xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 2bc0d5c782a271179e5f2d71b7baec8c7ad7b879)
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   if (!pcbddc->use_faces && !pcbddc->use_edges && !pcbddc->use_vertices) {
1417     pcbddc->use_vertices = PETSC_TRUE;
1418   }
1419   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,pcbddc->use_faces,pcbddc->use_edges,pcbddc->use_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
1420   /* HACKS (the two following code branches) */
1421   if (!ISForVertices && pcbddc->NullSpace && !pcbddc->user_ChangeOfBasisMatrix) {
1422     pcbddc->use_change_of_basis = PETSC_TRUE;
1423     pcbddc->use_change_on_faces = PETSC_FALSE;
1424   }
1425   if (pcbddc->NullSpace) {
1426     /* use_change_of_basis should be consistent among processors */
1427     PetscBool tbool = pcbddc->use_change_of_basis;
1428     ierr = MPI_Allreduce(&tbool,&(pcbddc->use_change_of_basis),1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1429   }
1430   /* print some info */
1431   if (pcbddc->dbg_flag) {
1432     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1433     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1434     i = 0;
1435     if (ISForVertices) {
1436       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
1437     }
1438     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
1439     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
1440     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
1441     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1442   }
1443   /* check if near null space is attached to global mat */
1444   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
1445   if (nearnullsp) {
1446     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1447     /* remove any stored info */
1448     ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
1449     ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1450     /* store information for BDDC solver reuse */
1451     ierr = PetscObjectReference((PetscObject)nearnullsp);CHKERRQ(ierr);
1452     pcbddc->onearnullspace = nearnullsp;
1453     ierr = PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1454     for (i=0;i<nnsp_size;i++) {
1455       ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);CHKERRQ(ierr);
1456     }
1457   } else { /* if near null space is not provided BDDC uses constants by default */
1458     nnsp_size = 0;
1459     nnsp_has_cnst = PETSC_TRUE;
1460   }
1461   /* get max number of constraints on a single cc */
1462   max_constraints = nnsp_size;
1463   if (nnsp_has_cnst) max_constraints++;
1464 
1465   /*
1466        Evaluate maximum storage size needed by the procedure
1467        - temp_indices will contain start index of each constraint stored as follows
1468        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
1469        - 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
1470        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
1471                                                                                                                                                          */
1472   total_counts = n_ISForFaces+n_ISForEdges;
1473   total_counts *= max_constraints;
1474   n_vertices = 0;
1475   if (ISForVertices) {
1476     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
1477   }
1478   total_counts += n_vertices;
1479   ierr = PetscMalloc1((total_counts+1),&temp_indices);CHKERRQ(ierr);
1480   ierr = PetscBTCreate(total_counts,&change_basis);CHKERRQ(ierr);
1481   total_counts = 0;
1482   max_size_of_constraint = 0;
1483   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1484     if (i<n_ISForEdges) {
1485       used_IS = &ISForEdges[i];
1486     } else {
1487       used_IS = &ISForFaces[i-n_ISForEdges];
1488     }
1489     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
1490     total_counts += j;
1491     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
1492   }
1493   total_counts *= max_constraints;
1494   total_counts += n_vertices;
1495   ierr = PetscMalloc1(total_counts,&temp_quadrature_constraint);CHKERRQ(ierr);
1496   ierr = PetscMalloc1(total_counts,&temp_indices_to_constraint);CHKERRQ(ierr);
1497   ierr = PetscMalloc1(total_counts,&temp_indices_to_constraint_B);CHKERRQ(ierr);
1498   /* get local part of global near null space vectors */
1499   ierr = PetscMalloc1(nnsp_size,&localnearnullsp);CHKERRQ(ierr);
1500   for (k=0;k<nnsp_size;k++) {
1501     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
1502     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1503     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1504   }
1505 
1506   /* whether or not to skip lapack calls */
1507   skip_lapack = PETSC_TRUE;
1508   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
1509 
1510   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
1511   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1512     PetscScalar temp_work;
1513 #if defined(PETSC_MISSING_LAPACK_GESVD)
1514     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
1515     ierr = PetscMalloc1(max_constraints*max_constraints,&correlation_mat);CHKERRQ(ierr);
1516     ierr = PetscMalloc1(max_constraints,&singular_vals);CHKERRQ(ierr);
1517     ierr = PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);CHKERRQ(ierr);
1518 #if defined(PETSC_USE_COMPLEX)
1519     ierr = PetscMalloc1(3*max_constraints,&rwork);CHKERRQ(ierr);
1520 #endif
1521     /* now we evaluate the optimal workspace using query with lwork=-1 */
1522     ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1523     ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
1524     lwork = -1;
1525     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1526 #if !defined(PETSC_USE_COMPLEX)
1527     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
1528 #else
1529     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
1530 #endif
1531     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1532     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
1533 #else /* on missing GESVD */
1534     /* SVD */
1535     PetscInt max_n,min_n;
1536     max_n = max_size_of_constraint;
1537     min_n = max_constraints;
1538     if (max_size_of_constraint < max_constraints) {
1539       min_n = max_size_of_constraint;
1540       max_n = max_constraints;
1541     }
1542     ierr = PetscMalloc1(min_n,&singular_vals);CHKERRQ(ierr);
1543 #if defined(PETSC_USE_COMPLEX)
1544     ierr = PetscMalloc1(5*min_n,&rwork);CHKERRQ(ierr);
1545 #endif
1546     /* now we evaluate the optimal workspace using query with lwork=-1 */
1547     lwork = -1;
1548     ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
1549     ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
1550     ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
1551     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1552 #if !defined(PETSC_USE_COMPLEX)
1553     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));
1554 #else
1555     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));
1556 #endif
1557     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1558     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
1559 #endif /* on missing GESVD */
1560     /* Allocate optimal workspace */
1561     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
1562     ierr = PetscMalloc1((PetscInt)lwork,&work);CHKERRQ(ierr);
1563   }
1564   /* Now we can loop on constraining sets */
1565   total_counts = 0;
1566   temp_indices[0] = 0;
1567   /* vertices */
1568   if (ISForVertices) {
1569     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1570     if (nnsp_has_cnst) { /* consider all vertices */
1571       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,n_vertices*sizeof(PetscInt));CHKERRQ(ierr);
1572       for (i=0;i<n_vertices;i++) {
1573         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1574         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1575         total_counts++;
1576       }
1577     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
1578       PetscBool used_vertex;
1579       for (i=0;i<n_vertices;i++) {
1580         used_vertex = PETSC_FALSE;
1581         k = 0;
1582         while (!used_vertex && k<nnsp_size) {
1583           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1584           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
1585             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
1586             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1587             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1588             total_counts++;
1589             used_vertex = PETSC_TRUE;
1590           }
1591           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1592           k++;
1593         }
1594       }
1595     }
1596     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1597     n_vertices = total_counts;
1598   }
1599 
1600   /* edges and faces */
1601   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1602     if (i<n_ISForEdges) {
1603       used_IS = &ISForEdges[i];
1604       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
1605     } else {
1606       used_IS = &ISForFaces[i-n_ISForEdges];
1607       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
1608     }
1609     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
1610     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
1611     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
1612     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1613     /* change of basis should not be performed on local periodic nodes */
1614     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
1615     if (nnsp_has_cnst) {
1616       PetscScalar quad_value;
1617       temp_constraints++;
1618       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
1619       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
1620       for (j=0;j<size_of_constraint;j++) {
1621         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
1622       }
1623       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1624       total_counts++;
1625     }
1626     for (k=0;k<nnsp_size;k++) {
1627       PetscReal real_value;
1628       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1629       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
1630       for (j=0;j<size_of_constraint;j++) {
1631         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
1632       }
1633       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1634       /* check if array is null on the connected component */
1635       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1636       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_one));
1637       if (real_value > 0.0) { /* keep indices and values */
1638         temp_constraints++;
1639         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1640         total_counts++;
1641       }
1642     }
1643     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1644     valid_constraints = temp_constraints;
1645     /* 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 */
1646     if (!pcbddc->use_nnsp_true && temp_constraints) {
1647       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
1648 
1649 #if defined(PETSC_MISSING_LAPACK_GESVD)
1650       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
1651          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
1652          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
1653             the constraints basis will differ (by a complex factor with absolute value equal to 1)
1654             from that computed using LAPACKgesvd
1655          -> This is due to a different computation of eigenvectors in LAPACKheev
1656          -> The quality of the POD-computed basis will be the same */
1657       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
1658       /* Store upper triangular part of correlation matrix */
1659       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1660       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1661       for (j=0;j<temp_constraints;j++) {
1662         for (k=0;k<j+1;k++) {
1663           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));
1664         }
1665       }
1666       /* compute eigenvalues and eigenvectors of correlation matrix */
1667       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1668       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
1669 #if !defined(PETSC_USE_COMPLEX)
1670       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
1671 #else
1672       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
1673 #endif
1674       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1675       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
1676       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
1677       j=0;
1678       while (j < temp_constraints && singular_vals[j] < tol) j++;
1679       total_counts=total_counts-j;
1680       valid_constraints = temp_constraints-j;
1681       /* scale and copy POD basis into used quadrature memory */
1682       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1683       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1684       ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
1685       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1686       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
1687       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1688       if (j<temp_constraints) {
1689         PetscInt ii;
1690         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
1691         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1692         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));
1693         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1694         for (k=0;k<temp_constraints-j;k++) {
1695           for (ii=0;ii<size_of_constraint;ii++) {
1696             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];
1697           }
1698         }
1699       }
1700 #else  /* on missing GESVD */
1701       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1702       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1703       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1704       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1705 #if !defined(PETSC_USE_COMPLEX)
1706       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));
1707 #else
1708       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));
1709 #endif
1710       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
1711       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1712       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
1713       k = temp_constraints;
1714       if (k > size_of_constraint) k = size_of_constraint;
1715       j = 0;
1716       while (j < k && singular_vals[k-j-1] < tol) j++;
1717       total_counts = total_counts-temp_constraints+k-j;
1718       valid_constraints = k-j;
1719 #endif /* on missing GESVD */
1720     }
1721     /* setting change_of_basis flag is safe now */
1722     if (boolforchange) {
1723       for (j=0;j<valid_constraints;j++) {
1724         PetscBTSet(change_basis,total_counts-j-1);
1725       }
1726     }
1727   }
1728   /* free index sets of faces, edges and vertices */
1729   for (i=0;i<n_ISForFaces;i++) {
1730     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1731   }
1732   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1733   for (i=0;i<n_ISForEdges;i++) {
1734     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1735   }
1736   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1737   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1738   /* map temp_indices_to_constraint in boundary numbering */
1739   ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,temp_indices[total_counts],temp_indices_to_constraint,&i,temp_indices_to_constraint_B);CHKERRQ(ierr);
1740   if (i != temp_indices[total_counts]) {
1741     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for constraints indices %d != %d\n",temp_indices[total_counts],i);
1742   }
1743 
1744   /* free workspace */
1745   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1746     ierr = PetscFree(work);CHKERRQ(ierr);
1747 #if defined(PETSC_USE_COMPLEX)
1748     ierr = PetscFree(rwork);CHKERRQ(ierr);
1749 #endif
1750     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1751 #if defined(PETSC_MISSING_LAPACK_GESVD)
1752     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1753     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1754 #endif
1755   }
1756   for (k=0;k<nnsp_size;k++) {
1757     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1758   }
1759   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1760 
1761   /* set quantities in pcbddc data structure and store previous primal size */
1762   /* n_vertices defines the number of subdomain corners in the primal space */
1763   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1764   olocal_primal_size = pcbddc->local_primal_size;
1765   pcbddc->local_primal_size = total_counts;
1766   pcbddc->n_vertices = n_vertices;
1767   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
1768 
1769   /* Create constraint matrix */
1770   /* The constraint matrix is used to compute the l2g map of primal dofs */
1771   /* so we need to set it up properly either with or without change of basis */
1772   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1773   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1774   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
1775   /* array to compute a local numbering of constraints : vertices first then constraints */
1776   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_numbering);CHKERRQ(ierr);
1777   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
1778   /* 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 */
1779   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_minloc);CHKERRQ(ierr);
1780   /* auxiliary stuff for basis change */
1781   ierr = PetscMalloc1(max_size_of_constraint,&global_indices);CHKERRQ(ierr);
1782   ierr = PetscBTCreate(pcis->n_B,&touched);CHKERRQ(ierr);
1783 
1784   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
1785   total_primal_vertices=0;
1786   for (i=0;i<pcbddc->local_primal_size;i++) {
1787     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1788     if (size_of_constraint == 1) {
1789       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]]);CHKERRQ(ierr);
1790       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
1791       aux_primal_minloc[total_primal_vertices]=0;
1792       total_primal_vertices++;
1793     } else if (PetscBTLookup(change_basis,i)) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
1794       PetscInt min_loc,min_index;
1795       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
1796       /* find first untouched local node */
1797       k = 0;
1798       while (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) k++;
1799       min_index = global_indices[k];
1800       min_loc = k;
1801       /* search the minimum among global nodes already untouched on the cc */
1802       for (k=1;k<size_of_constraint;k++) {
1803         /* there can be more than one constraint on a single connected component */
1804         if (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k]) && min_index > global_indices[k]) {
1805           min_index = global_indices[k];
1806           min_loc = k;
1807         }
1808       }
1809       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]+min_loc]);CHKERRQ(ierr);
1810       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
1811       aux_primal_minloc[total_primal_vertices]=min_loc;
1812       total_primal_vertices++;
1813     }
1814   }
1815   /* determine if a QR strategy is needed for change of basis */
1816   qr_needed = PETSC_FALSE;
1817   ierr = PetscBTCreate(pcbddc->local_primal_size,&qr_needed_idx);CHKERRQ(ierr);
1818   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1819     if (PetscBTLookup(change_basis,i)) {
1820       size_of_constraint = temp_indices[i+1]-temp_indices[i];
1821       j = 0;
1822       for (k=0;k<size_of_constraint;k++) {
1823         if (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) {
1824           j++;
1825         }
1826       }
1827       /* found more than one primal dof on the cc */
1828       if (j > 1) {
1829         PetscBTSet(qr_needed_idx,i);
1830         qr_needed = PETSC_TRUE;
1831       }
1832     }
1833   }
1834   /* free workspace */
1835   ierr = PetscFree(global_indices);CHKERRQ(ierr);
1836 
1837   /* permute indices in order to have a sorted set of vertices */
1838   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);CHKERRQ(ierr);
1839 
1840   /* nonzero structure of constraint matrix */
1841   ierr = PetscMalloc1(pcbddc->local_primal_size,&nnz);CHKERRQ(ierr);
1842   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
1843   j=total_primal_vertices;
1844   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1845     if (!PetscBTLookup(change_basis,i)) {
1846       nnz[j]=temp_indices[i+1]-temp_indices[i];
1847       j++;
1848     }
1849   }
1850   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1851   ierr = PetscFree(nnz);CHKERRQ(ierr);
1852   /* set values in constraint matrix */
1853   for (i=0;i<total_primal_vertices;i++) {
1854     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
1855   }
1856   total_counts = total_primal_vertices;
1857   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1858     if (!PetscBTLookup(change_basis,i)) {
1859       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1860       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);
1861       total_counts++;
1862     }
1863   }
1864   /* assembling */
1865   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1866   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1867   /*
1868   ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
1869   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
1870   */
1871   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1872   if (pcbddc->use_change_of_basis) {
1873     /* dual and primal dofs on a single cc */
1874     PetscInt     dual_dofs,primal_dofs;
1875     /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
1876     PetscInt     primal_counter;
1877     /* working stuff for GEQRF */
1878     PetscScalar  *qr_basis,*qr_tau = NULL,*qr_work,lqr_work_t;
1879     PetscBLASInt lqr_work;
1880     /* working stuff for UNGQR */
1881     PetscScalar  *gqr_work,lgqr_work_t;
1882     PetscBLASInt lgqr_work;
1883     /* working stuff for TRTRS */
1884     PetscScalar  *trs_rhs;
1885     PetscBLASInt Blas_NRHS;
1886     /* pointers for values insertion into change of basis matrix */
1887     PetscInt     *start_rows,*start_cols;
1888     PetscScalar  *start_vals;
1889     /* working stuff for values insertion */
1890     PetscBT      is_primal;
1891 
1892     /* change of basis acts on local interfaces -> dimension is n_B x n_B */
1893     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1894     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1895     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1896     /* work arrays */
1897     ierr = PetscMalloc1(pcis->n_B,&nnz);CHKERRQ(ierr);
1898     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
1899     /* nonzeros per row */
1900     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1901       if (PetscBTLookup(change_basis,i)) {
1902         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1903         if (PetscBTLookup(qr_needed_idx,i)) {
1904           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1905         } else {
1906           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = 2;
1907           /* get local primal index on the cc */
1908           j = 0;
1909           while (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+j])) j++;
1910           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1911         }
1912       }
1913     }
1914     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1915     ierr = PetscFree(nnz);CHKERRQ(ierr);
1916     /* Set initial identity in the matrix */
1917     for (i=0;i<pcis->n_B;i++) {
1918       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1919     }
1920 
1921     if (pcbddc->dbg_flag) {
1922       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1923       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
1924     }
1925 
1926 
1927     /* Now we loop on the constraints which need a change of basis */
1928     /*
1929        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
1930        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)
1931 
1932        Basic blocks of change of basis matrix T computed
1933 
1934           - Using the following block transformation if there is only a primal dof on the cc
1935             (in the example, primal dof is the last one of the edge in LOCAL ordering
1936              in this code, primal dof is the first one of the edge in GLOBAL ordering)
1937             | 1        0   ...        0     1 |
1938             | 0        1   ...        0     1 |
1939             |              ...                |
1940             | 0        ...            1     1 |
1941             | -s_1/s_n ...    -s_{n-1}/-s_n 1 |
1942 
1943           - via QR decomposition of constraints otherwise
1944     */
1945     if (qr_needed) {
1946       /* space to store Q */
1947       ierr = PetscMalloc1((max_size_of_constraint)*(max_size_of_constraint),&qr_basis);CHKERRQ(ierr);
1948       /* first we issue queries for optimal work */
1949       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1950       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1951       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1952       lqr_work = -1;
1953       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
1954       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
1955       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
1956       ierr = PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);CHKERRQ(ierr);
1957       lgqr_work = -1;
1958       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1959       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
1960       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
1961       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1962       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
1963       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
1964       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
1965       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
1966       ierr = PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);CHKERRQ(ierr);
1967       /* array to store scaling factors for reflectors */
1968       ierr = PetscMalloc1(max_constraints,&qr_tau);CHKERRQ(ierr);
1969       /* array to store rhs and solution of triangular solver */
1970       ierr = PetscMalloc1(max_constraints*max_constraints,&trs_rhs);CHKERRQ(ierr);
1971       /* allocating workspace for check */
1972       if (pcbddc->dbg_flag) {
1973         ierr = PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&work);CHKERRQ(ierr);
1974       }
1975     }
1976     /* array to store whether a node is primal or not */
1977     ierr = PetscBTCreate(pcis->n_B,&is_primal);CHKERRQ(ierr);
1978     ierr = PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);CHKERRQ(ierr);
1979     ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,aux_primal_numbering,&i,aux_primal_numbering_B);CHKERRQ(ierr);
1980     if (i != total_primal_vertices) {
1981       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",total_primal_vertices,i);
1982     }
1983     for (i=0;i<total_primal_vertices;i++) {
1984       ierr = PetscBTSet(is_primal,aux_primal_numbering_B[i]);CHKERRQ(ierr);
1985     }
1986     ierr = PetscFree(aux_primal_numbering_B);CHKERRQ(ierr);
1987 
1988     /* loop on constraints and see whether or not they need a change of basis and compute it */
1989     /* -> using implicit ordering contained in temp_indices data */
1990     total_counts = pcbddc->n_vertices;
1991     primal_counter = total_counts;
1992     while (total_counts<pcbddc->local_primal_size) {
1993       primal_dofs = 1;
1994       if (PetscBTLookup(change_basis,total_counts)) {
1995         /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
1996         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]]) {
1997           primal_dofs++;
1998         }
1999         /* get constraint info */
2000         size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
2001         dual_dofs = size_of_constraint-primal_dofs;
2002 
2003         if (pcbddc->dbg_flag) {
2004           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);
2005         }
2006 
2007         if (primal_dofs > 1) { /* QR */
2008 
2009           /* copy quadrature constraints for change of basis check */
2010           if (pcbddc->dbg_flag) {
2011             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2012           }
2013           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
2014           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2015 
2016           /* compute QR decomposition of constraints */
2017           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2018           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2019           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2020           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2021           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
2022           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
2023           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2024 
2025           /* explictly compute R^-T */
2026           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
2027           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
2028           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2029           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
2030           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2031           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2032           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2033           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
2034           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
2035           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2036 
2037           /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
2038           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2039           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2040           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2041           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2042           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2043           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
2044           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
2045           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2046 
2047           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
2048              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
2049              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
2050           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2051           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2052           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2053           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2054           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2055           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
2056           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2057           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));
2058           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2059           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2060 
2061           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
2062           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
2063           /* insert cols for primal dofs */
2064           for (j=0;j<primal_dofs;j++) {
2065             start_vals = &qr_basis[j*size_of_constraint];
2066             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
2067             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2068           }
2069           /* insert cols for dual dofs */
2070           for (j=0,k=0;j<dual_dofs;k++) {
2071             if (!PetscBTLookup(is_primal,temp_indices_to_constraint_B[temp_indices[total_counts]+k])) {
2072               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
2073               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2074               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2075               j++;
2076             }
2077           }
2078 
2079           /* check change of basis */
2080           if (pcbddc->dbg_flag) {
2081             PetscInt   ii,jj;
2082             PetscBool valid_qr=PETSC_TRUE;
2083             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
2084             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2085             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
2086             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2087             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
2088             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
2089             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2090             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));
2091             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2092             for (jj=0;jj<size_of_constraint;jj++) {
2093               for (ii=0;ii<primal_dofs;ii++) {
2094                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
2095                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
2096               }
2097             }
2098             if (!valid_qr) {
2099               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");CHKERRQ(ierr);
2100               for (jj=0;jj<size_of_constraint;jj++) {
2101                 for (ii=0;ii<primal_dofs;ii++) {
2102                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
2103                     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]));
2104                   }
2105                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
2106                     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]));
2107                   }
2108                 }
2109               }
2110             } else {
2111               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");CHKERRQ(ierr);
2112             }
2113           }
2114         } else { /* simple transformation block */
2115           PetscInt row,col;
2116           PetscScalar val;
2117           for (j=0;j<size_of_constraint;j++) {
2118             row = temp_indices_to_constraint_B[temp_indices[total_counts]+j];
2119             if (!PetscBTLookup(is_primal,row)) {
2120               col = temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2121               ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);CHKERRQ(ierr);
2122               ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,col,1.0,INSERT_VALUES);CHKERRQ(ierr);
2123             } else {
2124               for (k=0;k<size_of_constraint;k++) {
2125                 col = temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2126                 if (row != col) {
2127                   val = -temp_quadrature_constraint[temp_indices[total_counts]+k]/temp_quadrature_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2128                 } else {
2129                   val = 1.0;
2130                 }
2131                 ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,col,val,INSERT_VALUES);CHKERRQ(ierr);
2132               }
2133             }
2134           }
2135           if (pcbddc->dbg_flag) {
2136             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");CHKERRQ(ierr);
2137           }
2138         }
2139         /* increment primal counter */
2140         primal_counter += primal_dofs;
2141       } else {
2142         if (pcbddc->dbg_flag) {
2143           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);
2144         }
2145       }
2146       /* increment constraint counter total_counts */
2147       total_counts += primal_dofs;
2148     }
2149 
2150     /* free workspace */
2151     if (qr_needed) {
2152       if (pcbddc->dbg_flag) {
2153         ierr = PetscFree(work);CHKERRQ(ierr);
2154       }
2155       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
2156       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
2157       ierr = PetscFree(qr_work);CHKERRQ(ierr);
2158       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
2159       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
2160     }
2161     ierr = PetscBTDestroy(&is_primal);CHKERRQ(ierr);
2162     /* assembling */
2163     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2164     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2165     /*
2166     ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
2167     ierr = MatView(pcbddc->ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
2168     */
2169   }
2170   /* Change of basis as provided by the user in local numbering (internal and boundary) or boundary only */
2171   if (pcbddc->user_ChangeOfBasisMatrix) {
2172     PetscInt rows,cols;
2173     ierr = MatGetSize(pcbddc->user_ChangeOfBasisMatrix,&rows,&cols);CHKERRQ(ierr);
2174     if (rows == pcis->n && cols == pcis->n) {
2175       ierr = MatGetSubMatrix(pcbddc->user_ChangeOfBasisMatrix,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2176     } else {
2177       ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2178       pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
2179     }
2180   }
2181 
2182   /* get indices in local ordering for vertices and constraints */
2183   if (olocal_primal_size == pcbddc->local_primal_size) { /* if this is true, I need to check if a new primal space has been introduced */
2184     ierr = PetscMalloc1(olocal_primal_size,&oprimal_indices_local_idxs);CHKERRQ(ierr);
2185     ierr = PetscMemcpy(oprimal_indices_local_idxs,pcbddc->primal_indices_local_idxs,olocal_primal_size*sizeof(PetscInt));CHKERRQ(ierr);
2186   }
2187   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2188   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2189   ierr = PetscMalloc1(pcbddc->local_primal_size,&pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2190   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&i,&aux_primal_numbering);CHKERRQ(ierr);
2191   ierr = PetscMemcpy(pcbddc->primal_indices_local_idxs,aux_primal_numbering,i*sizeof(PetscInt));CHKERRQ(ierr);
2192   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2193   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&j,&aux_primal_numbering);CHKERRQ(ierr);
2194   ierr = PetscMemcpy(&pcbddc->primal_indices_local_idxs[i],aux_primal_numbering,j*sizeof(PetscInt));CHKERRQ(ierr);
2195   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2196   /* set quantities in PCBDDC data struct */
2197   pcbddc->n_actual_vertices = i;
2198   /* check if a new primal space has been introduced */
2199   pcbddc->new_primal_space_local = PETSC_TRUE;
2200   if (olocal_primal_size == pcbddc->local_primal_size) {
2201     ierr = PetscMemcmp(pcbddc->primal_indices_local_idxs,oprimal_indices_local_idxs,olocal_primal_size,&pcbddc->new_primal_space_local);CHKERRQ(ierr);
2202     pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
2203     ierr = PetscFree(oprimal_indices_local_idxs);CHKERRQ(ierr);
2204   }
2205   /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
2206   ierr = MPI_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
2207 
2208   /* flush dbg viewer */
2209   if (pcbddc->dbg_flag) {
2210     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2211   }
2212 
2213   /* free workspace */
2214   ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2215   ierr = PetscBTDestroy(&qr_needed_idx);CHKERRQ(ierr);
2216   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
2217   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2218   ierr = PetscBTDestroy(&change_basis);CHKERRQ(ierr);
2219   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
2220   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
2221   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
2222   PetscFunctionReturn(0);
2223 }
2224 
2225 #undef __FUNCT__
2226 #define __FUNCT__ "PCBDDCAnalyzeInterface"
2227 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
2228 {
2229   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
2230   PC_IS       *pcis = (PC_IS*)pc->data;
2231   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
2232   PetscInt    ierr,i,vertex_size;
2233   PetscViewer viewer=pcbddc->dbg_viewer;
2234 
2235   PetscFunctionBegin;
2236   /* Reset previously computed graph */
2237   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
2238   /* Init local Graph struct */
2239   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
2240 
2241   /* Check validity of the csr graph passed in by the user */
2242   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
2243     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
2244   }
2245 
2246   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
2247   if (pcbddc->use_local_adj && (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy)) {
2248     Mat mat_adj;
2249     const PetscInt *xadj,*adjncy;
2250     PetscBool flg_row=PETSC_TRUE;
2251 
2252     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
2253     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2254     if (!flg_row) {
2255       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
2256     }
2257     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
2258     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2259     if (!flg_row) {
2260       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2261     }
2262     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
2263     pcbddc->deluxe_compute_rowadj = PETSC_FALSE;
2264   }
2265 
2266   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
2267   vertex_size = 1;
2268   if (pcbddc->user_provided_isfordofs) {
2269     if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
2270       ierr = PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2271       for (i=0;i<pcbddc->n_ISForDofs;i++) {
2272         ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2273         ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
2274       }
2275       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
2276       pcbddc->n_ISForDofs = 0;
2277       ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
2278     }
2279     /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
2280     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
2281   } else {
2282     if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
2283       ierr = MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);CHKERRQ(ierr);
2284       ierr = PetscMalloc(pcbddc->n_ISForDofsLocal*sizeof(IS),&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2285       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
2286         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2287       }
2288     }
2289   }
2290 
2291   /* Setup of Graph */
2292   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
2293     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
2294   }
2295   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
2296     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
2297   }
2298   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices);
2299 
2300   /* Graph's connected components analysis */
2301   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
2302 
2303   /* print some info to stdout */
2304   if (pcbddc->dbg_flag) {
2305     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
2306   }
2307 
2308   /* mark topography has done */
2309   pcbddc->recompute_topography = PETSC_FALSE;
2310   PetscFunctionReturn(0);
2311 }
2312 
2313 #undef __FUNCT__
2314 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
2315 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt **vertices_idx)
2316 {
2317   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2318   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
2319   PetscErrorCode ierr;
2320 
2321   PetscFunctionBegin;
2322   n = 0;
2323   vertices = 0;
2324   if (pcbddc->ConstraintMatrix) {
2325     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
2326     for (i=0;i<local_primal_size;i++) {
2327       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2328       if (size_of_constraint == 1) n++;
2329       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2330     }
2331     if (vertices_idx) {
2332       ierr = PetscMalloc1(n,&vertices);CHKERRQ(ierr);
2333       n = 0;
2334       for (i=0;i<local_primal_size;i++) {
2335         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2336         if (size_of_constraint == 1) {
2337           vertices[n++]=row_cmat_indices[0];
2338         }
2339         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2340       }
2341     }
2342   }
2343   *n_vertices = n;
2344   if (vertices_idx) *vertices_idx = vertices;
2345   PetscFunctionReturn(0);
2346 }
2347 
2348 #undef __FUNCT__
2349 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
2350 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt **constraints_idx)
2351 {
2352   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2353   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
2354   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
2355   PetscBT        touched;
2356   PetscErrorCode ierr;
2357 
2358     /* This function assumes that the number of local constraints per connected component
2359        is not greater than the number of nodes defined for the connected component
2360        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
2361   PetscFunctionBegin;
2362   n = 0;
2363   constraints_index = 0;
2364   if (pcbddc->ConstraintMatrix) {
2365     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
2366     max_size_of_constraint = 0;
2367     for (i=0;i<local_primal_size;i++) {
2368       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2369       if (size_of_constraint > 1) {
2370         n++;
2371       }
2372       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
2373       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2374     }
2375     if (constraints_idx) {
2376       ierr = PetscMalloc1(n,&constraints_index);CHKERRQ(ierr);
2377       ierr = PetscMalloc1(max_size_of_constraint,&row_cmat_global_indices);CHKERRQ(ierr);
2378       ierr = PetscBTCreate(local_size,&touched);CHKERRQ(ierr);
2379       n = 0;
2380       for (i=0;i<local_primal_size;i++) {
2381         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2382         if (size_of_constraint > 1) {
2383           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
2384           /* find first untouched local node */
2385           j = 0;
2386           while (PetscBTLookup(touched,row_cmat_indices[j])) j++;
2387           min_index = row_cmat_global_indices[j];
2388           min_loc = j;
2389           /* search the minimum among nodes not yet touched on the connected component
2390              since there can be more than one constraint on a single cc */
2391           for (j=1;j<size_of_constraint;j++) {
2392             if (!PetscBTLookup(touched,row_cmat_indices[j]) && min_index > row_cmat_global_indices[j]) {
2393               min_index = row_cmat_global_indices[j];
2394               min_loc = j;
2395             }
2396           }
2397           ierr = PetscBTSet(touched,row_cmat_indices[min_loc]);CHKERRQ(ierr);
2398           constraints_index[n++] = row_cmat_indices[min_loc];
2399         }
2400         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2401       }
2402       ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2403       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
2404     }
2405   }
2406   *n_constraints = n;
2407   if (constraints_idx) *constraints_idx = constraints_index;
2408   PetscFunctionReturn(0);
2409 }
2410 
2411 /* the next two functions has been adapted from pcis.c */
2412 #undef __FUNCT__
2413 #define __FUNCT__ "PCBDDCApplySchur"
2414 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2415 {
2416   PetscErrorCode ierr;
2417   PC_IS          *pcis = (PC_IS*)(pc->data);
2418 
2419   PetscFunctionBegin;
2420   if (!vec2_B) { vec2_B = v; }
2421   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2422   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
2423   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2424   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
2425   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2426   PetscFunctionReturn(0);
2427 }
2428 
2429 #undef __FUNCT__
2430 #define __FUNCT__ "PCBDDCApplySchurTranspose"
2431 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2432 {
2433   PetscErrorCode ierr;
2434   PC_IS          *pcis = (PC_IS*)(pc->data);
2435 
2436   PetscFunctionBegin;
2437   if (!vec2_B) { vec2_B = v; }
2438   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2439   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
2440   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2441   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
2442   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2443   PetscFunctionReturn(0);
2444 }
2445 
2446 #undef __FUNCT__
2447 #define __FUNCT__ "PCBDDCSubsetNumbering"
2448 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[])
2449 {
2450   Vec            local_vec,global_vec;
2451   IS             seqis,paris;
2452   VecScatter     scatter_ctx;
2453   PetscScalar    *array;
2454   PetscInt       *temp_global_dofs;
2455   PetscScalar    globalsum;
2456   PetscInt       i,j,s;
2457   PetscInt       nlocals,first_index,old_index,max_local;
2458   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
2459   PetscMPIInt    *dof_sizes,*dof_displs;
2460   PetscBool      first_found;
2461   PetscErrorCode ierr;
2462 
2463   PetscFunctionBegin;
2464   /* mpi buffers */
2465   ierr = MPI_Comm_size(comm,&size_prec_comm);CHKERRQ(ierr);
2466   ierr = MPI_Comm_rank(comm,&rank_prec_comm);CHKERRQ(ierr);
2467   j = ( !rank_prec_comm ? size_prec_comm : 0);
2468   ierr = PetscMalloc1(j,&dof_sizes);CHKERRQ(ierr);
2469   ierr = PetscMalloc1(j,&dof_displs);CHKERRQ(ierr);
2470   /* get maximum size of subset */
2471   ierr = PetscMalloc1(n_local_dofs,&temp_global_dofs);CHKERRQ(ierr);
2472   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
2473   max_local = 0;
2474   for (i=0;i<n_local_dofs;i++) {
2475     if (max_local < temp_global_dofs[i] ) {
2476       max_local = temp_global_dofs[i];
2477     }
2478   }
2479   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
2480   max_global++;
2481   max_local = 0;
2482   for (i=0;i<n_local_dofs;i++) {
2483     if (max_local < local_dofs[i] ) {
2484       max_local = local_dofs[i];
2485     }
2486   }
2487   max_local++;
2488   /* allocate workspace */
2489   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
2490   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
2491   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
2492   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
2493   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
2494   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
2495   /* create scatter */
2496   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
2497   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
2498   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
2499   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
2500   ierr = ISDestroy(&paris);CHKERRQ(ierr);
2501   /* init array */
2502   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
2503   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2504   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2505   if (local_dofs_mult) {
2506     for (i=0;i<n_local_dofs;i++) {
2507       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
2508     }
2509   } else {
2510     for (i=0;i<n_local_dofs;i++) {
2511       array[local_dofs[i]]=1.0;
2512     }
2513   }
2514   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2515   /* scatter into global vec and get total number of global dofs */
2516   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2517   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2518   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
2519   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
2520   /* Fill global_vec with cumulative function for global numbering */
2521   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
2522   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
2523   nlocals = 0;
2524   first_index = -1;
2525   first_found = PETSC_FALSE;
2526   for (i=0;i<s;i++) {
2527     if (!first_found && PetscRealPart(array[i]) > 0.1) {
2528       first_found = PETSC_TRUE;
2529       first_index = i;
2530     }
2531     nlocals += (PetscInt)PetscRealPart(array[i]);
2532   }
2533   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2534   if (!rank_prec_comm) {
2535     dof_displs[0]=0;
2536     for (i=1;i<size_prec_comm;i++) {
2537       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
2538     }
2539   }
2540   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2541   if (first_found) {
2542     array[first_index] += (PetscScalar)nlocals;
2543     old_index = first_index;
2544     for (i=first_index+1;i<s;i++) {
2545       if (PetscRealPart(array[i]) > 0.1) {
2546         array[i] += array[old_index];
2547         old_index = i;
2548       }
2549     }
2550   }
2551   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
2552   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2553   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2554   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2555   /* get global ordering of local dofs */
2556   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2557   if (local_dofs_mult) {
2558     for (i=0;i<n_local_dofs;i++) {
2559       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
2560     }
2561   } else {
2562     for (i=0;i<n_local_dofs;i++) {
2563       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
2564     }
2565   }
2566   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2567   /* free workspace */
2568   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
2569   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
2570   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
2571   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
2572   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
2573   /* return pointer to global ordering of local dofs */
2574   *global_numbering_subset = temp_global_dofs;
2575   PetscFunctionReturn(0);
2576 }
2577 
2578 #undef __FUNCT__
2579 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
2580 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
2581 {
2582   PetscInt       i,j;
2583   PetscScalar    *alphas;
2584   PetscErrorCode ierr;
2585 
2586   PetscFunctionBegin;
2587   /* this implements stabilized Gram-Schmidt */
2588   ierr = PetscMalloc1(n,&alphas);CHKERRQ(ierr);
2589   for (i=0;i<n;i++) {
2590     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
2591     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
2592     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
2593   }
2594   ierr = PetscFree(alphas);CHKERRQ(ierr);
2595   PetscFunctionReturn(0);
2596 }
2597 
2598 #undef __FUNCT__
2599 #define __FUNCT__ "MatISGetSubassemblingPattern"
2600 PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscBool contiguous, IS* is_sends)
2601 {
2602   Mat             subdomain_adj;
2603   IS              new_ranks,ranks_send_to;
2604   MatPartitioning partitioner;
2605   Mat_IS          *matis;
2606   PetscInt        n_neighs,*neighs,*n_shared,**shared;
2607   PetscInt        prank;
2608   PetscMPIInt     size,rank,color;
2609   PetscInt        *xadj,*adjncy,*oldranks;
2610   PetscInt        *adjncy_wgt,*v_wgt,*is_indices,*ranks_send_to_idx;
2611   PetscInt        i,j,local_size,threshold=0;
2612   PetscErrorCode  ierr;
2613   PetscBool       use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
2614   PetscSubcomm    subcomm;
2615 
2616   PetscFunctionBegin;
2617   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_square",&use_square,NULL);CHKERRQ(ierr);
2618   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);CHKERRQ(ierr);
2619   ierr = PetscOptionsGetInt(NULL,"-matis_partitioning_threshold",&threshold,NULL);CHKERRQ(ierr);
2620 
2621   /* Get info on mapping */
2622   matis = (Mat_IS*)(mat->data);
2623   ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&local_size);CHKERRQ(ierr);
2624   ierr = ISLocalToGlobalMappingGetInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2625 
2626   /* build local CSR graph of subdomains' connectivity */
2627   ierr = PetscMalloc1(2,&xadj);CHKERRQ(ierr);
2628   xadj[0] = 0;
2629   xadj[1] = PetscMax(n_neighs-1,0);
2630   ierr = PetscMalloc1(xadj[1],&adjncy);CHKERRQ(ierr);
2631   ierr = PetscMalloc1(xadj[1],&adjncy_wgt);CHKERRQ(ierr);
2632 
2633   if (threshold) {
2634     PetscInt* count,min_threshold;
2635     ierr = PetscMalloc1(local_size,&count);CHKERRQ(ierr);
2636     ierr = PetscMemzero(count,local_size*sizeof(PetscInt));CHKERRQ(ierr);
2637     for (i=1;i<n_neighs;i++) {/* i=1 so I don't count myself -> faces nodes counts to 1 */
2638       for (j=0;j<n_shared[i];j++) {
2639         count[shared[i][j]] += 1;
2640       }
2641     }
2642     /* adapt threshold since we dont want to lose significant connections */
2643     min_threshold = n_neighs;
2644     for (i=1;i<n_neighs;i++) {
2645       for (j=0;j<n_shared[i];j++) {
2646         min_threshold = PetscMin(count[shared[i][j]],min_threshold);
2647       }
2648     }
2649     threshold = PetscMax(min_threshold+1,threshold);
2650     xadj[1] = 0;
2651     for (i=1;i<n_neighs;i++) {
2652       for (j=0;j<n_shared[i];j++) {
2653         if (count[shared[i][j]] < threshold) {
2654           adjncy[xadj[1]] = neighs[i];
2655           adjncy_wgt[xadj[1]] = n_shared[i];
2656           xadj[1]++;
2657           break;
2658         }
2659       }
2660     }
2661     ierr = PetscFree(count);CHKERRQ(ierr);
2662   } else {
2663     if (xadj[1]) {
2664       ierr = PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));CHKERRQ(ierr);
2665       ierr = PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));CHKERRQ(ierr);
2666     }
2667   }
2668   ierr = ISLocalToGlobalMappingRestoreInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2669   if (use_square) {
2670     for (i=0;i<xadj[1];i++) {
2671       adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
2672     }
2673   }
2674   ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2675 
2676   ierr = PetscMalloc(sizeof(PetscInt),&ranks_send_to_idx);CHKERRQ(ierr);
2677 
2678   /*
2679     Restrict work on active processes only.
2680   */
2681   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);CHKERRQ(ierr);
2682   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr); /* 2 groups, active process and not active processes */
2683   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
2684   ierr = PetscMPIIntCast(!local_size,&color);CHKERRQ(ierr);
2685   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2686   if (color) {
2687     ierr = PetscFree(xadj);CHKERRQ(ierr);
2688     ierr = PetscFree(adjncy);CHKERRQ(ierr);
2689     ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
2690   } else {
2691     PetscInt coarsening_ratio;
2692     ierr = MPI_Comm_size(subcomm->comm,&size);CHKERRQ(ierr);
2693     ierr = PetscMalloc1(size,&oldranks);CHKERRQ(ierr);
2694     prank = rank;
2695     ierr = MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm->comm);CHKERRQ(ierr);
2696     /*
2697     for (i=0;i<size;i++) {
2698       PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
2699     }
2700     */
2701     for (i=0;i<xadj[1];i++) {
2702       ierr = PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);CHKERRQ(ierr);
2703     }
2704     ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2705     ierr = MatCreateMPIAdj(subcomm->comm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);CHKERRQ(ierr);
2706     /* ierr = MatView(subdomain_adj,0);CHKERRQ(ierr); */
2707 
2708     /* Partition */
2709     ierr = MatPartitioningCreate(subcomm->comm,&partitioner);CHKERRQ(ierr);
2710     ierr = MatPartitioningSetAdjacency(partitioner,subdomain_adj);CHKERRQ(ierr);
2711     if (use_vwgt) {
2712       ierr = PetscMalloc(sizeof(*v_wgt),&v_wgt);CHKERRQ(ierr);
2713       v_wgt[0] = local_size;
2714       ierr = MatPartitioningSetVertexWeights(partitioner,v_wgt);CHKERRQ(ierr);
2715     }
2716     n_subdomains = PetscMin((PetscInt)size,n_subdomains);
2717     coarsening_ratio = size/n_subdomains;
2718     /* Parmetis does not always give back nparts with small graphs! this should be taken into account */
2719     ierr = MatPartitioningSetNParts(partitioner,n_subdomains);CHKERRQ(ierr);
2720     ierr = MatPartitioningSetFromOptions(partitioner);CHKERRQ(ierr);
2721     ierr = MatPartitioningApply(partitioner,&new_ranks);CHKERRQ(ierr);
2722     /* ierr = MatPartitioningView(partitioner,0);CHKERRQ(ierr); */
2723 
2724     ierr = ISGetIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2725     if (contiguous) {
2726       ranks_send_to_idx[0] = oldranks[is_indices[0]]; /* contiguos set of processes */
2727     } else {
2728       ranks_send_to_idx[0] = coarsening_ratio*oldranks[is_indices[0]]; /* scattered set of processes */
2729     }
2730     ierr = ISRestoreIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2731     /* clean up */
2732     ierr = PetscFree(oldranks);CHKERRQ(ierr);
2733     ierr = ISDestroy(&new_ranks);CHKERRQ(ierr);
2734     ierr = MatDestroy(&subdomain_adj);CHKERRQ(ierr);
2735     ierr = MatPartitioningDestroy(&partitioner);CHKERRQ(ierr);
2736   }
2737   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
2738 
2739   /* assemble parallel IS for sends */
2740   i = 1;
2741   if (color) i=0;
2742   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);CHKERRQ(ierr);
2743 
2744   /* get back IS */
2745   *is_sends = ranks_send_to;
2746   PetscFunctionReturn(0);
2747 }
2748 
2749 typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;
2750 
2751 #undef __FUNCT__
2752 #define __FUNCT__ "MatISSubassemble"
2753 PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
2754 {
2755   Mat                    local_mat;
2756   Mat_IS                 *matis;
2757   IS                     is_sends_internal;
2758   PetscInt               rows,cols;
2759   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
2760   PetscBool              ismatis,isdense,destroy_mat;
2761   ISLocalToGlobalMapping l2gmap;
2762   PetscInt*              l2gmap_indices;
2763   const PetscInt*        is_indices;
2764   MatType                new_local_type;
2765   /* buffers */
2766   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
2767   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
2768   PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
2769   /* MPI */
2770   MPI_Comm               comm,comm_n;
2771   PetscSubcomm           subcomm;
2772   PetscMPIInt            n_sends,n_recvs,commsize;
2773   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
2774   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
2775   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
2776   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
2777   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
2778   PetscErrorCode         ierr;
2779 
2780   PetscFunctionBegin;
2781   /* TODO: add missing checks */
2782   PetscValidLogicalCollectiveInt(mat,n_subdomains,3);
2783   PetscValidLogicalCollectiveBool(mat,restrict_comm,4);
2784   PetscValidLogicalCollectiveEnum(mat,reuse,5);
2785   PetscValidLogicalCollectiveInt(mat,nis,7);
2786   ierr = PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);CHKERRQ(ierr);
2787   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
2788   ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
2789   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);CHKERRQ(ierr);
2790   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
2791   ierr = MatGetSize(local_mat,&rows,&cols);CHKERRQ(ierr);
2792   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
2793   if (reuse == MAT_REUSE_MATRIX && *mat_n) {
2794     PetscInt mrows,mcols,mnrows,mncols;
2795     ierr = PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);CHKERRQ(ierr);
2796     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
2797     ierr = MatGetSize(mat,&mrows,&mcols);CHKERRQ(ierr);
2798     ierr = MatGetSize(*mat_n,&mnrows,&mncols);CHKERRQ(ierr);
2799     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
2800     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
2801   }
2802   ierr = MatGetBlockSize(local_mat,&bs);CHKERRQ(ierr);
2803   PetscValidLogicalCollectiveInt(mat,bs,0);
2804   /* prepare IS for sending if not provided */
2805   if (!is_sends) {
2806     PetscBool pcontig = PETSC_TRUE;
2807     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
2808     ierr = MatISGetSubassemblingPattern(mat,n_subdomains,pcontig,&is_sends_internal);CHKERRQ(ierr);
2809   } else {
2810     ierr = PetscObjectReference((PetscObject)is_sends);CHKERRQ(ierr);
2811     is_sends_internal = is_sends;
2812   }
2813 
2814   /* get pointer of MATIS data */
2815   matis = (Mat_IS*)mat->data;
2816 
2817   /* get comm */
2818   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2819 
2820   /* compute number of sends */
2821   ierr = ISGetLocalSize(is_sends_internal,&i);CHKERRQ(ierr);
2822   ierr = PetscMPIIntCast(i,&n_sends);CHKERRQ(ierr);
2823 
2824   /* compute number of receives */
2825   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
2826   ierr = PetscMalloc1(commsize,&iflags);CHKERRQ(ierr);
2827   ierr = PetscMemzero(iflags,commsize*sizeof(*iflags));CHKERRQ(ierr);
2828   ierr = ISGetIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
2829   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
2830   ierr = PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);CHKERRQ(ierr);
2831   ierr = PetscFree(iflags);CHKERRQ(ierr);
2832 
2833   /* restrict comm if requested */
2834   subcomm = 0;
2835   destroy_mat = PETSC_FALSE;
2836   if (restrict_comm) {
2837     PetscMPIInt color,rank,subcommsize;
2838     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2839     color = 0;
2840     if (n_sends && !n_recvs) color = 1; /* sending only processes will not partecipate in new comm */
2841     ierr = MPI_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
2842     subcommsize = commsize - subcommsize;
2843     /* check if reuse has been requested */
2844     if (reuse == MAT_REUSE_MATRIX) {
2845       if (*mat_n) {
2846         PetscMPIInt subcommsize2;
2847         ierr = MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);CHKERRQ(ierr);
2848         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
2849         comm_n = PetscObjectComm((PetscObject)*mat_n);
2850       } else {
2851         comm_n = PETSC_COMM_SELF;
2852       }
2853     } else { /* MAT_INITIAL_MATRIX */
2854       ierr = PetscSubcommCreate(comm,&subcomm);CHKERRQ(ierr);
2855       ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
2856       ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2857       comm_n = subcomm->comm;
2858     }
2859     /* flag to destroy *mat_n if not significative */
2860     if (color) destroy_mat = PETSC_TRUE;
2861   } else {
2862     comm_n = comm;
2863   }
2864 
2865   /* prepare send/receive buffers */
2866   ierr = PetscMalloc1(commsize,&ilengths_idxs);CHKERRQ(ierr);
2867   ierr = PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));CHKERRQ(ierr);
2868   ierr = PetscMalloc1(commsize,&ilengths_vals);CHKERRQ(ierr);
2869   ierr = PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));CHKERRQ(ierr);
2870   if (nis) {
2871     ierr = PetscMalloc(commsize*sizeof(*ilengths_idxs_is),&ilengths_idxs_is);CHKERRQ(ierr);
2872     ierr = PetscMemzero(ilengths_idxs_is,commsize*sizeof(*ilengths_idxs_is));CHKERRQ(ierr);
2873   }
2874 
2875   /* Get data from local matrices */
2876   if (!isdense) {
2877     /* TODO: See below some guidelines on how to prepare the local buffers */
2878     /*
2879        send_buffer_vals should contain the raw values of the local matrix
2880        send_buffer_idxs should contain:
2881        - MatType_PRIVATE type
2882        - PetscInt        size_of_l2gmap
2883        - PetscInt        global_row_indices[size_of_l2gmap]
2884        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
2885     */
2886   } else {
2887     ierr = MatDenseGetArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
2888     ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&i);CHKERRQ(ierr);
2889     ierr = PetscMalloc1((i+2),&send_buffer_idxs);CHKERRQ(ierr);
2890     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
2891     send_buffer_idxs[1] = i;
2892     ierr = ISLocalToGlobalMappingGetIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
2893     ierr = PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));CHKERRQ(ierr);
2894     ierr = ISLocalToGlobalMappingRestoreIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
2895     ierr = PetscMPIIntCast(i,&len);CHKERRQ(ierr);
2896     for (i=0;i<n_sends;i++) {
2897       ilengths_vals[is_indices[i]] = len*len;
2898       ilengths_idxs[is_indices[i]] = len+2;
2899     }
2900   }
2901   ierr = PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);CHKERRQ(ierr);
2902   /* additional is (if any) */
2903   if (nis) {
2904     PetscMPIInt psum;
2905     PetscInt j;
2906     for (j=0,psum=0;j<nis;j++) {
2907       PetscInt plen;
2908       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
2909       ierr = PetscMPIIntCast(plen,&len);CHKERRQ(ierr);
2910       psum += len+1; /* indices + lenght */
2911     }
2912     ierr = PetscMalloc(psum*sizeof(PetscInt),&send_buffer_idxs_is);CHKERRQ(ierr);
2913     for (j=0,psum=0;j<nis;j++) {
2914       PetscInt plen;
2915       const PetscInt *is_array_idxs;
2916       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
2917       send_buffer_idxs_is[psum] = plen;
2918       ierr = ISGetIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
2919       ierr = PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));CHKERRQ(ierr);
2920       ierr = ISRestoreIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
2921       psum += plen+1; /* indices + lenght */
2922     }
2923     for (i=0;i<n_sends;i++) {
2924       ilengths_idxs_is[is_indices[i]] = psum;
2925     }
2926     ierr = PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);CHKERRQ(ierr);
2927   }
2928 
2929   buf_size_idxs = 0;
2930   buf_size_vals = 0;
2931   buf_size_idxs_is = 0;
2932   for (i=0;i<n_recvs;i++) {
2933     buf_size_idxs += (PetscInt)olengths_idxs[i];
2934     buf_size_vals += (PetscInt)olengths_vals[i];
2935     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
2936   }
2937   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);CHKERRQ(ierr);
2938   ierr = PetscMalloc1(buf_size_vals,&recv_buffer_vals);CHKERRQ(ierr);
2939   ierr = PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);CHKERRQ(ierr);
2940 
2941   /* get new tags for clean communications */
2942   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);CHKERRQ(ierr);
2943   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_vals);CHKERRQ(ierr);
2944   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);CHKERRQ(ierr);
2945 
2946   /* allocate for requests */
2947   ierr = PetscMalloc1(n_sends,&send_req_idxs);CHKERRQ(ierr);
2948   ierr = PetscMalloc1(n_sends,&send_req_vals);CHKERRQ(ierr);
2949   ierr = PetscMalloc1(n_sends,&send_req_idxs_is);CHKERRQ(ierr);
2950   ierr = PetscMalloc1(n_recvs,&recv_req_idxs);CHKERRQ(ierr);
2951   ierr = PetscMalloc1(n_recvs,&recv_req_vals);CHKERRQ(ierr);
2952   ierr = PetscMalloc1(n_recvs,&recv_req_idxs_is);CHKERRQ(ierr);
2953 
2954   /* communications */
2955   ptr_idxs = recv_buffer_idxs;
2956   ptr_vals = recv_buffer_vals;
2957   ptr_idxs_is = recv_buffer_idxs_is;
2958   for (i=0;i<n_recvs;i++) {
2959     source_dest = onodes[i];
2960     ierr = MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);CHKERRQ(ierr);
2961     ierr = MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);CHKERRQ(ierr);
2962     ptr_idxs += olengths_idxs[i];
2963     ptr_vals += olengths_vals[i];
2964     if (nis) {
2965       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);
2966       ptr_idxs_is += olengths_idxs_is[i];
2967     }
2968   }
2969   for (i=0;i<n_sends;i++) {
2970     ierr = PetscMPIIntCast(is_indices[i],&source_dest);CHKERRQ(ierr);
2971     ierr = MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);CHKERRQ(ierr);
2972     ierr = MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);CHKERRQ(ierr);
2973     if (nis) {
2974       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);
2975     }
2976   }
2977   ierr = ISRestoreIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
2978   ierr = ISDestroy(&is_sends_internal);CHKERRQ(ierr);
2979 
2980   /* assemble new l2g map */
2981   ierr = MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
2982   ptr_idxs = recv_buffer_idxs;
2983   buf_size_idxs = 0;
2984   for (i=0;i<n_recvs;i++) {
2985     buf_size_idxs += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
2986     ptr_idxs += olengths_idxs[i];
2987   }
2988   ierr = PetscMalloc1(buf_size_idxs,&l2gmap_indices);CHKERRQ(ierr);
2989   ptr_idxs = recv_buffer_idxs;
2990   buf_size_idxs = 0;
2991   for (i=0;i<n_recvs;i++) {
2992     ierr = PetscMemcpy(&l2gmap_indices[buf_size_idxs],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));CHKERRQ(ierr);
2993     buf_size_idxs += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
2994     ptr_idxs += olengths_idxs[i];
2995   }
2996   ierr = PetscSortRemoveDupsInt(&buf_size_idxs,l2gmap_indices);CHKERRQ(ierr);
2997   ierr = ISLocalToGlobalMappingCreate(comm_n,1,buf_size_idxs,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);CHKERRQ(ierr);
2998   ierr = PetscFree(l2gmap_indices);CHKERRQ(ierr);
2999 
3000   /* infer new local matrix type from received local matrices type */
3001   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
3002   /* 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) */
3003   if (n_recvs) {
3004     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
3005     ptr_idxs = recv_buffer_idxs;
3006     for (i=0;i<n_recvs;i++) {
3007       if ((PetscInt)new_local_type_private != *ptr_idxs) {
3008         new_local_type_private = MATAIJ_PRIVATE;
3009         break;
3010       }
3011       ptr_idxs += olengths_idxs[i];
3012     }
3013     switch (new_local_type_private) {
3014       case MATDENSE_PRIVATE:
3015         if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
3016           new_local_type = MATSEQAIJ;
3017           bs = 1;
3018         } else { /* if I receive only 1 dense matrix */
3019           new_local_type = MATSEQDENSE;
3020           bs = 1;
3021         }
3022         break;
3023       case MATAIJ_PRIVATE:
3024         new_local_type = MATSEQAIJ;
3025         bs = 1;
3026         break;
3027       case MATBAIJ_PRIVATE:
3028         new_local_type = MATSEQBAIJ;
3029         break;
3030       case MATSBAIJ_PRIVATE:
3031         new_local_type = MATSEQSBAIJ;
3032         break;
3033       default:
3034         SETERRQ2(comm,PETSC_ERR_PLIB,"Unkwown private type %d in %s",new_local_type_private,__FUNCT__);
3035         break;
3036     }
3037   } else { /* by default, new_local_type is seqdense */
3038     new_local_type = MATSEQDENSE;
3039     bs = 1;
3040   }
3041 
3042   /* create MATIS object if needed */
3043   if (reuse == MAT_INITIAL_MATRIX) {
3044     ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
3045     ierr = MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,mat_n);CHKERRQ(ierr);
3046   } else {
3047     /* it also destroys the local matrices */
3048     ierr = MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);CHKERRQ(ierr);
3049   }
3050   ierr = ISLocalToGlobalMappingDestroy(&l2gmap);CHKERRQ(ierr);
3051   ierr = MatISGetLocalMat(*mat_n,&local_mat);CHKERRQ(ierr);
3052   ierr = MatSetType(local_mat,new_local_type);CHKERRQ(ierr);
3053   ierr = MatSetUp(local_mat);CHKERRQ(ierr); /* WARNING -> no preallocation yet */
3054 
3055   /* set values */
3056   ierr = MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3057   ptr_vals = recv_buffer_vals;
3058   ptr_idxs = recv_buffer_idxs;
3059   for (i=0;i<n_recvs;i++) {
3060     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
3061       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
3062       ierr = MatSetValues(*mat_n,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);CHKERRQ(ierr);
3063       ierr = MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3064       ierr = MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3065       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
3066     } else {
3067       /* TODO */
3068     }
3069     ptr_idxs += olengths_idxs[i];
3070     ptr_vals += olengths_vals[i];
3071   }
3072   ierr = MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3073   ierr = MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3074   ierr = MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3075   ierr = MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3076 
3077 #if 0
3078   if (!restrict_comm) { /* check */
3079     Vec       lvec,rvec;
3080     PetscReal infty_error;
3081 
3082     ierr = MatGetVecs(mat,&rvec,&lvec);CHKERRQ(ierr);
3083     ierr = VecSetRandom(rvec,NULL);CHKERRQ(ierr);
3084     ierr = MatMult(mat,rvec,lvec);CHKERRQ(ierr);
3085     ierr = VecScale(lvec,-1.0);CHKERRQ(ierr);
3086     ierr = MatMultAdd(*mat_n,rvec,lvec,lvec);CHKERRQ(ierr);
3087     ierr = VecNorm(lvec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3088     ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
3089     ierr = VecDestroy(&rvec);CHKERRQ(ierr);
3090     ierr = VecDestroy(&lvec);CHKERRQ(ierr);
3091   }
3092 #endif
3093 
3094   /* assemble new additional is (if any) */
3095   if (nis) {
3096     PetscInt **temp_idxs,*count_is,j,psum;
3097 
3098     ierr = MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3099     ierr = PetscMalloc(nis*sizeof(PetscInt),&count_is);CHKERRQ(ierr);
3100     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3101     ptr_idxs = recv_buffer_idxs_is;
3102     psum = 0;
3103     for (i=0;i<n_recvs;i++) {
3104       for (j=0;j<nis;j++) {
3105         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3106         count_is[j] += plen; /* increment counting of buffer for j-th IS */
3107         psum += plen;
3108         ptr_idxs += plen+1; /* shift pointer to received data */
3109       }
3110     }
3111     ierr = PetscMalloc(nis*sizeof(PetscInt*),&temp_idxs);CHKERRQ(ierr);
3112     ierr = PetscMalloc(psum*sizeof(PetscInt),&temp_idxs[0]);CHKERRQ(ierr);
3113     for (i=1;i<nis;i++) {
3114       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
3115     }
3116     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3117     ptr_idxs = recv_buffer_idxs_is;
3118     for (i=0;i<n_recvs;i++) {
3119       for (j=0;j<nis;j++) {
3120         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3121         ierr = PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));CHKERRQ(ierr);
3122         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
3123         ptr_idxs += plen+1; /* shift pointer to received data */
3124       }
3125     }
3126     for (i=0;i<nis;i++) {
3127       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3128       ierr = PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);CHKERRQ(ierr);CHKERRQ(ierr);
3129       ierr = ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3130     }
3131     ierr = PetscFree(count_is);CHKERRQ(ierr);
3132     ierr = PetscFree(temp_idxs[0]);CHKERRQ(ierr);
3133     ierr = PetscFree(temp_idxs);CHKERRQ(ierr);
3134   }
3135   /* free workspace */
3136   ierr = PetscFree(recv_buffer_idxs);CHKERRQ(ierr);
3137   ierr = PetscFree(recv_buffer_vals);CHKERRQ(ierr);
3138   ierr = PetscFree(recv_buffer_idxs_is);CHKERRQ(ierr);
3139   ierr = MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3140   ierr = PetscFree(send_buffer_idxs);CHKERRQ(ierr);
3141   ierr = MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3142   if (isdense) {
3143     ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
3144     ierr = MatDenseRestoreArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3145   } else {
3146     /* ierr = PetscFree(send_buffer_vals);CHKERRQ(ierr); */
3147   }
3148   if (nis) {
3149     ierr = MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3150     ierr = PetscFree(send_buffer_idxs_is);CHKERRQ(ierr);
3151   }
3152   ierr = PetscFree(recv_req_idxs);CHKERRQ(ierr);
3153   ierr = PetscFree(recv_req_vals);CHKERRQ(ierr);
3154   ierr = PetscFree(recv_req_idxs_is);CHKERRQ(ierr);
3155   ierr = PetscFree(send_req_idxs);CHKERRQ(ierr);
3156   ierr = PetscFree(send_req_vals);CHKERRQ(ierr);
3157   ierr = PetscFree(send_req_idxs_is);CHKERRQ(ierr);
3158   ierr = PetscFree(ilengths_vals);CHKERRQ(ierr);
3159   ierr = PetscFree(ilengths_idxs);CHKERRQ(ierr);
3160   ierr = PetscFree(olengths_vals);CHKERRQ(ierr);
3161   ierr = PetscFree(olengths_idxs);CHKERRQ(ierr);
3162   ierr = PetscFree(onodes);CHKERRQ(ierr);
3163   if (nis) {
3164     ierr = PetscFree(ilengths_idxs_is);CHKERRQ(ierr);
3165     ierr = PetscFree(olengths_idxs_is);CHKERRQ(ierr);
3166     ierr = PetscFree(onodes_is);CHKERRQ(ierr);
3167   }
3168   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
3169   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
3170     ierr = MatDestroy(mat_n);CHKERRQ(ierr);
3171     for (i=0;i<nis;i++) {
3172       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3173     }
3174   }
3175   PetscFunctionReturn(0);
3176 }
3177 
3178 /* temporary hack into ksp private data structure */
3179 #include <petsc-private/kspimpl.h>
3180 
3181 #undef __FUNCT__
3182 #define __FUNCT__ "PCBDDCSetUpCoarseSolver"
3183 PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
3184 {
3185   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
3186   PC_IS                  *pcis = (PC_IS*)pc->data;
3187   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
3188   MatNullSpace           CoarseNullSpace=NULL;
3189   ISLocalToGlobalMapping coarse_islg;
3190   IS                     coarse_is,*isarray;
3191   PetscInt               i,im_active=-1,active_procs=-1;
3192   PetscInt               nis,nisdofs,nisneu;
3193   PC                     pc_temp;
3194   PCType                 coarse_pc_type;
3195   KSPType                coarse_ksp_type;
3196   PetscBool              multilevel_requested,multilevel_allowed;
3197   PetscBool              isredundant,isbddc,isnn,coarse_reuse;
3198   Mat                    t_coarse_mat_is;
3199   PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
3200   PetscMPIInt            all_procs;
3201   PetscBool              csin_ml,csin_ds,csin,csin_type_simple;
3202   PetscBool              compute_vecs = PETSC_FALSE;
3203   PetscErrorCode         ierr;
3204 
3205   PetscFunctionBegin;
3206   /* Assign global numbering to coarse dofs */
3207   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 */
3208     compute_vecs = PETSC_TRUE;
3209     PetscInt ocoarse_size;
3210     ocoarse_size = pcbddc->coarse_size;
3211     ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
3212     ierr = PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);CHKERRQ(ierr);
3213     /* see if we can avoid some work */
3214     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
3215       if (ocoarse_size != pcbddc->coarse_size) { /* ...but with different size, so reset it and set reuse flag to false */
3216         ierr = KSPReset(pcbddc->coarse_ksp);CHKERRQ(ierr);
3217         coarse_reuse = PETSC_FALSE;
3218       } else { /* we can safely reuse already computed coarse matrix */
3219         coarse_reuse = PETSC_TRUE;
3220       }
3221     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
3222       coarse_reuse = PETSC_FALSE;
3223     }
3224     /* reset any subassembling information */
3225     ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3226     ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3227   } else { /* primal space is unchanged, so we can reuse coarse matrix */
3228     coarse_reuse = PETSC_TRUE;
3229   }
3230 
3231   /* count "active" (i.e. with positive local size) and "void" processes */
3232   im_active = !!(pcis->n);
3233   ierr = MPI_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3234   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);CHKERRQ(ierr);
3235   void_procs = all_procs-active_procs;
3236   csin_type_simple = PETSC_TRUE;
3237   if (pcbddc->current_level) {
3238     csin_ml = PETSC_TRUE;
3239     ncoarse_ml = void_procs;
3240     csin_ds = PETSC_TRUE;
3241     ncoarse_ds = void_procs;
3242     if (!void_procs) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
3243   } else {
3244     csin_ml = PETSC_FALSE;
3245     ncoarse_ml = all_procs;
3246     if (void_procs) {
3247       csin_ds = PETSC_TRUE;
3248       ncoarse_ds = void_procs;
3249       csin_type_simple = PETSC_FALSE;
3250     } else {
3251       csin_ds = PETSC_FALSE;
3252       ncoarse_ds = all_procs;
3253     }
3254   }
3255 
3256   /*
3257     test if we can go multilevel: three conditions must be satisfied:
3258     - we have not exceeded the number of levels requested
3259     - we can actually subassemble the active processes
3260     - we can find a suitable number of MPI processes where we can place the subassembled problem
3261   */
3262   multilevel_allowed = PETSC_FALSE;
3263   multilevel_requested = PETSC_FALSE;
3264   if (pcbddc->current_level < pcbddc->max_levels) {
3265     multilevel_requested = PETSC_TRUE;
3266     if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
3267       multilevel_allowed = PETSC_FALSE;
3268     } else {
3269       multilevel_allowed = PETSC_TRUE;
3270     }
3271   }
3272   /* determine number of process partecipating to coarse solver */
3273   if (multilevel_allowed) {
3274     ncoarse = ncoarse_ml;
3275     csin = csin_ml;
3276   } else {
3277     ncoarse = ncoarse_ds;
3278     csin = csin_ds;
3279   }
3280 
3281   /* creates temporary l2gmap and IS for coarse indexes */
3282   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);CHKERRQ(ierr);
3283   ierr = ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);CHKERRQ(ierr);
3284 
3285   /* creates temporary MATIS object for coarse matrix */
3286   ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_submat_dense);CHKERRQ(ierr);
3287 #if 0
3288   {
3289     PetscViewer viewer;
3290     char filename[256];
3291     sprintf(filename,"local_coarse_mat%d.m",PetscGlobalRank);
3292     ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
3293     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3294     ierr = MatView(coarse_submat_dense,viewer);CHKERRQ(ierr);
3295     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3296   }
3297 #endif
3298   ierr = MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,&t_coarse_mat_is);CHKERRQ(ierr);
3299   ierr = MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);CHKERRQ(ierr);
3300   ierr = MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3301   ierr = MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3302   ierr = MatDestroy(&coarse_submat_dense);CHKERRQ(ierr);
3303 
3304   /* compute dofs splitting and neumann boundaries for coarse dofs */
3305   if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal) ) { /* protects from unneded computations */
3306     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
3307     const PetscInt         *idxs;
3308     ISLocalToGlobalMapping tmap;
3309 
3310     /* create map between primal indices (in local representative ordering) and local primal numbering */
3311     ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);CHKERRQ(ierr);
3312     /* allocate space for temporary storage */
3313     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs);CHKERRQ(ierr);
3314     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs2);CHKERRQ(ierr);
3315     /* allocate for IS array */
3316     nisdofs = pcbddc->n_ISForDofsLocal;
3317     nisneu = !!pcbddc->NeumannBoundariesLocal;
3318     nis = nisdofs + nisneu;
3319     ierr = PetscMalloc(nis*sizeof(IS),&isarray);CHKERRQ(ierr);
3320     /* dofs splitting */
3321     for (i=0;i<nisdofs;i++) {
3322       /* ierr = ISView(pcbddc->ISForDofsLocal[i],0);CHKERRQ(ierr); */
3323       ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);CHKERRQ(ierr);
3324       ierr = ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3325       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3326       ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3327       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3328       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->ISForDofsLocal[i]),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3329       /* ierr = ISView(isarray[i],0);CHKERRQ(ierr); */
3330     }
3331     /* neumann boundaries */
3332     if (pcbddc->NeumannBoundariesLocal) {
3333       /* ierr = ISView(pcbddc->NeumannBoundariesLocal,0);CHKERRQ(ierr); */
3334       ierr = ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);CHKERRQ(ierr);
3335       ierr = ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3336       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3337       ierr = ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3338       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3339       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->NeumannBoundariesLocal),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);CHKERRQ(ierr);
3340       /* ierr = ISView(isarray[nisdofs],0);CHKERRQ(ierr); */
3341     }
3342     /* free memory */
3343     ierr = PetscFree(tidxs);CHKERRQ(ierr);
3344     ierr = PetscFree(tidxs2);CHKERRQ(ierr);
3345     ierr = ISLocalToGlobalMappingDestroy(&tmap);CHKERRQ(ierr);
3346   } else {
3347     nis = 0;
3348     nisdofs = 0;
3349     nisneu = 0;
3350     isarray = NULL;
3351   }
3352   /* destroy no longer needed map */
3353   ierr = ISLocalToGlobalMappingDestroy(&coarse_islg);CHKERRQ(ierr);
3354 
3355   /* restrict on coarse candidates (if needed) */
3356   coarse_mat_is = NULL;
3357   if (csin) {
3358     if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
3359       PetscInt j,tissize,*nisindices;
3360       PetscInt *coarse_candidates;
3361       const PetscInt* tisindices;
3362       /* get coarse candidates' ranks in pc communicator */
3363       ierr = PetscMalloc(all_procs*sizeof(PetscInt),&coarse_candidates);CHKERRQ(ierr);
3364       ierr = MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3365       for (i=0,j=0;i<all_procs;i++) {
3366         if (!coarse_candidates[i]) {
3367           coarse_candidates[j]=i;
3368           j++;
3369         }
3370       }
3371       if (j < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",j,ncoarse);
3372       /* get a suitable subassembling pattern */
3373       if (csin_type_simple) {
3374         PetscMPIInt rank;
3375         PetscInt    issize,isidx;
3376         ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
3377         if (im_active) {
3378           issize = 1;
3379           isidx = (PetscInt)rank;
3380         } else {
3381           issize = 0;
3382           isidx = -1;
3383         }
3384         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3385       } else {
3386         ierr = MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,PETSC_TRUE,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3387       }
3388       if (pcbddc->dbg_flag) {
3389         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3390         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");CHKERRQ(ierr);
3391         ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3392         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");CHKERRQ(ierr);
3393         for (i=0;i<j;i++) {
3394           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);CHKERRQ(ierr);
3395         }
3396         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");CHKERRQ(ierr);
3397         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3398       }
3399       /* shift the pattern on coarse candidates */
3400       ierr = ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);CHKERRQ(ierr);
3401       ierr = ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3402       ierr = PetscMalloc(tissize*sizeof(PetscInt),&nisindices);CHKERRQ(ierr);
3403       for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
3404       ierr = ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3405       ierr = ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);CHKERRQ(ierr);
3406       ierr = PetscFree(coarse_candidates);CHKERRQ(ierr);
3407     }
3408     if (pcbddc->dbg_flag) {
3409       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3410       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");CHKERRQ(ierr);
3411       ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3412       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3413     }
3414     /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
3415     ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
3416   } else {
3417     if (pcbddc->dbg_flag) {
3418       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3419       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");CHKERRQ(ierr);
3420       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3421     }
3422     ierr = PetscObjectReference((PetscObject)t_coarse_mat_is);CHKERRQ(ierr);
3423     coarse_mat_is = t_coarse_mat_is;
3424   }
3425 
3426   /* create local to global scatters for coarse problem */
3427   if (compute_vecs) {
3428     PetscInt lrows;
3429     ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
3430     if (coarse_mat_is) {
3431       ierr = MatGetLocalSize(coarse_mat_is,&lrows,NULL);CHKERRQ(ierr);
3432     } else {
3433       lrows = 0;
3434     }
3435     ierr = VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);CHKERRQ(ierr);
3436     ierr = VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);CHKERRQ(ierr);
3437     ierr = VecSetType(pcbddc->coarse_vec,VECSTANDARD);CHKERRQ(ierr);
3438     ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3439     ierr = VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3440   }
3441   ierr = ISDestroy(&coarse_is);CHKERRQ(ierr);
3442   ierr = MatDestroy(&t_coarse_mat_is);CHKERRQ(ierr);
3443 
3444   /* set defaults for coarse KSP and PC */
3445   if (multilevel_allowed) {
3446     coarse_ksp_type = KSPRICHARDSON;
3447     coarse_pc_type = PCBDDC;
3448   } else {
3449     coarse_ksp_type = KSPPREONLY;
3450     coarse_pc_type = PCREDUNDANT;
3451   }
3452 
3453   /* print some info if requested */
3454   if (pcbddc->dbg_flag) {
3455     if (!multilevel_allowed) {
3456       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3457       if (multilevel_requested) {
3458         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);
3459       } else if (pcbddc->max_levels) {
3460         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);CHKERRQ(ierr);
3461       }
3462       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3463     }
3464   }
3465 
3466   /* create the coarse KSP object only once with defaults */
3467   if (coarse_mat_is) {
3468     MatReuse coarse_mat_reuse;
3469     PetscViewer dbg_viewer;
3470     if (pcbddc->dbg_flag) {
3471       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
3472       ierr = PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3473     }
3474     if (!pcbddc->coarse_ksp) {
3475       char prefix[256],str_level[16];
3476       size_t len;
3477       ierr = KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);CHKERRQ(ierr);
3478       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3479       ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
3480       ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);CHKERRQ(ierr);
3481       ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3482       ierr = KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);CHKERRQ(ierr);
3483       ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3484       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3485       /* prefix */
3486       ierr = PetscStrcpy(prefix,"");CHKERRQ(ierr);
3487       ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
3488       if (!pcbddc->current_level) {
3489         ierr = PetscStrcpy(prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
3490         ierr = PetscStrcat(prefix,"pc_bddc_coarse_");CHKERRQ(ierr);
3491       } else {
3492         ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
3493         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
3494         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
3495         ierr = PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
3496         sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
3497         ierr = PetscStrcat(prefix,str_level);CHKERRQ(ierr);
3498       }
3499       ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);CHKERRQ(ierr);
3500       /* allow user customization */
3501       ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3502       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
3503     }
3504 
3505     /* get some info after set from options */
3506     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3507     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);CHKERRQ(ierr);
3508     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);CHKERRQ(ierr);
3509     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);CHKERRQ(ierr);
3510     if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
3511       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3512       isbddc = PETSC_FALSE;
3513     }
3514     if (isredundant) {
3515       KSP inner_ksp;
3516       PC inner_pc;
3517       ierr = PCRedundantGetKSP(pc_temp,&inner_ksp);CHKERRQ(ierr);
3518       ierr = KSPGetPC(inner_ksp,&inner_pc);CHKERRQ(ierr);
3519       ierr = PCFactorSetReuseFill(inner_pc,PETSC_TRUE);CHKERRQ(ierr);
3520     }
3521 
3522     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
3523     ierr = PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);CHKERRQ(ierr);
3524     ierr = PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);CHKERRQ(ierr);
3525     ierr = PCBDDCSetLevels(pc_temp,pcbddc->max_levels);CHKERRQ(ierr);
3526     if (nisdofs) {
3527       ierr = PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);CHKERRQ(ierr);
3528       for (i=0;i<nisdofs;i++) {
3529         ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3530       }
3531     }
3532     if (nisneu) {
3533       ierr = PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);CHKERRQ(ierr);
3534       ierr = ISDestroy(&isarray[nisdofs]);CHKERRQ(ierr);
3535     }
3536 
3537     /* assemble coarse matrix */
3538     if (coarse_reuse) {
3539       ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
3540       ierr = PetscObjectReference((PetscObject)coarse_mat);CHKERRQ(ierr);
3541       coarse_mat_reuse = MAT_REUSE_MATRIX;
3542     } else {
3543       coarse_mat_reuse = MAT_INITIAL_MATRIX;
3544     }
3545     if (isbddc || isnn) {
3546       if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
3547         ierr = MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,PETSC_TRUE,&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3548         if (pcbddc->dbg_flag) {
3549           ierr = PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3550           ierr = PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");CHKERRQ(ierr);
3551           ierr = ISView(pcbddc->coarse_subassembling,dbg_viewer);CHKERRQ(ierr);
3552           ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3553         }
3554       }
3555       ierr = MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);CHKERRQ(ierr);
3556     } else {
3557       ierr = MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);CHKERRQ(ierr);
3558     }
3559     ierr = MatDestroy(&coarse_mat_is);CHKERRQ(ierr);
3560 
3561     /* propagate symmetry info to coarse matrix */
3562     ierr = MatSetOption(coarse_mat,MAT_SYMMETRIC,pcbddc->issym);CHKERRQ(ierr);
3563     ierr = MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
3564 
3565     /* set operators */
3566     ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3567     if (pcbddc->dbg_flag) {
3568       ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3569     }
3570   } else { /* processes non partecipating to coarse solver (if any) */
3571     coarse_mat = 0;
3572   }
3573   ierr = PetscFree(isarray);CHKERRQ(ierr);
3574 #if 0
3575   {
3576     PetscViewer viewer;
3577     char filename[256];
3578     sprintf(filename,"coarse_mat.m");
3579     ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,&viewer);CHKERRQ(ierr);
3580     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3581     ierr = MatView(coarse_mat,viewer);CHKERRQ(ierr);
3582     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3583   }
3584 #endif
3585 
3586   /* Compute coarse null space (special handling by BDDC only) */
3587   if (pcbddc->NullSpace) {
3588     ierr = PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);CHKERRQ(ierr);
3589   }
3590 
3591   if (pcbddc->coarse_ksp) {
3592     Vec crhs,csol;
3593     PetscBool ispreonly;
3594     if (CoarseNullSpace) {
3595       if (isbddc) {
3596         ierr = PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);CHKERRQ(ierr);
3597       } else {
3598         ierr = KSPSetNullSpace(pcbddc->coarse_ksp,CoarseNullSpace);CHKERRQ(ierr);
3599       }
3600     }
3601     /* setup coarse ksp */
3602     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3603     ierr = KSPGetSolution(pcbddc->coarse_ksp,&csol);CHKERRQ(ierr);
3604     ierr = KSPGetRhs(pcbddc->coarse_ksp,&crhs);CHKERRQ(ierr);
3605     /* hack */
3606     if (!csol) {
3607       ierr = MatGetVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);CHKERRQ(ierr);
3608     }
3609     if (!crhs) {
3610       ierr = MatGetVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));CHKERRQ(ierr);
3611     }
3612     /* Check coarse problem if in debug mode or if solving with an iterative method */
3613     ierr = PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);CHKERRQ(ierr);
3614     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
3615       KSP       check_ksp;
3616       KSPType   check_ksp_type;
3617       PC        check_pc;
3618       Vec       check_vec,coarse_vec;
3619       PetscReal abs_infty_error,infty_error,lambda_min,lambda_max;
3620       PetscInt  its;
3621       PetscBool compute_eigs;
3622       PetscReal *eigs_r,*eigs_c;
3623       PetscInt  neigs;
3624       const char *prefix;
3625 
3626       /* Create ksp object suitable for estimation of extreme eigenvalues */
3627       ierr = KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);CHKERRQ(ierr);
3628       ierr = KSPSetOperators(check_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3629       ierr = KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3630       if (ispreonly) {
3631         check_ksp_type = KSPPREONLY;
3632         compute_eigs = PETSC_FALSE;
3633       } else {
3634         check_ksp_type = KSPGMRES;
3635         compute_eigs = PETSC_TRUE;
3636       }
3637       ierr = KSPSetType(check_ksp,check_ksp_type);CHKERRQ(ierr);
3638       ierr = KSPSetComputeSingularValues(check_ksp,compute_eigs);CHKERRQ(ierr);
3639       ierr = KSPSetComputeEigenvalues(check_ksp,compute_eigs);CHKERRQ(ierr);
3640       ierr = KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);CHKERRQ(ierr);
3641       ierr = KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);CHKERRQ(ierr);
3642       ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
3643       ierr = KSPAppendOptionsPrefix(check_ksp,"check_");CHKERRQ(ierr);
3644       ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
3645       ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
3646       ierr = KSPGetPC(pcbddc->coarse_ksp,&check_pc);CHKERRQ(ierr);
3647       ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
3648       /* create random vec */
3649       ierr = KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);CHKERRQ(ierr);
3650       ierr = VecDuplicate(coarse_vec,&check_vec);CHKERRQ(ierr);
3651       ierr = VecSetRandom(check_vec,NULL);CHKERRQ(ierr);
3652       if (CoarseNullSpace) {
3653         ierr = MatNullSpaceRemove(CoarseNullSpace,check_vec);CHKERRQ(ierr);
3654       }
3655       ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3656       /* solve coarse problem */
3657       ierr = KSPSolve(check_ksp,coarse_vec,coarse_vec);CHKERRQ(ierr);
3658       if (CoarseNullSpace) {
3659         ierr = MatNullSpaceRemove(CoarseNullSpace,coarse_vec);CHKERRQ(ierr);
3660       }
3661       /* set eigenvalue estimation if preonly has not been requested */
3662       if (compute_eigs) {
3663         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_r);CHKERRQ(ierr);
3664         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_c);CHKERRQ(ierr);
3665         ierr = KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);CHKERRQ(ierr);
3666         lambda_max = eigs_r[neigs-1];
3667         lambda_min = eigs_r[0];
3668         if (pcbddc->use_coarse_estimates) {
3669           if (lambda_max>lambda_min) {
3670             ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3671             ierr = KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));CHKERRQ(ierr);
3672           }
3673         }
3674       }
3675 
3676       /* check coarse problem residual error */
3677       if (pcbddc->dbg_flag) {
3678         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
3679         ierr = PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3680         ierr = VecAXPY(check_vec,-1.0,coarse_vec);CHKERRQ(ierr);
3681         ierr = VecNorm(check_vec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3682         ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3683         ierr = VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);CHKERRQ(ierr);
3684         ierr = VecDestroy(&check_vec);CHKERRQ(ierr);
3685         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (%d)\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
3686         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);CHKERRQ(ierr);
3687         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);CHKERRQ(ierr);
3688         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);CHKERRQ(ierr);
3689         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);CHKERRQ(ierr);
3690         if (compute_eigs) {
3691           PetscReal lambda_max_s,lambda_min_s;
3692           ierr = KSPGetIterationNumber(check_ksp,&its);CHKERRQ(ierr);
3693           ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);CHKERRQ(ierr);
3694           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);
3695           for (i=0;i<neigs;i++) {
3696             ierr = PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);CHKERRQ(ierr);
3697           }
3698         }
3699         ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3700         ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3701       }
3702       ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
3703       if (compute_eigs) {
3704         ierr = PetscFree(eigs_r);CHKERRQ(ierr);
3705         ierr = PetscFree(eigs_c);CHKERRQ(ierr);
3706       }
3707     }
3708   }
3709   /* print additional info */
3710   if (pcbddc->dbg_flag) {
3711     /* waits until all processes reaches this point */
3712     ierr = PetscBarrier((PetscObject)pc);CHKERRQ(ierr);
3713     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);CHKERRQ(ierr);
3714     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3715   }
3716 
3717   /* free memory */
3718   ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
3719   ierr = MatDestroy(&coarse_mat);CHKERRQ(ierr);
3720   PetscFunctionReturn(0);
3721 }
3722 
3723 #undef __FUNCT__
3724 #define __FUNCT__ "PCBDDCComputePrimalNumbering"
3725 PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
3726 {
3727   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
3728   PC_IS*         pcis = (PC_IS*)pc->data;
3729   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
3730   PetscInt       i,coarse_size;
3731   PetscInt       *local_primal_indices;
3732   PetscErrorCode ierr;
3733 
3734   PetscFunctionBegin;
3735   /* Compute global number of coarse dofs */
3736   if (!pcbddc->primal_indices_local_idxs && pcbddc->local_primal_size) {
3737     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Local primal indices have not been created");
3738   }
3739   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);
3740 
3741   /* check numbering */
3742   if (pcbddc->dbg_flag) {
3743     PetscScalar coarsesum,*array;
3744     PetscBool set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;
3745 
3746     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3747     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3748     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");CHKERRQ(ierr);
3749     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
3750     ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
3751     for (i=0;i<pcbddc->local_primal_size;i++) {
3752       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
3753     }
3754     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
3755     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
3756     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3757     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3758     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3759     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3760     ierr = VecScatterEnd(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3761     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3762     for (i=0;i<pcis->n;i++) {
3763       if (array[i] == 1.0) {
3764         set_error = PETSC_TRUE;
3765         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a single process!\n",PetscGlobalRank,i);CHKERRQ(ierr);
3766       }
3767     }
3768     ierr = MPI_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3769     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3770     for (i=0;i<pcis->n;i++) {
3771       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
3772     }
3773     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3774     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3775     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3776     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3777     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
3778     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));CHKERRQ(ierr);
3779     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
3780       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");CHKERRQ(ierr);
3781       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3782       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
3783       for (i=0;i<pcbddc->local_primal_size;i++) {
3784         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%d]=%d (%d)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i]);
3785       }
3786       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3787     }
3788     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3789     if (set_error_reduced) {
3790       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
3791     }
3792   }
3793   /* get back data */
3794   *coarse_size_n = coarse_size;
3795   *local_primal_indices_n = local_primal_indices;
3796   PetscFunctionReturn(0);
3797 }
3798 
3799 #undef __FUNCT__
3800 #define __FUNCT__ "PCBDDCGlobalToLocal"
3801 PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
3802 {
3803   IS             localis_t;
3804   PetscInt       i,lsize,*idxs,n;
3805   PetscScalar    *vals;
3806   PetscErrorCode ierr;
3807 
3808   PetscFunctionBegin;
3809   /* get indices in local ordering exploiting local to global map */
3810   ierr = ISGetLocalSize(globalis,&lsize);CHKERRQ(ierr);
3811   ierr = PetscMalloc(lsize*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3812   for (i=0;i<lsize;i++) vals[i] = 1.0;
3813   ierr = ISGetIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
3814   ierr = VecSet(gwork,0.0);CHKERRQ(ierr);
3815   ierr = VecSet(lwork,0.0);CHKERRQ(ierr);
3816   if (idxs) { /* multilevel guard */
3817     ierr = VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
3818   }
3819   ierr = VecAssemblyBegin(gwork);CHKERRQ(ierr);
3820   ierr = ISRestoreIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
3821   ierr = PetscFree(vals);CHKERRQ(ierr);
3822   ierr = VecAssemblyEnd(gwork);CHKERRQ(ierr);
3823   /* now compute set in local ordering */
3824   ierr = VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3825   ierr = VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3826   ierr = VecGetArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
3827   ierr = VecGetSize(lwork,&n);CHKERRQ(ierr);
3828   for (i=0,lsize=0;i<n;i++) {
3829     if (PetscRealPart(vals[i]) > 0.5) {
3830       lsize++;
3831     }
3832   }
3833   ierr = PetscMalloc(lsize*sizeof(PetscInt),&idxs);CHKERRQ(ierr);
3834   for (i=0,lsize=0;i<n;i++) {
3835     if (PetscRealPart(vals[i]) > 0.5) {
3836       idxs[lsize++] = i;
3837     }
3838   }
3839   ierr = VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
3840   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);CHKERRQ(ierr);
3841   *localis = localis_t;
3842   PetscFunctionReturn(0);
3843 }
3844