xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 95a0def0f3a2cdbb9441427df63e57f830d950d1)
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 /* uncomment for testing purposes */
628 /* #define PETSC_MISSING_LAPACK_GESVD 1 */
629 #undef __FUNCT__
630 #define __FUNCT__ "PCBDDCConstraintsSetUp"
631 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
632 {
633   PetscErrorCode    ierr;
634   PC_IS*            pcis = (PC_IS*)(pc->data);
635   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
636   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
637   /* constraint and (optionally) change of basis matrix implemented as SeqAIJ */
638   MatType           impMatType=MATSEQAIJ;
639   /* one and zero */
640   PetscScalar       one=1.0,zero=0.0;
641   /* space to store constraints and their local indices */
642   PetscScalar       *temp_quadrature_constraint;
643   PetscInt          *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B;
644   /* iterators */
645   PetscInt          i,j,k,total_counts,temp_start_ptr;
646   /* stuff to store connected components stored in pcbddc->mat_graph */
647   IS                ISForVertices,*ISForFaces,*ISForEdges,*used_IS;
648   PetscInt          n_ISForFaces,n_ISForEdges;
649   PetscBool         get_faces,get_edges,get_vertices;
650   /* near null space stuff */
651   MatNullSpace      nearnullsp;
652   const Vec         *nearnullvecs;
653   Vec               *localnearnullsp;
654   PetscBool         nnsp_has_cnst;
655   PetscInt          nnsp_size;
656   PetscScalar       *array;
657   /* BLAS integers */
658   PetscBLASInt      lwork,lierr;
659   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
660   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
661   /* LAPACK working arrays for SVD or POD */
662   PetscBool         skip_lapack;
663   PetscScalar       *work;
664   PetscReal         *singular_vals;
665 #if defined(PETSC_USE_COMPLEX)
666   PetscReal         *rwork;
667 #endif
668 #if defined(PETSC_MISSING_LAPACK_GESVD)
669   PetscBLASInt      Blas_one_2=1;
670   PetscScalar       *temp_basis,*correlation_mat;
671 #else
672   PetscBLASInt      dummy_int_1=1,dummy_int_2=1;
673   PetscScalar       dummy_scalar_1=0.0,dummy_scalar_2=0.0;
674 #endif
675   /* change of basis */
676   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
677   PetscBool         boolforchange,*change_basis,*touched;
678   /* auxiliary stuff */
679   PetscInt          *nnz,*is_indices,*local_to_B;
680   /* some quantities */
681   PetscInt          n_vertices,total_primal_vertices;
682   PetscInt          size_of_constraint,max_size_of_constraint,max_constraints,temp_constraints;
683 
684 
685   PetscFunctionBegin;
686   /* Get index sets for faces, edges and vertices from graph */
687   get_faces = PETSC_TRUE;
688   get_edges = PETSC_TRUE;
689   get_vertices = PETSC_TRUE;
690   if (pcbddc->vertices_flag) {
691     get_faces = PETSC_FALSE;
692     get_edges = PETSC_FALSE;
693   }
694   if (pcbddc->constraints_flag) {
695     get_vertices = PETSC_FALSE;
696   }
697   if (pcbddc->faces_flag) {
698     get_edges = PETSC_FALSE;
699   }
700   if (pcbddc->edges_flag) {
701     get_faces = PETSC_FALSE;
702   }
703   /* default */
704   if (!get_faces && !get_edges && !get_vertices) {
705     get_vertices = PETSC_TRUE;
706   }
707   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
708   /* print some info */
709   if (pcbddc->dbg_flag) {
710     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
711     i = 0;
712     if (ISForVertices) {
713       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
714     }
715     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
716     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
717     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
718     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
719   }
720   /* check if near null space is attached to global mat */
721   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
722   if (nearnullsp) {
723     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
724   } else { /* if near null space is not provided BDDC uses constants by default */
725     nnsp_size = 0;
726     nnsp_has_cnst = PETSC_TRUE;
727   }
728   /* get max number of constraints on a single cc */
729   max_constraints = nnsp_size;
730   if (nnsp_has_cnst) max_constraints++;
731 
732   /*
733        Evaluate maximum storage size needed by the procedure
734        - temp_indices will contain start index of each constraint stored as follows
735        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
736        - 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
737        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
738                                                                                                                                                          */
739   total_counts = n_ISForFaces+n_ISForEdges;
740   total_counts *= max_constraints;
741   n_vertices = 0;
742   if (ISForVertices) {
743     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
744   }
745   total_counts += n_vertices;
746   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
747   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
748   total_counts = 0;
749   max_size_of_constraint = 0;
750   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
751     if (i<n_ISForEdges) {
752       used_IS = &ISForEdges[i];
753     } else {
754       used_IS = &ISForFaces[i-n_ISForEdges];
755     }
756     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
757     total_counts += j;
758     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
759   }
760   total_counts *= max_constraints;
761   total_counts += n_vertices;
762   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
763   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
764   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
765   /* local to boundary numbering */
766   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
767   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
768   for (i=0;i<pcis->n;i++) local_to_B[i]=-1;
769   for (i=0;i<pcis->n_B;i++) local_to_B[is_indices[i]]=i;
770   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
771   /* get local part of global near null space vectors */
772   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
773   for (k=0;k<nnsp_size;k++) {
774     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
775     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
776     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
777   }
778 
779   /* whether or not to skip lapack calls */
780   skip_lapack = PETSC_TRUE;
781   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
782 
783   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
784   if (!pcbddc->use_nnsp_true && !skip_lapack) {
785     PetscScalar temp_work;
786 #if defined(PETSC_MISSING_LAPACK_GESVD)
787     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
788     ierr = PetscMalloc(max_constraints*max_constraints*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
789     ierr = PetscMalloc(max_constraints*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
790     ierr = PetscMalloc(max_size_of_constraint*max_constraints*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
791 #if defined(PETSC_USE_COMPLEX)
792     ierr = PetscMalloc(3*max_constraints*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
793 #endif
794     /* now we evaluate the optimal workspace using query with lwork=-1 */
795     ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
796     ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
797     lwork = -1;
798     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
799 #if !defined(PETSC_USE_COMPLEX)
800     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
801 #else
802     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
803 #endif
804     ierr = PetscFPTrapPop();CHKERRQ(ierr);
805     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
806 #else /* on missing GESVD */
807     /* SVD */
808     PetscInt max_n,min_n;
809     max_n = max_size_of_constraint;
810     min_n = max_constraints;
811     if (max_size_of_constraint < max_constraints) {
812       min_n = max_size_of_constraint;
813       max_n = max_constraints;
814     }
815     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
816 #if defined(PETSC_USE_COMPLEX)
817     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
818 #endif
819     /* now we evaluate the optimal workspace using query with lwork=-1 */
820     lwork = -1;
821     ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
822     ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
823     ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
824     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
825 #if !defined(PETSC_USE_COMPLEX)
826     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&temp_quadrature_constraint[0],&Blas_LDA,singular_vals,&dummy_scalar_1,&dummy_int_1,&dummy_scalar_2,&dummy_int_2,&temp_work,&lwork,&lierr));
827 #else
828     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&temp_quadrature_constraint[0],&Blas_LDA,singular_vals,&dummy_scalar_1,&dummy_int_1,&dummy_scalar_2,&dummy_int_2,&temp_work,&lwork,rwork,&lierr));
829 #endif
830     ierr = PetscFPTrapPop();CHKERRQ(ierr);
831     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
832 #endif /* on missing GESVD */
833     /* Allocate optimal workspace */
834     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
835     ierr = PetscMalloc((PetscInt)lwork*sizeof(PetscScalar),&work);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       PetscBool used_vertex;
854       for (i=0;i<n_vertices;i++) {
855         used_vertex = PETSC_FALSE;
856         k = 0;
857         while (!used_vertex && k<nnsp_size) {
858           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
859           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
860             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
861             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
862             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
863             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
864             change_basis[total_counts]=PETSC_FALSE;
865             total_counts++;
866             used_vertex = PETSC_TRUE;
867           }
868           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
869           k++;
870         }
871       }
872     }
873     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
874     n_vertices = total_counts;
875   }
876 
877   /* edges and faces */
878   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
879     if (i<n_ISForEdges) {
880       used_IS = &ISForEdges[i];
881       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
882     } else {
883       used_IS = &ISForFaces[i-n_ISForEdges];
884       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
885     }
886     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
887     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
888     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
889     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
890     /* change of basis should not be performed on local periodic nodes */
891     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
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       PetscReal real_value;
907       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
908       for (j=0;j<size_of_constraint;j++) {
909         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
910         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
911         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
912       }
913       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
914       /* check if array is null on the connected component */
915       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
916       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_one));
917       if (real_value > 0.0) { /* keep indices and values */
918         temp_constraints++;
919         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
920         change_basis[total_counts]=boolforchange;
921         total_counts++;
922       }
923     }
924     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
925     /* perform SVD on the constraints if use_nnsp_true has not be requested by the user */
926     if (!pcbddc->use_nnsp_true) {
927       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
928 
929 #if defined(PETSC_MISSING_LAPACK_GESVD)
930       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
931          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
932          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
933             the constraints basis will differ (by a complex factor with absolute value equal to 1)
934             from that computed using LAPACKgesvd
935          -> This is due to a different computation of eigenvectors in LAPACKheev
936          -> The quality of the POD-computed basis will be the same */
937       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
938       /* Store upper triangular part of correlation matrix */
939       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
940       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
941       for (j=0;j<temp_constraints;j++) {
942         for (k=0;k<j+1;k++) {
943           PetscStackCallBLAS("BLASdot",correlation_mat[j*temp_constraints+k]=BLASdot_(&Blas_N,&temp_quadrature_constraint[temp_indices[temp_start_ptr+k]],&Blas_one,&temp_quadrature_constraint[temp_indices[temp_start_ptr+j]],&Blas_one_2));
944         }
945       }
946       /* compute eigenvalues and eigenvectors of correlation matrix */
947       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
948       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
949 #if !defined(PETSC_USE_COMPLEX)
950       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
951 #else
952       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
953 #endif
954       ierr = PetscFPTrapPop();CHKERRQ(ierr);
955       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
956       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
957       j=0;
958       while (j < temp_constraints && singular_vals[j] < tol) j++;
959       total_counts=total_counts-j;
960       /* scale and copy POD basis into used quadrature memory */
961       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
962       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
963       ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
964       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
965       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
966       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
967       if (j<temp_constraints) {
968         PetscInt ii;
969         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
970         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
971         PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Blas_M,&Blas_N,&Blas_K,&one,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Blas_LDA,correlation_mat,&Blas_LDB,&zero,temp_basis,&Blas_LDC));
972         ierr = PetscFPTrapPop();CHKERRQ(ierr);
973         for (k=0;k<temp_constraints-j;k++) {
974           for (ii=0;ii<size_of_constraint;ii++) {
975             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[temp_constraints-1-k]*temp_basis[(temp_constraints-1-k)*size_of_constraint+ii];
976           }
977         }
978       }
979 #else  /* on missing GESVD */
980       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
981       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
982       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
983       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
984 #if !defined(PETSC_USE_COMPLEX)
985       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Blas_LDA,singular_vals,&dummy_scalar_1,&dummy_int_1,&dummy_scalar_2,&dummy_int_2,work,&lwork,&lierr));
986 #else
987       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Blas_LDA,singular_vals,&dummy_scalar_1,&dummy_int_1,&dummy_scalar_2,&dummy_int_2,work,&lwork,rwork,&lierr));
988 #endif
989       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
990       ierr = PetscFPTrapPop();CHKERRQ(ierr);
991       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
992       k = temp_constraints;
993       if (k > size_of_constraint) k = size_of_constraint;
994       j = 0;
995       while (j < k && singular_vals[k-j-1] < tol) j++;
996       total_counts = total_counts-temp_constraints+k-j;
997 #endif /* on missing GESVD */
998     }
999   }
1000   /* free index sets of faces, edges and vertices */
1001   for (i=0;i<n_ISForFaces;i++) {
1002     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1003   }
1004   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1005   for (i=0;i<n_ISForEdges;i++) {
1006     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1007   }
1008   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1009   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1010 
1011   /* free workspace */
1012   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1013     ierr = PetscFree(work);CHKERRQ(ierr);
1014 #if defined(PETSC_USE_COMPLEX)
1015     ierr = PetscFree(rwork);CHKERRQ(ierr);
1016 #endif
1017     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1018 #if defined(PETSC_MISSING_LAPACK_GESVD)
1019     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1020     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1021 #endif
1022   }
1023   for (k=0;k<nnsp_size;k++) {
1024     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1025   }
1026   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1027 
1028   /* set quantities in pcbddc data structure */
1029   /* n_vertices defines the number of subdomain corners in the primal space */
1030   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1031   pcbddc->local_primal_size = total_counts;
1032   pcbddc->n_vertices = n_vertices;
1033   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
1034 
1035   /* Create constraint matrix */
1036   /* The constraint matrix is used to compute the l2g map of primal dofs */
1037   /* so we need to set it up properly either with or without change of basis */
1038   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1039   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1040   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
1041   /* array to compute a local numbering of constraints : vertices first then constraints */
1042   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
1043   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
1044   /* note: it should not be needed since IS for faces and edges are already sorted by global ordering when analyzing the graph but... just in case */
1045   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_minloc);CHKERRQ(ierr);
1046   /* auxiliary stuff for basis change */
1047   ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&global_indices);CHKERRQ(ierr);
1048   ierr = PetscMalloc(pcis->n_B*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1049   ierr = PetscMemzero(touched,pcis->n_B*sizeof(PetscBool));CHKERRQ(ierr);
1050 
1051   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
1052   total_primal_vertices=0;
1053   for (i=0;i<pcbddc->local_primal_size;i++) {
1054     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1055     if (size_of_constraint == 1) {
1056       touched[temp_indices_to_constraint_B[temp_indices[i]]]=PETSC_TRUE;
1057       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
1058       aux_primal_minloc[total_primal_vertices]=0;
1059       total_primal_vertices++;
1060     } else if (change_basis[i]) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
1061       PetscInt min_loc,min_index;
1062       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
1063       /* find first untouched local node */
1064       k = 0;
1065       while (touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) k++;
1066       min_index = global_indices[k];
1067       min_loc = k;
1068       /* search the minimum among global nodes already untouched on the cc */
1069       for (k=1;k<size_of_constraint;k++) {
1070         /* there can be more than one constraint on a single connected component */
1071         if (min_index > global_indices[k] && !touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) {
1072           min_index = global_indices[k];
1073           min_loc = k;
1074         }
1075       }
1076       touched[temp_indices_to_constraint_B[temp_indices[i]+min_loc]] = PETSC_TRUE;
1077       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
1078       aux_primal_minloc[total_primal_vertices]=min_loc;
1079       total_primal_vertices++;
1080     }
1081   }
1082   /* free workspace */
1083   ierr = PetscFree(global_indices);CHKERRQ(ierr);
1084   ierr = PetscFree(touched);CHKERRQ(ierr);
1085   /* permute indices in order to have a sorted set of vertices */
1086   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);
1087 
1088   /* nonzero structure of constraint matrix */
1089   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1090   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
1091   j=total_primal_vertices;
1092   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1093     if (!change_basis[i]) {
1094       nnz[j]=temp_indices[i+1]-temp_indices[i];
1095       j++;
1096     }
1097   }
1098   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1099   ierr = PetscFree(nnz);CHKERRQ(ierr);
1100   /* set values in constraint matrix */
1101   for (i=0;i<total_primal_vertices;i++) {
1102     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
1103   }
1104   total_counts = total_primal_vertices;
1105   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1106     if (!change_basis[i]) {
1107       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1108       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);
1109       total_counts++;
1110     }
1111   }
1112   /* assembling */
1113   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1114   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1115   /*
1116   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
1117   */
1118   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1119   if (pcbddc->use_change_of_basis) {
1120     PetscBool qr_needed = PETSC_FALSE;
1121     /* change of basis acts on local interfaces -> dimension is n_B x n_B */
1122     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1123     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1124     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1125     /* work arrays */
1126     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1127     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
1128     /* nonzeros per row */
1129     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1130       if (change_basis[i]) {
1131         qr_needed = PETSC_TRUE;
1132         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1133         for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1134       }
1135     }
1136     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1137     ierr = PetscFree(nnz);CHKERRQ(ierr);
1138     /* Set initial identity in the matrix */
1139     for (i=0;i<pcis->n_B;i++) {
1140       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1141     }
1142 
1143     /* Now we loop on the constraints which need a change of basis */
1144     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
1145     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1) */
1146     /* Change of basis matrix T computed via QR decomposition of constraints */
1147     if (qr_needed) {
1148       /* dual and primal dofs on a single cc */
1149       PetscInt     dual_dofs,primal_dofs;
1150       /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
1151       PetscInt     primal_counter;
1152       /* working stuff for GEQRF */
1153       PetscScalar  *qr_basis,*qr_tau,*qr_work,lqr_work_t;
1154       PetscBLASInt lqr_work;
1155       /* working stuff for UNGQR */
1156       PetscScalar  *gqr_work,lgqr_work_t;
1157       PetscBLASInt lgqr_work;
1158       /* working stuff for TRTRS */
1159       PetscScalar  *trs_rhs;
1160       PetscBLASInt Blas_NRHS;
1161       /* pointers for values insertion into change of basis matrix */
1162       PetscInt     *start_rows,*start_cols;
1163       PetscScalar  *start_vals;
1164       /* working stuff for values insertion */
1165       PetscBool    *is_primal;
1166 
1167       /* space to store Q */
1168       ierr = PetscMalloc((max_size_of_constraint)*(max_size_of_constraint)*sizeof(PetscScalar),&qr_basis);CHKERRQ(ierr);
1169       /* first we issue queries for optimal work */
1170       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1171       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1172       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1173       lqr_work = -1;
1174       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
1175       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
1176       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
1177       ierr = PetscMalloc((PetscInt)PetscRealPart(lqr_work_t)*sizeof(*qr_work),&qr_work);CHKERRQ(ierr);
1178       lgqr_work = -1;
1179       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1180       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
1181       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
1182       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1183       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
1184       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
1185       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
1186       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
1187       ierr = PetscMalloc((PetscInt)PetscRealPart(lgqr_work_t)*sizeof(*gqr_work),&gqr_work);CHKERRQ(ierr);
1188       /* array to store scaling factors for reflectors */
1189       ierr = PetscMalloc(max_constraints*sizeof(*qr_tau),&qr_tau);CHKERRQ(ierr);
1190       /* array to store rhs and solution of triangular solver */
1191       ierr = PetscMalloc(max_constraints*max_constraints*sizeof(*trs_rhs),&trs_rhs);CHKERRQ(ierr);
1192       /* array to store whether a node is primal or not */
1193       ierr = PetscMalloc(pcis->n_B*sizeof(*is_primal),&is_primal);CHKERRQ(ierr);
1194       ierr = PetscMemzero(is_primal,pcis->n_B*sizeof(*is_primal));CHKERRQ(ierr);
1195       for (i=0;i<total_primal_vertices;i++) is_primal[local_to_B[aux_primal_numbering[i]]] = PETSC_TRUE;
1196 
1197       /* allocating workspace for check */
1198       if (pcbddc->dbg_flag) {
1199         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1200         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
1201         ierr = PetscMalloc(max_size_of_constraint*(max_constraints+max_size_of_constraint)*sizeof(*work),&work);CHKERRQ(ierr);
1202       }
1203 
1204       /* loop on constraints and see whether or not they need a change of basis */
1205       /* -> using implicit ordering contained in temp_indices data */
1206       total_counts = pcbddc->n_vertices;
1207       primal_counter = total_counts;
1208       while (total_counts<pcbddc->local_primal_size) {
1209         primal_dofs = 1;
1210         if (change_basis[total_counts]) {
1211           /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
1212           while (total_counts+primal_dofs < pcbddc->local_primal_size && temp_indices_to_constraint_B[temp_indices[total_counts]] == temp_indices_to_constraint_B[temp_indices[total_counts+primal_dofs]]) {
1213             primal_dofs++;
1214           }
1215           /* get constraint info */
1216           size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
1217           dual_dofs = size_of_constraint-primal_dofs;
1218 
1219           /* copy quadrature constraints for change of basis check */
1220           if (pcbddc->dbg_flag) {
1221             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %d to %d need a change of basis (size %d)\n",total_counts,total_counts+primal_dofs,size_of_constraint);CHKERRQ(ierr);
1222             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1223           }
1224 
1225           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
1226           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1227 
1228           /* compute QR decomposition of constraints */
1229           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1230           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1231           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1232           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1233           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
1234           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
1235           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1236 
1237           /* explictly compute R^-T */
1238           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
1239           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
1240           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1241           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
1242           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1243           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
1244           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1245           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
1246           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
1247           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1248 
1249           /* explcitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
1250           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1251           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1252           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
1253           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1254           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1255           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
1256           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
1257           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1258 
1259           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
1260              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
1261              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
1262           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1263           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1264           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
1265           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1266           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
1267           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1268           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1269           PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Blas_M,&Blas_N,&Blas_K,&one,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&zero,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_LDC));
1270           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1271           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1272 
1273           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
1274           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
1275           /* insert cols for primal dofs */
1276           for (j=0;j<primal_dofs;j++) {
1277             start_vals = &qr_basis[j*size_of_constraint];
1278             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
1279             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
1280           }
1281           /* insert cols for dual dofs */
1282           for (j=0,k=0;j<dual_dofs;k++) {
1283             if (!is_primal[temp_indices_to_constraint_B[temp_indices[total_counts]+k]]) {
1284               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
1285               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
1286               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
1287               j++;
1288             }
1289           }
1290 
1291           /* check change of basis */
1292           if (pcbddc->dbg_flag) {
1293             PetscInt   ii,jj;
1294             PetscBool valid_qr=PETSC_TRUE;
1295             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
1296             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1297             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
1298             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1299             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
1300             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
1301             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1302             PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&Blas_M,&Blas_N,&Blas_K,&one,work,&Blas_LDA,qr_basis,&Blas_LDB,&zero,&work[size_of_constraint*primal_dofs],&Blas_LDC));
1303             ierr = PetscFPTrapPop();CHKERRQ(ierr);
1304             for (jj=0;jj<size_of_constraint;jj++) {
1305               for (ii=0;ii<primal_dofs;ii++) {
1306                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
1307                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
1308               }
1309             }
1310             if (!valid_qr) {
1311               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
1312               for (jj=0;jj<size_of_constraint;jj++) {
1313                 for (ii=0;ii<primal_dofs;ii++) {
1314                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
1315                     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %d is not orthogonal to constraint %d (%1.14e)!\n",jj,ii,PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
1316                   }
1317                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
1318                     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %d is not unitary w.r.t constraint %d (%1.14e)!\n",jj,ii,PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
1319                   }
1320                 }
1321               }
1322             } else {
1323               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
1324             }
1325           }
1326           /* increment primal counter */
1327           primal_counter += primal_dofs;
1328         } else {
1329           if (pcbddc->dbg_flag) {
1330             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %d does not need a change of basis (size %d)\n",total_counts,temp_indices[total_counts+1]-temp_indices[total_counts]);CHKERRQ(ierr);
1331           }
1332         }
1333         /* increment constraint counter total_counts */
1334         total_counts += primal_dofs;
1335       }
1336       if (pcbddc->dbg_flag) {
1337         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1338         ierr = PetscFree(work);CHKERRQ(ierr);
1339       }
1340       /* free workspace */
1341       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
1342       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
1343       ierr = PetscFree(qr_work);CHKERRQ(ierr);
1344       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
1345       ierr = PetscFree(is_primal);CHKERRQ(ierr);
1346       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
1347     }
1348     /* assembling */
1349     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1350     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1351     /*
1352     ierr = MatView(pcbddc->ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
1353     */
1354   }
1355   /* free workspace */
1356   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
1357   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
1358   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
1359   ierr = PetscFree(change_basis);CHKERRQ(ierr);
1360   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
1361   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
1362   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
1363   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
1364   PetscFunctionReturn(0);
1365 }
1366 
1367 #undef __FUNCT__
1368 #define __FUNCT__ "PCBDDCAnalyzeInterface"
1369 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
1370 {
1371   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
1372   PC_IS       *pcis = (PC_IS*)pc->data;
1373   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
1374   PetscInt    bs,ierr,i,vertex_size;
1375   PetscViewer viewer=pcbddc->dbg_viewer;
1376 
1377   PetscFunctionBegin;
1378   /* Init local Graph struct */
1379   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
1380 
1381   /* Check validity of the csr graph passed in by the user */
1382   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
1383     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
1384   }
1385   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
1386   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
1387     Mat mat_adj;
1388     const PetscInt *xadj,*adjncy;
1389     PetscBool flg_row=PETSC_TRUE;
1390 
1391     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
1392     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1393     if (!flg_row) {
1394       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
1395     }
1396     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
1397     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1398     if (!flg_row) {
1399       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
1400     }
1401     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
1402   }
1403 
1404   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
1405   vertex_size = 1;
1406   if (!pcbddc->n_ISForDofs) {
1407     IS *custom_ISForDofs;
1408 
1409     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
1410     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
1411     for (i=0;i<bs;i++) {
1412       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1413     }
1414     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1415     /* remove my references to IS objects */
1416     for (i=0;i<bs;i++) {
1417       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1418     }
1419     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1420   } else { /* mat block size as vertex size (used for elasticity) */
1421     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1422   }
1423 
1424   /* Setup of Graph */
1425   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1426 
1427   /* Graph's connected components analysis */
1428   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1429 
1430   /* print some info to stdout */
1431   if (pcbddc->dbg_flag) {
1432     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1433   }
1434   PetscFunctionReturn(0);
1435 }
1436 
1437 #undef __FUNCT__
1438 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1439 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1440 {
1441   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1442   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1443   PetscErrorCode ierr;
1444 
1445   PetscFunctionBegin;
1446   n = 0;
1447   vertices = 0;
1448   if (pcbddc->ConstraintMatrix) {
1449     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1450     for (i=0;i<local_primal_size;i++) {
1451       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1452       if (size_of_constraint == 1) n++;
1453       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1454     }
1455     if (vertices_idx) {
1456       ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1457       n = 0;
1458       for (i=0;i<local_primal_size;i++) {
1459         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1460         if (size_of_constraint == 1) {
1461           vertices[n++]=row_cmat_indices[0];
1462         }
1463         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1464       }
1465     }
1466   }
1467   *n_vertices = n;
1468   if (vertices_idx) *vertices_idx = vertices;
1469   PetscFunctionReturn(0);
1470 }
1471 
1472 #undef __FUNCT__
1473 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
1474 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
1475 {
1476   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1477   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
1478   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
1479   PetscBool      *touched;
1480   PetscErrorCode ierr;
1481 
1482   PetscFunctionBegin;
1483   n = 0;
1484   constraints_index = 0;
1485   if (pcbddc->ConstraintMatrix) {
1486     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
1487     max_size_of_constraint = 0;
1488     for (i=0;i<local_primal_size;i++) {
1489       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1490       if (size_of_constraint > 1) {
1491         n++;
1492       }
1493       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
1494       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1495     }
1496     if (constraints_idx) {
1497       ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
1498       ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
1499       ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1500       ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
1501       n = 0;
1502       for (i=0;i<local_primal_size;i++) {
1503         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1504         if (size_of_constraint > 1) {
1505           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
1506           /* find first untouched local node */
1507           j = 0;
1508           while(touched[row_cmat_indices[j]]) j++;
1509           min_index = row_cmat_global_indices[j];
1510           min_loc = j;
1511           /* search the minimum among nodes not yet touched on the connected component
1512              since there can be more than one constraint on a single cc */
1513           for (j=1;j<size_of_constraint;j++) {
1514             if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
1515               min_index = row_cmat_global_indices[j];
1516               min_loc = j;
1517             }
1518           }
1519           touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
1520           constraints_index[n++] = row_cmat_indices[min_loc];
1521         }
1522         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1523       }
1524       ierr = PetscFree(touched);CHKERRQ(ierr);
1525       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
1526     }
1527   }
1528   *n_constraints = n;
1529   if (constraints_idx) *constraints_idx = constraints_index;
1530   PetscFunctionReturn(0);
1531 }
1532 
1533 /* the next two functions has been adapted from pcis.c */
1534 #undef __FUNCT__
1535 #define __FUNCT__ "PCBDDCApplySchur"
1536 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1537 {
1538   PetscErrorCode ierr;
1539   PC_IS          *pcis = (PC_IS*)(pc->data);
1540 
1541   PetscFunctionBegin;
1542   if (!vec2_B) { vec2_B = v; }
1543   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1544   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
1545   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1546   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
1547   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1548   PetscFunctionReturn(0);
1549 }
1550 
1551 #undef __FUNCT__
1552 #define __FUNCT__ "PCBDDCApplySchurTranspose"
1553 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1554 {
1555   PetscErrorCode ierr;
1556   PC_IS          *pcis = (PC_IS*)(pc->data);
1557 
1558   PetscFunctionBegin;
1559   if (!vec2_B) { vec2_B = v; }
1560   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1561   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
1562   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1563   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
1564   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1565   PetscFunctionReturn(0);
1566 }
1567 
1568 #undef __FUNCT__
1569 #define __FUNCT__ "PCBDDCSubsetNumbering"
1570 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[])
1571 {
1572   Vec            local_vec,global_vec;
1573   IS             seqis,paris;
1574   VecScatter     scatter_ctx;
1575   PetscScalar    *array;
1576   PetscInt       *temp_global_dofs;
1577   PetscScalar    globalsum;
1578   PetscInt       i,j,s;
1579   PetscInt       nlocals,first_index,old_index,max_local;
1580   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
1581   PetscMPIInt    *dof_sizes,*dof_displs;
1582   PetscBool      first_found;
1583   PetscErrorCode ierr;
1584 
1585   PetscFunctionBegin;
1586   /* mpi buffers */
1587   MPI_Comm_size(comm,&size_prec_comm);
1588   MPI_Comm_rank(comm,&rank_prec_comm);
1589   j = ( !rank_prec_comm ? size_prec_comm : 0);
1590   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1591   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1592   /* get maximum size of subset */
1593   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
1594   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
1595   max_local = 0;
1596   if (n_local_dofs) {
1597     max_local = temp_global_dofs[0];
1598     for (i=1;i<n_local_dofs;i++) {
1599       if (max_local < temp_global_dofs[i] ) {
1600         max_local = temp_global_dofs[i];
1601       }
1602     }
1603   }
1604   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
1605   max_global++;
1606   max_local = 0;
1607   if (n_local_dofs) {
1608     max_local = local_dofs[0];
1609     for (i=1;i<n_local_dofs;i++) {
1610       if (max_local < local_dofs[i] ) {
1611         max_local = local_dofs[i];
1612       }
1613     }
1614   }
1615   max_local++;
1616   /* allocate workspace */
1617   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
1618   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
1619   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
1620   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
1621   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
1622   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
1623   /* create scatter */
1624   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
1625   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
1626   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
1627   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
1628   ierr = ISDestroy(&paris);CHKERRQ(ierr);
1629   /* init array */
1630   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1631   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1632   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1633   if (local_dofs_mult) {
1634     for (i=0;i<n_local_dofs;i++) {
1635       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
1636     }
1637   } else {
1638     for (i=0;i<n_local_dofs;i++) {
1639       array[local_dofs[i]]=1.0;
1640     }
1641   }
1642   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1643   /* scatter into global vec and get total number of global dofs */
1644   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1645   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1646   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
1647   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
1648   /* Fill global_vec with cumulative function for global numbering */
1649   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
1650   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
1651   nlocals = 0;
1652   first_index = -1;
1653   first_found = PETSC_FALSE;
1654   for (i=0;i<s;i++) {
1655     if (!first_found && PetscRealPart(array[i]) > 0.0) {
1656       first_found = PETSC_TRUE;
1657       first_index = i;
1658     }
1659     nlocals += (PetscInt)PetscRealPart(array[i]);
1660   }
1661   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1662   if (!rank_prec_comm) {
1663     dof_displs[0]=0;
1664     for (i=1;i<size_prec_comm;i++) {
1665       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1666     }
1667   }
1668   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1669   if (first_found) {
1670     array[first_index] += (PetscScalar)nlocals;
1671     old_index = first_index;
1672     for (i=first_index+1;i<s;i++) {
1673       if (PetscRealPart(array[i]) > 0.0) {
1674         array[i] += array[old_index];
1675         old_index = i;
1676       }
1677     }
1678   }
1679   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
1680   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1681   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1682   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1683   /* get global ordering of local dofs */
1684   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1685   if (local_dofs_mult) {
1686     for (i=0;i<n_local_dofs;i++) {
1687       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
1688     }
1689   } else {
1690     for (i=0;i<n_local_dofs;i++) {
1691       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
1692     }
1693   }
1694   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1695   /* free workspace */
1696   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1697   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1698   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1699   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1700   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1701   /* return pointer to global ordering of local dofs */
1702   *global_numbering_subset = temp_global_dofs;
1703   PetscFunctionReturn(0);
1704 }
1705 
1706 #undef __FUNCT__
1707 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
1708 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
1709 {
1710   PetscInt       i,j;
1711   PetscScalar    *alphas;
1712   PetscErrorCode ierr;
1713 
1714   PetscFunctionBegin;
1715   /* this implements stabilized Gram-Schmidt */
1716   ierr = PetscMalloc(n*sizeof(PetscScalar),&alphas);CHKERRQ(ierr);
1717   for (i=0;i<n;i++) {
1718     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
1719     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
1720     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
1721   }
1722   ierr = PetscFree(alphas);CHKERRQ(ierr);
1723   PetscFunctionReturn(0);
1724 }
1725 
1726 
1727