKERRQ(ierr);
552       }
553       switch(pcbddc->coarse_problem_type){
554         case SEQUENTIAL_BDDC:
555           if (smode == SCATTER_FORWARD) {
556             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);
557             if (vec_to) {
558               if (imode == ADD_VALUES) {
559                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
560                   array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
561                 }
562               } else {
563                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
564                   array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
565                 }
566               }
567             }
568           } else {
569             if (vec_from) {
570               if (imode == ADD_VALUES) {
571                 MPI_Comm vec_from_comm;
572                 ierr = PetscObjectGetComm((PetscObject)(vec_from),&vec_from_comm);CHKERRQ(ierr);
573                 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);
574               }
575               for (i=0;i<pcbddc->replicated_primal_size;i++) {
576                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
577               }
578             }
579             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);
580           }
581           break;
582         case REPLICATED_BDDC:
583           if (smode == SCATTER_FORWARD) {
584             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);
585             if (imode == ADD_VALUES) {
586               for (i=0;i<pcbddc->replicated_primal_size;i++) {
587                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
588               }
589             } else {
590               for (i=0;i<pcbddc->replicated_primal_size;i++) {
591                 array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
592               }
593             }
594           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
595             if (imode == ADD_VALUES) {
596               for (i=0;i<pcbddc->local_primal_size;i++) {
597                 array_to[i]+=array_from[pcbddc->local_primal_indices[i]];
598               }
599             } else {
600               for (i=0;i<pcbddc->local_primal_size;i++) {
601                 array_to[i]=array_from[pcbddc->local_primal_indices[i]];
602               }
603             }
604           }
605           break;
606         case MULTILEVEL_BDDC:
607           break;
608         case PARALLEL_BDDC:
609           break;
610       }
611       if (vec_from) {
612         ierr = VecRestoreArray(vec_from,&array_from);CHKERRQ(ierr);
613       }
614       if (vec_to) {
615         ierr = VecRestoreArray(vec_to,&array_to);CHKERRQ(ierr);
616       }
617       break;
618   }
619   PetscFunctionReturn(0);
620 }
621 
622 #undef __FUNCT__
623 #define __FUNCT__ "PCBDDCConstraintsSetUp"
624 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
625 {
626   PetscErrorCode ierr;
627   PC_IS*         pcis = (PC_IS*)(pc->data);
628   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
629   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
630   PetscInt       *nnz,*is_indices;
631   PetscScalar    *temp_quadrature_constraint;
632   PetscInt       *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B,*local_to_B;
633   PetscInt       local_primal_size,i,j,k,total_counts,max_size_of_constraint;
634   PetscInt       n_vertices,size_of_constraint;
635   PetscReal      real_value;
636   PetscBool      nnsp_has_cnst=PETSC_FALSE,use_nnsp_true=pcbddc->use_nnsp_true;
637   PetscInt       nnsp_size=0,nnsp_addone=0,temp_constraints,temp_start_ptr,n_ISForFaces,n_ISForEdges;
638   IS             *used_IS,ISForVertices,*ISForFaces,*ISForEdges;
639   MatType        impMatType=MATSEQAIJ;
640   PetscBLASInt   Bs,Bt,lwork,lierr;
641   PetscReal      tol=1.0e-8;
642   MatNullSpace   nearnullsp;
643   const Vec      *nearnullvecs;
644   Vec            *localnearnullsp;
645   PetscScalar    *work,*temp_basis,*array_vector,*correlation_mat;
646   PetscReal      *rwork,*singular_vals;
647   PetscBLASInt   Bone=1,*ipiv;
648   Vec            temp_vec;
649   Mat            temp_mat;
650   KSP            temp_ksp;
651   PC             temp_pc;
652   PetscInt       s,start_constraint,dual_dofs;
653   PetscBool      compute_submatrix,useksp=PETSC_FALSE;
654   PetscInt       *aux_primal_permutation,*aux_primal_numbering;
655   PetscBool      boolforchange,*change_basis;
656 /* some ugly conditional declarations */
657 #if defined(PETSC_MISSING_LAPACK_GESVD)
658   PetscScalar    one=1.0,zero=0.0;
659   PetscInt       ii;
660   PetscScalar    *singular_vectors;
661   PetscBLASInt   *iwork,*ifail;
662   PetscReal      dummy_real,abs_tol;
663   PetscBLASInt   eigs_found;
664 #endif
665   PetscBLASInt   dummy_int;
666   PetscScalar    dummy_scalar;
667   PetscBool      used_vertex,get_faces,get_edges,get_vertices;
668 
669   PetscFunctionBegin;
670   /* Get index sets for faces, edges and vertices from graph */
671   get_faces = PETSC_TRUE;
672   get_edges = PETSC_TRUE;
673   get_vertices = PETSC_TRUE;
674   if (pcbddc->vertices_flag) {
675     get_faces = PETSC_FALSE;
676     get_edges = PETSC_FALSE;
677   }
678   if (pcbddc->constraints_flag) {
679     get_vertices = PETSC_FALSE;
680   }
681   if (pcbddc->faces_flag) {
682     get_edges = PETSC_FALSE;
683   }
684   if (pcbddc->edges_flag) {
685     get_faces = PETSC_FALSE;
686   }
687   /* default */
688   if (!get_faces && !get_edges && !get_vertices) {
689     get_vertices = PETSC_TRUE;
690   }
691   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
692   if (pcbddc->dbg_flag) {
693     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
694     i = 0;
695     if (ISForVertices) {
696       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
697     }
698     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
699     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
700     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
701     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
702   }
703   /* check if near null space is attached to global mat */
704   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
705   if (nearnullsp) {
706     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
707   } else { /* if near null space is not provided it uses constants */
708     nnsp_has_cnst = PETSC_TRUE;
709     use_nnsp_true = PETSC_TRUE;
710   }
711   if (nnsp_has_cnst) {
712     nnsp_addone = 1;
713   }
714   /*
715        Evaluate maximum storage size needed by the procedure
716        - temp_indices will contain start index of each constraint stored as follows
717        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
718        - 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
719        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
720                                                                                                                                                          */
721   total_counts = n_ISForFaces+n_ISForEdges;
722   total_counts *= (nnsp_addone+nnsp_size);
723   n_vertices = 0;
724   if (ISForVertices) {
725     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
726   }
727   total_counts += n_vertices;
728   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
729   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
730   total_counts = 0;
731   max_size_of_constraint = 0;
732   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
733     if (i<n_ISForEdges) {
734       used_IS = &ISForEdges[i];
735     } else {
736       used_IS = &ISForFaces[i-n_ISForEdges];
737     }
738     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
739     total_counts += j;
740     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
741   }
742   total_counts *= (nnsp_addone+nnsp_size);
743   total_counts += n_vertices;
744   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
745   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
746   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
747   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
748   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
749   for (i=0;i<pcis->n;i++) {
750     local_to_B[i]=-1;
751   }
752   for (i=0;i<pcis->n_B;i++) {
753     local_to_B[is_indices[i]]=i;
754   }
755   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
756 
757   /* First we issue queries to allocate optimal workspace for LAPACKgesvd or LAPACKsyev/LAPACKheev */
758   rwork = 0;
759   work = 0;
760   singular_vals = 0;
761   temp_basis = 0;
762   correlation_mat = 0;
763   if (!pcbddc->use_nnsp_true) {
764     PetscScalar temp_work;
765 #if defined(PETSC_MISSING_LAPACK_GESVD)
766     /* POD */
767     PetscInt max_n;
768     max_n = nnsp_addone+nnsp_size;
769     /* using some techniques borrowed from Proper Orthogonal Decomposition */
770     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
771     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&singular_vectors);CHKERRQ(ierr);
772     ierr = PetscMalloc(max_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
773     ierr = PetscMalloc(max_size_of_constraint*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
774 #if defined(PETSC_USE_COMPLEX)
775     ierr = PetscMalloc(3*max_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
776 #endif
777     ierr = PetscMalloc(5*max_n*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
778     ierr = PetscMalloc(max_n*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
779     /* now we evaluate the optimal workspace using query with lwork=-1 */
780     ierr = PetscBLASIntCast(max_n,&Bt);CHKERRQ(ierr);
781     lwork=-1;
782     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
783 #if !defined(PETSC_USE_COMPLEX)
784     abs_tol=1.e-8;
785 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,&lierr); */
786     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));
787 #else
788 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,rwork,&lierr); */
789 /*  LAPACK call is missing here! TODO */
790     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
791 #endif
792     if ( lierr ) {
793       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEVX Lapack routine %d",(int)lierr);
794     }
795     ierr = PetscFPTrapPop();CHKERRQ(ierr);
796 #else /* on missing GESVD */
797     /* SVD */
798     PetscInt max_n,min_n;
799     max_n = max_size_of_constraint;
800     min_n = nnsp_addone+nnsp_size;
801     if (max_size_of_constraint < ( nnsp_addone+nnsp_size ) ) {
802       min_n = max_size_of_constraint;
803       max_n = nnsp_addone+nnsp_size;
804     }
805     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
806 #if defined(PETSC_USE_COMPLEX)
807     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
808 #endif
809     /* now we evaluate the optimal workspace using query with lwork=-1 */
810     lwork=-1;
811     ierr = PetscBLASIntCast(max_n,&Bs);CHKERRQ(ierr);
812     ierr = PetscBLASIntCast(min_n,&Bt);CHKERRQ(ierr);
813     dummy_int = Bs;
814     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
815 #if !defined(PETSC_USE_COMPLEX)
816     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));
817 #else
818     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));
819 #endif
820     if ( lierr ) {
821       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SVD Lapack routine %d",(int)lierr);
822     }
823     ierr = PetscFPTrapPop();CHKERRQ(ierr);
824 #endif
825     /* Allocate optimal workspace */
826     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
827     total_counts = (PetscInt)lwork;
828     ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&work);CHKERRQ(ierr);
829   }
830   /* get local part of global near null space vectors */
831   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
832   for (k=0;k<nnsp_size;k++) {
833     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
834     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
835     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
836   }
837   /* Now we can loop on constraining sets */
838   total_counts = 0;
839   temp_indices[0] = 0;
840   /* vertices */
841   if (ISForVertices) {
842     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
843     if (nnsp_has_cnst) { /* consider all vertices */
844       for (i=0;i<n_vertices;i++) {
845         temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
846         temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
847         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
848         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
849         change_basis[total_counts]=PETSC_FALSE;
850         total_counts++;
851       }
852     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
853       for (i=0;i<n_vertices;i++) {
854         used_vertex=PETSC_FALSE;
855         k=0;
856         while (!used_vertex && k<nnsp_size) {
857           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
858           if (PetscAbsScalar(array_vector[is_indices[i]])>0.0) {
859             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
860             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
861             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
862             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
863             change_basis[total_counts]=PETSC_FALSE;
864             total_counts++;
865             used_vertex=PETSC_TRUE;
866           }
867           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
868           k++;
869         }
870       }
871     }
872     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
873     n_vertices = total_counts;
874   }
875   /* edges and faces */
876   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
877     if (i<n_ISForEdges) {
878       used_IS = &ISForEdges[i];
879       boolforchange = pcbddc->use_change_of_basis;
880     } else {
881       used_IS = &ISForFaces[i-n_ISForEdges];
882       boolforchange = pcbddc->use_change_on_faces;
883     }
884     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
885     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
886     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
887     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
888     /* HACK: change of basis should not performed on local periodic nodes */
889     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) {
890       boolforchange = PETSC_FALSE;
891     }
892     if (nnsp_has_cnst) {
893       PetscScalar quad_value;
894       temp_constraints++;
895       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
896       for (j=0;j<size_of_constraint;j++) {
897         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
898         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
899         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
900       }
901       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
902       change_basis[total_counts]=boolforchange;
903       total_counts++;
904     }
905     for (k=0;k<nnsp_size;k++) {
906       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
907       for (j=0;j<size_of_constraint;j++) {
908         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
909         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
910         temp_quadrature_constraint[temp_indices[total_counts]+j]=array_vector[is_indices[j]];
911       }
912       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
913       real_value = 1.0;
914       if (use_nnsp_true) { /* check if array is null on the connected component in case use_nnsp_true has been requested */
915         ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
916         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone));
917       }
918       if (real_value > 0.0) { /* keep indices and values */
919         temp_constraints++;
920         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
921         change_basis[total_counts]=boolforchange;
922         total_counts++;
923       }
924     }
925     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
926     /* perform SVD on the constraint if use_nnsp_true has not be requested by the user */
927     if (!use_nnsp_true) {
928       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
929       ierr = PetscBLASIntCast(temp_constraints,&Bt);CHKERRQ(ierr);
930 
931 #if defined(PETSC_MISSING_LAPACK_GESVD)
932       ierr = PetscMemzero(correlation_mat,Bt*Bt*sizeof(PetscScalar));CHKERRQ(ierr);
933       /* Store upper triangular part of correlation matrix */
934       for (j=0;j<temp_constraints;j++) {
935         for (k=0;k<j+1;k++) {
936           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));
937 
938         }
939       }
940       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
941 #if !defined(PETSC_USE_COMPLEX)
942 /*      LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,&lierr); */
943       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));
944 #else
945 /*  LAPACK call is missing here! TODO */
946       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
947 #endif
948       if (lierr) {
949         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEVX Lapack routine %d",(int)lierr);
950       }
951       ierr = PetscFPTrapPop();CHKERRQ(ierr);
952       /* retain eigenvalues greater than tol: note that lapack SYEV gives eigs in ascending order */
953       j=0;
954       while (j < Bt && singular_vals[j] < tol) j++;
955       total_counts=total_counts-j;
956       if (j<temp_constraints) {
957         for (k=j;k<Bt;k++) {
958           singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
959         }
960         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
961         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));
962         ierr = PetscFPTrapPop();CHKERRQ(ierr);
963         /* copy POD basis into used quadrature memory */
964         for (k=0;k<Bt-j;k++) {
965           for (ii=0;ii<size_of_constraint;ii++) {
966             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[Bt-1-k]*temp_basis[(Bt-1-k)*size_of_constraint+ii];
967           }
968         }
969       }
970 
971 #else  /* on missing GESVD */
972       PetscInt min_n = temp_constraints;
973       if (min_n > size_of_constraint) min_n = size_of_constraint;
974       dummy_int = Bs;
975       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
976 #if !defined(PETSC_USE_COMPLEX)
977       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));
978 #else
979       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));
980 #endif
981       if (lierr) {
982         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD Lapack routine %d",(int)lierr);
983       }
984       ierr = PetscFPTrapPop();CHKERRQ(ierr);
985       /* retain eigenvalues greater than tol: note that lapack SVD gives eigs in descending order */
986       j = 0;
987       while (j < min_n && singular_vals[min_n-j-1] < tol) j++;
988       total_counts = total_counts-(PetscInt)Bt+(min_n-j);
989 #endif
990     }
991   }
992   /* free index sets of faces, edges and vertices */
993   for (i=0;i<n_ISForFaces;i++) {
994     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
995   }
996   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
997   for (i=0;i<n_ISForEdges;i++) {
998     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
999   }
1000   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1001   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1002 
1003   /* set quantities in pcbddc data structure */
1004   /* n_vertices defines the number of point primal dofs */
1005   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1006   local_primal_size = total_counts;
1007   pcbddc->n_vertices = n_vertices;
1008   pcbddc->n_constraints = total_counts-n_vertices;
1009   pcbddc->local_primal_size = local_primal_size;
1010 
1011   /* Create constraint matrix */
1012   /* The constraint matrix is used to compute the l2g map of primal dofs */
1013   /* so we need to set it up properly either with or without change of basis */
1014   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1015   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1016   ierr = MatSetSizes(pcbddc->ConstraintMatrix,local_primal_size,pcis->n,local_primal_size,pcis->n);CHKERRQ(ierr);
1017   /* compute a local numbering of constraints : vertices first then constraints */
1018   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
1019   ierr = VecGetArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
1020   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
1021   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_permutation);CHKERRQ(ierr);
1022   total_counts=0;
1023   /* find vertices: subdomain corners plus dofs with basis changed */
1024   for (i=0;i<local_primal_size;i++) {
1025     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1026     if (change_basis[i] || size_of_constraint == 1) {
1027       k=0;
1028       while(k < size_of_constraint && array_vector[temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1]] != 0.0) {
1029         k=k+1;
1030       }
1031       j=temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1];
1032       array_vector[j] = 1.0;
1033       aux_primal_numbering[total_counts]=j;
1034       aux_primal_permutation[total_counts]=total_counts;
1035       total_counts++;
1036     }
1037   }
1038   ierr = VecRestoreArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
1039   /* permute indices in order to have a sorted set of vertices */
1040   ierr = PetscSortIntWithPermutation(total_counts,aux_primal_numbering,aux_primal_permutation);
1041   /* nonzero structure */
1042   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1043   for (i=0;i<total_counts;i++) {
1044     nnz[i]=1;
1045   }
1046   j=total_counts;
1047   for (i=n_vertices;i<local_primal_size;i++) {
1048     if (!change_basis[i]) {
1049       nnz[j]=temp_indices[i+1]-temp_indices[i];
1050       j++;
1051     }
1052   }
1053   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1054   ierr = PetscFree(nnz);CHKERRQ(ierr);
1055   /* set values in constraint matrix */
1056   for (i=0;i<total_counts;i++) {
1057     j = aux_primal_permutation[i];
1058     k = aux_primal_numbering[j];
1059     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,k,1.0,INSERT_VALUES);CHKERRQ(ierr);
1060   }
1061   for (i=n_vertices;i<local_primal_size;i++) {
1062     if (!change_basis[i]) {
1063       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1064       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);
1065       total_counts++;
1066     }
1067   }
1068   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
1069   ierr = PetscFree(aux_primal_permutation);CHKERRQ(ierr);
1070   /* assembling */
1071   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1072   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1073 
1074   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1075   if (pcbddc->use_change_of_basis) {
1076     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1077     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1078     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1079     /* work arrays */
1080     /* we need to reuse these arrays, so we free them */
1081     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1082     ierr = PetscFree(work);CHKERRQ(ierr);
1083     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1084     ierr = PetscMalloc((nnsp_addone+nnsp_size)*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
1085     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscScalar),&work);CHKERRQ(ierr);
1086     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscBLASInt),&ipiv);CHKERRQ(ierr);
1087     for (i=0;i<pcis->n_B;i++) {
1088       nnz[i]=1;
1089     }
1090     /* Overestimated nonzeros per row */
1091     k=1;
1092     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
1093       if (change_basis[i]) {
1094         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1095         if (k < size_of_constraint) {
1096           k = size_of_constraint;
1097         }
1098         for (j=0;j<size_of_constraint;j++) {
1099           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1100         }
1101       }
1102     }
1103     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1104     ierr = PetscFree(nnz);CHKERRQ(ierr);
1105     /* Temporary array to store indices */
1106     ierr = PetscMalloc(k*sizeof(PetscInt),&is_indices);CHKERRQ(ierr);
1107     /* Set initial identity in the matrix */
1108     for (i=0;i<pcis->n_B;i++) {
1109       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1110     }
1111     /* Now we loop on the constraints which need a change of basis */
1112     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
1113     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (6.2.1) */
1114     temp_constraints = 0;
1115     if (pcbddc->n_vertices < local_primal_size) {
1116       temp_start_ptr = temp_indices_to_constraint_B[temp_indices[pcbddc->n_vertices]];
1117     }
1118     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
1119       if (change_basis[i]) {
1120         compute_submatrix = PETSC_FALSE;
1121         useksp = PETSC_FALSE;
1122         if (temp_start_ptr == temp_indices_to_constraint_B[temp_indices[i]]) {
1123           temp_constraints++;
1124           if (i == local_primal_size -1 ||  temp_start_ptr != temp_indices_to_constraint_B[temp_indices[i+1]]) {
1125             compute_submatrix = PETSC_TRUE;
1126           }
1127         }
1128         if (compute_submatrix) {
1129           if (temp_constraints > 1 || pcbddc->use_nnsp_true) {
1130             useksp = PETSC_TRUE;
1131           }
1132           size_of_constraint = temp_indices[i+1]-temp_indices[i];
1133           if (useksp) { /* experimental TODO: reuse KSP and MAT instead of creating them each time */
1134             ierr = MatCreate(PETSC_COMM_SELF,&temp_mat);CHKERRQ(ierr);
1135             ierr = MatSetType(temp_mat,impMatType);CHKERRQ(ierr);
1136             ierr = MatSetSizes(temp_mat,size_of_constraint,size_of_constraint,size_of_constraint,size_of_constraint);CHKERRQ(ierr);
1137             ierr = MatSeqAIJSetPreallocation(temp_mat,size_of_constraint,NULL);CHKERRQ(ierr);
1138           }
1139           /* First _size_of_constraint-temp_constraints_ columns */
1140           dual_dofs = size_of_constraint-temp_constraints;
1141           start_constraint = i+1-temp_constraints;
1142           for (s=0;s<dual_dofs;s++) {
1143             is_indices[0] = s;
1144             for (j=0;j<temp_constraints;j++) {
1145               for (k=0;k<temp_constraints;k++) {
1146                 temp_basis[j*temp_constraints+k]=temp_quadrature_constraint[temp_indices[start_constraint+k]+s+j+1];
1147               }
1148               work[j]=-temp_quadrature_constraint[temp_indices[start_constraint+j]+s];
1149               is_indices[j+1]=s+j+1;
1150             }
1151             Bt = temp_constraints;
1152             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1153             PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&Bt,&Bone,temp_basis,&Bt,ipiv,work,&Bt,&lierr));
1154             if ( lierr ) {
1155               SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESV Lapack routine %d",(int)lierr);
1156             }
1157             ierr = PetscFPTrapPop();CHKERRQ(ierr);
1158             j = temp_indices_to_constraint_B[temp_indices[start_constraint]+s];
1159             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,temp_constraints,&temp_indices_to_constraint_B[temp_indices[start_constraint]+s+1],1,&j,work,INSERT_VALUES);CHKERRQ(ierr);
1160             if (useksp) {
1161               /* temp mat with transposed rows and columns */
1162               ierr = MatSetValues(temp_mat,1,&s,temp_constraints,&is_indices[1],work,INSERT_VALUES);CHKERRQ(ierr);
1163               ierr = MatSetValue(temp_mat,is_indices[0],is_indices[0],1.0,INSERT_VALUES);CHKERRQ(ierr);
1164             }
1165           }
1166           if (useksp) {
1167             /* last rows of temp_mat */
1168             for (j=0;j<size_of_constraint;j++) {
1169               is_indices[j] = j;
1170             }
1171             for (s=0;s<temp_constraints;s++) {
1172               k = s + dual_dofs;
1173               ierr = MatSetValues(temp_mat,1,&k,size_of_constraint,is_indices,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
1174             }
1175             ierr = MatAssemblyBegin(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1176             ierr = MatAssemblyEnd(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1177             ierr = MatGetVecs(temp_mat,&temp_vec,NULL);CHKERRQ(ierr);
1178             ierr = KSPCreate(PETSC_COMM_SELF,&temp_ksp);CHKERRQ(ierr);
1179             ierr = KSPSetOperators(temp_ksp,temp_mat,temp_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
1180             ierr = KSPSetType(temp_ksp,KSPPREONLY);CHKERRQ(ierr);
1181             ierr = KSPGetPC(temp_ksp,&temp_pc);CHKERRQ(ierr);
1182             ierr = PCSetType(temp_pc,PCLU);CHKERRQ(ierr);
1183             ierr = KSPSetUp(temp_ksp);CHKERRQ(ierr);
1184             for (s=0;s<temp_constraints;s++) {
1185               ierr = VecSet(temp_vec,0.0);CHKERRQ(ierr);
1186               ierr = VecSetValue(temp_vec,s+dual_dofs,1.0,INSERT_VALUES);CHKERRQ(ierr);
1187               ierr = VecAssemblyBegin(temp_vec);CHKERRQ(ierr);
1188               ierr = VecAssemblyEnd(temp_vec);CHKERRQ(ierr);
1189               ierr = KSPSolve(temp_ksp,temp_vec,temp_vec);CHKERRQ(ierr);
1190               ierr = VecGetArray(temp_vec,&array_vector);CHKERRQ(ierr);
1191               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
1192               /* last columns of change of basis matrix associated to new primal dofs */
1193               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);
1194               ierr = VecRestoreArray(temp_vec,&array_vector);CHKERRQ(ierr);
1195             }
1196             ierr = MatDestroy(&temp_mat);CHKERRQ(ierr);
1197             ierr = KSPDestroy(&temp_ksp);CHKERRQ(ierr);
1198             ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
1199           } else {
1200             /* last columns of change of basis matrix associated to new primal dofs */
1201             for (s=0;s<temp_constraints;s++) {
1202               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
1203               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);
1204             }
1205           }
1206           /* prepare for the next cycle */
1207           temp_constraints = 0;
1208           if (i != local_primal_size -1 ) {
1209             temp_start_ptr = temp_indices_to_constraint_B[temp_indices[i+1]];
1210           }
1211         }
1212       }
1213     }
1214     /* assembling */
1215     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1216     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1217     ierr = PetscFree(ipiv);CHKERRQ(ierr);
1218     ierr = PetscFree(is_indices);CHKERRQ(ierr);
1219   }
1220   /* free workspace no longer needed */
1221   ierr = PetscFree(rwork);CHKERRQ(ierr);
1222   ierr = PetscFree(work);CHKERRQ(ierr);
1223   ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1224   ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1225   ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1226   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
1227   ierr = PetscFree(change_basis);CHKERRQ(ierr);
1228   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
1229   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
1230   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
1231   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
1232 #if defined(PETSC_MISSING_LAPACK_GESVD)
1233   ierr = PetscFree(iwork);CHKERRQ(ierr);
1234   ierr = PetscFree(ifail);CHKERRQ(ierr);
1235   ierr = PetscFree(singular_vectors);CHKERRQ(ierr);
1236 #endif
1237   for (k=0;k<nnsp_size;k++) {
1238     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1239   }
1240   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1241   PetscFunctionReturn(0);
1242 }
1243 
1244 #undef __FUNCT__
1245 #define __FUNCT__ "PCBDDCAnalyzeInterface"
1246 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
1247 {
1248   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
1249   PC_IS       *pcis = (PC_IS*)pc->data;
1250   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
1251   PetscInt    bs,ierr,i,vertex_size;
1252   PetscViewer viewer=pcbddc->dbg_viewer;
1253 
1254   PetscFunctionBegin;
1255   /* Init local Graph struct */
1256   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
1257 
1258   /* Check validity of the csr graph passed in by the user */
1259   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
1260     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
1261   }
1262   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
1263   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
1264     Mat mat_adj;
1265     const PetscInt *xadj,*adjncy;
1266     PetscBool flg_row=PETSC_TRUE;
1267 
1268     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
1269     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1270     if (!flg_row) {
1271       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
1272     }
1273     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
1274     ierr = MatRestoreRowIJ(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 MatRestoreRowIJ called in %s\n",__FUNCT__);
1277     }
1278     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
1279   }
1280 
1281   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
1282   vertex_size = 1;
1283   if (!pcbddc->n_ISForDofs) {
1284     IS *custom_ISForDofs;
1285 
1286     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
1287     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
1288     for (i=0;i<bs;i++) {
1289       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1290     }
1291     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1292     /* remove my references to IS objects */
1293     for (i=0;i<bs;i++) {
1294       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1295     }
1296     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1297   } else { /* mat block size as vertex size (used for elasticity) */
1298     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1299   }
1300 
1301   /* Setup of Graph */
1302   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1303 
1304   /* Graph's connected components analysis */
1305   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1306 
1307   /* print some info to stdout */
1308   if (pcbddc->dbg_flag) {
1309     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1310   }
1311   PetscFunctionReturn(0);
1312 }
1313 
1314 #undef __FUNCT__
1315 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1316 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1317 {
1318   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1319   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1320   PetscErrorCode ierr;
1321 
1322   PetscFunctionBegin;
1323   n = 0;
1324   vertices = 0;
1325   if (pcbddc->ConstraintMatrix) {
1326     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1327     for (i=0;i<local_primal_size;i++) {
1328       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1329       if (size_of_constraint == 1) n++;
1330       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1331     }
1332     if (vertices_idx) {
1333       ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1334       n = 0;
1335       for (i=0;i<local_primal_size;i++) {
1336         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1337         if (size_of_constraint == 1) {
1338           vertices[n++]=row_cmat_indices[0];
1339         }
1340         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1341       }
1342     }
1343   }
1344   *n_vertices = n;
1345   if (vertices_idx) *vertices_idx = vertices;
1346   PetscFunctionReturn(0);
1347 }
1348 
1349 #undef __FUNCT__
1350 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
1351 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
1352 {
1353   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1354   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
1355   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
1356   PetscBool      *touched;
1357   PetscErrorCode ierr;
1358 
1359   PetscFunctionBegin;
1360   n = 0;
1361   constraints_index = 0;
1362   if (pcbddc->ConstraintMatrix) {
1363     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
1364     max_size_of_constraint = 0;
1365     for (i=0;i<local_primal_size;i++) {
1366       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1367       if (size_of_constraint > 1) {
1368         n++;
1369       }
1370       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
1371       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1372     }
1373     if (constraints_idx) {
1374       ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
1375       ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
1376       ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1377       ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
1378       n = 0;
1379       for (i=0;i<local_primal_size;i++) {
1380         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1381         if (size_of_constraint > 1) {
1382           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
1383           /* find first untouched local node */
1384           j = 0;
1385           while(touched[row_cmat_indices[j]]) j++;
1386           min_index = row_cmat_global_indices[j];
1387           min_loc = j;
1388           /* search the minimum among nodes not yet touched on the connected component
1389              since there can be more than one constraint on a single cc */
1390           for (j=1;j<size_of_constraint;j++) {
1391             if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
1392               min_index = row_cmat_global_indices[j];
1393               min_loc = j;
1394             }
1395           }
1396           touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
1397           constraints_index[n++] = row_cmat_indices[min_loc];
1398         }
1399         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1400       }
1401       ierr = PetscFree(touched);CHKERRQ(ierr);
1402       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
1403     }
1404   }
1405   *n_constraints = n;
1406   if (constraints_idx) *constraints_idx = constraints_index;
1407   PetscFunctionReturn(0);
1408 }
1409 
1410 /* the next two functions has been adapted from pcis.c */
1411 #undef __FUNCT__
1412 #define __FUNCT__ "PCBDDCApplySchur"
1413 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1414 {
1415   PetscErrorCode ierr;
1416   PC_IS          *pcis = (PC_IS*)(pc->data);
1417 
1418   PetscFunctionBegin;
1419   if (!vec2_B) { vec2_B = v; }
1420   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1421   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
1422   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1423   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
1424   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1425   PetscFunctionReturn(0);
1426 }
1427 
1428 #undef __FUNCT__
1429 #define __FUNCT__ "PCBDDCApplySchurTranspose"
1430 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1431 {
1432   PetscErrorCode ierr;
1433   PC_IS          *pcis = (PC_IS*)(pc->data);
1434 
1435   PetscFunctionBegin;
1436   if (!vec2_B) { vec2_B = v; }
1437   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1438   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
1439   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1440   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
1441   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1442   PetscFunctionReturn(0);
1443 }
1444 
1445 #undef __FUNCT__
1446 #define __FUNCT__ "PCBDDCSubsetNumbering"
1447 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[])
1448 {
1449   Vec            local_vec,global_vec;
1450   IS             seqis,paris;
1451   VecScatter     scatter_ctx;
1452   PetscScalar    *array;
1453   PetscInt       *temp_global_dofs;
1454   PetscScalar    globalsum;
1455   PetscInt       i,j,s;
1456   PetscInt       nlocals,first_index,old_index,max_local;
1457   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
1458   PetscMPIInt    *dof_sizes,*dof_displs;
1459   PetscBool      first_found;
1460   PetscErrorCode ierr;
1461 
1462   PetscFunctionBegin;
1463   /* mpi buffers */
1464   MPI_Comm_size(comm,&size_prec_comm);
1465   MPI_Comm_rank(comm,&rank_prec_comm);
1466   j = ( !rank_prec_comm ? size_prec_comm : 0);
1467   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1468   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1469   /* get maximum size of subset */
1470   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
1471   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
1472   max_local = 0;
1473   if (n_local_dofs) {
1474     max_local = temp_global_dofs[0];
1475     for (i=1;i<n_local_dofs;i++) {
1476       if (max_local < temp_global_dofs[i] ) {
1477         max_local = temp_global_dofs[i];
1478       }
1479     }
1480   }
1481   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
1482   max_global++;
1483   max_local = 0;
1484   if (n_local_dofs) {
1485     max_local = local_dofs[0];
1486     for (i=1;i<n_local_dofs;i++) {
1487       if (max_local < local_dofs[i] ) {
1488         max_local = local_dofs[i];
1489       }
1490     }
1491   }
1492   max_local++;
1493   /* allocate workspace */
1494   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
1495   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
1496   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
1497   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
1498   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
1499   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
1500   /* create scatter */
1501   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
1502   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
1503   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
1504   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
1505   ierr = ISDestroy(&paris);CHKERRQ(ierr);
1506   /* init array */
1507   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1508   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1509   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1510   if (local_dofs_mult) {
1511     for (i=0;i<n_local_dofs;i++) {
1512       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
1513     }
1514   } else {
1515     for (i=0;i<n_local_dofs;i++) {
1516       array[local_dofs[i]]=1.0;
1517     }
1518   }
1519   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1520   /* scatter into global vec and get total number of global dofs */
1521   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1522   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1523   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
1524   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
1525   /* Fill global_vec with cumulative function for global numbering */
1526   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
1527   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
1528   nlocals = 0;
1529   first_index = -1;
1530   first_found = PETSC_FALSE;
1531   for (i=0;i<s;i++) {
1532     if (!first_found && PetscRealPart(array[i]) > 0.0) {
1533       first_found = PETSC_TRUE;
1534       first_index = i;
1535     }
1536     nlocals += (PetscInt)PetscRealPart(array[i]);
1537   }
1538   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1539   if (!rank_prec_comm) {
1540     dof_displs[0]=0;
1541     for (i=1;i<size_prec_comm;i++) {
1542       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1543     }
1544   }
1545   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1546   if (first_found) {
1547     array[first_index] += (PetscScalar)nlocals;
1548     old_index = first_index;
1549     for (i=first_index+1;i<s;i++) {
1550       if (PetscRealPart(array[i]) > 0.0) {
1551         array[i] += array[old_index];
1552         old_index = i;
1553       }
1554     }
1555   }
1556   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
1557   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1558   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1559   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1560   /* get global ordering of local dofs */
1561   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1562   if (local_dofs_mult) {
1563     for (i=0;i<n_local_dofs;i++) {
1564       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
1565     }
1566   } else {
1567     for (i=0;i<n_local_dofs;i++) {
1568       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
1569     }
1570   }
1571   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1572   /* free workspace */
1573   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1574   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1575   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1576   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1577   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1578   /* return pointer to global ordering of local dofs */
1579   *global_numbering_subset = temp_global_dofs;
1580   PetscFunctionReturn(0);
1581 }
1582