xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision d06fc5fdc14868351a0b98e4bca8d71e559dfa1f)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <petscblaslapack.h>
4 
5 #undef __FUNCT__
6 #define __FUNCT__ "PCBDDCSetUpSolvers"
7 PetscErrorCode PCBDDCSetUpSolvers(PC pc)
8 {
9   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
10   PetscScalar    *coarse_submat_vals;
11   PetscErrorCode ierr;
12 
13   PetscFunctionBegin;
14   /* Compute matrix after change of basis and extract local submatrices */
15   ierr = PCBDDCSetUpLocalMatrices(pc);CHKERRQ(ierr);
16 
17   /* Setup local scatters R_to_B and (optionally) R_to_D */
18   /* PCBDDCSetUpLocalWorkVectors and PCBDDCSetUpLocalMatrices should be called first! */
19   ierr = PCBDDCSetUpLocalScatters(pc);CHKERRQ(ierr);
20 
21   /* Setup local solvers ksp_D and ksp_R */
22   /* PCBDDCSetUpLocalScatters should be called first! */
23   ierr = PCBDDCSetUpLocalSolvers(pc);CHKERRQ(ierr);
24 
25   /* Change global null space passed in by the user if change of basis has been requested */
26   if (pcbddc->NullSpace && pcbddc->ChangeOfBasisMatrix) {
27     ierr = PCBDDCNullSpaceAdaptGlobal(pc);CHKERRQ(ierr);
28   }
29 
30   /*
31      Setup local correction and local part of coarse basis.
32      Gives back the dense local part of the coarse matrix in column major ordering
33   */
34   ierr = PCBDDCSetUpCorrection(pc,&coarse_submat_vals);CHKERRQ(ierr);
35 
36   /* Compute total number of coarse nodes and setup coarse solver */
37   ierr = PCBDDCSetUpCoarseSolver(pc,coarse_submat_vals);CHKERRQ(ierr);
38 
39   /* free */
40   ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
41   PetscFunctionReturn(0);
42 }
43 
44 #undef __FUNCT__
45 #define __FUNCT__ "PCBDDCResetCustomization"
46 PetscErrorCode PCBDDCResetCustomization(PC pc)
47 {
48   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
49   PetscErrorCode ierr;
50 
51   PetscFunctionBegin;
52   ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
53   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
54   ierr = MatNullSpaceDestroy(&pcbddc->NullSpace);CHKERRQ(ierr);
55   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
56   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
57   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
58   ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
59   ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
60   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
61   ierr = PCBDDCSetDofsSplitting(pc,0,NULL);CHKERRQ(ierr);
62   ierr = PCBDDCSetDofsSplittingLocal(pc,0,NULL);CHKERRQ(ierr);
63   PetscFunctionReturn(0);
64 }
65 
66 #undef __FUNCT__
67 #define __FUNCT__ "PCBDDCResetTopography"
68 PetscErrorCode PCBDDCResetTopography(PC pc)
69 {
70   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
71   PetscErrorCode ierr;
72 
73   PetscFunctionBegin;
74   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
75   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
76   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
77   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
78   PetscFunctionReturn(0);
79 }
80 
81 #undef __FUNCT__
82 #define __FUNCT__ "PCBDDCResetSolvers"
83 PetscErrorCode PCBDDCResetSolvers(PC pc)
84 {
85   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
86   PetscErrorCode ierr;
87 
88   PetscFunctionBegin;
89   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
90   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
91   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
92   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
93   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
94   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
95   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
96   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
97   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
98   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
99   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
100   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
101   ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
102   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
103   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
104   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
105   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
106   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
107   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
108   ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
109   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
110   ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
111   ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
112   ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
113   PetscFunctionReturn(0);
114 }
115 
116 #undef __FUNCT__
117 #define __FUNCT__ "PCBDDCSetUpLocalWorkVectors"
118 PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
119 {
120   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
121   PC_IS          *pcis = (PC_IS*)pc->data;
122   VecType        impVecType;
123   PetscInt       n_constraints,n_R,old_size;
124   PetscErrorCode ierr;
125 
126   PetscFunctionBegin;
127   if (!pcbddc->ConstraintMatrix) {
128     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Constraint matrix has not been created");
129   }
130   /* get sizes */
131   n_constraints = pcbddc->local_primal_size - pcbddc->n_actual_vertices;
132   n_R = pcis->n-pcbddc->n_actual_vertices;
133   ierr = VecGetType(pcis->vec1_N,&impVecType);CHKERRQ(ierr);
134   /* local work vectors (try to avoid unneeded work)*/
135   /* R nodes */
136   old_size = -1;
137   if (pcbddc->vec1_R) {
138     ierr = VecGetSize(pcbddc->vec1_R,&old_size);CHKERRQ(ierr);
139   }
140   if (n_R != old_size) {
141     ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
142     ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
143     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);CHKERRQ(ierr);
144     ierr = VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);CHKERRQ(ierr);
145     ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
146     ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
147   }
148   /* local primal dofs */
149   old_size = -1;
150   if (pcbddc->vec1_P) {
151     ierr = VecGetSize(pcbddc->vec1_P,&old_size);CHKERRQ(ierr);
152   }
153   if (pcbddc->local_primal_size != old_size) {
154     ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
155     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);CHKERRQ(ierr);
156     ierr = VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,pcbddc->local_primal_size);CHKERRQ(ierr);
157     ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
158   }
159   /* local explicit constraints */
160   old_size = -1;
161   if (pcbddc->vec1_C) {
162     ierr = VecGetSize(pcbddc->vec1_C,&old_size);CHKERRQ(ierr);
163   }
164   if (n_constraints && n_constraints != old_size) {
165     ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
166     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);CHKERRQ(ierr);
167     ierr = VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);CHKERRQ(ierr);
168     ierr = VecSetType(pcbddc->vec1_C,impVecType);CHKERRQ(ierr);
169   }
170   PetscFunctionReturn(0);
171 }
172 
173 #undef __FUNCT__
174 #define __FUNCT__ "PCBDDCSetUpCorrection"
175 PetscErrorCode PCBDDCSetUpCorrection(PC pc, PetscScalar **coarse_submat_vals_n)
176 {
177   PetscErrorCode         ierr;
178   /* pointers to pcis and pcbddc */
179   PC_IS*                 pcis = (PC_IS*)pc->data;
180   PC_BDDC*               pcbddc = (PC_BDDC*)pc->data;
181   /* submatrices of local problem */
182   Mat                    A_RV,A_VR,A_VV;
183   /* working matrices */
184   Mat                    M1,M2,M3,C_CR;
185   /* working vectors */
186   Vec                    vec1_C,vec2_C,vec1_V,vec2_V;
187   /* additional working stuff */
188   IS                     is_aux;
189   PetscScalar            *coarse_submat_vals; /* TODO: use a PETSc matrix */
190   const PetscScalar      *array,*row_cmat_values;
191   const PetscInt         *row_cmat_indices,*idx_R_local;
192   PetscInt               *idx_V_B,*auxindices;
193   PetscInt               n_vertices,n_constraints,size_of_constraint;
194   PetscInt               i,j,n_R,n_D,n_B;
195   PetscBool              unsymmetric_check;
196   /* matrix type (vector type propagated downstream from vec1_C and local matrix type) */
197   MatType                impMatType;
198   /* some shortcuts to scalars */
199   PetscScalar            zero=0.0,one=1.0,m_one=-1.0;
200   /* for debugging purposes */
201   PetscReal              *coarsefunctions_errors,*constraints_errors;
202 
203   PetscFunctionBegin;
204   /* get number of vertices (corners plus constraints with change of basis)
205      pcbddc->n_actual_vertices stores the actual number of vertices, pcbddc->n_vertices the number of corners computed */
206   n_vertices = pcbddc->n_actual_vertices;
207   n_constraints = pcbddc->local_primal_size-n_vertices;
208   /* Set Non-overlapping dimensions */
209   n_B = pcis->n_B; n_D = pcis->n - n_B;
210   n_R = pcis->n-n_vertices;
211 
212   /* Set types for local objects needed by BDDC precondtioner */
213   impMatType = MATSEQDENSE;
214 
215   /* Allocating some extra storage just to be safe */
216   ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&auxindices);CHKERRQ(ierr);
217   for (i=0;i<pcis->n;i++) auxindices[i]=i;
218 
219   /* vertices in boundary numbering */
220   ierr = PetscMalloc1(n_vertices,&idx_V_B);CHKERRQ(ierr);
221   ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,n_vertices,pcbddc->primal_indices_local_idxs,&i,idx_V_B);CHKERRQ(ierr);
222   if (i != n_vertices) {
223     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for BDDC vertices! %d != %d\n",n_vertices,i);
224   }
225 
226   /* Precompute stuffs needed for preprocessing and application of BDDC*/
227   if (n_constraints) {
228     /* see if we can save some allocations */
229     if (pcbddc->local_auxmat2) {
230       PetscInt on_R,on_constraints;
231       ierr = MatGetSize(pcbddc->local_auxmat2,&on_R,&on_constraints);CHKERRQ(ierr);
232       if (on_R != n_R || on_constraints != n_constraints) {
233         ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
234         ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
235       }
236     }
237     /* work vectors */
238     ierr = VecDuplicate(pcbddc->vec1_C,&vec1_C);CHKERRQ(ierr);
239     ierr = VecDuplicate(pcbddc->vec1_C,&vec2_C);CHKERRQ(ierr);
240     /* auxiliary matrices */
241     if (!pcbddc->local_auxmat2) {
242       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->local_auxmat2);CHKERRQ(ierr);
243       ierr = MatSetSizes(pcbddc->local_auxmat2,n_R,n_constraints,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
244       ierr = MatSetType(pcbddc->local_auxmat2,impMatType);CHKERRQ(ierr);
245       ierr = MatSetUp(pcbddc->local_auxmat2);CHKERRQ(ierr);
246     }
247 
248     /* Extract constraints on R nodes: C_{CR}  */
249     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);CHKERRQ(ierr);
250     ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
251     ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
252 
253     /* Assemble local_auxmat2 = - A_{RR}^{-1} C^T_{CR} needed by BDDC application */
254     for (i=0;i<n_constraints;i++) {
255       ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
256       /* Get row of constraint matrix in R numbering */
257       ierr = MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
258       ierr = VecSetValues(pcbddc->vec1_R,size_of_constraint,row_cmat_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
259       ierr = MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
260       ierr = VecAssemblyBegin(pcbddc->vec1_R);CHKERRQ(ierr);
261       ierr = VecAssemblyEnd(pcbddc->vec1_R);CHKERRQ(ierr);
262       /* Solve for row of constraint matrix in R numbering */
263       ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
264       /* Set values in local_auxmat2 */
265       ierr = VecGetArrayRead(pcbddc->vec2_R,&array);CHKERRQ(ierr);
266       ierr = MatSetValues(pcbddc->local_auxmat2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
267       ierr = VecRestoreArrayRead(pcbddc->vec2_R,&array);CHKERRQ(ierr);
268     }
269     ierr = MatAssemblyBegin(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
270     ierr = MatAssemblyEnd(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
271     ierr = MatScale(pcbddc->local_auxmat2,m_one);CHKERRQ(ierr);
272 
273     /* Assemble explicitly M1 = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} needed in preproc  */
274     ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);CHKERRQ(ierr);
275     ierr = MatLUFactor(M3,NULL,NULL,NULL);CHKERRQ(ierr);
276     ierr = MatCreate(PETSC_COMM_SELF,&M1);CHKERRQ(ierr);
277     ierr = MatSetSizes(M1,n_constraints,n_constraints,n_constraints,n_constraints);CHKERRQ(ierr);
278     ierr = MatSetType(M1,impMatType);CHKERRQ(ierr);
279     ierr = MatSetUp(M1);CHKERRQ(ierr);
280     ierr = MatDuplicate(M1,MAT_DO_NOT_COPY_VALUES,&M2);CHKERRQ(ierr);
281     ierr = MatZeroEntries(M2);CHKERRQ(ierr);
282     ierr = VecSet(vec1_C,m_one);CHKERRQ(ierr);
283     ierr = MatDiagonalSet(M2,vec1_C,INSERT_VALUES);CHKERRQ(ierr);
284     ierr = MatMatSolve(M3,M2,M1);CHKERRQ(ierr);
285     ierr = MatDestroy(&M2);CHKERRQ(ierr);
286     ierr = MatDestroy(&M3);CHKERRQ(ierr);
287     /* Assemble local_auxmat1 = M1*C_{CR} needed by BDDC application in KSP and in preproc */
288     if (!pcbddc->local_auxmat1) {
289       ierr = MatMatMult(M1,C_CR,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
290     } else {
291       ierr = MatMatMult(M1,C_CR,MAT_REUSE_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
292     }
293   }
294 
295   /* Get submatrices from subdomain matrix */
296   if (n_vertices) {
297     PetscInt ibs,mbs;
298     PetscBool issbaij;
299     Mat newmat;
300 
301     ierr = ISComplement(pcbddc->is_R_local,0,pcis->n,&is_aux);CHKERRQ(ierr);
302     ierr = MatGetBlockSize(pcbddc->local_mat,&mbs);CHKERRQ(ierr);
303     ierr = ISGetBlockSize(pcbddc->is_R_local,&ibs);CHKERRQ(ierr);
304     if (ibs != mbs) { /* need to convert to SEQAIJ */
305       ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
306       ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
307       ierr = MatGetSubMatrix(newmat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
308       ierr = MatGetSubMatrix(newmat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
309       ierr = MatDestroy(&newmat);CHKERRQ(ierr);
310     } else {
311       /* this is safe */
312       ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
313       ierr = PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
314       if (issbaij) { /* need to convert to BAIJ to get offdiagonal blocks */
315         ierr = MatConvert(pcbddc->local_mat,MATSEQBAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
316         /* which of the two approaches is faster? */
317         /* ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
318         ierr = MatCreateTranspose(A_RV,&A_VR);CHKERRQ(ierr);*/
319         ierr = MatGetSubMatrix(newmat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
320         ierr = MatCreateTranspose(A_VR,&A_RV);CHKERRQ(ierr);
321         ierr = MatDestroy(&newmat);CHKERRQ(ierr);
322       } else {
323         ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
324         ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
325       }
326     }
327     ierr = MatGetVecs(A_RV,&vec1_V,NULL);CHKERRQ(ierr);
328     ierr = VecDuplicate(vec1_V,&vec2_V);CHKERRQ(ierr);
329     ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
330   }
331 
332   /* Matrix of coarse basis functions (local) */
333   if (pcbddc->coarse_phi_B) {
334     PetscInt on_B,on_primal;
335     ierr = MatGetSize(pcbddc->coarse_phi_B,&on_B,&on_primal);CHKERRQ(ierr);
336     if (on_B != n_B || on_primal != pcbddc->local_primal_size) {
337       ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
338       ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
339     }
340   }
341   if (pcbddc->coarse_phi_D) {
342     PetscInt on_D,on_primal;
343     ierr = MatGetSize(pcbddc->coarse_phi_D,&on_D,&on_primal);CHKERRQ(ierr);
344     if (on_D != n_D || on_primal != pcbddc->local_primal_size) {
345       ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
346       ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
347     }
348   }
349   if (!pcbddc->coarse_phi_B) {
350     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
351     ierr = MatSetSizes(pcbddc->coarse_phi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
352     ierr = MatSetType(pcbddc->coarse_phi_B,impMatType);CHKERRQ(ierr);
353     ierr = MatSetUp(pcbddc->coarse_phi_B);CHKERRQ(ierr);
354   }
355   if ( (pcbddc->switch_static || pcbddc->dbg_flag) && !pcbddc->coarse_phi_D ) {
356     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
357     ierr = MatSetSizes(pcbddc->coarse_phi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
358     ierr = MatSetType(pcbddc->coarse_phi_D,impMatType);CHKERRQ(ierr);
359     ierr = MatSetUp(pcbddc->coarse_phi_D);CHKERRQ(ierr);
360   }
361 
362   if (pcbddc->dbg_flag) {
363     ierr = ISGetIndices(pcbddc->is_R_local,&idx_R_local);CHKERRQ(ierr);
364     ierr = PetscMalloc1(2*pcbddc->local_primal_size,&coarsefunctions_errors);CHKERRQ(ierr);
365     ierr = PetscMalloc1(2*pcbddc->local_primal_size,&constraints_errors);CHKERRQ(ierr);
366   }
367   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
368   ierr = PetscMalloc1((pcbddc->local_primal_size)*(pcbddc->local_primal_size),&coarse_submat_vals);CHKERRQ(ierr);
369 
370   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
371 
372   /* vertices */
373   for (i=0;i<n_vertices;i++) {
374     /* this should not be needed, but MatMult_BAIJ is broken when using compressed row routines */
375     ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr); /* TODO: REMOVE IT */
376     ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
377     ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
378     ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
379     ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
380     /* simplified solution of saddle point problem with null rhs on constraints multipliers */
381     ierr = MatMult(A_RV,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
382     ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
383     ierr = VecScale(pcbddc->vec1_R,m_one);CHKERRQ(ierr);
384     if (n_constraints) {
385       ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec1_R,vec1_C);CHKERRQ(ierr);
386       ierr = MatMultAdd(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
387       ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
388     }
389     ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
390     ierr = MatMultAdd(A_VV,vec1_V,vec2_V,vec2_V);CHKERRQ(ierr);
391 
392     /* Set values in coarse basis function and subdomain part of coarse_mat */
393     /* coarse basis functions */
394     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
395     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
396     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
397     ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
398     ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
399     ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
400     ierr = MatSetValue(pcbddc->coarse_phi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
401     if (pcbddc->switch_static || pcbddc->dbg_flag) {
402       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
403       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
404       ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
405       ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
406       ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
407     }
408     /* subdomain contribution to coarse matrix. WARNING -> column major ordering */
409     ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
410     ierr = PetscMemcpy(&coarse_submat_vals[i*pcbddc->local_primal_size],array,n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
411     ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
412     if (n_constraints) {
413       ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
414       ierr = PetscMemcpy(&coarse_submat_vals[i*pcbddc->local_primal_size+n_vertices],array,n_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
415       ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
416     }
417 
418     /* check */
419     if (pcbddc->dbg_flag) {
420       /* assemble subdomain vector on local nodes */
421       ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
422       ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
423       ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
424       ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
425       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],one,INSERT_VALUES);CHKERRQ(ierr);
426       ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
427       ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
428       /* assemble subdomain vector of lagrange multipliers (i.e. primal nodes) */
429       ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
430       ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
431       ierr = VecSetValues(pcbddc->vec1_P,n_vertices,auxindices,array,INSERT_VALUES);CHKERRQ(ierr);
432       ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
433       if (n_constraints) {
434         ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
435         ierr = VecSetValues(pcbddc->vec1_P,n_constraints,&auxindices[n_vertices],array,INSERT_VALUES);CHKERRQ(ierr);
436         ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
437       }
438       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
439       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
440       ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
441       /* check saddle point solution */
442       ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
443       ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
444       ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i]);CHKERRQ(ierr);
445       ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
446       /* shift by the identity matrix */
447       ierr = VecSetValue(pcbddc->vec1_P,i,m_one,ADD_VALUES);CHKERRQ(ierr);
448       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
449       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
450       ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i]);CHKERRQ(ierr);
451     }
452   }
453 
454   /* constraints */
455   for (i=0;i<n_constraints;i++) {
456     ierr = VecSet(vec2_C,zero);CHKERRQ(ierr);
457     ierr = VecSetValue(vec2_C,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
458     ierr = VecAssemblyBegin(vec2_C);CHKERRQ(ierr);
459     ierr = VecAssemblyEnd(vec2_C);CHKERRQ(ierr);
460     /* simplified solution of saddle point problem with null rhs on vertices multipliers */
461     ierr = MatMult(M1,vec2_C,vec1_C);CHKERRQ(ierr);
462     ierr = MatMult(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
463     ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
464     if (n_vertices) {
465       ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
466     }
467     /* Set values in coarse basis function and subdomain part of coarse_mat */
468     /* coarse basis functions */
469     j = i+n_vertices; /* don't touch this! */
470     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
471     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
472     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
473     ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
474     ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&j,array,INSERT_VALUES);CHKERRQ(ierr);
475     ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
476     if (pcbddc->switch_static || pcbddc->dbg_flag) {
477       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
478       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
479       ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
480       ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&j,array,INSERT_VALUES);CHKERRQ(ierr);
481       ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
482     }
483     /* subdomain contribution to coarse matrix. WARNING -> column major ordering */
484     if (n_vertices) {
485       ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
486       ierr = PetscMemcpy(&coarse_submat_vals[j*pcbddc->local_primal_size],array,n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
487       ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
488     }
489     ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
490     ierr = PetscMemcpy(&coarse_submat_vals[j*pcbddc->local_primal_size+n_vertices],array,n_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
491     ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
492 
493     if (pcbddc->dbg_flag) {
494       /* assemble subdomain vector on nodes */
495       ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
496       ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
497       ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
498       ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
499       ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
500       ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
501       /* assemble subdomain vector of lagrange multipliers */
502       ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
503       if (n_vertices) {
504         ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
505         ierr = VecSetValues(pcbddc->vec1_P,n_vertices,auxindices,array,INSERT_VALUES);CHKERRQ(ierr);
506         ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
507       }
508       ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
509       ierr = VecSetValues(pcbddc->vec1_P,n_constraints,&auxindices[n_vertices],array,INSERT_VALUES);CHKERRQ(ierr);
510       ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
511       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
512       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
513       ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
514       /* check saddle point solution */
515       ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
516       ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
517       ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[j]);CHKERRQ(ierr);
518       ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
519       /* shift by the identity matrix */
520       ierr = VecSetValue(pcbddc->vec1_P,j,m_one,ADD_VALUES);CHKERRQ(ierr);
521       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
522       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
523       ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[j]);CHKERRQ(ierr);
524     }
525   }
526   /* call assembling routines for local coarse basis */
527   ierr = MatAssemblyBegin(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
528   ierr = MatAssemblyEnd(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
529   if (pcbddc->switch_static || pcbddc->dbg_flag) {
530     ierr = MatAssemblyBegin(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
531     ierr = MatAssemblyEnd(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
532   }
533 
534   /* compute other basis functions for non-symmetric problems */
535   ierr = MatIsSymmetric(pc->pmat,1.e-4,&pcbddc->issym);CHKERRQ(ierr);
536   if (!pcbddc->issym) {
537     if (!pcbddc->coarse_psi_B) {
538       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_psi_B);CHKERRQ(ierr);
539       ierr = MatSetSizes(pcbddc->coarse_psi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
540       ierr = MatSetType(pcbddc->coarse_psi_B,impMatType);CHKERRQ(ierr);
541       ierr = MatSetUp(pcbddc->coarse_psi_B);CHKERRQ(ierr);
542     }
543     if ( (pcbddc->switch_static || pcbddc->dbg_flag) && !pcbddc->coarse_psi_D) {
544       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_psi_D);CHKERRQ(ierr);
545       ierr = MatSetSizes(pcbddc->coarse_psi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
546       ierr = MatSetType(pcbddc->coarse_psi_D,impMatType);CHKERRQ(ierr);
547       ierr = MatSetUp(pcbddc->coarse_psi_D);CHKERRQ(ierr);
548     }
549     for (i=0;i<pcbddc->local_primal_size;i++) {
550       if (n_constraints) {
551         ierr = VecSet(vec1_C,zero);CHKERRQ(ierr);
552         for (j=0;j<n_constraints;j++) {
553           ierr = VecSetValue(vec1_C,j,coarse_submat_vals[(j+n_vertices)*pcbddc->local_primal_size+i],INSERT_VALUES);CHKERRQ(ierr);
554         }
555         ierr = VecAssemblyBegin(vec1_C);CHKERRQ(ierr);
556         ierr = VecAssemblyEnd(vec1_C);CHKERRQ(ierr);
557       }
558       if (i<n_vertices) {
559         ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
560         ierr = VecSetValue(vec1_V,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
561         ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
562         ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
563         ierr = MatMultTranspose(A_VR,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
564         if (n_constraints) {
565           ierr = MatMultTransposeAdd(C_CR,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
566         }
567       } else {
568         ierr = MatMultTranspose(C_CR,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
569       }
570       ierr = KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
571       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
572       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
573       ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
574       ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
575       ierr = MatSetValues(pcbddc->coarse_psi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
576       ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
577       if (i<n_vertices) {
578         ierr = MatSetValue(pcbddc->coarse_psi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
579       }
580       if (pcbddc->switch_static || pcbddc->dbg_flag) {
581         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
582         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
583         ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
584         ierr = MatSetValues(pcbddc->coarse_psi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
585         ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
586       }
587 
588       if (pcbddc->dbg_flag) {
589         /* assemble subdomain vector on nodes */
590         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
591         ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
592         ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
593         ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
594         if (i<n_vertices) {
595           ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],one,INSERT_VALUES);CHKERRQ(ierr);
596         }
597         ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
598         ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
599         /* assemble subdomain vector of lagrange multipliers */
600         for (j=0;j<pcbddc->local_primal_size;j++) {
601           ierr = VecSetValue(pcbddc->vec1_P,j,-coarse_submat_vals[j*pcbddc->local_primal_size+i],INSERT_VALUES);CHKERRQ(ierr);
602         }
603         ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
604         ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
605         /* check saddle point solution */
606         ierr = MatMultTranspose(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
607         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
608         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i+pcbddc->local_primal_size]);CHKERRQ(ierr);
609         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
610         /* shift by the identity matrix */
611         ierr = VecSetValue(pcbddc->vec1_P,i,m_one,ADD_VALUES);CHKERRQ(ierr);
612         ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
613         ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
614         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i+pcbddc->local_primal_size]);CHKERRQ(ierr);
615       }
616     }
617     ierr = MatAssemblyBegin(pcbddc->coarse_psi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
618     ierr = MatAssemblyEnd(pcbddc->coarse_psi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
619     if (pcbddc->switch_static || pcbddc->dbg_flag) {
620       ierr = MatAssemblyBegin(pcbddc->coarse_psi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
621       ierr = MatAssemblyEnd(pcbddc->coarse_psi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
622     }
623     unsymmetric_check = PETSC_TRUE;
624   } else { /* take references to already computed coarse basis */
625     unsymmetric_check = PETSC_FALSE;
626     ierr = PetscObjectReference((PetscObject)pcbddc->coarse_phi_B);CHKERRQ(ierr);
627     pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
628     if (pcbddc->coarse_phi_D) {
629       ierr = PetscObjectReference((PetscObject)pcbddc->coarse_phi_D);CHKERRQ(ierr);
630       pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
631     }
632   }
633   ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
634   /* Checking coarse_sub_mat and coarse basis functios */
635   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
636   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
637   if (pcbddc->dbg_flag) {
638     Mat         coarse_sub_mat;
639     Mat         AUXMAT,TM1,TM2,TM3,TM4;
640     Mat         coarse_phi_D,coarse_phi_B;
641     Mat         coarse_psi_D,coarse_psi_B;
642     Mat         A_II,A_BB,A_IB,A_BI;
643     MatType     checkmattype=MATSEQAIJ;
644     PetscReal   real_value;
645 
646     ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
647     ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
648     ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
649     ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
650     ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
651     ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
652     if (unsymmetric_check) {
653       ierr = MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);CHKERRQ(ierr);
654       ierr = MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);CHKERRQ(ierr);
655     }
656     ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);
657 
658     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
659     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat and local basis functions\n");CHKERRQ(ierr);
660     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
661     if (unsymmetric_check) {
662       ierr = MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
663       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
664       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
665       ierr = MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
666       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
667       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
668       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
669       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
670       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
671       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
672       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
673       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
674     } else {
675       ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
676       ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
677       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
678       ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
679       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
680       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
681       ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
682       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
683     }
684     ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
685     ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
686     ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
687     ierr = MatConvert(TM1,MATSEQDENSE,MAT_REUSE_MATRIX,&TM1);CHKERRQ(ierr);
688     ierr = MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
689     ierr = MatNorm(TM1,NORM_INFINITY,&real_value);CHKERRQ(ierr);
690     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
691     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"----------------------------------\n");CHKERRQ(ierr);
692     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d \n",PetscGlobalRank);CHKERRQ(ierr);
693     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"matrix error = % 1.14e\n",real_value);CHKERRQ(ierr);
694     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"coarse functions (phi) errors\n");CHKERRQ(ierr);
695     for (i=0;i<pcbddc->local_primal_size;i++) {
696       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i,coarsefunctions_errors[i]);CHKERRQ(ierr);
697     }
698     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"constraints (phi) errors\n");CHKERRQ(ierr);
699     for (i=0;i<pcbddc->local_primal_size;i++) {
700       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i,constraints_errors[i]);CHKERRQ(ierr);
701     }
702     if (unsymmetric_check) {
703       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"coarse functions (psi) errors\n");CHKERRQ(ierr);
704       for (i=pcbddc->local_primal_size;i<2*pcbddc->local_primal_size;i++) {
705         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i-pcbddc->local_primal_size,coarsefunctions_errors[i]);CHKERRQ(ierr);
706       }
707       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"constraints (psi) errors\n");CHKERRQ(ierr);
708       for (i=pcbddc->local_primal_size;i<2*pcbddc->local_primal_size;i++) {
709         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i-pcbddc->local_primal_size,constraints_errors[i]);CHKERRQ(ierr);
710       }
711     }
712     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
713     ierr = MatDestroy(&A_II);CHKERRQ(ierr);
714     ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
715     ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
716     ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
717     ierr = MatDestroy(&TM1);CHKERRQ(ierr);
718     ierr = MatDestroy(&TM2);CHKERRQ(ierr);
719     ierr = MatDestroy(&TM3);CHKERRQ(ierr);
720     ierr = MatDestroy(&TM4);CHKERRQ(ierr);
721     ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
722     ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
723     if (unsymmetric_check) {
724       ierr = MatDestroy(&coarse_psi_D);CHKERRQ(ierr);
725       ierr = MatDestroy(&coarse_psi_B);CHKERRQ(ierr);
726     }
727     ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
728     ierr = ISRestoreIndices(pcbddc->is_R_local,&idx_R_local);CHKERRQ(ierr);
729     ierr = PetscFree(coarsefunctions_errors);CHKERRQ(ierr);
730     ierr = PetscFree(constraints_errors);CHKERRQ(ierr);
731   }
732   /* free memory */
733   if (n_vertices) {
734     ierr = VecDestroy(&vec1_V);CHKERRQ(ierr);
735     ierr = VecDestroy(&vec2_V);CHKERRQ(ierr);
736     ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
737     ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
738     ierr = MatDestroy(&A_VV);CHKERRQ(ierr);
739   }
740   if (n_constraints) {
741     ierr = VecDestroy(&vec1_C);CHKERRQ(ierr);
742     ierr = VecDestroy(&vec2_C);CHKERRQ(ierr);
743     ierr = MatDestroy(&M1);CHKERRQ(ierr);
744     ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
745   }
746   ierr = PetscFree(auxindices);CHKERRQ(ierr);
747   /* get back data */
748   *coarse_submat_vals_n = coarse_submat_vals;
749   PetscFunctionReturn(0);
750 }
751 
752 #undef __FUNCT__
753 #define __FUNCT__ "PCBDDCSetUpLocalMatrices"
754 PetscErrorCode PCBDDCSetUpLocalMatrices(PC pc)
755 {
756   PC_IS*            pcis = (PC_IS*)(pc->data);
757   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
758   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
759   PetscBool         issbaij,isseqaij;
760   /* manage repeated solves */
761   MatReuse          reuse;
762   PetscErrorCode    ierr;
763 
764   PetscFunctionBegin;
765   if ( (pcbddc->use_change_of_basis && !pcbddc->ChangeOfBasisMatrix) || (pcbddc->user_ChangeOfBasisMatrix && !pcbddc->ChangeOfBasisMatrix) ) {
766     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Change of basis matrix has not been created");
767   }
768   /* get mat flags */
769   reuse = MAT_INITIAL_MATRIX;
770   if (pc->setupcalled) {
771     if (pc->flag == SAME_NONZERO_PATTERN) {
772       reuse = MAT_REUSE_MATRIX;
773     } else {
774       reuse = MAT_INITIAL_MATRIX;
775     }
776   }
777   if (reuse == MAT_INITIAL_MATRIX) {
778     ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
779     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
780     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
781     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
782     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
783   }
784 
785   /* transform local matrices if needed */
786   if (pcbddc->ChangeOfBasisMatrix) {
787     Mat         change_mat_all;
788     PetscScalar *row_cmat_values;
789     PetscInt    *row_cmat_indices;
790     PetscInt    *nnz,*is_indices,*temp_indices;
791     PetscInt    i,j,k,n_D,n_B;
792 
793     /* Get Non-overlapping dimensions */
794     n_B = pcis->n_B;
795     n_D = pcis->n-n_B;
796 
797     /* compute nonzero structure of change of basis on all local nodes */
798     ierr = PetscMalloc1(pcis->n,&nnz);CHKERRQ(ierr);
799     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
800     for (i=0;i<n_D;i++) nnz[is_indices[i]] = 1;
801     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
802     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
803     k=1;
804     for (i=0;i<n_B;i++) {
805       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
806       nnz[is_indices[i]]=j;
807       if (k < j) k = j;
808       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
809     }
810     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
811     /* assemble change of basis matrix on the whole set of local dofs */
812     ierr = PetscMalloc1(k,&temp_indices);CHKERRQ(ierr);
813     ierr = MatCreate(PETSC_COMM_SELF,&change_mat_all);CHKERRQ(ierr);
814     ierr = MatSetSizes(change_mat_all,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
815     ierr = MatSetType(change_mat_all,MATSEQAIJ);CHKERRQ(ierr);
816     ierr = MatSeqAIJSetPreallocation(change_mat_all,0,nnz);CHKERRQ(ierr);
817     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
818     for (i=0;i<n_D;i++) {
819       ierr = MatSetValue(change_mat_all,is_indices[i],is_indices[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
820     }
821     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
822     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
823     for (i=0;i<n_B;i++) {
824       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
825       for (k=0; k<j; k++) temp_indices[k]=is_indices[row_cmat_indices[k]];
826       ierr = MatSetValues(change_mat_all,1,&is_indices[i],j,temp_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
827       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
828     }
829     ierr = MatAssemblyBegin(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
830     ierr = MatAssemblyEnd(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
831     /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
832     ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQBAIJ,&isseqaij);CHKERRQ(ierr);
833     if (isseqaij) {
834       ierr = MatPtAP(matis->A,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
835     } else {
836       Mat work_mat;
837       ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
838       ierr = MatPtAP(work_mat,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
839       ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
840     }
841     /*
842     ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
843     ierr = MatView(change_mat_all,(PetscViewer)0);CHKERRQ(ierr);
844     */
845     ierr = MatDestroy(&change_mat_all);CHKERRQ(ierr);
846     ierr = PetscFree(nnz);CHKERRQ(ierr);
847     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
848   } else {
849     /* without change of basis, the local matrix is unchanged */
850     if (!pcbddc->local_mat) {
851       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
852       pcbddc->local_mat = matis->A;
853     }
854   }
855 
856   /* get submatrices */
857   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_I_local,reuse,&pcis->A_II);CHKERRQ(ierr);
858   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,reuse,&pcis->A_BB);CHKERRQ(ierr);
859   ierr = PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
860   if (!issbaij) {
861     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
862     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
863   } else {
864     Mat newmat;
865     ierr = MatConvert(pcbddc->local_mat,MATSEQBAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
866     ierr = MatGetSubMatrix(newmat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
867     ierr = MatGetSubMatrix(newmat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
868     ierr = MatDestroy(&newmat);CHKERRQ(ierr);
869   }
870   PetscFunctionReturn(0);
871 }
872 
873 #undef __FUNCT__
874 #define __FUNCT__ "PCBDDCSetUpLocalScatters"
875 PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
876 {
877   PC_IS*         pcis = (PC_IS*)(pc->data);
878   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
879   IS             is_aux1,is_aux2;
880   PetscInt       *aux_array1,*aux_array2,*is_indices,*idx_R_local;
881   PetscInt       n_vertices,i,j,n_R,n_D,n_B;
882   PetscInt       vbs,bs;
883   PetscBT        bitmask;
884   PetscErrorCode ierr;
885 
886   PetscFunctionBegin;
887   /*
888     No need to setup local scatters if
889       - primal space is unchanged
890         AND
891       - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
892         AND
893       - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
894   */
895   if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) {
896     PetscFunctionReturn(0);
897   }
898   /* destroy old objects */
899   ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
900   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
901   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
902   /* Set Non-overlapping dimensions */
903   n_B = pcis->n_B; n_D = pcis->n - n_B;
904   n_vertices = pcbddc->n_actual_vertices;
905   /* create auxiliary bitmask */
906   ierr = PetscBTCreate(pcis->n,&bitmask);CHKERRQ(ierr);
907   for (i=0;i<n_vertices;i++) {
908     ierr = PetscBTSet(bitmask,pcbddc->primal_indices_local_idxs[i]);CHKERRQ(ierr);
909   }
910 
911   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
912   ierr = PetscMalloc1((pcis->n-n_vertices),&idx_R_local);CHKERRQ(ierr);
913   for (i=0, n_R=0; i<pcis->n; i++) {
914     if (!PetscBTLookup(bitmask,i)) {
915       idx_R_local[n_R] = i;
916       n_R++;
917     }
918   }
919 
920   /* Block code */
921   vbs = 1;
922   ierr = MatGetBlockSize(pcbddc->local_mat,&bs);CHKERRQ(ierr);
923   if (bs>1 && !(n_vertices%bs)) {
924     PetscBool is_blocked = PETSC_TRUE;
925     PetscInt  *vary;
926     /* Verify if the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
927     ierr = PetscMalloc1(pcis->n/bs,&vary);CHKERRQ(ierr);
928     ierr = PetscMemzero(vary,pcis->n/bs*sizeof(PetscInt));CHKERRQ(ierr);
929     for (i=0; i<n_vertices; i++) vary[pcbddc->primal_indices_local_idxs[i]/bs]++;
930     for (i=0; i<n_vertices; i++) {
931       if (vary[i]!=0 && vary[i]!=bs) {
932         is_blocked = PETSC_FALSE;
933         break;
934       }
935     }
936     if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
937       vbs = bs;
938       for (i=0;i<n_R/vbs;i++) {
939         idx_R_local[i] = idx_R_local[vbs*i]/vbs;
940       }
941     }
942     ierr = PetscFree(vary);CHKERRQ(ierr);
943   }
944   ierr = ISCreateBlock(PETSC_COMM_SELF,vbs,n_R/vbs,idx_R_local,PETSC_COPY_VALUES,&pcbddc->is_R_local);CHKERRQ(ierr);
945   ierr = PetscFree(idx_R_local);CHKERRQ(ierr);
946 
947   /* print some info if requested */
948   if (pcbddc->dbg_flag) {
949     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
950     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
951     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
952     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
953     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
954     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"r_size = %d, v_size = %d, constraints = %d, local_primal_size = %d\n",n_R,n_vertices,pcbddc->local_primal_size-n_vertices,pcbddc->local_primal_size);CHKERRQ(ierr);
955     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
956     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
957   }
958 
959   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
960   ierr = ISGetIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
961   ierr = PetscMalloc1((pcis->n_B-n_vertices),&aux_array1);CHKERRQ(ierr);
962   ierr = PetscMalloc1((pcis->n_B-n_vertices),&aux_array2);CHKERRQ(ierr);
963   ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
964   for (i=0; i<n_D; i++) {
965     ierr = PetscBTSet(bitmask,is_indices[i]);CHKERRQ(ierr);
966   }
967   ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
968   for (i=0, j=0; i<n_R; i++) {
969     if (!PetscBTLookup(bitmask,idx_R_local[i])) {
970       aux_array1[j++] = i;
971     }
972   }
973   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
974   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
975   for (i=0, j=0; i<n_B; i++) {
976     if (!PetscBTLookup(bitmask,is_indices[i])) {
977       aux_array2[j++] = i;
978     }
979   }
980   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
981   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);CHKERRQ(ierr);
982   ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
983   ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
984   ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
985 
986   if (pcbddc->switch_static || pcbddc->dbg_flag) {
987     ierr = PetscMalloc1(n_D,&aux_array1);CHKERRQ(ierr);
988     for (i=0, j=0; i<n_R; i++) {
989       if (PetscBTLookup(bitmask,idx_R_local[i])) {
990         aux_array1[j++] = i;
991       }
992     }
993     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
994     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
995     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
996   }
997   ierr = PetscBTDestroy(&bitmask);CHKERRQ(ierr);
998   ierr = ISRestoreIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
999   PetscFunctionReturn(0);
1000 }
1001 
1002 
1003 #undef __FUNCT__
1004 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
1005 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc)
1006 {
1007   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1008   PC_IS          *pcis = (PC_IS*)pc->data;
1009   PC             pc_temp;
1010   Mat            A_RR;
1011   MatReuse       reuse;
1012   PetscScalar    m_one = -1.0;
1013   PetscReal      value;
1014   PetscInt       n_D,n_R,ibs,mbs;
1015   PetscBool      use_exact,use_exact_reduced,issbaij;
1016   PetscErrorCode ierr;
1017   /* prefixes stuff */
1018   char           dir_prefix[256],neu_prefix[256],str_level[16];
1019   size_t         len;
1020 
1021   PetscFunctionBegin;
1022 
1023   /* compute prefixes */
1024   ierr = PetscStrcpy(dir_prefix,"");CHKERRQ(ierr);
1025   ierr = PetscStrcpy(neu_prefix,"");CHKERRQ(ierr);
1026   if (!pcbddc->current_level) {
1027     ierr = PetscStrcpy(dir_prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
1028     ierr = PetscStrcpy(neu_prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
1029     ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
1030     ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
1031   } else {
1032     ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
1033     sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
1034     ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
1035     len -= 15; /* remove "pc_bddc_coarse_" */
1036     if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
1037     if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
1038     ierr = PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
1039     ierr = PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
1040     ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
1041     ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
1042     ierr = PetscStrcat(dir_prefix,str_level);CHKERRQ(ierr);
1043     ierr = PetscStrcat(neu_prefix,str_level);CHKERRQ(ierr);
1044   }
1045 
1046   /* DIRICHLET PROBLEM */
1047   /* Matrix for Dirichlet problem is pcis->A_II */
1048   ierr = ISGetSize(pcis->is_I_local,&n_D);CHKERRQ(ierr);
1049   if (!pcbddc->ksp_D) { /* create object if not yet build */
1050     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
1051     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
1052     /* default */
1053     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
1054     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);CHKERRQ(ierr);
1055     ierr = PetscObjectTypeCompare((PetscObject)pcis->A_II,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
1056     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
1057     if (issbaij) {
1058       ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
1059     } else {
1060       ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
1061     }
1062     /* Allow user's customization */
1063     ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
1064     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
1065   }
1066   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II);CHKERRQ(ierr);
1067   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
1068   if (!n_D) {
1069     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
1070     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
1071   }
1072   /* Set Up KSP for Dirichlet problem of BDDC */
1073   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
1074   /* set ksp_D into pcis data */
1075   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
1076   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
1077   pcis->ksp_D = pcbddc->ksp_D;
1078 
1079   /* NEUMANN PROBLEM */
1080   /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
1081   ierr = ISGetSize(pcbddc->is_R_local,&n_R);CHKERRQ(ierr);
1082   if (pcbddc->ksp_R) { /* already created ksp */
1083     PetscInt nn_R;
1084     ierr = KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);CHKERRQ(ierr);
1085     ierr = PetscObjectReference((PetscObject)A_RR);CHKERRQ(ierr);
1086     ierr = MatGetSize(A_RR,&nn_R,NULL);CHKERRQ(ierr);
1087     if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
1088       ierr = KSPReset(pcbddc->ksp_R);CHKERRQ(ierr);
1089       ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1090       reuse = MAT_INITIAL_MATRIX;
1091     } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
1092       if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
1093         ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1094         reuse = MAT_INITIAL_MATRIX;
1095       } else { /* safe to reuse the matrix */
1096         reuse = MAT_REUSE_MATRIX;
1097       }
1098     }
1099     /* last check */
1100     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
1101       ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1102       reuse = MAT_INITIAL_MATRIX;
1103     }
1104   } else { /* first time, so we need to create the matrix */
1105     reuse = MAT_INITIAL_MATRIX;
1106   }
1107   /* extract A_RR */
1108   ierr = MatGetBlockSize(pcbddc->local_mat,&mbs);CHKERRQ(ierr);
1109   ierr = ISGetBlockSize(pcbddc->is_R_local,&ibs);CHKERRQ(ierr);
1110   if (ibs != mbs) {
1111     Mat newmat;
1112     ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
1113     ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
1114     ierr = MatDestroy(&newmat);CHKERRQ(ierr);
1115   } else {
1116     ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
1117   }
1118   if (!pcbddc->ksp_R) { /* create object if not present */
1119     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
1120     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
1121     /* default */
1122     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
1123     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);CHKERRQ(ierr);
1124     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
1125     ierr = PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
1126     if (issbaij) {
1127       ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
1128     } else {
1129       ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
1130     }
1131     /* Allow user's customization */
1132     ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
1133     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
1134   }
1135   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);CHKERRQ(ierr);
1136   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
1137   if (!n_R) {
1138     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
1139     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
1140   }
1141   /* Set Up KSP for Neumann problem of BDDC */
1142   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
1143 
1144   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
1145   if (pcbddc->NullSpace || pcbddc->dbg_flag) {
1146     /* Dirichlet */
1147     ierr = VecSetRandom(pcis->vec1_D,NULL);CHKERRQ(ierr);
1148     ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1149     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);CHKERRQ(ierr);
1150     ierr = VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);CHKERRQ(ierr);
1151     ierr = VecNorm(pcis->vec1_D,NORM_INFINITY,&value);CHKERRQ(ierr);
1152     /* need to be adapted? */
1153     use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
1154     ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1155     ierr = PCBDDCSetUseExactDirichlet(pc,use_exact_reduced);CHKERRQ(ierr);
1156     /* print info */
1157     if (pcbddc->dbg_flag) {
1158       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1159       ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1160       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
1161       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
1162       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve (%s) = % 1.14e \n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_D))->prefix,value);CHKERRQ(ierr);
1163       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1164     }
1165     if (pcbddc->NullSpace && !use_exact_reduced && !pcbddc->switch_static) {
1166       ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcis->is_I_local);CHKERRQ(ierr);
1167     }
1168 
1169     /* Neumann */
1170     ierr = VecSetRandom(pcbddc->vec1_R,NULL);CHKERRQ(ierr);
1171     ierr = MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
1172     ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
1173     ierr = VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);CHKERRQ(ierr);
1174     ierr = VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);CHKERRQ(ierr);
1175     /* need to be adapted? */
1176     use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
1177     ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1178     /* print info */
1179     if (pcbddc->dbg_flag) {
1180       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann solve (%s) = % 1.14e \n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_R))->prefix,value);CHKERRQ(ierr);
1181       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1182     }
1183     if (pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
1184       ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcbddc->is_R_local);CHKERRQ(ierr);
1185     }
1186   }
1187   /* free Neumann problem's matrix */
1188   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 #undef __FUNCT__
1193 #define __FUNCT__ "PCBDDCSolveSubstructureCorrection"
1194 static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec rhs, Vec sol, Vec work, PetscBool applytranspose)
1195 {
1196   PetscErrorCode ierr;
1197   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1198 
1199   PetscFunctionBegin;
1200   if (applytranspose) {
1201     if (pcbddc->local_auxmat1) {
1202       ierr = MatMultTranspose(pcbddc->local_auxmat2,rhs,work);CHKERRQ(ierr);
1203       ierr = MatMultTransposeAdd(pcbddc->local_auxmat1,work,rhs,rhs);CHKERRQ(ierr);
1204     }
1205     ierr = KSPSolveTranspose(pcbddc->ksp_R,rhs,sol);CHKERRQ(ierr);
1206   } else {
1207     ierr = KSPSolve(pcbddc->ksp_R,rhs,sol);CHKERRQ(ierr);
1208     if (pcbddc->local_auxmat1) {
1209       ierr = MatMult(pcbddc->local_auxmat1,sol,work);CHKERRQ(ierr);
1210       ierr = MatMultAdd(pcbddc->local_auxmat2,work,sol,sol);CHKERRQ(ierr);
1211     }
1212   }
1213   PetscFunctionReturn(0);
1214 }
1215 
1216 /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
1217 #undef __FUNCT__
1218 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
1219 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
1220 {
1221   PetscErrorCode ierr;
1222   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
1223   PC_IS*            pcis = (PC_IS*)  (pc->data);
1224   const PetscScalar zero = 0.0;
1225 
1226   PetscFunctionBegin;
1227   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
1228   if (applytranspose) {
1229     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1230     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1231   } else {
1232     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1233     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1234   }
1235   /* start communications from local primal nodes to rhs of coarse solver */
1236   ierr = VecSet(pcbddc->coarse_vec,zero);CHKERRQ(ierr);
1237   ierr = PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1238   ierr = PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1239 
1240   /* Coarse solution -> rhs and sol updated in PCBDDCScattarCoarseDataBegin/End */
1241   /* TODO remove null space when doing multilevel */
1242   if (pcbddc->coarse_ksp) {
1243     if (applytranspose) {
1244       ierr = KSPSolveTranspose(pcbddc->coarse_ksp,NULL,NULL);CHKERRQ(ierr);
1245     } else {
1246       ierr = KSPSolve(pcbddc->coarse_ksp,NULL,NULL);CHKERRQ(ierr);
1247     }
1248   }
1249   /* start communications from coarse solver solution to local primal nodes */
1250   ierr = PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1251 
1252   /* Local solution on R nodes */
1253   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
1254   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1255   ierr = VecScatterEnd(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1256   if (pcbddc->switch_static) {
1257     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1258     ierr = VecScatterEnd(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1259   }
1260   ierr = PCBDDCSolveSubstructureCorrection(pc,pcbddc->vec1_R,pcbddc->vec2_R,pcbddc->vec1_C,applytranspose);CHKERRQ(ierr);
1261   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1262   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1263   ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1264   if (pcbddc->switch_static) {
1265     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1266     ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1267   }
1268 
1269   /* complete communications from coarse sol to local primal nodes */
1270   ierr = PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1271 
1272   /* Sum contributions from two levels */
1273   if (applytranspose) {
1274     ierr = MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1275     if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1276   } else {
1277     ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1278     if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1279   }
1280   PetscFunctionReturn(0);
1281 }
1282 
1283 /* TODO: the following two function can be optimized using VecPlaceArray whenever possible and using overlap flag */
1284 #undef __FUNCT__
1285 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
1286 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
1287 {
1288   PetscErrorCode ierr;
1289   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1290   PetscScalar    *array,*array2;
1291   Vec            from,to;
1292 
1293   PetscFunctionBegin;
1294   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
1295     from = pcbddc->coarse_vec;
1296     to = pcbddc->vec1_P;
1297     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
1298       Vec tvec;
1299       PetscInt lsize;
1300       ierr = KSPGetSolution(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1301       ierr = VecGetLocalSize(tvec,&lsize);CHKERRQ(ierr);
1302       ierr = VecGetArrayRead(tvec,(const PetscScalar**)&array);CHKERRQ(ierr);
1303       ierr = VecGetArray(from,&array2);CHKERRQ(ierr);
1304       ierr = PetscMemcpy(array2,array,lsize*sizeof(PetscScalar));CHKERRQ(ierr);
1305       ierr = VecRestoreArrayRead(tvec,(const PetscScalar**)&array);CHKERRQ(ierr);
1306       ierr = VecRestoreArray(from,&array2);CHKERRQ(ierr);
1307     }
1308   } else { /* from local to global -> put data in coarse right hand side */
1309     from = pcbddc->vec1_P;
1310     to = pcbddc->coarse_vec;
1311   }
1312   ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
1313   PetscFunctionReturn(0);
1314 }
1315 
1316 #undef __FUNCT__
1317 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
1318 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
1319 {
1320   PetscErrorCode ierr;
1321   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1322   PetscScalar    *array,*array2;
1323   Vec            from,to;
1324 
1325   PetscFunctionBegin;
1326   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
1327     from = pcbddc->coarse_vec;
1328     to = pcbddc->vec1_P;
1329   } else { /* from local to global -> put data in coarse right hand side */
1330     from = pcbddc->vec1_P;
1331     to = pcbddc->coarse_vec;
1332   }
1333   ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
1334   if (smode == SCATTER_FORWARD) {
1335     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
1336       Vec tvec;
1337       PetscInt lsize;
1338       ierr = KSPGetRhs(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1339       ierr = VecGetLocalSize(tvec,&lsize);CHKERRQ(ierr);
1340       ierr = VecGetArrayRead(to,(const PetscScalar**)&array);CHKERRQ(ierr);
1341       ierr = VecGetArray(tvec,&array2);CHKERRQ(ierr);
1342       ierr = PetscMemcpy(array2,array,lsize*sizeof(PetscScalar));CHKERRQ(ierr);
1343       ierr = VecRestoreArrayRead(to,(const PetscScalar**)&array);CHKERRQ(ierr);
1344       ierr = VecRestoreArray(tvec,&array2);CHKERRQ(ierr);
1345     }
1346   }
1347   PetscFunctionReturn(0);
1348 }
1349 
1350 /* uncomment for testing purposes */
1351 /* #define PETSC_MISSING_LAPACK_GESVD 1 */
1352 #undef __FUNCT__
1353 #define __FUNCT__ "PCBDDCConstraintsSetUp"
1354 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
1355 {
1356   PetscErrorCode    ierr;
1357   PC_IS*            pcis = (PC_IS*)(pc->data);
1358   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
1359   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
1360   /* constraint and (optionally) change of basis matrix implemented as SeqAIJ */
1361   MatType           impMatType=MATSEQAIJ;
1362   /* one and zero */
1363   PetscScalar       one=1.0,zero=0.0;
1364   /* space to store constraints and their local indices */
1365   PetscScalar       *temp_quadrature_constraint;
1366   PetscInt          *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B;
1367   /* iterators */
1368   PetscInt          i,j,k,total_counts,temp_start_ptr;
1369   /* stuff to store connected components stored in pcbddc->mat_graph */
1370   IS                ISForVertices,*ISForFaces,*ISForEdges,*used_IS;
1371   PetscInt          n_ISForFaces,n_ISForEdges;
1372   /* near null space stuff */
1373   MatNullSpace      nearnullsp;
1374   const Vec         *nearnullvecs;
1375   Vec               *localnearnullsp;
1376   PetscBool         nnsp_has_cnst;
1377   PetscInt          nnsp_size;
1378   PetscScalar       *array;
1379   /* BLAS integers */
1380   PetscBLASInt      lwork,lierr;
1381   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
1382   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
1383   /* LAPACK working arrays for SVD or POD */
1384   PetscBool         skip_lapack;
1385   PetscScalar       *work;
1386   PetscReal         *singular_vals;
1387 #if defined(PETSC_USE_COMPLEX)
1388   PetscReal         *rwork;
1389 #endif
1390 #if defined(PETSC_MISSING_LAPACK_GESVD)
1391   PetscBLASInt      Blas_one_2=1;
1392   PetscScalar       *temp_basis,*correlation_mat;
1393 #else
1394   PetscBLASInt      dummy_int_1=1,dummy_int_2=1;
1395   PetscScalar       dummy_scalar_1=0.0,dummy_scalar_2=0.0;
1396 #endif
1397   /* reuse */
1398   PetscInt          olocal_primal_size;
1399   PetscInt          *oprimal_indices_local_idxs;
1400   /* change of basis */
1401   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
1402   PetscBool         boolforchange,qr_needed;
1403   PetscBT           touched,change_basis,qr_needed_idx;
1404   /* auxiliary stuff */
1405   PetscInt          *nnz,*is_indices,*aux_primal_numbering_B;
1406   /* some quantities */
1407   PetscInt          n_vertices,total_primal_vertices,valid_constraints;
1408   PetscInt          size_of_constraint,max_size_of_constraint,max_constraints,temp_constraints;
1409 
1410 
1411   PetscFunctionBegin;
1412   /* Destroy Mat objects computed previously */
1413   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1414   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1415   /* Get index sets for faces, edges and vertices from graph */
1416   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);CHKERRQ(ierr);
1417   /* free unneeded index sets */
1418   if (!pcbddc->use_vertices) {
1419     ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1420   }
1421   if (!pcbddc->use_edges) {
1422     for (i=0;i<n_ISForEdges;i++) {
1423       ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1424     }
1425     ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1426     n_ISForEdges = 0;
1427   }
1428   if (!pcbddc->use_faces) {
1429     for (i=0;i<n_ISForFaces;i++) {
1430       ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1431     }
1432     ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1433     n_ISForFaces = 0;
1434   }
1435   /* HACKS (the following two blocks of code) */
1436   if (!ISForVertices && pcbddc->NullSpace && !pcbddc->user_ChangeOfBasisMatrix) {
1437     pcbddc->use_change_of_basis = PETSC_TRUE;
1438     if (!ISForEdges) {
1439       pcbddc->use_change_on_faces = PETSC_TRUE;
1440     }
1441   }
1442   if (pcbddc->NullSpace) {
1443     /* use_change_of_basis should be consistent among processors */
1444     PetscBool tbool[2],gbool[2];
1445     tbool [0] = pcbddc->use_change_of_basis;
1446     tbool [1] = pcbddc->use_change_on_faces;
1447     ierr = MPI_Allreduce(tbool,gbool,2,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1448     pcbddc->use_change_of_basis = gbool[0];
1449     pcbddc->use_change_on_faces = gbool[1];
1450   }
1451   /* print some info */
1452   if (pcbddc->dbg_flag) {
1453     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1454     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1455     i = 0;
1456     if (ISForVertices) {
1457       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
1458     }
1459     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
1460     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
1461     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
1462     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1463   }
1464   /* check if near null space is attached to global mat */
1465   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
1466   if (nearnullsp) {
1467     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1468     /* remove any stored info */
1469     ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
1470     ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1471     /* store information for BDDC solver reuse */
1472     ierr = PetscObjectReference((PetscObject)nearnullsp);CHKERRQ(ierr);
1473     pcbddc->onearnullspace = nearnullsp;
1474     ierr = PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1475     for (i=0;i<nnsp_size;i++) {
1476       ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);CHKERRQ(ierr);
1477     }
1478   } else { /* if near null space is not provided BDDC uses constants by default */
1479     nnsp_size = 0;
1480     nnsp_has_cnst = PETSC_TRUE;
1481   }
1482   /* get max number of constraints on a single cc */
1483   max_constraints = nnsp_size;
1484   if (nnsp_has_cnst) max_constraints++;
1485 
1486   /*
1487        Evaluate maximum storage size needed by the procedure
1488        - temp_indices will contain start index of each constraint stored as follows
1489        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
1490        - 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
1491        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
1492                                                                                                                                                          */
1493   total_counts = n_ISForFaces+n_ISForEdges;
1494   total_counts *= max_constraints;
1495   n_vertices = 0;
1496   if (ISForVertices) {
1497     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
1498   }
1499   total_counts += n_vertices;
1500   ierr = PetscMalloc1((total_counts+1),&temp_indices);CHKERRQ(ierr);
1501   ierr = PetscBTCreate(total_counts,&change_basis);CHKERRQ(ierr);
1502   total_counts = 0;
1503   max_size_of_constraint = 0;
1504   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1505     if (i<n_ISForEdges) {
1506       used_IS = &ISForEdges[i];
1507     } else {
1508       used_IS = &ISForFaces[i-n_ISForEdges];
1509     }
1510     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
1511     total_counts += j;
1512     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
1513   }
1514   total_counts *= max_constraints;
1515   total_counts += n_vertices;
1516   ierr = PetscMalloc1(total_counts,&temp_quadrature_constraint);CHKERRQ(ierr);
1517   ierr = PetscMalloc1(total_counts,&temp_indices_to_constraint);CHKERRQ(ierr);
1518   ierr = PetscMalloc1(total_counts,&temp_indices_to_constraint_B);CHKERRQ(ierr);
1519   /* get local part of global near null space vectors */
1520   ierr = PetscMalloc1(nnsp_size,&localnearnullsp);CHKERRQ(ierr);
1521   for (k=0;k<nnsp_size;k++) {
1522     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
1523     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1524     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1525   }
1526 
1527   /* whether or not to skip lapack calls */
1528   skip_lapack = PETSC_TRUE;
1529   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
1530 
1531   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
1532   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1533     PetscScalar temp_work;
1534 #if defined(PETSC_MISSING_LAPACK_GESVD)
1535     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
1536     ierr = PetscMalloc1(max_constraints*max_constraints,&correlation_mat);CHKERRQ(ierr);
1537     ierr = PetscMalloc1(max_constraints,&singular_vals);CHKERRQ(ierr);
1538     ierr = PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);CHKERRQ(ierr);
1539 #if defined(PETSC_USE_COMPLEX)
1540     ierr = PetscMalloc1(3*max_constraints,&rwork);CHKERRQ(ierr);
1541 #endif
1542     /* now we evaluate the optimal workspace using query with lwork=-1 */
1543     ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1544     ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
1545     lwork = -1;
1546     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1547 #if !defined(PETSC_USE_COMPLEX)
1548     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
1549 #else
1550     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
1551 #endif
1552     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1553     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
1554 #else /* on missing GESVD */
1555     /* SVD */
1556     PetscInt max_n,min_n;
1557     max_n = max_size_of_constraint;
1558     min_n = max_constraints;
1559     if (max_size_of_constraint < max_constraints) {
1560       min_n = max_size_of_constraint;
1561       max_n = max_constraints;
1562     }
1563     ierr = PetscMalloc1(min_n,&singular_vals);CHKERRQ(ierr);
1564 #if defined(PETSC_USE_COMPLEX)
1565     ierr = PetscMalloc1(5*min_n,&rwork);CHKERRQ(ierr);
1566 #endif
1567     /* now we evaluate the optimal workspace using query with lwork=-1 */
1568     lwork = -1;
1569     ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
1570     ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
1571     ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
1572     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1573 #if !defined(PETSC_USE_COMPLEX)
1574     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));
1575 #else
1576     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));
1577 #endif
1578     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1579     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
1580 #endif /* on missing GESVD */
1581     /* Allocate optimal workspace */
1582     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
1583     ierr = PetscMalloc1((PetscInt)lwork,&work);CHKERRQ(ierr);
1584   }
1585   /* Now we can loop on constraining sets */
1586   total_counts = 0;
1587   temp_indices[0] = 0;
1588   /* vertices */
1589   if (ISForVertices) {
1590     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1591     if (nnsp_has_cnst) { /* consider all vertices */
1592       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,n_vertices*sizeof(PetscInt));CHKERRQ(ierr);
1593       for (i=0;i<n_vertices;i++) {
1594         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1595         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1596         total_counts++;
1597       }
1598     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
1599       PetscBool used_vertex;
1600       for (i=0;i<n_vertices;i++) {
1601         used_vertex = PETSC_FALSE;
1602         k = 0;
1603         while (!used_vertex && k<nnsp_size) {
1604           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1605           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
1606             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
1607             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1608             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1609             total_counts++;
1610             used_vertex = PETSC_TRUE;
1611           }
1612           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1613           k++;
1614         }
1615       }
1616     }
1617     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1618     n_vertices = total_counts;
1619   }
1620 
1621   /* edges and faces */
1622   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1623     if (i<n_ISForEdges) {
1624       used_IS = &ISForEdges[i];
1625       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
1626     } else {
1627       used_IS = &ISForFaces[i-n_ISForEdges];
1628       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
1629     }
1630     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
1631     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
1632     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
1633     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1634     /* change of basis should not be performed on local periodic nodes */
1635     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
1636     if (nnsp_has_cnst) {
1637       PetscScalar quad_value;
1638       temp_constraints++;
1639       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
1640       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
1641       for (j=0;j<size_of_constraint;j++) {
1642         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
1643       }
1644       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1645       total_counts++;
1646     }
1647     for (k=0;k<nnsp_size;k++) {
1648       PetscReal real_value;
1649       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1650       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
1651       for (j=0;j<size_of_constraint;j++) {
1652         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
1653       }
1654       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1655       /* check if array is null on the connected component */
1656       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1657       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_one));
1658       if (real_value > 0.0) { /* keep indices and values */
1659         temp_constraints++;
1660         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1661         total_counts++;
1662       }
1663     }
1664     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1665     valid_constraints = temp_constraints;
1666     /* perform SVD on the constraints if use_nnsp_true has not be requested by the user and there are non-null constraints on the cc */
1667     if (!pcbddc->use_nnsp_true && temp_constraints) {
1668       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
1669 
1670 #if defined(PETSC_MISSING_LAPACK_GESVD)
1671       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
1672          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
1673          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
1674             the constraints basis will differ (by a complex factor with absolute value equal to 1)
1675             from that computed using LAPACKgesvd
1676          -> This is due to a different computation of eigenvectors in LAPACKheev
1677          -> The quality of the POD-computed basis will be the same */
1678       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
1679       /* Store upper triangular part of correlation matrix */
1680       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1681       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1682       for (j=0;j<temp_constraints;j++) {
1683         for (k=0;k<j+1;k++) {
1684           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));
1685         }
1686       }
1687       /* compute eigenvalues and eigenvectors of correlation matrix */
1688       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1689       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
1690 #if !defined(PETSC_USE_COMPLEX)
1691       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
1692 #else
1693       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
1694 #endif
1695       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1696       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
1697       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
1698       j=0;
1699       while (j < temp_constraints && singular_vals[j] < tol) j++;
1700       total_counts=total_counts-j;
1701       valid_constraints = temp_constraints-j;
1702       /* scale and copy POD basis into used quadrature memory */
1703       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1704       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1705       ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
1706       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1707       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
1708       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1709       if (j<temp_constraints) {
1710         PetscInt ii;
1711         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
1712         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1713         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));
1714         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1715         for (k=0;k<temp_constraints-j;k++) {
1716           for (ii=0;ii<size_of_constraint;ii++) {
1717             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];
1718           }
1719         }
1720       }
1721 #else  /* on missing GESVD */
1722       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1723       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1724       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1725       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1726 #if !defined(PETSC_USE_COMPLEX)
1727       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));
1728 #else
1729       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));
1730 #endif
1731       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
1732       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1733       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
1734       k = temp_constraints;
1735       if (k > size_of_constraint) k = size_of_constraint;
1736       j = 0;
1737       while (j < k && singular_vals[k-j-1] < tol) j++;
1738       total_counts = total_counts-temp_constraints+k-j;
1739       valid_constraints = k-j;
1740 #endif /* on missing GESVD */
1741     }
1742     /* setting change_of_basis flag is safe now */
1743     if (boolforchange) {
1744       for (j=0;j<valid_constraints;j++) {
1745         PetscBTSet(change_basis,total_counts-j-1);
1746       }
1747     }
1748   }
1749   /* free index sets of faces, edges and vertices */
1750   for (i=0;i<n_ISForFaces;i++) {
1751     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1752   }
1753   if (n_ISForFaces) {
1754     ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1755   }
1756   for (i=0;i<n_ISForEdges;i++) {
1757     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1758   }
1759   if (n_ISForEdges) {
1760     ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1761   }
1762   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1763   /* map temp_indices_to_constraint in boundary numbering */
1764   ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,temp_indices[total_counts],temp_indices_to_constraint,&i,temp_indices_to_constraint_B);CHKERRQ(ierr);
1765   if (i != temp_indices[total_counts]) {
1766     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for constraints indices %d != %d\n",temp_indices[total_counts],i);
1767   }
1768 
1769   /* free workspace */
1770   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1771     ierr = PetscFree(work);CHKERRQ(ierr);
1772 #if defined(PETSC_USE_COMPLEX)
1773     ierr = PetscFree(rwork);CHKERRQ(ierr);
1774 #endif
1775     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1776 #if defined(PETSC_MISSING_LAPACK_GESVD)
1777     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1778     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1779 #endif
1780   }
1781   for (k=0;k<nnsp_size;k++) {
1782     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1783   }
1784   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1785 
1786   /* set quantities in pcbddc data structure and store previous primal size */
1787   /* n_vertices defines the number of subdomain corners in the primal space */
1788   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1789   olocal_primal_size = pcbddc->local_primal_size;
1790   pcbddc->local_primal_size = total_counts;
1791   pcbddc->n_vertices = n_vertices;
1792   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
1793 
1794   /* Create constraint matrix */
1795   /* The constraint matrix is used to compute the l2g map of primal dofs */
1796   /* so we need to set it up properly either with or without change of basis */
1797   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1798   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1799   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
1800   /* array to compute a local numbering of constraints : vertices first then constraints */
1801   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_numbering);CHKERRQ(ierr);
1802   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
1803   /* 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 */
1804   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_minloc);CHKERRQ(ierr);
1805   /* auxiliary stuff for basis change */
1806   ierr = PetscMalloc1(max_size_of_constraint,&global_indices);CHKERRQ(ierr);
1807   ierr = PetscBTCreate(pcis->n_B,&touched);CHKERRQ(ierr);
1808 
1809   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
1810   total_primal_vertices=0;
1811   for (i=0;i<pcbddc->local_primal_size;i++) {
1812     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1813     if (size_of_constraint == 1) {
1814       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]]);CHKERRQ(ierr);
1815       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
1816       aux_primal_minloc[total_primal_vertices]=0;
1817       total_primal_vertices++;
1818     } else if (PetscBTLookup(change_basis,i)) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
1819       PetscInt min_loc,min_index;
1820       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
1821       /* find first untouched local node */
1822       k = 0;
1823       while (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) k++;
1824       min_index = global_indices[k];
1825       min_loc = k;
1826       /* search the minimum among global nodes already untouched on the cc */
1827       for (k=1;k<size_of_constraint;k++) {
1828         /* there can be more than one constraint on a single connected component */
1829         if (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k]) && min_index > global_indices[k]) {
1830           min_index = global_indices[k];
1831           min_loc = k;
1832         }
1833       }
1834       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]+min_loc]);CHKERRQ(ierr);
1835       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
1836       aux_primal_minloc[total_primal_vertices]=min_loc;
1837       total_primal_vertices++;
1838     }
1839   }
1840   /* determine if a QR strategy is needed for change of basis */
1841   qr_needed = PETSC_FALSE;
1842   ierr = PetscBTCreate(pcbddc->local_primal_size,&qr_needed_idx);CHKERRQ(ierr);
1843   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1844     if (PetscBTLookup(change_basis,i)) {
1845       size_of_constraint = temp_indices[i+1]-temp_indices[i];
1846       j = 0;
1847       for (k=0;k<size_of_constraint;k++) {
1848         if (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) {
1849           j++;
1850         }
1851       }
1852       /* found more than one primal dof on the cc */
1853       if (j > 1) {
1854         PetscBTSet(qr_needed_idx,i);
1855         qr_needed = PETSC_TRUE;
1856       }
1857     }
1858   }
1859   /* free workspace */
1860   ierr = PetscFree(global_indices);CHKERRQ(ierr);
1861 
1862   /* permute indices in order to have a sorted set of vertices */
1863   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);CHKERRQ(ierr);
1864 
1865   /* nonzero structure of constraint matrix */
1866   ierr = PetscMalloc1(pcbddc->local_primal_size,&nnz);CHKERRQ(ierr);
1867   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
1868   j=total_primal_vertices;
1869   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1870     if (!PetscBTLookup(change_basis,i)) {
1871       nnz[j]=temp_indices[i+1]-temp_indices[i];
1872       j++;
1873     }
1874   }
1875   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1876   ierr = PetscFree(nnz);CHKERRQ(ierr);
1877   /* set values in constraint matrix */
1878   for (i=0;i<total_primal_vertices;i++) {
1879     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
1880   }
1881   total_counts = total_primal_vertices;
1882   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1883     if (!PetscBTLookup(change_basis,i)) {
1884       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1885       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);
1886       total_counts++;
1887     }
1888   }
1889   /* assembling */
1890   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1891   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1892   /*
1893   ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
1894   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
1895   */
1896   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1897   if (pcbddc->use_change_of_basis) {
1898     /* dual and primal dofs on a single cc */
1899     PetscInt     dual_dofs,primal_dofs;
1900     /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
1901     PetscInt     primal_counter;
1902     /* working stuff for GEQRF */
1903     PetscScalar  *qr_basis,*qr_tau = NULL,*qr_work,lqr_work_t;
1904     PetscBLASInt lqr_work;
1905     /* working stuff for UNGQR */
1906     PetscScalar  *gqr_work,lgqr_work_t;
1907     PetscBLASInt lgqr_work;
1908     /* working stuff for TRTRS */
1909     PetscScalar  *trs_rhs;
1910     PetscBLASInt Blas_NRHS;
1911     /* pointers for values insertion into change of basis matrix */
1912     PetscInt     *start_rows,*start_cols;
1913     PetscScalar  *start_vals;
1914     /* working stuff for values insertion */
1915     PetscBT      is_primal;
1916 
1917     /* change of basis acts on local interfaces -> dimension is n_B x n_B */
1918     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1919     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1920     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1921     /* work arrays */
1922     ierr = PetscMalloc1(pcis->n_B,&nnz);CHKERRQ(ierr);
1923     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
1924     /* nonzeros per row */
1925     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1926       if (PetscBTLookup(change_basis,i)) {
1927         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1928         if (PetscBTLookup(qr_needed_idx,i)) {
1929           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1930         } else {
1931           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = 2;
1932           /* get local primal index on the cc */
1933           j = 0;
1934           while (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+j])) j++;
1935           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1936         }
1937       }
1938     }
1939     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1940     ierr = PetscFree(nnz);CHKERRQ(ierr);
1941     /* Set initial identity in the matrix */
1942     for (i=0;i<pcis->n_B;i++) {
1943       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1944     }
1945 
1946     if (pcbddc->dbg_flag) {
1947       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1948       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
1949     }
1950 
1951 
1952     /* Now we loop on the constraints which need a change of basis */
1953     /*
1954        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
1955        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)
1956 
1957        Basic blocks of change of basis matrix T computed
1958 
1959           - Using the following block transformation if there is only a primal dof on the cc
1960             (in the example, primal dof is the last one of the edge in LOCAL ordering
1961              in this code, primal dof is the first one of the edge in GLOBAL ordering)
1962             | 1        0   ...        0     1 |
1963             | 0        1   ...        0     1 |
1964             |              ...                |
1965             | 0        ...            1     1 |
1966             | -s_1/s_n ...    -s_{n-1}/-s_n 1 |
1967 
1968           - via QR decomposition of constraints otherwise
1969     */
1970     if (qr_needed) {
1971       /* space to store Q */
1972       ierr = PetscMalloc1((max_size_of_constraint)*(max_size_of_constraint),&qr_basis);CHKERRQ(ierr);
1973       /* first we issue queries for optimal work */
1974       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1975       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1976       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1977       lqr_work = -1;
1978       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
1979       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
1980       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
1981       ierr = PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);CHKERRQ(ierr);
1982       lgqr_work = -1;
1983       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1984       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
1985       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
1986       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1987       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
1988       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
1989       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
1990       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
1991       ierr = PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);CHKERRQ(ierr);
1992       /* array to store scaling factors for reflectors */
1993       ierr = PetscMalloc1(max_constraints,&qr_tau);CHKERRQ(ierr);
1994       /* array to store rhs and solution of triangular solver */
1995       ierr = PetscMalloc1(max_constraints*max_constraints,&trs_rhs);CHKERRQ(ierr);
1996       /* allocating workspace for check */
1997       if (pcbddc->dbg_flag) {
1998         ierr = PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&work);CHKERRQ(ierr);
1999       }
2000     }
2001     /* array to store whether a node is primal or not */
2002     ierr = PetscBTCreate(pcis->n_B,&is_primal);CHKERRQ(ierr);
2003     ierr = PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);CHKERRQ(ierr);
2004     ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,aux_primal_numbering,&i,aux_primal_numbering_B);CHKERRQ(ierr);
2005     if (i != total_primal_vertices) {
2006       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",total_primal_vertices,i);
2007     }
2008     for (i=0;i<total_primal_vertices;i++) {
2009       ierr = PetscBTSet(is_primal,aux_primal_numbering_B[i]);CHKERRQ(ierr);
2010     }
2011     ierr = PetscFree(aux_primal_numbering_B);CHKERRQ(ierr);
2012 
2013     /* loop on constraints and see whether or not they need a change of basis and compute it */
2014     /* -> using implicit ordering contained in temp_indices data */
2015     total_counts = pcbddc->n_vertices;
2016     primal_counter = total_counts;
2017     while (total_counts<pcbddc->local_primal_size) {
2018       primal_dofs = 1;
2019       if (PetscBTLookup(change_basis,total_counts)) {
2020         /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
2021         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]]) {
2022           primal_dofs++;
2023         }
2024         /* get constraint info */
2025         size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
2026         dual_dofs = size_of_constraint-primal_dofs;
2027 
2028         if (pcbddc->dbg_flag) {
2029           ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraints %d to %d (incl) need a change of basis (size %d)\n",total_counts,total_counts+primal_dofs-1,size_of_constraint);CHKERRQ(ierr);
2030         }
2031 
2032         if (primal_dofs > 1) { /* QR */
2033 
2034           /* copy quadrature constraints for change of basis check */
2035           if (pcbddc->dbg_flag) {
2036             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2037           }
2038           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
2039           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2040 
2041           /* compute QR decomposition of constraints */
2042           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2043           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2044           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2045           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2046           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
2047           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
2048           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2049 
2050           /* explictly compute R^-T */
2051           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
2052           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
2053           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2054           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
2055           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2056           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2057           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2058           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
2059           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
2060           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2061 
2062           /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
2063           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2064           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2065           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2066           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2067           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2068           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
2069           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
2070           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2071 
2072           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
2073              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
2074              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
2075           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2076           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2077           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2078           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2079           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2080           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
2081           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2082           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));
2083           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2084           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2085 
2086           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
2087           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
2088           /* insert cols for primal dofs */
2089           for (j=0;j<primal_dofs;j++) {
2090             start_vals = &qr_basis[j*size_of_constraint];
2091             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
2092             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2093           }
2094           /* insert cols for dual dofs */
2095           for (j=0,k=0;j<dual_dofs;k++) {
2096             if (!PetscBTLookup(is_primal,temp_indices_to_constraint_B[temp_indices[total_counts]+k])) {
2097               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
2098               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2099               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2100               j++;
2101             }
2102           }
2103 
2104           /* check change of basis */
2105           if (pcbddc->dbg_flag) {
2106             PetscInt   ii,jj;
2107             PetscBool valid_qr=PETSC_TRUE;
2108             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
2109             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2110             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
2111             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2112             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
2113             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
2114             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2115             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));
2116             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2117             for (jj=0;jj<size_of_constraint;jj++) {
2118               for (ii=0;ii<primal_dofs;ii++) {
2119                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
2120                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
2121               }
2122             }
2123             if (!valid_qr) {
2124               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");CHKERRQ(ierr);
2125               for (jj=0;jj<size_of_constraint;jj++) {
2126                 for (ii=0;ii<primal_dofs;ii++) {
2127                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
2128                     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]));
2129                   }
2130                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
2131                     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]));
2132                   }
2133                 }
2134               }
2135             } else {
2136               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");CHKERRQ(ierr);
2137             }
2138           }
2139         } else { /* simple transformation block */
2140           PetscInt row,col;
2141           PetscScalar val;
2142           for (j=0;j<size_of_constraint;j++) {
2143             row = temp_indices_to_constraint_B[temp_indices[total_counts]+j];
2144             if (!PetscBTLookup(is_primal,row)) {
2145               col = temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2146               ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);CHKERRQ(ierr);
2147               ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,col,1.0,INSERT_VALUES);CHKERRQ(ierr);
2148             } else {
2149               for (k=0;k<size_of_constraint;k++) {
2150                 col = temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2151                 if (row != col) {
2152                   val = -temp_quadrature_constraint[temp_indices[total_counts]+k]/temp_quadrature_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2153                 } else {
2154                   val = 1.0;
2155                 }
2156                 ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,col,val,INSERT_VALUES);CHKERRQ(ierr);
2157               }
2158             }
2159           }
2160           if (pcbddc->dbg_flag) {
2161             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");CHKERRQ(ierr);
2162           }
2163         }
2164         /* increment primal counter */
2165         primal_counter += primal_dofs;
2166       } else {
2167         if (pcbddc->dbg_flag) {
2168           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);
2169         }
2170       }
2171       /* increment constraint counter total_counts */
2172       total_counts += primal_dofs;
2173     }
2174 
2175     /* free workspace */
2176     if (qr_needed) {
2177       if (pcbddc->dbg_flag) {
2178         ierr = PetscFree(work);CHKERRQ(ierr);
2179       }
2180       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
2181       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
2182       ierr = PetscFree(qr_work);CHKERRQ(ierr);
2183       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
2184       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
2185     }
2186     ierr = PetscBTDestroy(&is_primal);CHKERRQ(ierr);
2187     /* assembling */
2188     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2189     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2190     /*
2191     ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
2192     ierr = MatView(pcbddc->ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
2193     */
2194   }
2195   /* Change of basis as provided by the user in local numbering (internal and boundary) or boundary only */
2196   if (pcbddc->user_ChangeOfBasisMatrix) {
2197     PetscInt rows,cols;
2198     ierr = MatGetSize(pcbddc->user_ChangeOfBasisMatrix,&rows,&cols);CHKERRQ(ierr);
2199     if (rows == pcis->n && cols == pcis->n) {
2200       ierr = MatGetSubMatrix(pcbddc->user_ChangeOfBasisMatrix,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2201     } else {
2202       ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2203       pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
2204     }
2205   }
2206 
2207   /* get indices in local ordering for vertices and constraints */
2208   if (olocal_primal_size == pcbddc->local_primal_size) { /* if this is true, I need to check if a new primal space has been introduced */
2209     ierr = PetscMalloc1(olocal_primal_size,&oprimal_indices_local_idxs);CHKERRQ(ierr);
2210     ierr = PetscMemcpy(oprimal_indices_local_idxs,pcbddc->primal_indices_local_idxs,olocal_primal_size*sizeof(PetscInt));CHKERRQ(ierr);
2211   }
2212   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2213   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2214   ierr = PetscMalloc1(pcbddc->local_primal_size,&pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2215   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&i,&aux_primal_numbering);CHKERRQ(ierr);
2216   ierr = PetscMemcpy(pcbddc->primal_indices_local_idxs,aux_primal_numbering,i*sizeof(PetscInt));CHKERRQ(ierr);
2217   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2218   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&j,&aux_primal_numbering);CHKERRQ(ierr);
2219   ierr = PetscMemcpy(&pcbddc->primal_indices_local_idxs[i],aux_primal_numbering,j*sizeof(PetscInt));CHKERRQ(ierr);
2220   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2221   /* set quantities in PCBDDC data struct */
2222   pcbddc->n_actual_vertices = i;
2223   /* check if a new primal space has been introduced */
2224   pcbddc->new_primal_space_local = PETSC_TRUE;
2225   if (olocal_primal_size == pcbddc->local_primal_size) {
2226     ierr = PetscMemcmp(pcbddc->primal_indices_local_idxs,oprimal_indices_local_idxs,olocal_primal_size,&pcbddc->new_primal_space_local);CHKERRQ(ierr);
2227     pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
2228     ierr = PetscFree(oprimal_indices_local_idxs);CHKERRQ(ierr);
2229   }
2230   /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
2231   ierr = MPI_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
2232 
2233   /* flush dbg viewer */
2234   if (pcbddc->dbg_flag) {
2235     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2236   }
2237 
2238   /* free workspace */
2239   ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2240   ierr = PetscBTDestroy(&qr_needed_idx);CHKERRQ(ierr);
2241   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
2242   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2243   ierr = PetscBTDestroy(&change_basis);CHKERRQ(ierr);
2244   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
2245   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
2246   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
2247   PetscFunctionReturn(0);
2248 }
2249 
2250 #undef __FUNCT__
2251 #define __FUNCT__ "PCBDDCAnalyzeInterface"
2252 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
2253 {
2254   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
2255   PC_IS       *pcis = (PC_IS*)pc->data;
2256   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
2257   PetscInt    ierr,i,vertex_size;
2258   PetscViewer viewer=pcbddc->dbg_viewer;
2259 
2260   PetscFunctionBegin;
2261   /* Reset previously computed graph */
2262   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
2263   /* Init local Graph struct */
2264   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
2265 
2266   /* Check validity of the csr graph passed in by the user */
2267   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
2268     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
2269   }
2270 
2271   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
2272   if (pcbddc->use_local_adj && (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy)) {
2273     Mat mat_adj;
2274     const PetscInt *xadj,*adjncy;
2275     PetscBool flg_row=PETSC_TRUE;
2276 
2277     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
2278     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2279     if (!flg_row) {
2280       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
2281     }
2282     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
2283     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2284     if (!flg_row) {
2285       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2286     }
2287     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
2288   }
2289 
2290   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
2291   vertex_size = 1;
2292   if (pcbddc->user_provided_isfordofs) {
2293     if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
2294       ierr = PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2295       for (i=0;i<pcbddc->n_ISForDofs;i++) {
2296         ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2297         ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
2298       }
2299       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
2300       pcbddc->n_ISForDofs = 0;
2301       ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
2302     }
2303     /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
2304     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
2305   } else {
2306     if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
2307       ierr = MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);CHKERRQ(ierr);
2308       ierr = PetscMalloc(pcbddc->n_ISForDofsLocal*sizeof(IS),&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2309       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
2310         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2311       }
2312     }
2313   }
2314 
2315   /* Setup of Graph */
2316   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
2317     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
2318   }
2319   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
2320     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
2321   }
2322   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices);
2323 
2324   /* Graph's connected components analysis */
2325   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
2326 
2327   /* print some info to stdout */
2328   if (pcbddc->dbg_flag) {
2329     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
2330   }
2331 
2332   /* mark topography has done */
2333   pcbddc->recompute_topography = PETSC_FALSE;
2334   PetscFunctionReturn(0);
2335 }
2336 
2337 #undef __FUNCT__
2338 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
2339 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt **vertices_idx)
2340 {
2341   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2342   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
2343   PetscErrorCode ierr;
2344 
2345   PetscFunctionBegin;
2346   n = 0;
2347   vertices = 0;
2348   if (pcbddc->ConstraintMatrix) {
2349     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
2350     for (i=0;i<local_primal_size;i++) {
2351       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2352       if (size_of_constraint == 1) n++;
2353       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2354     }
2355     if (vertices_idx) {
2356       ierr = PetscMalloc1(n,&vertices);CHKERRQ(ierr);
2357       n = 0;
2358       for (i=0;i<local_primal_size;i++) {
2359         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2360         if (size_of_constraint == 1) {
2361           vertices[n++]=row_cmat_indices[0];
2362         }
2363         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2364       }
2365     }
2366   }
2367   *n_vertices = n;
2368   if (vertices_idx) *vertices_idx = vertices;
2369   PetscFunctionReturn(0);
2370 }
2371 
2372 #undef __FUNCT__
2373 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
2374 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt **constraints_idx)
2375 {
2376   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2377   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
2378   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
2379   PetscBT        touched;
2380   PetscErrorCode ierr;
2381 
2382     /* This function assumes that the number of local constraints per connected component
2383        is not greater than the number of nodes defined for the connected component
2384        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
2385   PetscFunctionBegin;
2386   n = 0;
2387   constraints_index = 0;
2388   if (pcbddc->ConstraintMatrix) {
2389     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
2390     max_size_of_constraint = 0;
2391     for (i=0;i<local_primal_size;i++) {
2392       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2393       if (size_of_constraint > 1) {
2394         n++;
2395       }
2396       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
2397       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2398     }
2399     if (constraints_idx) {
2400       ierr = PetscMalloc1(n,&constraints_index);CHKERRQ(ierr);
2401       ierr = PetscMalloc1(max_size_of_constraint,&row_cmat_global_indices);CHKERRQ(ierr);
2402       ierr = PetscBTCreate(local_size,&touched);CHKERRQ(ierr);
2403       n = 0;
2404       for (i=0;i<local_primal_size;i++) {
2405         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2406         if (size_of_constraint > 1) {
2407           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
2408           /* find first untouched local node */
2409           j = 0;
2410           while (PetscBTLookup(touched,row_cmat_indices[j])) j++;
2411           min_index = row_cmat_global_indices[j];
2412           min_loc = j;
2413           /* search the minimum among nodes not yet touched on the connected component
2414              since there can be more than one constraint on a single cc */
2415           for (j=1;j<size_of_constraint;j++) {
2416             if (!PetscBTLookup(touched,row_cmat_indices[j]) && min_index > row_cmat_global_indices[j]) {
2417               min_index = row_cmat_global_indices[j];
2418               min_loc = j;
2419             }
2420           }
2421           ierr = PetscBTSet(touched,row_cmat_indices[min_loc]);CHKERRQ(ierr);
2422           constraints_index[n++] = row_cmat_indices[min_loc];
2423         }
2424         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2425       }
2426       ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2427       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
2428     }
2429   }
2430   *n_constraints = n;
2431   if (constraints_idx) *constraints_idx = constraints_index;
2432   PetscFunctionReturn(0);
2433 }
2434 
2435 /* the next two functions has been adapted from pcis.c */
2436 #undef __FUNCT__
2437 #define __FUNCT__ "PCBDDCApplySchur"
2438 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2439 {
2440   PetscErrorCode ierr;
2441   PC_IS          *pcis = (PC_IS*)(pc->data);
2442 
2443   PetscFunctionBegin;
2444   if (!vec2_B) { vec2_B = v; }
2445   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2446   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
2447   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2448   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
2449   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2450   PetscFunctionReturn(0);
2451 }
2452 
2453 #undef __FUNCT__
2454 #define __FUNCT__ "PCBDDCApplySchurTranspose"
2455 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2456 {
2457   PetscErrorCode ierr;
2458   PC_IS          *pcis = (PC_IS*)(pc->data);
2459 
2460   PetscFunctionBegin;
2461   if (!vec2_B) { vec2_B = v; }
2462   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2463   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
2464   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2465   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
2466   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2467   PetscFunctionReturn(0);
2468 }
2469 
2470 #undef __FUNCT__
2471 #define __FUNCT__ "PCBDDCSubsetNumbering"
2472 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[])
2473 {
2474   Vec            local_vec,global_vec;
2475   IS             seqis,paris;
2476   VecScatter     scatter_ctx;
2477   PetscScalar    *array;
2478   PetscInt       *temp_global_dofs;
2479   PetscScalar    globalsum;
2480   PetscInt       i,j,s;
2481   PetscInt       nlocals,first_index,old_index,max_local;
2482   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
2483   PetscMPIInt    *dof_sizes,*dof_displs;
2484   PetscBool      first_found;
2485   PetscErrorCode ierr;
2486 
2487   PetscFunctionBegin;
2488   /* mpi buffers */
2489   ierr = MPI_Comm_size(comm,&size_prec_comm);CHKERRQ(ierr);
2490   ierr = MPI_Comm_rank(comm,&rank_prec_comm);CHKERRQ(ierr);
2491   j = ( !rank_prec_comm ? size_prec_comm : 0);
2492   ierr = PetscMalloc1(j,&dof_sizes);CHKERRQ(ierr);
2493   ierr = PetscMalloc1(j,&dof_displs);CHKERRQ(ierr);
2494   /* get maximum size of subset */
2495   ierr = PetscMalloc1(n_local_dofs,&temp_global_dofs);CHKERRQ(ierr);
2496   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
2497   max_local = 0;
2498   for (i=0;i<n_local_dofs;i++) {
2499     if (max_local < temp_global_dofs[i] ) {
2500       max_local = temp_global_dofs[i];
2501     }
2502   }
2503   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
2504   max_global++;
2505   max_local = 0;
2506   for (i=0;i<n_local_dofs;i++) {
2507     if (max_local < local_dofs[i] ) {
2508       max_local = local_dofs[i];
2509     }
2510   }
2511   max_local++;
2512   /* allocate workspace */
2513   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
2514   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
2515   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
2516   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
2517   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
2518   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
2519   /* create scatter */
2520   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
2521   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
2522   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
2523   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
2524   ierr = ISDestroy(&paris);CHKERRQ(ierr);
2525   /* init array */
2526   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
2527   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2528   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2529   if (local_dofs_mult) {
2530     for (i=0;i<n_local_dofs;i++) {
2531       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
2532     }
2533   } else {
2534     for (i=0;i<n_local_dofs;i++) {
2535       array[local_dofs[i]]=1.0;
2536     }
2537   }
2538   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2539   /* scatter into global vec and get total number of global dofs */
2540   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2541   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2542   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
2543   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
2544   /* Fill global_vec with cumulative function for global numbering */
2545   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
2546   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
2547   nlocals = 0;
2548   first_index = -1;
2549   first_found = PETSC_FALSE;
2550   for (i=0;i<s;i++) {
2551     if (!first_found && PetscRealPart(array[i]) > 0.1) {
2552       first_found = PETSC_TRUE;
2553       first_index = i;
2554     }
2555     nlocals += (PetscInt)PetscRealPart(array[i]);
2556   }
2557   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2558   if (!rank_prec_comm) {
2559     dof_displs[0]=0;
2560     for (i=1;i<size_prec_comm;i++) {
2561       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
2562     }
2563   }
2564   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2565   if (first_found) {
2566     array[first_index] += (PetscScalar)nlocals;
2567     old_index = first_index;
2568     for (i=first_index+1;i<s;i++) {
2569       if (PetscRealPart(array[i]) > 0.1) {
2570         array[i] += array[old_index];
2571         old_index = i;
2572       }
2573     }
2574   }
2575   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
2576   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2577   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2578   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2579   /* get global ordering of local dofs */
2580   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2581   if (local_dofs_mult) {
2582     for (i=0;i<n_local_dofs;i++) {
2583       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
2584     }
2585   } else {
2586     for (i=0;i<n_local_dofs;i++) {
2587       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
2588     }
2589   }
2590   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2591   /* free workspace */
2592   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
2593   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
2594   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
2595   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
2596   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
2597   /* return pointer to global ordering of local dofs */
2598   *global_numbering_subset = temp_global_dofs;
2599   PetscFunctionReturn(0);
2600 }
2601 
2602 #undef __FUNCT__
2603 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
2604 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
2605 {
2606   PetscInt       i,j;
2607   PetscScalar    *alphas;
2608   PetscErrorCode ierr;
2609 
2610   PetscFunctionBegin;
2611   /* this implements stabilized Gram-Schmidt */
2612   ierr = PetscMalloc1(n,&alphas);CHKERRQ(ierr);
2613   for (i=0;i<n;i++) {
2614     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
2615     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
2616     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
2617   }
2618   ierr = PetscFree(alphas);CHKERRQ(ierr);
2619   PetscFunctionReturn(0);
2620 }
2621 
2622 #undef __FUNCT__
2623 #define __FUNCT__ "MatISGetSubassemblingPattern"
2624 PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscBool contiguous, IS* is_sends)
2625 {
2626   Mat             subdomain_adj;
2627   IS              new_ranks,ranks_send_to;
2628   MatPartitioning partitioner;
2629   Mat_IS          *matis;
2630   PetscInt        n_neighs,*neighs,*n_shared,**shared;
2631   PetscInt        prank;
2632   PetscMPIInt     size,rank,color;
2633   PetscInt        *xadj,*adjncy,*oldranks;
2634   PetscInt        *adjncy_wgt,*v_wgt,*is_indices,*ranks_send_to_idx;
2635   PetscInt        i,j,local_size,threshold=0;
2636   PetscErrorCode  ierr;
2637   PetscBool       use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
2638   PetscSubcomm    subcomm;
2639 
2640   PetscFunctionBegin;
2641   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_square",&use_square,NULL);CHKERRQ(ierr);
2642   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);CHKERRQ(ierr);
2643   ierr = PetscOptionsGetInt(NULL,"-matis_partitioning_threshold",&threshold,NULL);CHKERRQ(ierr);
2644 
2645   /* Get info on mapping */
2646   matis = (Mat_IS*)(mat->data);
2647   ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&local_size);CHKERRQ(ierr);
2648   ierr = ISLocalToGlobalMappingGetInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2649 
2650   /* build local CSR graph of subdomains' connectivity */
2651   ierr = PetscMalloc1(2,&xadj);CHKERRQ(ierr);
2652   xadj[0] = 0;
2653   xadj[1] = PetscMax(n_neighs-1,0);
2654   ierr = PetscMalloc1(xadj[1],&adjncy);CHKERRQ(ierr);
2655   ierr = PetscMalloc1(xadj[1],&adjncy_wgt);CHKERRQ(ierr);
2656 
2657   if (threshold) {
2658     PetscInt* count,min_threshold;
2659     ierr = PetscMalloc1(local_size,&count);CHKERRQ(ierr);
2660     ierr = PetscMemzero(count,local_size*sizeof(PetscInt));CHKERRQ(ierr);
2661     for (i=1;i<n_neighs;i++) {/* i=1 so I don't count myself -> faces nodes counts to 1 */
2662       for (j=0;j<n_shared[i];j++) {
2663         count[shared[i][j]] += 1;
2664       }
2665     }
2666     /* adapt threshold since we dont want to lose significant connections */
2667     min_threshold = n_neighs;
2668     for (i=1;i<n_neighs;i++) {
2669       for (j=0;j<n_shared[i];j++) {
2670         min_threshold = PetscMin(count[shared[i][j]],min_threshold);
2671       }
2672     }
2673     threshold = PetscMax(min_threshold+1,threshold);
2674     xadj[1] = 0;
2675     for (i=1;i<n_neighs;i++) {
2676       for (j=0;j<n_shared[i];j++) {
2677         if (count[shared[i][j]] < threshold) {
2678           adjncy[xadj[1]] = neighs[i];
2679           adjncy_wgt[xadj[1]] = n_shared[i];
2680           xadj[1]++;
2681           break;
2682         }
2683       }
2684     }
2685     ierr = PetscFree(count);CHKERRQ(ierr);
2686   } else {
2687     if (xadj[1]) {
2688       ierr = PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));CHKERRQ(ierr);
2689       ierr = PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));CHKERRQ(ierr);
2690     }
2691   }
2692   ierr = ISLocalToGlobalMappingRestoreInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2693   if (use_square) {
2694     for (i=0;i<xadj[1];i++) {
2695       adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
2696     }
2697   }
2698   ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2699 
2700   ierr = PetscMalloc(sizeof(PetscInt),&ranks_send_to_idx);CHKERRQ(ierr);
2701 
2702   /*
2703     Restrict work on active processes only.
2704   */
2705   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);CHKERRQ(ierr);
2706   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr); /* 2 groups, active process and not active processes */
2707   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
2708   ierr = PetscMPIIntCast(!local_size,&color);CHKERRQ(ierr);
2709   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2710   if (color) {
2711     ierr = PetscFree(xadj);CHKERRQ(ierr);
2712     ierr = PetscFree(adjncy);CHKERRQ(ierr);
2713     ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
2714   } else {
2715     PetscInt coarsening_ratio;
2716     ierr = MPI_Comm_size(subcomm->comm,&size);CHKERRQ(ierr);
2717     ierr = PetscMalloc1(size,&oldranks);CHKERRQ(ierr);
2718     prank = rank;
2719     ierr = MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm->comm);CHKERRQ(ierr);
2720     /*
2721     for (i=0;i<size;i++) {
2722       PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
2723     }
2724     */
2725     for (i=0;i<xadj[1];i++) {
2726       ierr = PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);CHKERRQ(ierr);
2727     }
2728     ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2729     ierr = MatCreateMPIAdj(subcomm->comm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);CHKERRQ(ierr);
2730     /* ierr = MatView(subdomain_adj,0);CHKERRQ(ierr); */
2731 
2732     /* Partition */
2733     ierr = MatPartitioningCreate(subcomm->comm,&partitioner);CHKERRQ(ierr);
2734     ierr = MatPartitioningSetAdjacency(partitioner,subdomain_adj);CHKERRQ(ierr);
2735     if (use_vwgt) {
2736       ierr = PetscMalloc(sizeof(*v_wgt),&v_wgt);CHKERRQ(ierr);
2737       v_wgt[0] = local_size;
2738       ierr = MatPartitioningSetVertexWeights(partitioner,v_wgt);CHKERRQ(ierr);
2739     }
2740     n_subdomains = PetscMin((PetscInt)size,n_subdomains);
2741     coarsening_ratio = size/n_subdomains;
2742     /* Parmetis does not always give back nparts with small graphs! this should be taken into account */
2743     ierr = MatPartitioningSetNParts(partitioner,n_subdomains);CHKERRQ(ierr);
2744     ierr = MatPartitioningSetFromOptions(partitioner);CHKERRQ(ierr);
2745     ierr = MatPartitioningApply(partitioner,&new_ranks);CHKERRQ(ierr);
2746     /* ierr = MatPartitioningView(partitioner,0);CHKERRQ(ierr); */
2747 
2748     ierr = ISGetIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2749     if (contiguous) {
2750       ranks_send_to_idx[0] = oldranks[is_indices[0]]; /* contiguos set of processes */
2751     } else {
2752       ranks_send_to_idx[0] = coarsening_ratio*oldranks[is_indices[0]]; /* scattered set of processes */
2753     }
2754     ierr = ISRestoreIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2755     /* clean up */
2756     ierr = PetscFree(oldranks);CHKERRQ(ierr);
2757     ierr = ISDestroy(&new_ranks);CHKERRQ(ierr);
2758     ierr = MatDestroy(&subdomain_adj);CHKERRQ(ierr);
2759     ierr = MatPartitioningDestroy(&partitioner);CHKERRQ(ierr);
2760   }
2761   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
2762 
2763   /* assemble parallel IS for sends */
2764   i = 1;
2765   if (color) i=0;
2766   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);CHKERRQ(ierr);
2767 
2768   /* get back IS */
2769   *is_sends = ranks_send_to;
2770   PetscFunctionReturn(0);
2771 }
2772 
2773 typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;
2774 
2775 #undef __FUNCT__
2776 #define __FUNCT__ "MatISSubassemble"
2777 PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
2778 {
2779   Mat                    local_mat;
2780   Mat_IS                 *matis;
2781   IS                     is_sends_internal;
2782   PetscInt               rows,cols;
2783   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
2784   PetscBool              ismatis,isdense,destroy_mat;
2785   ISLocalToGlobalMapping l2gmap;
2786   PetscInt*              l2gmap_indices;
2787   const PetscInt*        is_indices;
2788   MatType                new_local_type;
2789   /* buffers */
2790   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
2791   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
2792   PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
2793   /* MPI */
2794   MPI_Comm               comm,comm_n;
2795   PetscSubcomm           subcomm;
2796   PetscMPIInt            n_sends,n_recvs,commsize;
2797   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
2798   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
2799   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
2800   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
2801   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
2802   PetscErrorCode         ierr;
2803 
2804   PetscFunctionBegin;
2805   /* TODO: add missing checks */
2806   PetscValidLogicalCollectiveInt(mat,n_subdomains,3);
2807   PetscValidLogicalCollectiveBool(mat,restrict_comm,4);
2808   PetscValidLogicalCollectiveEnum(mat,reuse,5);
2809   PetscValidLogicalCollectiveInt(mat,nis,7);
2810   ierr = PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);CHKERRQ(ierr);
2811   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
2812   ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
2813   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);CHKERRQ(ierr);
2814   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
2815   ierr = MatGetSize(local_mat,&rows,&cols);CHKERRQ(ierr);
2816   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
2817   if (reuse == MAT_REUSE_MATRIX && *mat_n) {
2818     PetscInt mrows,mcols,mnrows,mncols;
2819     ierr = PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);CHKERRQ(ierr);
2820     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
2821     ierr = MatGetSize(mat,&mrows,&mcols);CHKERRQ(ierr);
2822     ierr = MatGetSize(*mat_n,&mnrows,&mncols);CHKERRQ(ierr);
2823     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
2824     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
2825   }
2826   ierr = MatGetBlockSize(local_mat,&bs);CHKERRQ(ierr);
2827   PetscValidLogicalCollectiveInt(mat,bs,0);
2828   /* prepare IS for sending if not provided */
2829   if (!is_sends) {
2830     PetscBool pcontig = PETSC_TRUE;
2831     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
2832     ierr = MatISGetSubassemblingPattern(mat,n_subdomains,pcontig,&is_sends_internal);CHKERRQ(ierr);
2833   } else {
2834     ierr = PetscObjectReference((PetscObject)is_sends);CHKERRQ(ierr);
2835     is_sends_internal = is_sends;
2836   }
2837 
2838   /* get pointer of MATIS data */
2839   matis = (Mat_IS*)mat->data;
2840 
2841   /* get comm */
2842   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2843 
2844   /* compute number of sends */
2845   ierr = ISGetLocalSize(is_sends_internal,&i);CHKERRQ(ierr);
2846   ierr = PetscMPIIntCast(i,&n_sends);CHKERRQ(ierr);
2847 
2848   /* compute number of receives */
2849   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
2850   ierr = PetscMalloc1(commsize,&iflags);CHKERRQ(ierr);
2851   ierr = PetscMemzero(iflags,commsize*sizeof(*iflags));CHKERRQ(ierr);
2852   ierr = ISGetIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
2853   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
2854   ierr = PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);CHKERRQ(ierr);
2855   ierr = PetscFree(iflags);CHKERRQ(ierr);
2856 
2857   /* restrict comm if requested */
2858   subcomm = 0;
2859   destroy_mat = PETSC_FALSE;
2860   if (restrict_comm) {
2861     PetscMPIInt color,rank,subcommsize;
2862     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2863     color = 0;
2864     if (n_sends && !n_recvs) color = 1; /* sending only processes will not partecipate in new comm */
2865     ierr = MPI_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
2866     subcommsize = commsize - subcommsize;
2867     /* check if reuse has been requested */
2868     if (reuse == MAT_REUSE_MATRIX) {
2869       if (*mat_n) {
2870         PetscMPIInt subcommsize2;
2871         ierr = MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);CHKERRQ(ierr);
2872         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
2873         comm_n = PetscObjectComm((PetscObject)*mat_n);
2874       } else {
2875         comm_n = PETSC_COMM_SELF;
2876       }
2877     } else { /* MAT_INITIAL_MATRIX */
2878       ierr = PetscSubcommCreate(comm,&subcomm);CHKERRQ(ierr);
2879       ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
2880       ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2881       comm_n = subcomm->comm;
2882     }
2883     /* flag to destroy *mat_n if not significative */
2884     if (color) destroy_mat = PETSC_TRUE;
2885   } else {
2886     comm_n = comm;
2887   }
2888 
2889   /* prepare send/receive buffers */
2890   ierr = PetscMalloc1(commsize,&ilengths_idxs);CHKERRQ(ierr);
2891   ierr = PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));CHKERRQ(ierr);
2892   ierr = PetscMalloc1(commsize,&ilengths_vals);CHKERRQ(ierr);
2893   ierr = PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));CHKERRQ(ierr);
2894   if (nis) {
2895     ierr = PetscMalloc(commsize*sizeof(*ilengths_idxs_is),&ilengths_idxs_is);CHKERRQ(ierr);
2896     ierr = PetscMemzero(ilengths_idxs_is,commsize*sizeof(*ilengths_idxs_is));CHKERRQ(ierr);
2897   }
2898 
2899   /* Get data from local matrices */
2900   if (!isdense) {
2901     /* TODO: See below some guidelines on how to prepare the local buffers */
2902     /*
2903        send_buffer_vals should contain the raw values of the local matrix
2904        send_buffer_idxs should contain:
2905        - MatType_PRIVATE type
2906        - PetscInt        size_of_l2gmap
2907        - PetscInt        global_row_indices[size_of_l2gmap]
2908        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
2909     */
2910   } else {
2911     ierr = MatDenseGetArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
2912     ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&i);CHKERRQ(ierr);
2913     ierr = PetscMalloc1((i+2),&send_buffer_idxs);CHKERRQ(ierr);
2914     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
2915     send_buffer_idxs[1] = i;
2916     ierr = ISLocalToGlobalMappingGetIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
2917     ierr = PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));CHKERRQ(ierr);
2918     ierr = ISLocalToGlobalMappingRestoreIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
2919     ierr = PetscMPIIntCast(i,&len);CHKERRQ(ierr);
2920     for (i=0;i<n_sends;i++) {
2921       ilengths_vals[is_indices[i]] = len*len;
2922       ilengths_idxs[is_indices[i]] = len+2;
2923     }
2924   }
2925   ierr = PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);CHKERRQ(ierr);
2926   /* additional is (if any) */
2927   if (nis) {
2928     PetscMPIInt psum;
2929     PetscInt j;
2930     for (j=0,psum=0;j<nis;j++) {
2931       PetscInt plen;
2932       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
2933       ierr = PetscMPIIntCast(plen,&len);CHKERRQ(ierr);
2934       psum += len+1; /* indices + lenght */
2935     }
2936     ierr = PetscMalloc(psum*sizeof(PetscInt),&send_buffer_idxs_is);CHKERRQ(ierr);
2937     for (j=0,psum=0;j<nis;j++) {
2938       PetscInt plen;
2939       const PetscInt *is_array_idxs;
2940       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
2941       send_buffer_idxs_is[psum] = plen;
2942       ierr = ISGetIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
2943       ierr = PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));CHKERRQ(ierr);
2944       ierr = ISRestoreIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
2945       psum += plen+1; /* indices + lenght */
2946     }
2947     for (i=0;i<n_sends;i++) {
2948       ilengths_idxs_is[is_indices[i]] = psum;
2949     }
2950     ierr = PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);CHKERRQ(ierr);
2951   }
2952 
2953   buf_size_idxs = 0;
2954   buf_size_vals = 0;
2955   buf_size_idxs_is = 0;
2956   for (i=0;i<n_recvs;i++) {
2957     buf_size_idxs += (PetscInt)olengths_idxs[i];
2958     buf_size_vals += (PetscInt)olengths_vals[i];
2959     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
2960   }
2961   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);CHKERRQ(ierr);
2962   ierr = PetscMalloc1(buf_size_vals,&recv_buffer_vals);CHKERRQ(ierr);
2963   ierr = PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);CHKERRQ(ierr);
2964 
2965   /* get new tags for clean communications */
2966   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);CHKERRQ(ierr);
2967   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_vals);CHKERRQ(ierr);
2968   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);CHKERRQ(ierr);
2969 
2970   /* allocate for requests */
2971   ierr = PetscMalloc1(n_sends,&send_req_idxs);CHKERRQ(ierr);
2972   ierr = PetscMalloc1(n_sends,&send_req_vals);CHKERRQ(ierr);
2973   ierr = PetscMalloc1(n_sends,&send_req_idxs_is);CHKERRQ(ierr);
2974   ierr = PetscMalloc1(n_recvs,&recv_req_idxs);CHKERRQ(ierr);
2975   ierr = PetscMalloc1(n_recvs,&recv_req_vals);CHKERRQ(ierr);
2976   ierr = PetscMalloc1(n_recvs,&recv_req_idxs_is);CHKERRQ(ierr);
2977 
2978   /* communications */
2979   ptr_idxs = recv_buffer_idxs;
2980   ptr_vals = recv_buffer_vals;
2981   ptr_idxs_is = recv_buffer_idxs_is;
2982   for (i=0;i<n_recvs;i++) {
2983     source_dest = onodes[i];
2984     ierr = MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);CHKERRQ(ierr);
2985     ierr = MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);CHKERRQ(ierr);
2986     ptr_idxs += olengths_idxs[i];
2987     ptr_vals += olengths_vals[i];
2988     if (nis) {
2989       ierr = MPI_Irecv(ptr_idxs_is,olengths_idxs_is[i],MPIU_INT,source_dest,tag_idxs_is,comm,&recv_req_idxs_is[i]);CHKERRQ(ierr);
2990       ptr_idxs_is += olengths_idxs_is[i];
2991     }
2992   }
2993   for (i=0;i<n_sends;i++) {
2994     ierr = PetscMPIIntCast(is_indices[i],&source_dest);CHKERRQ(ierr);
2995     ierr = MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);CHKERRQ(ierr);
2996     ierr = MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);CHKERRQ(ierr);
2997     if (nis) {
2998       ierr = MPI_Isend(send_buffer_idxs_is,ilengths_idxs_is[source_dest],MPIU_INT,source_dest,tag_idxs_is,comm,&send_req_idxs_is[i]);CHKERRQ(ierr);
2999     }
3000   }
3001   ierr = ISRestoreIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
3002   ierr = ISDestroy(&is_sends_internal);CHKERRQ(ierr);
3003 
3004   /* assemble new l2g map */
3005   ierr = MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3006   ptr_idxs = recv_buffer_idxs;
3007   buf_size_idxs = 0;
3008   for (i=0;i<n_recvs;i++) {
3009     buf_size_idxs += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3010     ptr_idxs += olengths_idxs[i];
3011   }
3012   ierr = PetscMalloc1(buf_size_idxs,&l2gmap_indices);CHKERRQ(ierr);
3013   ptr_idxs = recv_buffer_idxs;
3014   buf_size_idxs = 0;
3015   for (i=0;i<n_recvs;i++) {
3016     ierr = PetscMemcpy(&l2gmap_indices[buf_size_idxs],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));CHKERRQ(ierr);
3017     buf_size_idxs += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3018     ptr_idxs += olengths_idxs[i];
3019   }
3020   ierr = PetscSortRemoveDupsInt(&buf_size_idxs,l2gmap_indices);CHKERRQ(ierr);
3021   ierr = ISLocalToGlobalMappingCreate(comm_n,1,buf_size_idxs,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);CHKERRQ(ierr);
3022   ierr = PetscFree(l2gmap_indices);CHKERRQ(ierr);
3023 
3024   /* infer new local matrix type from received local matrices type */
3025   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
3026   /* it also assumes that if the block size is set, than it is the same among all local matrices (see checks at the beginning of the function) */
3027   if (n_recvs) {
3028     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
3029     ptr_idxs = recv_buffer_idxs;
3030     for (i=0;i<n_recvs;i++) {
3031       if ((PetscInt)new_local_type_private != *ptr_idxs) {
3032         new_local_type_private = MATAIJ_PRIVATE;
3033         break;
3034       }
3035       ptr_idxs += olengths_idxs[i];
3036     }
3037     switch (new_local_type_private) {
3038       case MATDENSE_PRIVATE:
3039         if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
3040           new_local_type = MATSEQAIJ;
3041           bs = 1;
3042         } else { /* if I receive only 1 dense matrix */
3043           new_local_type = MATSEQDENSE;
3044           bs = 1;
3045         }
3046         break;
3047       case MATAIJ_PRIVATE:
3048         new_local_type = MATSEQAIJ;
3049         bs = 1;
3050         break;
3051       case MATBAIJ_PRIVATE:
3052         new_local_type = MATSEQBAIJ;
3053         break;
3054       case MATSBAIJ_PRIVATE:
3055         new_local_type = MATSEQSBAIJ;
3056         break;
3057       default:
3058         SETERRQ2(comm,PETSC_ERR_PLIB,"Unkwown private type %d in %s",new_local_type_private,__FUNCT__);
3059         break;
3060     }
3061   } else { /* by default, new_local_type is seqdense */
3062     new_local_type = MATSEQDENSE;
3063     bs = 1;
3064   }
3065 
3066   /* create MATIS object if needed */
3067   if (reuse == MAT_INITIAL_MATRIX) {
3068     ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
3069     ierr = MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,mat_n);CHKERRQ(ierr);
3070   } else {
3071     /* it also destroys the local matrices */
3072     ierr = MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);CHKERRQ(ierr);
3073   }
3074   ierr = ISLocalToGlobalMappingDestroy(&l2gmap);CHKERRQ(ierr);
3075   ierr = MatISGetLocalMat(*mat_n,&local_mat);CHKERRQ(ierr);
3076   ierr = MatSetType(local_mat,new_local_type);CHKERRQ(ierr);
3077   ierr = MatSetUp(local_mat);CHKERRQ(ierr); /* WARNING -> no preallocation yet */
3078 
3079   /* set values */
3080   ierr = MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3081   ptr_vals = recv_buffer_vals;
3082   ptr_idxs = recv_buffer_idxs;
3083   for (i=0;i<n_recvs;i++) {
3084     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
3085       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
3086       ierr = MatSetValues(*mat_n,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);CHKERRQ(ierr);
3087       ierr = MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3088       ierr = MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3089       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
3090     } else {
3091       /* TODO */
3092     }
3093     ptr_idxs += olengths_idxs[i];
3094     ptr_vals += olengths_vals[i];
3095   }
3096   ierr = MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3097   ierr = MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3098   ierr = MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3099   ierr = MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3100 
3101 #if 0
3102   if (!restrict_comm) { /* check */
3103     Vec       lvec,rvec;
3104     PetscReal infty_error;
3105 
3106     ierr = MatGetVecs(mat,&rvec,&lvec);CHKERRQ(ierr);
3107     ierr = VecSetRandom(rvec,NULL);CHKERRQ(ierr);
3108     ierr = MatMult(mat,rvec,lvec);CHKERRQ(ierr);
3109     ierr = VecScale(lvec,-1.0);CHKERRQ(ierr);
3110     ierr = MatMultAdd(*mat_n,rvec,lvec,lvec);CHKERRQ(ierr);
3111     ierr = VecNorm(lvec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3112     ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
3113     ierr = VecDestroy(&rvec);CHKERRQ(ierr);
3114     ierr = VecDestroy(&lvec);CHKERRQ(ierr);
3115   }
3116 #endif
3117 
3118   /* assemble new additional is (if any) */
3119   if (nis) {
3120     PetscInt **temp_idxs,*count_is,j,psum;
3121 
3122     ierr = MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3123     ierr = PetscMalloc(nis*sizeof(PetscInt),&count_is);CHKERRQ(ierr);
3124     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3125     ptr_idxs = recv_buffer_idxs_is;
3126     psum = 0;
3127     for (i=0;i<n_recvs;i++) {
3128       for (j=0;j<nis;j++) {
3129         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3130         count_is[j] += plen; /* increment counting of buffer for j-th IS */
3131         psum += plen;
3132         ptr_idxs += plen+1; /* shift pointer to received data */
3133       }
3134     }
3135     ierr = PetscMalloc(nis*sizeof(PetscInt*),&temp_idxs);CHKERRQ(ierr);
3136     ierr = PetscMalloc(psum*sizeof(PetscInt),&temp_idxs[0]);CHKERRQ(ierr);
3137     for (i=1;i<nis;i++) {
3138       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
3139     }
3140     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3141     ptr_idxs = recv_buffer_idxs_is;
3142     for (i=0;i<n_recvs;i++) {
3143       for (j=0;j<nis;j++) {
3144         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3145         ierr = PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));CHKERRQ(ierr);
3146         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
3147         ptr_idxs += plen+1; /* shift pointer to received data */
3148       }
3149     }
3150     for (i=0;i<nis;i++) {
3151       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3152       ierr = PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);CHKERRQ(ierr);CHKERRQ(ierr);
3153       ierr = ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3154     }
3155     ierr = PetscFree(count_is);CHKERRQ(ierr);
3156     ierr = PetscFree(temp_idxs[0]);CHKERRQ(ierr);
3157     ierr = PetscFree(temp_idxs);CHKERRQ(ierr);
3158   }
3159   /* free workspace */
3160   ierr = PetscFree(recv_buffer_idxs);CHKERRQ(ierr);
3161   ierr = PetscFree(recv_buffer_vals);CHKERRQ(ierr);
3162   ierr = PetscFree(recv_buffer_idxs_is);CHKERRQ(ierr);
3163   ierr = MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3164   ierr = PetscFree(send_buffer_idxs);CHKERRQ(ierr);
3165   ierr = MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3166   if (isdense) {
3167     ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
3168     ierr = MatDenseRestoreArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3169   } else {
3170     /* ierr = PetscFree(send_buffer_vals);CHKERRQ(ierr); */
3171   }
3172   if (nis) {
3173     ierr = MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3174     ierr = PetscFree(send_buffer_idxs_is);CHKERRQ(ierr);
3175   }
3176   ierr = PetscFree(recv_req_idxs);CHKERRQ(ierr);
3177   ierr = PetscFree(recv_req_vals);CHKERRQ(ierr);
3178   ierr = PetscFree(recv_req_idxs_is);CHKERRQ(ierr);
3179   ierr = PetscFree(send_req_idxs);CHKERRQ(ierr);
3180   ierr = PetscFree(send_req_vals);CHKERRQ(ierr);
3181   ierr = PetscFree(send_req_idxs_is);CHKERRQ(ierr);
3182   ierr = PetscFree(ilengths_vals);CHKERRQ(ierr);
3183   ierr = PetscFree(ilengths_idxs);CHKERRQ(ierr);
3184   ierr = PetscFree(olengths_vals);CHKERRQ(ierr);
3185   ierr = PetscFree(olengths_idxs);CHKERRQ(ierr);
3186   ierr = PetscFree(onodes);CHKERRQ(ierr);
3187   if (nis) {
3188     ierr = PetscFree(ilengths_idxs_is);CHKERRQ(ierr);
3189     ierr = PetscFree(olengths_idxs_is);CHKERRQ(ierr);
3190     ierr = PetscFree(onodes_is);CHKERRQ(ierr);
3191   }
3192   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
3193   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
3194     ierr = MatDestroy(mat_n);CHKERRQ(ierr);
3195     for (i=0;i<nis;i++) {
3196       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3197     }
3198   }
3199   PetscFunctionReturn(0);
3200 }
3201 
3202 /* temporary hack into ksp private data structure */
3203 #include <petsc-private/kspimpl.h>
3204 
3205 #undef __FUNCT__
3206 #define __FUNCT__ "PCBDDCSetUpCoarseSolver"
3207 PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
3208 {
3209   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
3210   PC_IS                  *pcis = (PC_IS*)pc->data;
3211   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
3212   MatNullSpace           CoarseNullSpace=NULL;
3213   ISLocalToGlobalMapping coarse_islg;
3214   IS                     coarse_is,*isarray;
3215   PetscInt               i,im_active=-1,active_procs=-1;
3216   PetscInt               nis,nisdofs,nisneu;
3217   PC                     pc_temp;
3218   PCType                 coarse_pc_type;
3219   KSPType                coarse_ksp_type;
3220   PetscBool              multilevel_requested,multilevel_allowed;
3221   PetscBool              isredundant,isbddc,isnn,coarse_reuse;
3222   Mat                    t_coarse_mat_is;
3223   PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
3224   PetscMPIInt            all_procs;
3225   PetscBool              csin_ml,csin_ds,csin,csin_type_simple;
3226   PetscBool              compute_vecs = PETSC_FALSE;
3227   PetscErrorCode         ierr;
3228 
3229   PetscFunctionBegin;
3230   /* Assign global numbering to coarse dofs */
3231   if (pcbddc->new_primal_space || pcbddc->coarse_size == -1) { /* a new primal space is present or it is the first initialization, so recompute global numbering */
3232     compute_vecs = PETSC_TRUE;
3233     PetscInt ocoarse_size;
3234     ocoarse_size = pcbddc->coarse_size;
3235     ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
3236     ierr = PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);CHKERRQ(ierr);
3237     /* see if we can avoid some work */
3238     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
3239       if (ocoarse_size != pcbddc->coarse_size) { /* ...but with different size, so reset it and set reuse flag to false */
3240         ierr = KSPReset(pcbddc->coarse_ksp);CHKERRQ(ierr);
3241         coarse_reuse = PETSC_FALSE;
3242       } else { /* we can safely reuse already computed coarse matrix */
3243         coarse_reuse = PETSC_TRUE;
3244       }
3245     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
3246       coarse_reuse = PETSC_FALSE;
3247     }
3248     /* reset any subassembling information */
3249     ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3250     ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3251   } else { /* primal space is unchanged, so we can reuse coarse matrix */
3252     coarse_reuse = PETSC_TRUE;
3253   }
3254 
3255   /* count "active" (i.e. with positive local size) and "void" processes */
3256   im_active = !!(pcis->n);
3257   ierr = MPI_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3258   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);CHKERRQ(ierr);
3259   void_procs = all_procs-active_procs;
3260   csin_type_simple = PETSC_TRUE;
3261   if (pcbddc->current_level) {
3262     csin_ml = PETSC_TRUE;
3263     ncoarse_ml = void_procs;
3264     csin_ds = PETSC_TRUE;
3265     ncoarse_ds = void_procs;
3266     if (!void_procs) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
3267   } else {
3268     csin_ml = PETSC_FALSE;
3269     ncoarse_ml = all_procs;
3270     if (void_procs) {
3271       csin_ds = PETSC_TRUE;
3272       ncoarse_ds = void_procs;
3273       csin_type_simple = PETSC_FALSE;
3274     } else {
3275       csin_ds = PETSC_FALSE;
3276       ncoarse_ds = all_procs;
3277     }
3278   }
3279 
3280   /*
3281     test if we can go multilevel: three conditions must be satisfied:
3282     - we have not exceeded the number of levels requested
3283     - we can actually subassemble the active processes
3284     - we can find a suitable number of MPI processes where we can place the subassembled problem
3285   */
3286   multilevel_allowed = PETSC_FALSE;
3287   multilevel_requested = PETSC_FALSE;
3288   if (pcbddc->current_level < pcbddc->max_levels) {
3289     multilevel_requested = PETSC_TRUE;
3290     if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
3291       multilevel_allowed = PETSC_FALSE;
3292     } else {
3293       multilevel_allowed = PETSC_TRUE;
3294     }
3295   }
3296   /* determine number of process partecipating to coarse solver */
3297   if (multilevel_allowed) {
3298     ncoarse = ncoarse_ml;
3299     csin = csin_ml;
3300   } else {
3301     ncoarse = ncoarse_ds;
3302     csin = csin_ds;
3303   }
3304 
3305   /* creates temporary l2gmap and IS for coarse indexes */
3306   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);CHKERRQ(ierr);
3307   ierr = ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);CHKERRQ(ierr);
3308 
3309   /* creates temporary MATIS object for coarse matrix */
3310   ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_submat_dense);CHKERRQ(ierr);
3311 #if 0
3312   {
3313     PetscViewer viewer;
3314     char filename[256];
3315     sprintf(filename,"local_coarse_mat%d.m",PetscGlobalRank);
3316     ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
3317     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3318     ierr = MatView(coarse_submat_dense,viewer);CHKERRQ(ierr);
3319     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3320   }
3321 #endif
3322   ierr = MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,&t_coarse_mat_is);CHKERRQ(ierr);
3323   ierr = MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);CHKERRQ(ierr);
3324   ierr = MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3325   ierr = MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3326   ierr = MatDestroy(&coarse_submat_dense);CHKERRQ(ierr);
3327 
3328   /* compute dofs splitting and neumann boundaries for coarse dofs */
3329   if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal) ) { /* protects from unneded computations */
3330     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
3331     const PetscInt         *idxs;
3332     ISLocalToGlobalMapping tmap;
3333 
3334     /* create map between primal indices (in local representative ordering) and local primal numbering */
3335     ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);CHKERRQ(ierr);
3336     /* allocate space for temporary storage */
3337     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs);CHKERRQ(ierr);
3338     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs2);CHKERRQ(ierr);
3339     /* allocate for IS array */
3340     nisdofs = pcbddc->n_ISForDofsLocal;
3341     nisneu = !!pcbddc->NeumannBoundariesLocal;
3342     nis = nisdofs + nisneu;
3343     ierr = PetscMalloc(nis*sizeof(IS),&isarray);CHKERRQ(ierr);
3344     /* dofs splitting */
3345     for (i=0;i<nisdofs;i++) {
3346       /* ierr = ISView(pcbddc->ISForDofsLocal[i],0);CHKERRQ(ierr); */
3347       ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);CHKERRQ(ierr);
3348       ierr = ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3349       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3350       ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3351       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3352       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->ISForDofsLocal[i]),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3353       /* ierr = ISView(isarray[i],0);CHKERRQ(ierr); */
3354     }
3355     /* neumann boundaries */
3356     if (pcbddc->NeumannBoundariesLocal) {
3357       /* ierr = ISView(pcbddc->NeumannBoundariesLocal,0);CHKERRQ(ierr); */
3358       ierr = ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);CHKERRQ(ierr);
3359       ierr = ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3360       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3361       ierr = ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3362       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3363       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->NeumannBoundariesLocal),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);CHKERRQ(ierr);
3364       /* ierr = ISView(isarray[nisdofs],0);CHKERRQ(ierr); */
3365     }
3366     /* free memory */
3367     ierr = PetscFree(tidxs);CHKERRQ(ierr);
3368     ierr = PetscFree(tidxs2);CHKERRQ(ierr);
3369     ierr = ISLocalToGlobalMappingDestroy(&tmap);CHKERRQ(ierr);
3370   } else {
3371     nis = 0;
3372     nisdofs = 0;
3373     nisneu = 0;
3374     isarray = NULL;
3375   }
3376   /* destroy no longer needed map */
3377   ierr = ISLocalToGlobalMappingDestroy(&coarse_islg);CHKERRQ(ierr);
3378 
3379   /* restrict on coarse candidates (if needed) */
3380   coarse_mat_is = NULL;
3381   if (csin) {
3382     if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
3383       PetscInt j,tissize,*nisindices;
3384       PetscInt *coarse_candidates;
3385       const PetscInt* tisindices;
3386       /* get coarse candidates' ranks in pc communicator */
3387       ierr = PetscMalloc(all_procs*sizeof(PetscInt),&coarse_candidates);CHKERRQ(ierr);
3388       ierr = MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3389       for (i=0,j=0;i<all_procs;i++) {
3390         if (!coarse_candidates[i]) {
3391           coarse_candidates[j]=i;
3392           j++;
3393         }
3394       }
3395       if (j < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",j,ncoarse);
3396       /* get a suitable subassembling pattern */
3397       if (csin_type_simple) {
3398         PetscMPIInt rank;
3399         PetscInt    issize,isidx;
3400         ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
3401         if (im_active) {
3402           issize = 1;
3403           isidx = (PetscInt)rank;
3404         } else {
3405           issize = 0;
3406           isidx = -1;
3407         }
3408         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3409       } else {
3410         ierr = MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,PETSC_TRUE,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3411       }
3412       if (pcbddc->dbg_flag) {
3413         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3414         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");CHKERRQ(ierr);
3415         ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3416         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");CHKERRQ(ierr);
3417         for (i=0;i<j;i++) {
3418           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);CHKERRQ(ierr);
3419         }
3420         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");CHKERRQ(ierr);
3421         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3422       }
3423       /* shift the pattern on coarse candidates */
3424       ierr = ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);CHKERRQ(ierr);
3425       ierr = ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3426       ierr = PetscMalloc(tissize*sizeof(PetscInt),&nisindices);CHKERRQ(ierr);
3427       for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
3428       ierr = ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3429       ierr = ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);CHKERRQ(ierr);
3430       ierr = PetscFree(coarse_candidates);CHKERRQ(ierr);
3431     }
3432     if (pcbddc->dbg_flag) {
3433       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3434       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");CHKERRQ(ierr);
3435       ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3436       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3437     }
3438     /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
3439     ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
3440   } else {
3441     if (pcbddc->dbg_flag) {
3442       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3443       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");CHKERRQ(ierr);
3444       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3445     }
3446     ierr = PetscObjectReference((PetscObject)t_coarse_mat_is);CHKERRQ(ierr);
3447     coarse_mat_is = t_coarse_mat_is;
3448   }
3449 
3450   /* create local to global scatters for coarse problem */
3451   if (compute_vecs) {
3452     PetscInt lrows;
3453     ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
3454     if (coarse_mat_is) {
3455       ierr = MatGetLocalSize(coarse_mat_is,&lrows,NULL);CHKERRQ(ierr);
3456     } else {
3457       lrows = 0;
3458     }
3459     ierr = VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);CHKERRQ(ierr);
3460     ierr = VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);CHKERRQ(ierr);
3461     ierr = VecSetType(pcbddc->coarse_vec,VECSTANDARD);CHKERRQ(ierr);
3462     ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3463     ierr = VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3464   }
3465   ierr = ISDestroy(&coarse_is);CHKERRQ(ierr);
3466   ierr = MatDestroy(&t_coarse_mat_is);CHKERRQ(ierr);
3467 
3468   /* set defaults for coarse KSP and PC */
3469   if (multilevel_allowed) {
3470     coarse_ksp_type = KSPRICHARDSON;
3471     coarse_pc_type = PCBDDC;
3472   } else {
3473     coarse_ksp_type = KSPPREONLY;
3474     coarse_pc_type = PCREDUNDANT;
3475   }
3476 
3477   /* print some info if requested */
3478   if (pcbddc->dbg_flag) {
3479     if (!multilevel_allowed) {
3480       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3481       if (multilevel_requested) {
3482         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Not enough active processes on level %d (active processes %d, coarsening ratio %d)\n",pcbddc->current_level,active_procs,pcbddc->coarsening_ratio);CHKERRQ(ierr);
3483       } else if (pcbddc->max_levels) {
3484         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);CHKERRQ(ierr);
3485       }
3486       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3487     }
3488   }
3489 
3490   /* create the coarse KSP object only once with defaults */
3491   if (coarse_mat_is) {
3492     MatReuse coarse_mat_reuse;
3493     PetscViewer dbg_viewer = NULL;
3494     if (pcbddc->dbg_flag) {
3495       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
3496       ierr = PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3497     }
3498     if (!pcbddc->coarse_ksp) {
3499       char prefix[256],str_level[16];
3500       size_t len;
3501       ierr = KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);CHKERRQ(ierr);
3502       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3503       ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
3504       ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);CHKERRQ(ierr);
3505       ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3506       ierr = KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);CHKERRQ(ierr);
3507       ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3508       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3509       /* prefix */
3510       ierr = PetscStrcpy(prefix,"");CHKERRQ(ierr);
3511       ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
3512       if (!pcbddc->current_level) {
3513         ierr = PetscStrcpy(prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
3514         ierr = PetscStrcat(prefix,"pc_bddc_coarse_");CHKERRQ(ierr);
3515       } else {
3516         ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
3517         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
3518         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
3519         ierr = PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
3520         sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
3521         ierr = PetscStrcat(prefix,str_level);CHKERRQ(ierr);
3522       }
3523       ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);CHKERRQ(ierr);
3524       /* allow user customization */
3525       ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3526       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
3527     }
3528 
3529     /* get some info after set from options */
3530     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3531     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);CHKERRQ(ierr);
3532     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);CHKERRQ(ierr);
3533     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);CHKERRQ(ierr);
3534     if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
3535       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3536       isbddc = PETSC_FALSE;
3537     }
3538     if (isredundant) {
3539       KSP inner_ksp;
3540       PC inner_pc;
3541       ierr = PCRedundantGetKSP(pc_temp,&inner_ksp);CHKERRQ(ierr);
3542       ierr = KSPGetPC(inner_ksp,&inner_pc);CHKERRQ(ierr);
3543       ierr = PCFactorSetReuseFill(inner_pc,PETSC_TRUE);CHKERRQ(ierr);
3544     }
3545 
3546     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
3547     ierr = PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);CHKERRQ(ierr);
3548     ierr = PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);CHKERRQ(ierr);
3549     ierr = PCBDDCSetLevels(pc_temp,pcbddc->max_levels);CHKERRQ(ierr);
3550     if (nisdofs) {
3551       ierr = PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);CHKERRQ(ierr);
3552       for (i=0;i<nisdofs;i++) {
3553         ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3554       }
3555     }
3556     if (nisneu) {
3557       ierr = PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);CHKERRQ(ierr);
3558       ierr = ISDestroy(&isarray[nisdofs]);CHKERRQ(ierr);
3559     }
3560 
3561     /* assemble coarse matrix */
3562     if (coarse_reuse) {
3563       ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
3564       ierr = PetscObjectReference((PetscObject)coarse_mat);CHKERRQ(ierr);
3565       coarse_mat_reuse = MAT_REUSE_MATRIX;
3566     } else {
3567       coarse_mat_reuse = MAT_INITIAL_MATRIX;
3568     }
3569     if (isbddc || isnn) {
3570       if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
3571         ierr = MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,PETSC_TRUE,&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3572         if (pcbddc->dbg_flag) {
3573           ierr = PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3574           ierr = PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");CHKERRQ(ierr);
3575           ierr = ISView(pcbddc->coarse_subassembling,dbg_viewer);CHKERRQ(ierr);
3576           ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3577         }
3578       }
3579       ierr = MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);CHKERRQ(ierr);
3580     } else {
3581       ierr = MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);CHKERRQ(ierr);
3582     }
3583     ierr = MatDestroy(&coarse_mat_is);CHKERRQ(ierr);
3584 
3585     /* propagate symmetry info to coarse matrix */
3586     ierr = MatSetOption(coarse_mat,MAT_SYMMETRIC,pcbddc->issym);CHKERRQ(ierr);
3587     ierr = MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
3588 
3589     /* set operators */
3590     ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3591     if (pcbddc->dbg_flag) {
3592       ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3593     }
3594   } else { /* processes non partecipating to coarse solver (if any) */
3595     coarse_mat = 0;
3596   }
3597   ierr = PetscFree(isarray);CHKERRQ(ierr);
3598 #if 0
3599   {
3600     PetscViewer viewer;
3601     char filename[256];
3602     sprintf(filename,"coarse_mat.m");
3603     ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,&viewer);CHKERRQ(ierr);
3604     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3605     ierr = MatView(coarse_mat,viewer);CHKERRQ(ierr);
3606     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3607   }
3608 #endif
3609 
3610   /* Compute coarse null space (special handling by BDDC only) */
3611   if (pcbddc->NullSpace) {
3612     ierr = PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);CHKERRQ(ierr);
3613   }
3614 
3615   if (pcbddc->coarse_ksp) {
3616     Vec crhs,csol;
3617     PetscBool ispreonly;
3618     if (CoarseNullSpace) {
3619       if (isbddc) {
3620         ierr = PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);CHKERRQ(ierr);
3621       } else {
3622         ierr = KSPSetNullSpace(pcbddc->coarse_ksp,CoarseNullSpace);CHKERRQ(ierr);
3623       }
3624     }
3625     /* setup coarse ksp */
3626     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3627     ierr = KSPGetSolution(pcbddc->coarse_ksp,&csol);CHKERRQ(ierr);
3628     ierr = KSPGetRhs(pcbddc->coarse_ksp,&crhs);CHKERRQ(ierr);
3629     /* hack */
3630     if (!csol) {
3631       ierr = MatGetVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);CHKERRQ(ierr);
3632     }
3633     if (!crhs) {
3634       ierr = MatGetVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));CHKERRQ(ierr);
3635     }
3636     /* Check coarse problem if in debug mode or if solving with an iterative method */
3637     ierr = PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);CHKERRQ(ierr);
3638     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
3639       KSP       check_ksp;
3640       KSPType   check_ksp_type;
3641       PC        check_pc;
3642       Vec       check_vec,coarse_vec;
3643       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
3644       PetscInt  its;
3645       PetscBool compute_eigs;
3646       PetscReal *eigs_r,*eigs_c;
3647       PetscInt  neigs;
3648       const char *prefix;
3649 
3650       /* Create ksp object suitable for estimation of extreme eigenvalues */
3651       ierr = KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);CHKERRQ(ierr);
3652       ierr = KSPSetOperators(check_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3653       ierr = KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3654       if (ispreonly) {
3655         check_ksp_type = KSPPREONLY;
3656         compute_eigs = PETSC_FALSE;
3657       } else {
3658         check_ksp_type = KSPGMRES;
3659         compute_eigs = PETSC_TRUE;
3660       }
3661       ierr = KSPSetType(check_ksp,check_ksp_type);CHKERRQ(ierr);
3662       ierr = KSPSetComputeSingularValues(check_ksp,compute_eigs);CHKERRQ(ierr);
3663       ierr = KSPSetComputeEigenvalues(check_ksp,compute_eigs);CHKERRQ(ierr);
3664       ierr = KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);CHKERRQ(ierr);
3665       ierr = KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);CHKERRQ(ierr);
3666       ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
3667       ierr = KSPAppendOptionsPrefix(check_ksp,"check_");CHKERRQ(ierr);
3668       ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
3669       ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
3670       ierr = KSPGetPC(pcbddc->coarse_ksp,&check_pc);CHKERRQ(ierr);
3671       ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
3672       /* create random vec */
3673       ierr = KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);CHKERRQ(ierr);
3674       ierr = VecDuplicate(coarse_vec,&check_vec);CHKERRQ(ierr);
3675       ierr = VecSetRandom(check_vec,NULL);CHKERRQ(ierr);
3676       if (CoarseNullSpace) {
3677         ierr = MatNullSpaceRemove(CoarseNullSpace,check_vec);CHKERRQ(ierr);
3678       }
3679       ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3680       /* solve coarse problem */
3681       ierr = KSPSolve(check_ksp,coarse_vec,coarse_vec);CHKERRQ(ierr);
3682       if (CoarseNullSpace) {
3683         ierr = MatNullSpaceRemove(CoarseNullSpace,coarse_vec);CHKERRQ(ierr);
3684       }
3685       /* set eigenvalue estimation if preonly has not been requested */
3686       if (compute_eigs) {
3687         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_r);CHKERRQ(ierr);
3688         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_c);CHKERRQ(ierr);
3689         ierr = KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);CHKERRQ(ierr);
3690         lambda_max = eigs_r[neigs-1];
3691         lambda_min = eigs_r[0];
3692         if (pcbddc->use_coarse_estimates) {
3693           if (lambda_max>lambda_min) {
3694             ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3695             ierr = KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));CHKERRQ(ierr);
3696           }
3697         }
3698       }
3699 
3700       /* check coarse problem residual error */
3701       if (pcbddc->dbg_flag) {
3702         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
3703         ierr = PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3704         ierr = VecAXPY(check_vec,-1.0,coarse_vec);CHKERRQ(ierr);
3705         ierr = VecNorm(check_vec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3706         ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3707         ierr = VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);CHKERRQ(ierr);
3708         ierr = VecDestroy(&check_vec);CHKERRQ(ierr);
3709         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (%d)\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
3710         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);CHKERRQ(ierr);
3711         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);CHKERRQ(ierr);
3712         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);CHKERRQ(ierr);
3713         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);CHKERRQ(ierr);
3714         if (compute_eigs) {
3715           PetscReal lambda_max_s,lambda_min_s;
3716           ierr = KSPGetIterationNumber(check_ksp,&its);CHKERRQ(ierr);
3717           ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);CHKERRQ(ierr);
3718           ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem eigenvalues (estimated with %d iterations of %s): %1.6e %1.6e (%1.6e %1.6e)\n",its,check_ksp_type,lambda_min,lambda_max,lambda_min_s,lambda_max_s);CHKERRQ(ierr);
3719           for (i=0;i<neigs;i++) {
3720             ierr = PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);CHKERRQ(ierr);
3721           }
3722         }
3723         ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3724         ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3725       }
3726       ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
3727       if (compute_eigs) {
3728         ierr = PetscFree(eigs_r);CHKERRQ(ierr);
3729         ierr = PetscFree(eigs_c);CHKERRQ(ierr);
3730       }
3731     }
3732   }
3733   /* print additional info */
3734   if (pcbddc->dbg_flag) {
3735     /* waits until all processes reaches this point */
3736     ierr = PetscBarrier((PetscObject)pc);CHKERRQ(ierr);
3737     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);CHKERRQ(ierr);
3738     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3739   }
3740 
3741   /* free memory */
3742   ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
3743   ierr = MatDestroy(&coarse_mat);CHKERRQ(ierr);
3744   PetscFunctionReturn(0);
3745 }
3746 
3747 #undef __FUNCT__
3748 #define __FUNCT__ "PCBDDCComputePrimalNumbering"
3749 PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
3750 {
3751   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
3752   PC_IS*         pcis = (PC_IS*)pc->data;
3753   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
3754   PetscInt       i,coarse_size;
3755   PetscInt       *local_primal_indices;
3756   PetscErrorCode ierr;
3757 
3758   PetscFunctionBegin;
3759   /* Compute global number of coarse dofs */
3760   if (!pcbddc->primal_indices_local_idxs && pcbddc->local_primal_size) {
3761     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Local primal indices have not been created");
3762   }
3763   ierr = PCBDDCSubsetNumbering(PetscObjectComm((PetscObject)(pc->pmat)),matis->mapping,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,NULL,&coarse_size,&local_primal_indices);CHKERRQ(ierr);
3764 
3765   /* check numbering */
3766   if (pcbddc->dbg_flag) {
3767     PetscScalar coarsesum,*array;
3768     PetscBool set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;
3769 
3770     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3771     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3772     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");CHKERRQ(ierr);
3773     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
3774     ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
3775     for (i=0;i<pcbddc->local_primal_size;i++) {
3776       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
3777     }
3778     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
3779     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
3780     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3781     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3782     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3783     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3784     ierr = VecScatterEnd(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3785     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3786     for (i=0;i<pcis->n;i++) {
3787       if (array[i] == 1.0) {
3788         set_error = PETSC_TRUE;
3789         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a single process!\n",PetscGlobalRank,i);CHKERRQ(ierr);
3790       }
3791     }
3792     ierr = MPI_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3793     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3794     for (i=0;i<pcis->n;i++) {
3795       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
3796     }
3797     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3798     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3799     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3800     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3801     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
3802     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));CHKERRQ(ierr);
3803     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
3804       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");CHKERRQ(ierr);
3805       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3806       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
3807       for (i=0;i<pcbddc->local_primal_size;i++) {
3808         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%d]=%d (%d)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i]);
3809       }
3810       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3811     }
3812     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3813     if (set_error_reduced) {
3814       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
3815     }
3816   }
3817   /* get back data */
3818   *coarse_size_n = coarse_size;
3819   *local_primal_indices_n = local_primal_indices;
3820   PetscFunctionReturn(0);
3821 }
3822 
3823 #undef __FUNCT__
3824 #define __FUNCT__ "PCBDDCGlobalToLocal"
3825 PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
3826 {
3827   IS             localis_t;
3828   PetscInt       i,lsize,*idxs,n;
3829   PetscScalar    *vals;
3830   PetscErrorCode ierr;
3831 
3832   PetscFunctionBegin;
3833   /* get indices in local ordering exploiting local to global map */
3834   ierr = ISGetLocalSize(globalis,&lsize);CHKERRQ(ierr);
3835   ierr = PetscMalloc(lsize*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3836   for (i=0;i<lsize;i++) vals[i] = 1.0;
3837   ierr = ISGetIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
3838   ierr = VecSet(gwork,0.0);CHKERRQ(ierr);
3839   ierr = VecSet(lwork,0.0);CHKERRQ(ierr);
3840   if (idxs) { /* multilevel guard */
3841     ierr = VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
3842   }
3843   ierr = VecAssemblyBegin(gwork);CHKERRQ(ierr);
3844   ierr = ISRestoreIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
3845   ierr = PetscFree(vals);CHKERRQ(ierr);
3846   ierr = VecAssemblyEnd(gwork);CHKERRQ(ierr);
3847   /* now compute set in local ordering */
3848   ierr = VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3849   ierr = VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3850   ierr = VecGetArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
3851   ierr = VecGetSize(lwork,&n);CHKERRQ(ierr);
3852   for (i=0,lsize=0;i<n;i++) {
3853     if (PetscRealPart(vals[i]) > 0.5) {
3854       lsize++;
3855     }
3856   }
3857   ierr = PetscMalloc(lsize*sizeof(PetscInt),&idxs);CHKERRQ(ierr);
3858   for (i=0,lsize=0;i<n;i++) {
3859     if (PetscRealPart(vals[i]) > 0.5) {
3860       idxs[lsize++] = i;
3861     }
3862   }
3863   ierr = VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
3864   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);CHKERRQ(ierr);
3865   *localis = localis_t;
3866   PetscFunctionReturn(0);
3867 }
3868