xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 34a97f8c781d28c390054b7fe2045ae8e3fc2469)
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);CHKERRQ(ierr);
1039     ierr = PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len);CHKERRQ(ierr);
1040     *(dir_prefix+len)='\0';
1041     *(neu_prefix+len)='\0';
1042     ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
1043     ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
1044     ierr = PetscStrcat(dir_prefix,str_level);CHKERRQ(ierr);
1045     ierr = PetscStrcat(neu_prefix,str_level);CHKERRQ(ierr);
1046   }
1047 
1048   /* DIRICHLET PROBLEM */
1049   /* Matrix for Dirichlet problem is pcis->A_II */
1050   ierr = ISGetSize(pcis->is_I_local,&n_D);CHKERRQ(ierr);
1051   if (!pcbddc->ksp_D) { /* create object if not yet build */
1052     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
1053     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
1054     /* default */
1055     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
1056     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);CHKERRQ(ierr);
1057     ierr = PetscObjectTypeCompare((PetscObject)pcis->A_II,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
1058     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
1059     if (issbaij) {
1060       ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
1061     } else {
1062       ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
1063     }
1064     /* Allow user's customization */
1065     ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
1066     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
1067   }
1068   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II);CHKERRQ(ierr);
1069   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
1070   if (!n_D) {
1071     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
1072     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
1073   }
1074   /* Set Up KSP for Dirichlet problem of BDDC */
1075   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
1076   /* set ksp_D into pcis data */
1077   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
1078   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
1079   pcis->ksp_D = pcbddc->ksp_D;
1080 
1081   /* NEUMANN PROBLEM */
1082   /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
1083   ierr = ISGetSize(pcbddc->is_R_local,&n_R);CHKERRQ(ierr);
1084   if (pcbddc->ksp_R) { /* already created ksp */
1085     PetscInt nn_R;
1086     ierr = KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);CHKERRQ(ierr);
1087     ierr = PetscObjectReference((PetscObject)A_RR);CHKERRQ(ierr);
1088     ierr = MatGetSize(A_RR,&nn_R,NULL);CHKERRQ(ierr);
1089     if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
1090       ierr = KSPReset(pcbddc->ksp_R);CHKERRQ(ierr);
1091       ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1092       reuse = MAT_INITIAL_MATRIX;
1093     } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
1094       if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
1095         ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1096         reuse = MAT_INITIAL_MATRIX;
1097       } else { /* safe to reuse the matrix */
1098         reuse = MAT_REUSE_MATRIX;
1099       }
1100     }
1101     /* last check */
1102     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
1103       ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1104       reuse = MAT_INITIAL_MATRIX;
1105     }
1106   } else { /* first time, so we need to create the matrix */
1107     reuse = MAT_INITIAL_MATRIX;
1108   }
1109   /* extract A_RR */
1110   ierr = MatGetBlockSize(pcbddc->local_mat,&mbs);CHKERRQ(ierr);
1111   ierr = ISGetBlockSize(pcbddc->is_R_local,&ibs);CHKERRQ(ierr);
1112   if (ibs != mbs) {
1113     Mat newmat;
1114     ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
1115     ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
1116     ierr = MatDestroy(&newmat);CHKERRQ(ierr);
1117   } else {
1118     ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
1119   }
1120   if (!pcbddc->ksp_R) { /* create object if not present */
1121     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
1122     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
1123     /* default */
1124     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
1125     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);CHKERRQ(ierr);
1126     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
1127     ierr = PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
1128     if (issbaij) {
1129       ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
1130     } else {
1131       ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
1132     }
1133     /* Allow user's customization */
1134     ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
1135     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
1136   }
1137   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);CHKERRQ(ierr);
1138   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
1139   if (!n_R) {
1140     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
1141     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
1142   }
1143   /* Set Up KSP for Neumann problem of BDDC */
1144   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
1145 
1146   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
1147   if (pcbddc->NullSpace || pcbddc->dbg_flag) {
1148     /* Dirichlet */
1149     ierr = VecSetRandom(pcis->vec1_D,NULL);CHKERRQ(ierr);
1150     ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1151     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);CHKERRQ(ierr);
1152     ierr = VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);CHKERRQ(ierr);
1153     ierr = VecNorm(pcis->vec1_D,NORM_INFINITY,&value);CHKERRQ(ierr);
1154     /* need to be adapted? */
1155     use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
1156     ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1157     ierr = PCBDDCSetUseExactDirichlet(pc,use_exact_reduced);CHKERRQ(ierr);
1158     /* print info */
1159     if (pcbddc->dbg_flag) {
1160       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1161       ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1162       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
1163       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
1164       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);
1165       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1166     }
1167     if (pcbddc->NullSpace && !use_exact_reduced && !pcbddc->switch_static) {
1168       ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcis->is_I_local);CHKERRQ(ierr);
1169     }
1170 
1171     /* Neumann */
1172     ierr = VecSetRandom(pcbddc->vec1_R,NULL);CHKERRQ(ierr);
1173     ierr = MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
1174     ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
1175     ierr = VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);CHKERRQ(ierr);
1176     ierr = VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);CHKERRQ(ierr);
1177     /* need to be adapted? */
1178     use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
1179     ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1180     /* print info */
1181     if (pcbddc->dbg_flag) {
1182       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);
1183       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1184     }
1185     if (pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
1186       ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcbddc->is_R_local);CHKERRQ(ierr);
1187     }
1188   }
1189   /* free Neumann problem's matrix */
1190   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1191   PetscFunctionReturn(0);
1192 }
1193 
1194 #undef __FUNCT__
1195 #define __FUNCT__ "PCBDDCSolveSubstructureCorrection"
1196 static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec rhs, Vec sol, Vec work, PetscBool applytranspose)
1197 {
1198   PetscErrorCode ierr;
1199   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1200 
1201   PetscFunctionBegin;
1202   if (applytranspose) {
1203     if (pcbddc->local_auxmat1) {
1204       ierr = MatMultTranspose(pcbddc->local_auxmat2,rhs,work);CHKERRQ(ierr);
1205       ierr = MatMultTransposeAdd(pcbddc->local_auxmat1,work,rhs,rhs);CHKERRQ(ierr);
1206     }
1207     ierr = KSPSolveTranspose(pcbddc->ksp_R,rhs,sol);CHKERRQ(ierr);
1208   } else {
1209     ierr = KSPSolve(pcbddc->ksp_R,rhs,sol);CHKERRQ(ierr);
1210     if (pcbddc->local_auxmat1) {
1211       ierr = MatMult(pcbddc->local_auxmat1,sol,work);CHKERRQ(ierr);
1212       ierr = MatMultAdd(pcbddc->local_auxmat2,work,sol,sol);CHKERRQ(ierr);
1213     }
1214   }
1215   PetscFunctionReturn(0);
1216 }
1217 
1218 /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
1219 #undef __FUNCT__
1220 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
1221 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
1222 {
1223   PetscErrorCode ierr;
1224   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
1225   PC_IS*            pcis = (PC_IS*)  (pc->data);
1226   const PetscScalar zero = 0.0;
1227 
1228   PetscFunctionBegin;
1229   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
1230   if (applytranspose) {
1231     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1232     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1233   } else {
1234     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1235     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1236   }
1237   /* start communications from local primal nodes to rhs of coarse solver */
1238   ierr = VecSet(pcbddc->coarse_vec,zero);CHKERRQ(ierr);
1239   ierr = PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1240   ierr = PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1241 
1242   /* Coarse solution -> rhs and sol updated in PCBDDCScattarCoarseDataBegin/End */
1243   /* TODO remove null space when doing multilevel */
1244   if (pcbddc->coarse_ksp) {
1245     if (applytranspose) {
1246       ierr = KSPSolveTranspose(pcbddc->coarse_ksp,NULL,NULL);CHKERRQ(ierr);
1247     } else {
1248       ierr = KSPSolve(pcbddc->coarse_ksp,NULL,NULL);CHKERRQ(ierr);
1249     }
1250   }
1251   /* start communications from coarse solver solution to local primal nodes */
1252   ierr = PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1253 
1254   /* Local solution on R nodes */
1255   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
1256   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1257   ierr = VecScatterEnd(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1258   if (pcbddc->switch_static) {
1259     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1260     ierr = VecScatterEnd(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1261   }
1262   ierr = PCBDDCSolveSubstructureCorrection(pc,pcbddc->vec1_R,pcbddc->vec2_R,pcbddc->vec1_C,applytranspose);CHKERRQ(ierr);
1263   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1264   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1265   ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1266   if (pcbddc->switch_static) {
1267     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1268     ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1269   }
1270 
1271   /* complete communications from coarse sol to local primal nodes */
1272   ierr = PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1273 
1274   /* Sum contributions from two levels */
1275   if (applytranspose) {
1276     ierr = MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1277     if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1278   } else {
1279     ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1280     if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1281   }
1282   PetscFunctionReturn(0);
1283 }
1284 
1285 /* TODO: the following two function can be optimized using VecPlaceArray whenever possible and using overlap flag */
1286 #undef __FUNCT__
1287 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
1288 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
1289 {
1290   PetscErrorCode ierr;
1291   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1292   PetscScalar    *array,*array2;
1293   Vec            from,to;
1294 
1295   PetscFunctionBegin;
1296   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
1297     from = pcbddc->coarse_vec;
1298     to = pcbddc->vec1_P;
1299     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
1300       Vec tvec;
1301       PetscInt lsize;
1302       ierr = KSPGetSolution(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1303       ierr = VecGetLocalSize(tvec,&lsize);CHKERRQ(ierr);
1304       ierr = VecGetArrayRead(tvec,(const PetscScalar**)&array);CHKERRQ(ierr);
1305       ierr = VecGetArray(from,&array2);CHKERRQ(ierr);
1306       ierr = PetscMemcpy(array2,array,lsize*sizeof(PetscScalar));CHKERRQ(ierr);
1307       ierr = VecRestoreArrayRead(tvec,(const PetscScalar**)&array);CHKERRQ(ierr);
1308       ierr = VecRestoreArray(from,&array2);CHKERRQ(ierr);
1309     }
1310   } else { /* from local to global -> put data in coarse right hand side */
1311     from = pcbddc->vec1_P;
1312     to = pcbddc->coarse_vec;
1313   }
1314   ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
1315   PetscFunctionReturn(0);
1316 }
1317 
1318 #undef __FUNCT__
1319 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
1320 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
1321 {
1322   PetscErrorCode ierr;
1323   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1324   PetscScalar    *array,*array2;
1325   Vec            from,to;
1326 
1327   PetscFunctionBegin;
1328   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
1329     from = pcbddc->coarse_vec;
1330     to = pcbddc->vec1_P;
1331   } else { /* from local to global -> put data in coarse right hand side */
1332     from = pcbddc->vec1_P;
1333     to = pcbddc->coarse_vec;
1334   }
1335   ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
1336   if (smode == SCATTER_FORWARD) {
1337     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
1338       Vec tvec;
1339       PetscInt lsize;
1340       ierr = KSPGetRhs(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1341       ierr = VecGetLocalSize(tvec,&lsize);CHKERRQ(ierr);
1342       ierr = VecGetArrayRead(to,(const PetscScalar**)&array);CHKERRQ(ierr);
1343       ierr = VecGetArray(tvec,&array2);CHKERRQ(ierr);
1344       ierr = PetscMemcpy(array2,array,lsize*sizeof(PetscScalar));CHKERRQ(ierr);
1345       ierr = VecRestoreArrayRead(to,(const PetscScalar**)&array);CHKERRQ(ierr);
1346       ierr = VecRestoreArray(tvec,&array2);CHKERRQ(ierr);
1347     }
1348   }
1349   PetscFunctionReturn(0);
1350 }
1351 
1352 /* uncomment for testing purposes */
1353 /* #define PETSC_MISSING_LAPACK_GESVD 1 */
1354 #undef __FUNCT__
1355 #define __FUNCT__ "PCBDDCConstraintsSetUp"
1356 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
1357 {
1358   PetscErrorCode    ierr;
1359   PC_IS*            pcis = (PC_IS*)(pc->data);
1360   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
1361   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
1362   /* constraint and (optionally) change of basis matrix implemented as SeqAIJ */
1363   MatType           impMatType=MATSEQAIJ;
1364   /* one and zero */
1365   PetscScalar       one=1.0,zero=0.0;
1366   /* space to store constraints and their local indices */
1367   PetscScalar       *temp_quadrature_constraint;
1368   PetscInt          *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B;
1369   /* iterators */
1370   PetscInt          i,j,k,total_counts,temp_start_ptr;
1371   /* stuff to store connected components stored in pcbddc->mat_graph */
1372   IS                ISForVertices,*ISForFaces,*ISForEdges,*used_IS;
1373   PetscInt          n_ISForFaces,n_ISForEdges;
1374   /* near null space stuff */
1375   MatNullSpace      nearnullsp;
1376   const Vec         *nearnullvecs;
1377   Vec               *localnearnullsp;
1378   PetscBool         nnsp_has_cnst;
1379   PetscInt          nnsp_size;
1380   PetscScalar       *array;
1381   /* BLAS integers */
1382   PetscBLASInt      lwork,lierr;
1383   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
1384   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
1385   /* LAPACK working arrays for SVD or POD */
1386   PetscBool         skip_lapack;
1387   PetscScalar       *work;
1388   PetscReal         *singular_vals;
1389 #if defined(PETSC_USE_COMPLEX)
1390   PetscReal         *rwork;
1391 #endif
1392 #if defined(PETSC_MISSING_LAPACK_GESVD)
1393   PetscBLASInt      Blas_one_2=1;
1394   PetscScalar       *temp_basis,*correlation_mat;
1395 #else
1396   PetscBLASInt      dummy_int_1=1,dummy_int_2=1;
1397   PetscScalar       dummy_scalar_1=0.0,dummy_scalar_2=0.0;
1398 #endif
1399   /* reuse */
1400   PetscInt          olocal_primal_size;
1401   PetscInt          *oprimal_indices_local_idxs;
1402   /* change of basis */
1403   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
1404   PetscBool         boolforchange,qr_needed;
1405   PetscBT           touched,change_basis,qr_needed_idx;
1406   /* auxiliary stuff */
1407   PetscInt          *nnz,*is_indices,*aux_primal_numbering_B;
1408   /* some quantities */
1409   PetscInt          n_vertices,total_primal_vertices,valid_constraints;
1410   PetscInt          size_of_constraint,max_size_of_constraint,max_constraints,temp_constraints;
1411 
1412 
1413   PetscFunctionBegin;
1414   /* Destroy Mat objects computed previously */
1415   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1416   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1417   /* Get index sets for faces, edges and vertices from graph */
1418   if (!pcbddc->use_faces && !pcbddc->use_edges && !pcbddc->use_vertices) {
1419     pcbddc->use_vertices = PETSC_TRUE;
1420   }
1421   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,pcbddc->use_faces,pcbddc->use_edges,pcbddc->use_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
1422   /* HACKS (the two following code branches) */
1423   if (!ISForVertices && pcbddc->NullSpace && !pcbddc->user_ChangeOfBasisMatrix) {
1424     pcbddc->use_change_of_basis = PETSC_TRUE;
1425     pcbddc->use_change_on_faces = PETSC_FALSE;
1426   }
1427   if (pcbddc->NullSpace) {
1428     /* use_change_of_basis should be consistent among processors */
1429     PetscBool tbool = pcbddc->use_change_of_basis;
1430     ierr = MPI_Allreduce(&tbool,&(pcbddc->use_change_of_basis),1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1431   }
1432   /* print some info */
1433   if (pcbddc->dbg_flag) {
1434     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1435     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1436     i = 0;
1437     if (ISForVertices) {
1438       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
1439     }
1440     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
1441     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
1442     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
1443     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1444   }
1445   /* check if near null space is attached to global mat */
1446   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
1447   if (nearnullsp) {
1448     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1449     /* remove any stored info */
1450     ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
1451     ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1452     /* store information for BDDC solver reuse */
1453     ierr = PetscObjectReference((PetscObject)nearnullsp);CHKERRQ(ierr);
1454     pcbddc->onearnullspace = nearnullsp;
1455     ierr = PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1456     for (i=0;i<nnsp_size;i++) {
1457       ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);CHKERRQ(ierr);
1458     }
1459   } else { /* if near null space is not provided BDDC uses constants by default */
1460     nnsp_size = 0;
1461     nnsp_has_cnst = PETSC_TRUE;
1462   }
1463   /* get max number of constraints on a single cc */
1464   max_constraints = nnsp_size;
1465   if (nnsp_has_cnst) max_constraints++;
1466 
1467   /*
1468        Evaluate maximum storage size needed by the procedure
1469        - temp_indices will contain start index of each constraint stored as follows
1470        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
1471        - 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
1472        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
1473                                                                                                                                                          */
1474   total_counts = n_ISForFaces+n_ISForEdges;
1475   total_counts *= max_constraints;
1476   n_vertices = 0;
1477   if (ISForVertices) {
1478     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
1479   }
1480   total_counts += n_vertices;
1481   ierr = PetscMalloc1((total_counts+1),&temp_indices);CHKERRQ(ierr);
1482   ierr = PetscBTCreate(total_counts,&change_basis);CHKERRQ(ierr);
1483   total_counts = 0;
1484   max_size_of_constraint = 0;
1485   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1486     if (i<n_ISForEdges) {
1487       used_IS = &ISForEdges[i];
1488     } else {
1489       used_IS = &ISForFaces[i-n_ISForEdges];
1490     }
1491     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
1492     total_counts += j;
1493     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
1494   }
1495   total_counts *= max_constraints;
1496   total_counts += n_vertices;
1497   ierr = PetscMalloc1(total_counts,&temp_quadrature_constraint);CHKERRQ(ierr);
1498   ierr = PetscMalloc1(total_counts,&temp_indices_to_constraint);CHKERRQ(ierr);
1499   ierr = PetscMalloc1(total_counts,&temp_indices_to_constraint_B);CHKERRQ(ierr);
1500   /* get local part of global near null space vectors */
1501   ierr = PetscMalloc1(nnsp_size,&localnearnullsp);CHKERRQ(ierr);
1502   for (k=0;k<nnsp_size;k++) {
1503     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
1504     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1505     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1506   }
1507 
1508   /* whether or not to skip lapack calls */
1509   skip_lapack = PETSC_TRUE;
1510   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
1511 
1512   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
1513   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1514     PetscScalar temp_work;
1515 #if defined(PETSC_MISSING_LAPACK_GESVD)
1516     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
1517     ierr = PetscMalloc1(max_constraints*max_constraints,&correlation_mat);CHKERRQ(ierr);
1518     ierr = PetscMalloc1(max_constraints,&singular_vals);CHKERRQ(ierr);
1519     ierr = PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);CHKERRQ(ierr);
1520 #if defined(PETSC_USE_COMPLEX)
1521     ierr = PetscMalloc1(3*max_constraints,&rwork);CHKERRQ(ierr);
1522 #endif
1523     /* now we evaluate the optimal workspace using query with lwork=-1 */
1524     ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1525     ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
1526     lwork = -1;
1527     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1528 #if !defined(PETSC_USE_COMPLEX)
1529     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
1530 #else
1531     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
1532 #endif
1533     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1534     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
1535 #else /* on missing GESVD */
1536     /* SVD */
1537     PetscInt max_n,min_n;
1538     max_n = max_size_of_constraint;
1539     min_n = max_constraints;
1540     if (max_size_of_constraint < max_constraints) {
1541       min_n = max_size_of_constraint;
1542       max_n = max_constraints;
1543     }
1544     ierr = PetscMalloc1(min_n,&singular_vals);CHKERRQ(ierr);
1545 #if defined(PETSC_USE_COMPLEX)
1546     ierr = PetscMalloc1(5*min_n,&rwork);CHKERRQ(ierr);
1547 #endif
1548     /* now we evaluate the optimal workspace using query with lwork=-1 */
1549     lwork = -1;
1550     ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
1551     ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
1552     ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
1553     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1554 #if !defined(PETSC_USE_COMPLEX)
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,&lierr));
1556 #else
1557     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));
1558 #endif
1559     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1560     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
1561 #endif /* on missing GESVD */
1562     /* Allocate optimal workspace */
1563     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
1564     ierr = PetscMalloc1((PetscInt)lwork,&work);CHKERRQ(ierr);
1565   }
1566   /* Now we can loop on constraining sets */
1567   total_counts = 0;
1568   temp_indices[0] = 0;
1569   /* vertices */
1570   if (ISForVertices) {
1571     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1572     if (nnsp_has_cnst) { /* consider all vertices */
1573       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,n_vertices*sizeof(PetscInt));CHKERRQ(ierr);
1574       for (i=0;i<n_vertices;i++) {
1575         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1576         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1577         total_counts++;
1578       }
1579     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
1580       PetscBool used_vertex;
1581       for (i=0;i<n_vertices;i++) {
1582         used_vertex = PETSC_FALSE;
1583         k = 0;
1584         while (!used_vertex && k<nnsp_size) {
1585           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1586           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
1587             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
1588             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1589             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1590             total_counts++;
1591             used_vertex = PETSC_TRUE;
1592           }
1593           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1594           k++;
1595         }
1596       }
1597     }
1598     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1599     n_vertices = total_counts;
1600   }
1601 
1602   /* edges and faces */
1603   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1604     if (i<n_ISForEdges) {
1605       used_IS = &ISForEdges[i];
1606       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
1607     } else {
1608       used_IS = &ISForFaces[i-n_ISForEdges];
1609       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
1610     }
1611     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
1612     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
1613     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
1614     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1615     /* change of basis should not be performed on local periodic nodes */
1616     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
1617     if (nnsp_has_cnst) {
1618       PetscScalar quad_value;
1619       temp_constraints++;
1620       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
1621       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
1622       for (j=0;j<size_of_constraint;j++) {
1623         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
1624       }
1625       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1626       total_counts++;
1627     }
1628     for (k=0;k<nnsp_size;k++) {
1629       PetscReal real_value;
1630       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1631       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
1632       for (j=0;j<size_of_constraint;j++) {
1633         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
1634       }
1635       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1636       /* check if array is null on the connected component */
1637       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1638       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_one));
1639       if (real_value > 0.0) { /* keep indices and values */
1640         temp_constraints++;
1641         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1642         total_counts++;
1643       }
1644     }
1645     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1646     valid_constraints = temp_constraints;
1647     /* 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 */
1648     if (!pcbddc->use_nnsp_true && temp_constraints) {
1649       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
1650 
1651 #if defined(PETSC_MISSING_LAPACK_GESVD)
1652       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
1653          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
1654          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
1655             the constraints basis will differ (by a complex factor with absolute value equal to 1)
1656             from that computed using LAPACKgesvd
1657          -> This is due to a different computation of eigenvectors in LAPACKheev
1658          -> The quality of the POD-computed basis will be the same */
1659       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
1660       /* Store upper triangular part of correlation matrix */
1661       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1662       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1663       for (j=0;j<temp_constraints;j++) {
1664         for (k=0;k<j+1;k++) {
1665           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));
1666         }
1667       }
1668       /* compute eigenvalues and eigenvectors of correlation matrix */
1669       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1670       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
1671 #if !defined(PETSC_USE_COMPLEX)
1672       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
1673 #else
1674       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
1675 #endif
1676       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1677       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
1678       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
1679       j=0;
1680       while (j < temp_constraints && singular_vals[j] < tol) j++;
1681       total_counts=total_counts-j;
1682       valid_constraints = temp_constraints-j;
1683       /* scale and copy POD basis into used quadrature memory */
1684       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1685       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1686       ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
1687       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1688       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
1689       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1690       if (j<temp_constraints) {
1691         PetscInt ii;
1692         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
1693         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1694         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));
1695         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1696         for (k=0;k<temp_constraints-j;k++) {
1697           for (ii=0;ii<size_of_constraint;ii++) {
1698             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];
1699           }
1700         }
1701       }
1702 #else  /* on missing GESVD */
1703       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1704       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1705       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1706       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1707 #if !defined(PETSC_USE_COMPLEX)
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,&lierr));
1709 #else
1710       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));
1711 #endif
1712       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
1713       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1714       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
1715       k = temp_constraints;
1716       if (k > size_of_constraint) k = size_of_constraint;
1717       j = 0;
1718       while (j < k && singular_vals[k-j-1] < tol) j++;
1719       total_counts = total_counts-temp_constraints+k-j;
1720       valid_constraints = k-j;
1721 #endif /* on missing GESVD */
1722     }
1723     /* setting change_of_basis flag is safe now */
1724     if (boolforchange) {
1725       for (j=0;j<valid_constraints;j++) {
1726         PetscBTSet(change_basis,total_counts-j-1);
1727       }
1728     }
1729   }
1730   /* free index sets of faces, edges and vertices */
1731   for (i=0;i<n_ISForFaces;i++) {
1732     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1733   }
1734   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1735   for (i=0;i<n_ISForEdges;i++) {
1736     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1737   }
1738   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1739   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1740   /* map temp_indices_to_constraint in boundary numbering */
1741   ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,temp_indices[total_counts],temp_indices_to_constraint,&i,temp_indices_to_constraint_B);CHKERRQ(ierr);
1742   if (i != temp_indices[total_counts]) {
1743     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for constraints indices %d != %d\n",temp_indices[total_counts],i);
1744   }
1745 
1746   /* free workspace */
1747   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1748     ierr = PetscFree(work);CHKERRQ(ierr);
1749 #if defined(PETSC_USE_COMPLEX)
1750     ierr = PetscFree(rwork);CHKERRQ(ierr);
1751 #endif
1752     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1753 #if defined(PETSC_MISSING_LAPACK_GESVD)
1754     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1755     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1756 #endif
1757   }
1758   for (k=0;k<nnsp_size;k++) {
1759     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1760   }
1761   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1762 
1763   /* set quantities in pcbddc data structure and store previous primal size */
1764   /* n_vertices defines the number of subdomain corners in the primal space */
1765   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1766   olocal_primal_size = pcbddc->local_primal_size;
1767   pcbddc->local_primal_size = total_counts;
1768   pcbddc->n_vertices = n_vertices;
1769   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
1770 
1771   /* Create constraint matrix */
1772   /* The constraint matrix is used to compute the l2g map of primal dofs */
1773   /* so we need to set it up properly either with or without change of basis */
1774   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1775   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1776   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
1777   /* array to compute a local numbering of constraints : vertices first then constraints */
1778   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_numbering);CHKERRQ(ierr);
1779   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
1780   /* 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 */
1781   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_minloc);CHKERRQ(ierr);
1782   /* auxiliary stuff for basis change */
1783   ierr = PetscMalloc1(max_size_of_constraint,&global_indices);CHKERRQ(ierr);
1784   ierr = PetscBTCreate(pcis->n_B,&touched);CHKERRQ(ierr);
1785 
1786   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
1787   total_primal_vertices=0;
1788   for (i=0;i<pcbddc->local_primal_size;i++) {
1789     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1790     if (size_of_constraint == 1) {
1791       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]]);CHKERRQ(ierr);
1792       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
1793       aux_primal_minloc[total_primal_vertices]=0;
1794       total_primal_vertices++;
1795     } else if (PetscBTLookup(change_basis,i)) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
1796       PetscInt min_loc,min_index;
1797       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
1798       /* find first untouched local node */
1799       k = 0;
1800       while (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) k++;
1801       min_index = global_indices[k];
1802       min_loc = k;
1803       /* search the minimum among global nodes already untouched on the cc */
1804       for (k=1;k<size_of_constraint;k++) {
1805         /* there can be more than one constraint on a single connected component */
1806         if (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k]) && min_index > global_indices[k]) {
1807           min_index = global_indices[k];
1808           min_loc = k;
1809         }
1810       }
1811       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]+min_loc]);CHKERRQ(ierr);
1812       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
1813       aux_primal_minloc[total_primal_vertices]=min_loc;
1814       total_primal_vertices++;
1815     }
1816   }
1817   /* determine if a QR strategy is needed for change of basis */
1818   qr_needed = PETSC_FALSE;
1819   ierr = PetscBTCreate(pcbddc->local_primal_size,&qr_needed_idx);CHKERRQ(ierr);
1820   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1821     if (PetscBTLookup(change_basis,i)) {
1822       size_of_constraint = temp_indices[i+1]-temp_indices[i];
1823       j = 0;
1824       for (k=0;k<size_of_constraint;k++) {
1825         if (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) {
1826           j++;
1827         }
1828       }
1829       /* found more than one primal dof on the cc */
1830       if (j > 1) {
1831         PetscBTSet(qr_needed_idx,i);
1832         qr_needed = PETSC_TRUE;
1833       }
1834     }
1835   }
1836   /* free workspace */
1837   ierr = PetscFree(global_indices);CHKERRQ(ierr);
1838 
1839   /* permute indices in order to have a sorted set of vertices */
1840   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);CHKERRQ(ierr);
1841 
1842   /* nonzero structure of constraint matrix */
1843   ierr = PetscMalloc1(pcbddc->local_primal_size,&nnz);CHKERRQ(ierr);
1844   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
1845   j=total_primal_vertices;
1846   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1847     if (!PetscBTLookup(change_basis,i)) {
1848       nnz[j]=temp_indices[i+1]-temp_indices[i];
1849       j++;
1850     }
1851   }
1852   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1853   ierr = PetscFree(nnz);CHKERRQ(ierr);
1854   /* set values in constraint matrix */
1855   for (i=0;i<total_primal_vertices;i++) {
1856     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
1857   }
1858   total_counts = total_primal_vertices;
1859   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1860     if (!PetscBTLookup(change_basis,i)) {
1861       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1862       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);
1863       total_counts++;
1864     }
1865   }
1866   /* assembling */
1867   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1868   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1869   /*
1870   ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
1871   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
1872   */
1873   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1874   if (pcbddc->use_change_of_basis) {
1875     /* dual and primal dofs on a single cc */
1876     PetscInt     dual_dofs,primal_dofs;
1877     /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
1878     PetscInt     primal_counter;
1879     /* working stuff for GEQRF */
1880     PetscScalar  *qr_basis,*qr_tau = NULL,*qr_work,lqr_work_t;
1881     PetscBLASInt lqr_work;
1882     /* working stuff for UNGQR */
1883     PetscScalar  *gqr_work,lgqr_work_t;
1884     PetscBLASInt lgqr_work;
1885     /* working stuff for TRTRS */
1886     PetscScalar  *trs_rhs;
1887     PetscBLASInt Blas_NRHS;
1888     /* pointers for values insertion into change of basis matrix */
1889     PetscInt     *start_rows,*start_cols;
1890     PetscScalar  *start_vals;
1891     /* working stuff for values insertion */
1892     PetscBT      is_primal;
1893 
1894     /* change of basis acts on local interfaces -> dimension is n_B x n_B */
1895     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1896     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1897     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1898     /* work arrays */
1899     ierr = PetscMalloc1(pcis->n_B,&nnz);CHKERRQ(ierr);
1900     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
1901     /* nonzeros per row */
1902     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1903       if (PetscBTLookup(change_basis,i)) {
1904         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1905         if (PetscBTLookup(qr_needed_idx,i)) {
1906           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1907         } else {
1908           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = 2;
1909           /* get local primal index on the cc */
1910           j = 0;
1911           while (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+j])) j++;
1912           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1913         }
1914       }
1915     }
1916     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1917     ierr = PetscFree(nnz);CHKERRQ(ierr);
1918     /* Set initial identity in the matrix */
1919     for (i=0;i<pcis->n_B;i++) {
1920       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1921     }
1922 
1923     if (pcbddc->dbg_flag) {
1924       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1925       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
1926     }
1927 
1928 
1929     /* Now we loop on the constraints which need a change of basis */
1930     /*
1931        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
1932        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)
1933 
1934        Basic blocks of change of basis matrix T computed
1935 
1936           - Using the following block transformation if there is only a primal dof on the cc
1937             (in the example, primal dof is the last one of the edge in LOCAL ordering
1938              in this code, primal dof is the first one of the edge in GLOBAL ordering)
1939             | 1        0   ...        0     1 |
1940             | 0        1   ...        0     1 |
1941             |              ...                |
1942             | 0        ...            1     1 |
1943             | -s_1/s_n ...    -s_{n-1}/-s_n 1 |
1944 
1945           - via QR decomposition of constraints otherwise
1946     */
1947     if (qr_needed) {
1948       /* space to store Q */
1949       ierr = PetscMalloc1((max_size_of_constraint)*(max_size_of_constraint),&qr_basis);CHKERRQ(ierr);
1950       /* first we issue queries for optimal work */
1951       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1952       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1953       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1954       lqr_work = -1;
1955       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
1956       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
1957       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
1958       ierr = PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);CHKERRQ(ierr);
1959       lgqr_work = -1;
1960       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1961       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
1962       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
1963       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1964       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
1965       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
1966       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
1967       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
1968       ierr = PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);CHKERRQ(ierr);
1969       /* array to store scaling factors for reflectors */
1970       ierr = PetscMalloc1(max_constraints,&qr_tau);CHKERRQ(ierr);
1971       /* array to store rhs and solution of triangular solver */
1972       ierr = PetscMalloc1(max_constraints*max_constraints,&trs_rhs);CHKERRQ(ierr);
1973       /* allocating workspace for check */
1974       if (pcbddc->dbg_flag) {
1975         ierr = PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&work);CHKERRQ(ierr);
1976       }
1977     }
1978     /* array to store whether a node is primal or not */
1979     ierr = PetscBTCreate(pcis->n_B,&is_primal);CHKERRQ(ierr);
1980     ierr = PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);CHKERRQ(ierr);
1981     ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,aux_primal_numbering,&i,aux_primal_numbering_B);CHKERRQ(ierr);
1982     if (i != total_primal_vertices) {
1983       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",total_primal_vertices,i);
1984     }
1985     for (i=0;i<total_primal_vertices;i++) {
1986       ierr = PetscBTSet(is_primal,aux_primal_numbering_B[i]);CHKERRQ(ierr);
1987     }
1988     ierr = PetscFree(aux_primal_numbering_B);CHKERRQ(ierr);
1989 
1990     /* loop on constraints and see whether or not they need a change of basis and compute it */
1991     /* -> using implicit ordering contained in temp_indices data */
1992     total_counts = pcbddc->n_vertices;
1993     primal_counter = total_counts;
1994     while (total_counts<pcbddc->local_primal_size) {
1995       primal_dofs = 1;
1996       if (PetscBTLookup(change_basis,total_counts)) {
1997         /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
1998         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]]) {
1999           primal_dofs++;
2000         }
2001         /* get constraint info */
2002         size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
2003         dual_dofs = size_of_constraint-primal_dofs;
2004 
2005         if (pcbddc->dbg_flag) {
2006           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);
2007         }
2008 
2009         if (primal_dofs > 1) { /* QR */
2010 
2011           /* copy quadrature constraints for change of basis check */
2012           if (pcbddc->dbg_flag) {
2013             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2014           }
2015           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
2016           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2017 
2018           /* compute QR decomposition of constraints */
2019           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2020           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2021           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2022           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2023           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
2024           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
2025           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2026 
2027           /* explictly compute R^-T */
2028           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
2029           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
2030           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2031           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
2032           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2033           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2034           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2035           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
2036           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
2037           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2038 
2039           /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
2040           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2041           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2042           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2043           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2044           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2045           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
2046           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
2047           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2048 
2049           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
2050              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
2051              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
2052           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2053           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2054           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2055           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2056           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2057           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
2058           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2059           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));
2060           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2061           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2062 
2063           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
2064           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
2065           /* insert cols for primal dofs */
2066           for (j=0;j<primal_dofs;j++) {
2067             start_vals = &qr_basis[j*size_of_constraint];
2068             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
2069             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2070           }
2071           /* insert cols for dual dofs */
2072           for (j=0,k=0;j<dual_dofs;k++) {
2073             if (!PetscBTLookup(is_primal,temp_indices_to_constraint_B[temp_indices[total_counts]+k])) {
2074               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
2075               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2076               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2077               j++;
2078             }
2079           }
2080 
2081           /* check change of basis */
2082           if (pcbddc->dbg_flag) {
2083             PetscInt   ii,jj;
2084             PetscBool valid_qr=PETSC_TRUE;
2085             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
2086             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2087             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
2088             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2089             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
2090             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
2091             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2092             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));
2093             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2094             for (jj=0;jj<size_of_constraint;jj++) {
2095               for (ii=0;ii<primal_dofs;ii++) {
2096                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
2097                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
2098               }
2099             }
2100             if (!valid_qr) {
2101               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");CHKERRQ(ierr);
2102               for (jj=0;jj<size_of_constraint;jj++) {
2103                 for (ii=0;ii<primal_dofs;ii++) {
2104                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
2105                     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]));
2106                   }
2107                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
2108                     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]));
2109                   }
2110                 }
2111               }
2112             } else {
2113               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");CHKERRQ(ierr);
2114             }
2115           }
2116         } else { /* simple transformation block */
2117           PetscInt row,col;
2118           PetscScalar val;
2119           for (j=0;j<size_of_constraint;j++) {
2120             row = temp_indices_to_constraint_B[temp_indices[total_counts]+j];
2121             if (!PetscBTLookup(is_primal,row)) {
2122               col = temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2123               ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);CHKERRQ(ierr);
2124               ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,col,1.0,INSERT_VALUES);CHKERRQ(ierr);
2125             } else {
2126               for (k=0;k<size_of_constraint;k++) {
2127                 col = temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2128                 if (row != col) {
2129                   val = -temp_quadrature_constraint[temp_indices[total_counts]+k]/temp_quadrature_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2130                 } else {
2131                   val = 1.0;
2132                 }
2133                 ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,row,col,val,INSERT_VALUES);CHKERRQ(ierr);
2134               }
2135             }
2136           }
2137           if (pcbddc->dbg_flag) {
2138             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");CHKERRQ(ierr);
2139           }
2140         }
2141         /* increment primal counter */
2142         primal_counter += primal_dofs;
2143       } else {
2144         if (pcbddc->dbg_flag) {
2145           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);
2146         }
2147       }
2148       /* increment constraint counter total_counts */
2149       total_counts += primal_dofs;
2150     }
2151 
2152     /* free workspace */
2153     if (qr_needed) {
2154       if (pcbddc->dbg_flag) {
2155         ierr = PetscFree(work);CHKERRQ(ierr);
2156       }
2157       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
2158       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
2159       ierr = PetscFree(qr_work);CHKERRQ(ierr);
2160       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
2161       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
2162     }
2163     ierr = PetscBTDestroy(&is_primal);CHKERRQ(ierr);
2164     /* assembling */
2165     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2166     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2167     /*
2168     ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
2169     ierr = MatView(pcbddc->ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
2170     */
2171   }
2172   /* Change of basis as provided by the user in local numbering (internal and boundary) or boundary only */
2173   if (pcbddc->user_ChangeOfBasisMatrix) {
2174     PetscInt rows,cols;
2175     ierr = MatGetSize(pcbddc->user_ChangeOfBasisMatrix,&rows,&cols);CHKERRQ(ierr);
2176     if (rows == pcis->n && cols == pcis->n) {
2177       ierr = MatGetSubMatrix(pcbddc->user_ChangeOfBasisMatrix,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2178     } else {
2179       ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2180       pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
2181     }
2182   }
2183 
2184   /* get indices in local ordering for vertices and constraints */
2185   if (olocal_primal_size == pcbddc->local_primal_size) { /* if this is true, I need to check if a new primal space has been introduced */
2186     ierr = PetscMalloc1(olocal_primal_size,&oprimal_indices_local_idxs);CHKERRQ(ierr);
2187     ierr = PetscMemcpy(oprimal_indices_local_idxs,pcbddc->primal_indices_local_idxs,olocal_primal_size*sizeof(PetscInt));CHKERRQ(ierr);
2188   }
2189   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2190   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2191   ierr = PetscMalloc1(pcbddc->local_primal_size,&pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2192   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&i,&aux_primal_numbering);CHKERRQ(ierr);
2193   ierr = PetscMemcpy(pcbddc->primal_indices_local_idxs,aux_primal_numbering,i*sizeof(PetscInt));CHKERRQ(ierr);
2194   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2195   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&j,&aux_primal_numbering);CHKERRQ(ierr);
2196   ierr = PetscMemcpy(&pcbddc->primal_indices_local_idxs[i],aux_primal_numbering,j*sizeof(PetscInt));CHKERRQ(ierr);
2197   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2198   /* set quantities in PCBDDC data struct */
2199   pcbddc->n_actual_vertices = i;
2200   /* check if a new primal space has been introduced */
2201   pcbddc->new_primal_space_local = PETSC_TRUE;
2202   if (olocal_primal_size == pcbddc->local_primal_size) {
2203     ierr = PetscMemcmp(pcbddc->primal_indices_local_idxs,oprimal_indices_local_idxs,olocal_primal_size,&pcbddc->new_primal_space_local);CHKERRQ(ierr);
2204     pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
2205     ierr = PetscFree(oprimal_indices_local_idxs);CHKERRQ(ierr);
2206   }
2207   /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
2208   ierr = MPI_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
2209 
2210   /* flush dbg viewer */
2211   if (pcbddc->dbg_flag) {
2212     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2213   }
2214 
2215   /* free workspace */
2216   ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2217   ierr = PetscBTDestroy(&qr_needed_idx);CHKERRQ(ierr);
2218   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
2219   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2220   ierr = PetscBTDestroy(&change_basis);CHKERRQ(ierr);
2221   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
2222   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
2223   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
2224   PetscFunctionReturn(0);
2225 }
2226 
2227 #undef __FUNCT__
2228 #define __FUNCT__ "PCBDDCAnalyzeInterface"
2229 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
2230 {
2231   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
2232   PC_IS       *pcis = (PC_IS*)pc->data;
2233   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
2234   PetscInt    ierr,i,vertex_size;
2235   PetscViewer viewer=pcbddc->dbg_viewer;
2236 
2237   PetscFunctionBegin;
2238   /* Reset previously computed graph */
2239   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
2240   /* Init local Graph struct */
2241   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
2242 
2243   /* Check validity of the csr graph passed in by the user */
2244   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
2245     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
2246   }
2247 
2248   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
2249   if (pcbddc->use_local_adj && (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy)) {
2250     Mat mat_adj;
2251     const PetscInt *xadj,*adjncy;
2252     PetscBool flg_row=PETSC_TRUE;
2253 
2254     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
2255     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2256     if (!flg_row) {
2257       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
2258     }
2259     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
2260     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2261     if (!flg_row) {
2262       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2263     }
2264     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
2265     pcbddc->deluxe_compute_rowadj = PETSC_FALSE;
2266   }
2267 
2268   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
2269   vertex_size = 1;
2270   if (pcbddc->user_provided_isfordofs) {
2271     if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
2272       ierr = PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2273       for (i=0;i<pcbddc->n_ISForDofs;i++) {
2274         ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2275         ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
2276       }
2277       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
2278       pcbddc->n_ISForDofs = 0;
2279       ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
2280     }
2281     /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
2282     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
2283   } else {
2284     if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
2285       ierr = MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);CHKERRQ(ierr);
2286       ierr = PetscMalloc(pcbddc->n_ISForDofsLocal*sizeof(IS),&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2287       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
2288         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2289       }
2290     }
2291   }
2292 
2293   /* Setup of Graph */
2294   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
2295     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
2296   }
2297   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
2298     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
2299   }
2300   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices);
2301 
2302   /* Graph's connected components analysis */
2303   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
2304 
2305   /* print some info to stdout */
2306   if (pcbddc->dbg_flag) {
2307     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
2308   }
2309 
2310   /* mark topography has done */
2311   pcbddc->recompute_topography = PETSC_FALSE;
2312   PetscFunctionReturn(0);
2313 }
2314 
2315 #undef __FUNCT__
2316 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
2317 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt **vertices_idx)
2318 {
2319   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2320   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
2321   PetscErrorCode ierr;
2322 
2323   PetscFunctionBegin;
2324   n = 0;
2325   vertices = 0;
2326   if (pcbddc->ConstraintMatrix) {
2327     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
2328     for (i=0;i<local_primal_size;i++) {
2329       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2330       if (size_of_constraint == 1) n++;
2331       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2332     }
2333     if (vertices_idx) {
2334       ierr = PetscMalloc1(n,&vertices);CHKERRQ(ierr);
2335       n = 0;
2336       for (i=0;i<local_primal_size;i++) {
2337         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2338         if (size_of_constraint == 1) {
2339           vertices[n++]=row_cmat_indices[0];
2340         }
2341         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2342       }
2343     }
2344   }
2345   *n_vertices = n;
2346   if (vertices_idx) *vertices_idx = vertices;
2347   PetscFunctionReturn(0);
2348 }
2349 
2350 #undef __FUNCT__
2351 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
2352 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt **constraints_idx)
2353 {
2354   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2355   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
2356   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
2357   PetscBT        touched;
2358   PetscErrorCode ierr;
2359 
2360     /* This function assumes that the number of local constraints per connected component
2361        is not greater than the number of nodes defined for the connected component
2362        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
2363   PetscFunctionBegin;
2364   n = 0;
2365   constraints_index = 0;
2366   if (pcbddc->ConstraintMatrix) {
2367     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
2368     max_size_of_constraint = 0;
2369     for (i=0;i<local_primal_size;i++) {
2370       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2371       if (size_of_constraint > 1) {
2372         n++;
2373       }
2374       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
2375       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2376     }
2377     if (constraints_idx) {
2378       ierr = PetscMalloc1(n,&constraints_index);CHKERRQ(ierr);
2379       ierr = PetscMalloc1(max_size_of_constraint,&row_cmat_global_indices);CHKERRQ(ierr);
2380       ierr = PetscBTCreate(local_size,&touched);CHKERRQ(ierr);
2381       n = 0;
2382       for (i=0;i<local_primal_size;i++) {
2383         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2384         if (size_of_constraint > 1) {
2385           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
2386           /* find first untouched local node */
2387           j = 0;
2388           while (PetscBTLookup(touched,row_cmat_indices[j])) j++;
2389           min_index = row_cmat_global_indices[j];
2390           min_loc = j;
2391           /* search the minimum among nodes not yet touched on the connected component
2392              since there can be more than one constraint on a single cc */
2393           for (j=1;j<size_of_constraint;j++) {
2394             if (!PetscBTLookup(touched,row_cmat_indices[j]) && min_index > row_cmat_global_indices[j]) {
2395               min_index = row_cmat_global_indices[j];
2396               min_loc = j;
2397             }
2398           }
2399           ierr = PetscBTSet(touched,row_cmat_indices[min_loc]);CHKERRQ(ierr);
2400           constraints_index[n++] = row_cmat_indices[min_loc];
2401         }
2402         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2403       }
2404       ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2405       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
2406     }
2407   }
2408   *n_constraints = n;
2409   if (constraints_idx) *constraints_idx = constraints_index;
2410   PetscFunctionReturn(0);
2411 }
2412 
2413 /* the next two functions has been adapted from pcis.c */
2414 #undef __FUNCT__
2415 #define __FUNCT__ "PCBDDCApplySchur"
2416 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2417 {
2418   PetscErrorCode ierr;
2419   PC_IS          *pcis = (PC_IS*)(pc->data);
2420 
2421   PetscFunctionBegin;
2422   if (!vec2_B) { vec2_B = v; }
2423   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2424   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
2425   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2426   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
2427   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2428   PetscFunctionReturn(0);
2429 }
2430 
2431 #undef __FUNCT__
2432 #define __FUNCT__ "PCBDDCApplySchurTranspose"
2433 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2434 {
2435   PetscErrorCode ierr;
2436   PC_IS          *pcis = (PC_IS*)(pc->data);
2437 
2438   PetscFunctionBegin;
2439   if (!vec2_B) { vec2_B = v; }
2440   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2441   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
2442   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2443   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
2444   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2445   PetscFunctionReturn(0);
2446 }
2447 
2448 #undef __FUNCT__
2449 #define __FUNCT__ "PCBDDCSubsetNumbering"
2450 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[])
2451 {
2452   Vec            local_vec,global_vec;
2453   IS             seqis,paris;
2454   VecScatter     scatter_ctx;
2455   PetscScalar    *array;
2456   PetscInt       *temp_global_dofs;
2457   PetscScalar    globalsum;
2458   PetscInt       i,j,s;
2459   PetscInt       nlocals,first_index,old_index,max_local;
2460   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
2461   PetscMPIInt    *dof_sizes,*dof_displs;
2462   PetscBool      first_found;
2463   PetscErrorCode ierr;
2464 
2465   PetscFunctionBegin;
2466   /* mpi buffers */
2467   ierr = MPI_Comm_size(comm,&size_prec_comm);CHKERRQ(ierr);
2468   ierr = MPI_Comm_rank(comm,&rank_prec_comm);CHKERRQ(ierr);
2469   j = ( !rank_prec_comm ? size_prec_comm : 0);
2470   ierr = PetscMalloc1(j,&dof_sizes);CHKERRQ(ierr);
2471   ierr = PetscMalloc1(j,&dof_displs);CHKERRQ(ierr);
2472   /* get maximum size of subset */
2473   ierr = PetscMalloc1(n_local_dofs,&temp_global_dofs);CHKERRQ(ierr);
2474   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
2475   max_local = 0;
2476   for (i=0;i<n_local_dofs;i++) {
2477     if (max_local < temp_global_dofs[i] ) {
2478       max_local = temp_global_dofs[i];
2479     }
2480   }
2481   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
2482   max_global++;
2483   max_local = 0;
2484   for (i=0;i<n_local_dofs;i++) {
2485     if (max_local < local_dofs[i] ) {
2486       max_local = local_dofs[i];
2487     }
2488   }
2489   max_local++;
2490   /* allocate workspace */
2491   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
2492   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
2493   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
2494   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
2495   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
2496   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
2497   /* create scatter */
2498   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
2499   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
2500   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
2501   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
2502   ierr = ISDestroy(&paris);CHKERRQ(ierr);
2503   /* init array */
2504   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
2505   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2506   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2507   if (local_dofs_mult) {
2508     for (i=0;i<n_local_dofs;i++) {
2509       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
2510     }
2511   } else {
2512     for (i=0;i<n_local_dofs;i++) {
2513       array[local_dofs[i]]=1.0;
2514     }
2515   }
2516   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2517   /* scatter into global vec and get total number of global dofs */
2518   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2519   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2520   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
2521   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
2522   /* Fill global_vec with cumulative function for global numbering */
2523   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
2524   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
2525   nlocals = 0;
2526   first_index = -1;
2527   first_found = PETSC_FALSE;
2528   for (i=0;i<s;i++) {
2529     if (!first_found && PetscRealPart(array[i]) > 0.1) {
2530       first_found = PETSC_TRUE;
2531       first_index = i;
2532     }
2533     nlocals += (PetscInt)PetscRealPart(array[i]);
2534   }
2535   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2536   if (!rank_prec_comm) {
2537     dof_displs[0]=0;
2538     for (i=1;i<size_prec_comm;i++) {
2539       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
2540     }
2541   }
2542   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2543   if (first_found) {
2544     array[first_index] += (PetscScalar)nlocals;
2545     old_index = first_index;
2546     for (i=first_index+1;i<s;i++) {
2547       if (PetscRealPart(array[i]) > 0.1) {
2548         array[i] += array[old_index];
2549         old_index = i;
2550       }
2551     }
2552   }
2553   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
2554   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2555   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2556   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2557   /* get global ordering of local dofs */
2558   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2559   if (local_dofs_mult) {
2560     for (i=0;i<n_local_dofs;i++) {
2561       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
2562     }
2563   } else {
2564     for (i=0;i<n_local_dofs;i++) {
2565       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
2566     }
2567   }
2568   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2569   /* free workspace */
2570   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
2571   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
2572   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
2573   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
2574   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
2575   /* return pointer to global ordering of local dofs */
2576   *global_numbering_subset = temp_global_dofs;
2577   PetscFunctionReturn(0);
2578 }
2579 
2580 #undef __FUNCT__
2581 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
2582 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
2583 {
2584   PetscInt       i,j;
2585   PetscScalar    *alphas;
2586   PetscErrorCode ierr;
2587 
2588   PetscFunctionBegin;
2589   /* this implements stabilized Gram-Schmidt */
2590   ierr = PetscMalloc1(n,&alphas);CHKERRQ(ierr);
2591   for (i=0;i<n;i++) {
2592     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
2593     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
2594     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
2595   }
2596   ierr = PetscFree(alphas);CHKERRQ(ierr);
2597   PetscFunctionReturn(0);
2598 }
2599 
2600 #undef __FUNCT__
2601 #define __FUNCT__ "MatISGetSubassemblingPattern"
2602 PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscBool contiguous, IS* is_sends)
2603 {
2604   Mat             subdomain_adj;
2605   IS              new_ranks,ranks_send_to;
2606   MatPartitioning partitioner;
2607   Mat_IS          *matis;
2608   PetscInt        n_neighs,*neighs,*n_shared,**shared;
2609   PetscInt        prank;
2610   PetscMPIInt     size,rank,color;
2611   PetscInt        *xadj,*adjncy,*oldranks;
2612   PetscInt        *adjncy_wgt,*v_wgt,*is_indices,*ranks_send_to_idx;
2613   PetscInt        i,j,local_size,threshold=0;
2614   PetscErrorCode  ierr;
2615   PetscBool       use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
2616   PetscSubcomm    subcomm;
2617 
2618   PetscFunctionBegin;
2619   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_square",&use_square,NULL);CHKERRQ(ierr);
2620   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);CHKERRQ(ierr);
2621   ierr = PetscOptionsGetInt(NULL,"-matis_partitioning_threshold",&threshold,NULL);CHKERRQ(ierr);
2622 
2623   /* Get info on mapping */
2624   matis = (Mat_IS*)(mat->data);
2625   ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&local_size);CHKERRQ(ierr);
2626   ierr = ISLocalToGlobalMappingGetInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2627 
2628   /* build local CSR graph of subdomains' connectivity */
2629   ierr = PetscMalloc1(2,&xadj);CHKERRQ(ierr);
2630   xadj[0] = 0;
2631   xadj[1] = PetscMax(n_neighs-1,0);
2632   ierr = PetscMalloc1(xadj[1],&adjncy);CHKERRQ(ierr);
2633   ierr = PetscMalloc1(xadj[1],&adjncy_wgt);CHKERRQ(ierr);
2634 
2635   if (threshold) {
2636     PetscInt* count,min_threshold;
2637     ierr = PetscMalloc1(local_size,&count);CHKERRQ(ierr);
2638     ierr = PetscMemzero(count,local_size*sizeof(PetscInt));CHKERRQ(ierr);
2639     for (i=1;i<n_neighs;i++) {/* i=1 so I don't count myself -> faces nodes counts to 1 */
2640       for (j=0;j<n_shared[i];j++) {
2641         count[shared[i][j]] += 1;
2642       }
2643     }
2644     /* adapt threshold since we dont want to lose significant connections */
2645     min_threshold = n_neighs;
2646     for (i=1;i<n_neighs;i++) {
2647       for (j=0;j<n_shared[i];j++) {
2648         min_threshold = PetscMin(count[shared[i][j]],min_threshold);
2649       }
2650     }
2651     threshold = PetscMax(min_threshold+1,threshold);
2652     xadj[1] = 0;
2653     for (i=1;i<n_neighs;i++) {
2654       for (j=0;j<n_shared[i];j++) {
2655         if (count[shared[i][j]] < threshold) {
2656           adjncy[xadj[1]] = neighs[i];
2657           adjncy_wgt[xadj[1]] = n_shared[i];
2658           xadj[1]++;
2659           break;
2660         }
2661       }
2662     }
2663     ierr = PetscFree(count);CHKERRQ(ierr);
2664   } else {
2665     if (xadj[1]) {
2666       ierr = PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));CHKERRQ(ierr);
2667       ierr = PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));CHKERRQ(ierr);
2668     }
2669   }
2670   ierr = ISLocalToGlobalMappingRestoreInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2671   if (use_square) {
2672     for (i=0;i<xadj[1];i++) {
2673       adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
2674     }
2675   }
2676   ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2677 
2678   ierr = PetscMalloc(sizeof(PetscInt),&ranks_send_to_idx);CHKERRQ(ierr);
2679 
2680   /*
2681     Restrict work on active processes only.
2682   */
2683   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);CHKERRQ(ierr);
2684   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr); /* 2 groups, active process and not active processes */
2685   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
2686   ierr = PetscMPIIntCast(!local_size,&color);CHKERRQ(ierr);
2687   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2688   if (color) {
2689     ierr = PetscFree(xadj);CHKERRQ(ierr);
2690     ierr = PetscFree(adjncy);CHKERRQ(ierr);
2691     ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
2692   } else {
2693     PetscInt coarsening_ratio;
2694     ierr = MPI_Comm_size(subcomm->comm,&size);CHKERRQ(ierr);
2695     ierr = PetscMalloc1(size,&oldranks);CHKERRQ(ierr);
2696     prank = rank;
2697     ierr = MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm->comm);CHKERRQ(ierr);
2698     /*
2699     for (i=0;i<size;i++) {
2700       PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
2701     }
2702     */
2703     for (i=0;i<xadj[1];i++) {
2704       ierr = PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);CHKERRQ(ierr);
2705     }
2706     ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2707     ierr = MatCreateMPIAdj(subcomm->comm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);CHKERRQ(ierr);
2708     /* ierr = MatView(subdomain_adj,0);CHKERRQ(ierr); */
2709 
2710     /* Partition */
2711     ierr = MatPartitioningCreate(subcomm->comm,&partitioner);CHKERRQ(ierr);
2712     ierr = MatPartitioningSetAdjacency(partitioner,subdomain_adj);CHKERRQ(ierr);
2713     if (use_vwgt) {
2714       ierr = PetscMalloc(sizeof(*v_wgt),&v_wgt);CHKERRQ(ierr);
2715       v_wgt[0] = local_size;
2716       ierr = MatPartitioningSetVertexWeights(partitioner,v_wgt);CHKERRQ(ierr);
2717     }
2718     n_subdomains = PetscMin((PetscInt)size,n_subdomains);
2719     coarsening_ratio = size/n_subdomains;
2720     /* Parmetis does not always give back nparts with small graphs! this should be taken into account */
2721     ierr = MatPartitioningSetNParts(partitioner,n_subdomains);CHKERRQ(ierr);
2722     ierr = MatPartitioningSetFromOptions(partitioner);CHKERRQ(ierr);
2723     ierr = MatPartitioningApply(partitioner,&new_ranks);CHKERRQ(ierr);
2724     /* ierr = MatPartitioningView(partitioner,0);CHKERRQ(ierr); */
2725 
2726     ierr = ISGetIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2727     if (contiguous) {
2728       ranks_send_to_idx[0] = oldranks[is_indices[0]]; /* contiguos set of processes */
2729     } else {
2730       ranks_send_to_idx[0] = coarsening_ratio*oldranks[is_indices[0]]; /* scattered set of processes */
2731     }
2732     ierr = ISRestoreIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2733     /* clean up */
2734     ierr = PetscFree(oldranks);CHKERRQ(ierr);
2735     ierr = ISDestroy(&new_ranks);CHKERRQ(ierr);
2736     ierr = MatDestroy(&subdomain_adj);CHKERRQ(ierr);
2737     ierr = MatPartitioningDestroy(&partitioner);CHKERRQ(ierr);
2738   }
2739   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
2740 
2741   /* assemble parallel IS for sends */
2742   i = 1;
2743   if (color) i=0;
2744   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);CHKERRQ(ierr);
2745 
2746   /* get back IS */
2747   *is_sends = ranks_send_to;
2748   PetscFunctionReturn(0);
2749 }
2750 
2751 typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;
2752 
2753 #undef __FUNCT__
2754 #define __FUNCT__ "MatISSubassemble"
2755 PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
2756 {
2757   Mat                    local_mat;
2758   Mat_IS                 *matis;
2759   IS                     is_sends_internal;
2760   PetscInt               rows,cols;
2761   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
2762   PetscBool              ismatis,isdense,destroy_mat;
2763   ISLocalToGlobalMapping l2gmap;
2764   PetscInt*              l2gmap_indices;
2765   const PetscInt*        is_indices;
2766   MatType                new_local_type;
2767   /* buffers */
2768   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
2769   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
2770   PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
2771   /* MPI */
2772   MPI_Comm               comm,comm_n;
2773   PetscSubcomm           subcomm;
2774   PetscMPIInt            n_sends,n_recvs,commsize;
2775   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
2776   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
2777   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
2778   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
2779   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
2780   PetscErrorCode         ierr;
2781 
2782   PetscFunctionBegin;
2783   /* TODO: add missing checks */
2784   PetscValidLogicalCollectiveInt(mat,n_subdomains,3);
2785   PetscValidLogicalCollectiveBool(mat,restrict_comm,4);
2786   PetscValidLogicalCollectiveEnum(mat,reuse,5);
2787   PetscValidLogicalCollectiveInt(mat,nis,7);
2788   ierr = PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);CHKERRQ(ierr);
2789   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
2790   ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
2791   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);CHKERRQ(ierr);
2792   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
2793   ierr = MatGetSize(local_mat,&rows,&cols);CHKERRQ(ierr);
2794   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
2795   if (reuse == MAT_REUSE_MATRIX && *mat_n) {
2796     PetscInt mrows,mcols,mnrows,mncols;
2797     ierr = PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);CHKERRQ(ierr);
2798     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
2799     ierr = MatGetSize(mat,&mrows,&mcols);CHKERRQ(ierr);
2800     ierr = MatGetSize(*mat_n,&mnrows,&mncols);CHKERRQ(ierr);
2801     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
2802     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
2803   }
2804   ierr = MatGetBlockSize(local_mat,&bs);CHKERRQ(ierr);
2805   PetscValidLogicalCollectiveInt(mat,bs,0);
2806   /* prepare IS for sending if not provided */
2807   if (!is_sends) {
2808     PetscBool pcontig = PETSC_TRUE;
2809     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
2810     ierr = MatISGetSubassemblingPattern(mat,n_subdomains,pcontig,&is_sends_internal);CHKERRQ(ierr);
2811   } else {
2812     ierr = PetscObjectReference((PetscObject)is_sends);CHKERRQ(ierr);
2813     is_sends_internal = is_sends;
2814   }
2815 
2816   /* get pointer of MATIS data */
2817   matis = (Mat_IS*)mat->data;
2818 
2819   /* get comm */
2820   comm = PetscObjectComm((PetscObject)mat);
2821 
2822   /* compute number of sends */
2823   ierr = ISGetLocalSize(is_sends_internal,&i);CHKERRQ(ierr);
2824   ierr = PetscMPIIntCast(i,&n_sends);CHKERRQ(ierr);
2825 
2826   /* compute number of receives */
2827   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
2828   ierr = PetscMalloc1(commsize,&iflags);CHKERRQ(ierr);
2829   ierr = PetscMemzero(iflags,commsize*sizeof(*iflags));CHKERRQ(ierr);
2830   ierr = ISGetIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
2831   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
2832   ierr = PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);CHKERRQ(ierr);
2833   ierr = PetscFree(iflags);CHKERRQ(ierr);
2834 
2835   /* restrict comm if requested */
2836   subcomm = 0;
2837   destroy_mat = PETSC_FALSE;
2838   if (restrict_comm) {
2839     PetscMPIInt color,rank,subcommsize;
2840     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2841     color = 0;
2842     if (n_sends && !n_recvs) color = 1; /* sending only processes will not partecipate in new comm */
2843     ierr = MPI_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
2844     subcommsize = commsize - subcommsize;
2845     /* check if reuse has been requested */
2846     if (reuse == MAT_REUSE_MATRIX) {
2847       if (*mat_n) {
2848         PetscMPIInt subcommsize2;
2849         ierr = MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);CHKERRQ(ierr);
2850         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
2851         comm_n = PetscObjectComm((PetscObject)*mat_n);
2852       } else {
2853         comm_n = PETSC_COMM_SELF;
2854       }
2855     } else { /* MAT_INITIAL_MATRIX */
2856       ierr = PetscSubcommCreate(comm,&subcomm);CHKERRQ(ierr);
2857       ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
2858       ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2859       comm_n = subcomm->comm;
2860     }
2861     /* flag to destroy *mat_n if not significative */
2862     if (color) destroy_mat = PETSC_TRUE;
2863   } else {
2864     comm_n = comm;
2865   }
2866 
2867   /* prepare send/receive buffers */
2868   ierr = PetscMalloc1(commsize,&ilengths_idxs);CHKERRQ(ierr);
2869   ierr = PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));CHKERRQ(ierr);
2870   ierr = PetscMalloc1(commsize,&ilengths_vals);CHKERRQ(ierr);
2871   ierr = PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));CHKERRQ(ierr);
2872   if (nis) {
2873     ierr = PetscMalloc(commsize*sizeof(*ilengths_idxs_is),&ilengths_idxs_is);CHKERRQ(ierr);
2874     ierr = PetscMemzero(ilengths_idxs_is,commsize*sizeof(*ilengths_idxs_is));CHKERRQ(ierr);
2875   }
2876 
2877   /* Get data from local matrices */
2878   if (!isdense) {
2879     /* TODO: See below some guidelines on how to prepare the local buffers */
2880     /*
2881        send_buffer_vals should contain the raw values of the local matrix
2882        send_buffer_idxs should contain:
2883        - MatType_PRIVATE type
2884        - PetscInt        size_of_l2gmap
2885        - PetscInt        global_row_indices[size_of_l2gmap]
2886        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
2887     */
2888   } else {
2889     ierr = MatDenseGetArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
2890     ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&i);CHKERRQ(ierr);
2891     ierr = PetscMalloc1((i+2),&send_buffer_idxs);CHKERRQ(ierr);
2892     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
2893     send_buffer_idxs[1] = i;
2894     ierr = ISLocalToGlobalMappingGetIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
2895     ierr = PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));CHKERRQ(ierr);
2896     ierr = ISLocalToGlobalMappingRestoreIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
2897     ierr = PetscMPIIntCast(i,&len);CHKERRQ(ierr);
2898     for (i=0;i<n_sends;i++) {
2899       ilengths_vals[is_indices[i]] = len*len;
2900       ilengths_idxs[is_indices[i]] = len+2;
2901     }
2902   }
2903   ierr = PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);CHKERRQ(ierr);
2904   /* additional is (if any) */
2905   if (nis) {
2906     PetscMPIInt psum;
2907     PetscInt j;
2908     for (j=0,psum=0;j<nis;j++) {
2909       PetscInt plen;
2910       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
2911       ierr = PetscMPIIntCast(plen,&len);CHKERRQ(ierr);
2912       psum += len+1; /* indices + lenght */
2913     }
2914     ierr = PetscMalloc(psum*sizeof(PetscInt),&send_buffer_idxs_is);CHKERRQ(ierr);
2915     for (j=0,psum=0;j<nis;j++) {
2916       PetscInt plen;
2917       const PetscInt *is_array_idxs;
2918       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
2919       send_buffer_idxs_is[psum] = plen;
2920       ierr = ISGetIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
2921       ierr = PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));CHKERRQ(ierr);
2922       ierr = ISRestoreIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
2923       psum += plen+1; /* indices + lenght */
2924     }
2925     for (i=0;i<n_sends;i++) {
2926       ilengths_idxs_is[is_indices[i]] = psum;
2927     }
2928     ierr = PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);CHKERRQ(ierr);
2929   }
2930 
2931   buf_size_idxs = 0;
2932   buf_size_vals = 0;
2933   buf_size_idxs_is = 0;
2934   for (i=0;i<n_recvs;i++) {
2935     buf_size_idxs += (PetscInt)olengths_idxs[i];
2936     buf_size_vals += (PetscInt)olengths_vals[i];
2937     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
2938   }
2939   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);CHKERRQ(ierr);
2940   ierr = PetscMalloc1(buf_size_vals,&recv_buffer_vals);CHKERRQ(ierr);
2941   ierr = PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);CHKERRQ(ierr);
2942 
2943   /* get new tags for clean communications */
2944   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);CHKERRQ(ierr);
2945   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_vals);CHKERRQ(ierr);
2946   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);CHKERRQ(ierr);
2947 
2948   /* allocate for requests */
2949   ierr = PetscMalloc1(n_sends,&send_req_idxs);CHKERRQ(ierr);
2950   ierr = PetscMalloc1(n_sends,&send_req_vals);CHKERRQ(ierr);
2951   ierr = PetscMalloc1(n_sends,&send_req_idxs_is);CHKERRQ(ierr);
2952   ierr = PetscMalloc1(n_recvs,&recv_req_idxs);CHKERRQ(ierr);
2953   ierr = PetscMalloc1(n_recvs,&recv_req_vals);CHKERRQ(ierr);
2954   ierr = PetscMalloc1(n_recvs,&recv_req_idxs_is);CHKERRQ(ierr);
2955 
2956   /* communications */
2957   ptr_idxs = recv_buffer_idxs;
2958   ptr_vals = recv_buffer_vals;
2959   ptr_idxs_is = recv_buffer_idxs_is;
2960   for (i=0;i<n_recvs;i++) {
2961     source_dest = onodes[i];
2962     ierr = MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);CHKERRQ(ierr);
2963     ierr = MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);CHKERRQ(ierr);
2964     ptr_idxs += olengths_idxs[i];
2965     ptr_vals += olengths_vals[i];
2966     if (nis) {
2967       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);
2968       ptr_idxs_is += olengths_idxs_is[i];
2969     }
2970   }
2971   for (i=0;i<n_sends;i++) {
2972     ierr = PetscMPIIntCast(is_indices[i],&source_dest);CHKERRQ(ierr);
2973     ierr = MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);CHKERRQ(ierr);
2974     ierr = MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);CHKERRQ(ierr);
2975     if (nis) {
2976       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);
2977     }
2978   }
2979   ierr = ISRestoreIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
2980   ierr = ISDestroy(&is_sends_internal);CHKERRQ(ierr);
2981 
2982   /* assemble new l2g map */
2983   ierr = MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
2984   ptr_idxs = recv_buffer_idxs;
2985   buf_size_idxs = 0;
2986   for (i=0;i<n_recvs;i++) {
2987     buf_size_idxs += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
2988     ptr_idxs += olengths_idxs[i];
2989   }
2990   ierr = PetscMalloc1(buf_size_idxs,&l2gmap_indices);CHKERRQ(ierr);
2991   ptr_idxs = recv_buffer_idxs;
2992   buf_size_idxs = 0;
2993   for (i=0;i<n_recvs;i++) {
2994     ierr = PetscMemcpy(&l2gmap_indices[buf_size_idxs],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));CHKERRQ(ierr);
2995     buf_size_idxs += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
2996     ptr_idxs += olengths_idxs[i];
2997   }
2998   ierr = PetscSortRemoveDupsInt(&buf_size_idxs,l2gmap_indices);CHKERRQ(ierr);
2999   ierr = ISLocalToGlobalMappingCreate(comm,1,buf_size_idxs,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);CHKERRQ(ierr);
3000   ierr = PetscFree(l2gmap_indices);CHKERRQ(ierr);
3001 
3002   /* infer new local matrix type from received local matrices type */
3003   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
3004   /* 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) */
3005   if (n_recvs) {
3006     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
3007     ptr_idxs = recv_buffer_idxs;
3008     for (i=0;i<n_recvs;i++) {
3009       if ((PetscInt)new_local_type_private != *ptr_idxs) {
3010         new_local_type_private = MATAIJ_PRIVATE;
3011         break;
3012       }
3013       ptr_idxs += olengths_idxs[i];
3014     }
3015     switch (new_local_type_private) {
3016       case MATDENSE_PRIVATE:
3017         if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
3018           new_local_type = MATSEQAIJ;
3019           bs = 1;
3020         } else { /* if I receive only 1 dense matrix */
3021           new_local_type = MATSEQDENSE;
3022           bs = 1;
3023         }
3024         break;
3025       case MATAIJ_PRIVATE:
3026         new_local_type = MATSEQAIJ;
3027         bs = 1;
3028         break;
3029       case MATBAIJ_PRIVATE:
3030         new_local_type = MATSEQBAIJ;
3031         break;
3032       case MATSBAIJ_PRIVATE:
3033         new_local_type = MATSEQSBAIJ;
3034         break;
3035       default:
3036         SETERRQ2(comm,PETSC_ERR_PLIB,"Unkwown private type %d in %s",new_local_type_private,__FUNCT__);
3037         break;
3038     }
3039   } else { /* by default, new_local_type is seqdense */
3040     new_local_type = MATSEQDENSE;
3041     bs = 1;
3042   }
3043 
3044   /* create MATIS object if needed */
3045   if (reuse == MAT_INITIAL_MATRIX) {
3046     ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
3047     ierr = MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,mat_n);CHKERRQ(ierr);
3048   } else {
3049     /* it also destroys the local matrices */
3050     ierr = MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);CHKERRQ(ierr);
3051   }
3052   ierr = ISLocalToGlobalMappingDestroy(&l2gmap);CHKERRQ(ierr);
3053   ierr = MatISGetLocalMat(*mat_n,&local_mat);CHKERRQ(ierr);
3054   ierr = MatSetType(local_mat,new_local_type);CHKERRQ(ierr);
3055   ierr = MatSetUp(local_mat);CHKERRQ(ierr); /* WARNING -> no preallocation yet */
3056 
3057   /* set values */
3058   ierr = MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3059   ptr_vals = recv_buffer_vals;
3060   ptr_idxs = recv_buffer_idxs;
3061   for (i=0;i<n_recvs;i++) {
3062     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
3063       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
3064       ierr = MatSetValues(*mat_n,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);CHKERRQ(ierr);
3065       ierr = MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3066       ierr = MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3067       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
3068     } else {
3069       /* TODO */
3070     }
3071     ptr_idxs += olengths_idxs[i];
3072     ptr_vals += olengths_vals[i];
3073   }
3074   ierr = MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3075   ierr = MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3076   ierr = MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3077   ierr = MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3078 
3079 #if 0
3080   if (!restrict_comm) { /* check */
3081     Vec       lvec,rvec;
3082     PetscReal infty_error;
3083 
3084     ierr = MatGetVecs(mat,&rvec,&lvec);CHKERRQ(ierr);
3085     ierr = VecSetRandom(rvec,NULL);CHKERRQ(ierr);
3086     ierr = MatMult(mat,rvec,lvec);CHKERRQ(ierr);
3087     ierr = VecScale(lvec,-1.0);CHKERRQ(ierr);
3088     ierr = MatMultAdd(*mat_n,rvec,lvec,lvec);CHKERRQ(ierr);
3089     ierr = VecNorm(lvec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3090     ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
3091     ierr = VecDestroy(&rvec);CHKERRQ(ierr);
3092     ierr = VecDestroy(&lvec);CHKERRQ(ierr);
3093   }
3094 #endif
3095 
3096   /* assemble new additional is (if any) */
3097   if (nis) {
3098     PetscInt **temp_idxs,*count_is,j,psum;
3099 
3100     ierr = MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3101     ierr = PetscMalloc(nis*sizeof(PetscInt),&count_is);CHKERRQ(ierr);
3102     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3103     ptr_idxs = recv_buffer_idxs_is;
3104     psum = 0;
3105     for (i=0;i<n_recvs;i++) {
3106       for (j=0;j<nis;j++) {
3107         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3108         count_is[j] += plen; /* increment counting of buffer for j-th IS */
3109         psum += plen;
3110         ptr_idxs += plen+1; /* shift pointer to received data */
3111       }
3112     }
3113     ierr = PetscMalloc(nis*sizeof(PetscInt*),&temp_idxs);CHKERRQ(ierr);
3114     ierr = PetscMalloc(psum*sizeof(PetscInt),&temp_idxs[0]);CHKERRQ(ierr);
3115     for (i=1;i<nis;i++) {
3116       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
3117     }
3118     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3119     ptr_idxs = recv_buffer_idxs_is;
3120     for (i=0;i<n_recvs;i++) {
3121       for (j=0;j<nis;j++) {
3122         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3123         ierr = PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));CHKERRQ(ierr);
3124         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
3125         ptr_idxs += plen+1; /* shift pointer to received data */
3126       }
3127     }
3128     for (i=0;i<nis;i++) {
3129       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3130       ierr = PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);CHKERRQ(ierr);CHKERRQ(ierr);
3131       ierr = ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3132     }
3133     ierr = PetscFree(count_is);CHKERRQ(ierr);
3134     ierr = PetscFree(temp_idxs[0]);CHKERRQ(ierr);
3135     ierr = PetscFree(temp_idxs);CHKERRQ(ierr);
3136   }
3137   /* free workspace */
3138   ierr = PetscFree(recv_buffer_idxs);CHKERRQ(ierr);
3139   ierr = PetscFree(recv_buffer_vals);CHKERRQ(ierr);
3140   ierr = PetscFree(recv_buffer_idxs_is);CHKERRQ(ierr);
3141   ierr = MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3142   ierr = PetscFree(send_buffer_idxs);CHKERRQ(ierr);
3143   ierr = MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3144   if (isdense) {
3145     ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
3146     ierr = MatDenseRestoreArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3147   } else {
3148     /* ierr = PetscFree(send_buffer_vals);CHKERRQ(ierr); */
3149   }
3150   if (nis) {
3151     ierr = MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3152     ierr = PetscFree(send_buffer_idxs_is);CHKERRQ(ierr);
3153   }
3154   ierr = PetscFree(recv_req_idxs);CHKERRQ(ierr);
3155   ierr = PetscFree(recv_req_vals);CHKERRQ(ierr);
3156   ierr = PetscFree(recv_req_idxs_is);CHKERRQ(ierr);
3157   ierr = PetscFree(send_req_idxs);CHKERRQ(ierr);
3158   ierr = PetscFree(send_req_vals);CHKERRQ(ierr);
3159   ierr = PetscFree(send_req_idxs_is);CHKERRQ(ierr);
3160   ierr = PetscFree(ilengths_vals);CHKERRQ(ierr);
3161   ierr = PetscFree(ilengths_idxs);CHKERRQ(ierr);
3162   ierr = PetscFree(olengths_vals);CHKERRQ(ierr);
3163   ierr = PetscFree(olengths_idxs);CHKERRQ(ierr);
3164   ierr = PetscFree(onodes);CHKERRQ(ierr);
3165   if (nis) {
3166     ierr = PetscFree(ilengths_idxs_is);CHKERRQ(ierr);
3167     ierr = PetscFree(olengths_idxs_is);CHKERRQ(ierr);
3168     ierr = PetscFree(onodes_is);CHKERRQ(ierr);
3169   }
3170   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
3171   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
3172     ierr = MatDestroy(mat_n);CHKERRQ(ierr);
3173     for (i=0;i<nis;i++) {
3174       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3175     }
3176   }
3177   PetscFunctionReturn(0);
3178 }
3179 
3180 /* temporary hack into ksp private data structure */
3181 #include <petsc-private/kspimpl.h>
3182 
3183 #undef __FUNCT__
3184 #define __FUNCT__ "PCBDDCSetUpCoarseSolver"
3185 PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
3186 {
3187   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
3188   PC_IS                  *pcis = (PC_IS*)pc->data;
3189   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
3190   MatNullSpace           CoarseNullSpace=NULL;
3191   ISLocalToGlobalMapping coarse_islg;
3192   IS                     coarse_is,*isarray;
3193   PetscInt               i,im_active=-1,active_procs=-1;
3194   PetscInt               nis,nisdofs,nisneu;
3195   PC                     pc_temp;
3196   PCType                 coarse_pc_type;
3197   KSPType                coarse_ksp_type;
3198   PetscBool              multilevel_requested,multilevel_allowed;
3199   PetscBool              isredundant,isbddc,isnn,coarse_reuse;
3200   Mat                    t_coarse_mat_is;
3201   PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
3202   PetscMPIInt            all_procs;
3203   PetscBool              csin_ml,csin_ds,csin,csin_type_simple;
3204   PetscBool              compute_vecs = PETSC_FALSE;
3205   PetscErrorCode         ierr;
3206 
3207   PetscFunctionBegin;
3208   /* Assign global numbering to coarse dofs */
3209   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 */
3210     compute_vecs = PETSC_TRUE;
3211     PetscInt ocoarse_size;
3212     ocoarse_size = pcbddc->coarse_size;
3213     ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
3214     ierr = PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);CHKERRQ(ierr);
3215     /* see if we can avoid some work */
3216     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
3217       if (ocoarse_size != pcbddc->coarse_size) { /* ...but with different size, so reset it and set reuse flag to false */
3218         ierr = KSPReset(pcbddc->coarse_ksp);CHKERRQ(ierr);
3219         coarse_reuse = PETSC_FALSE;
3220       } else { /* we can safely reuse already computed coarse matrix */
3221         coarse_reuse = PETSC_TRUE;
3222       }
3223     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
3224       coarse_reuse = PETSC_FALSE;
3225     }
3226     /* reset any subassembling information */
3227     ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3228     ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3229   } else { /* primal space is unchanged, so we can reuse coarse matrix */
3230     coarse_reuse = PETSC_TRUE;
3231   }
3232 
3233   /* count "active" (i.e. with positive local size) and "void" processes */
3234   im_active = !!(pcis->n);
3235   ierr = MPI_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3236   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);CHKERRQ(ierr);
3237   void_procs = all_procs-active_procs;
3238   csin_type_simple = PETSC_TRUE;
3239   if (pcbddc->current_level) {
3240     csin_ml = PETSC_TRUE;
3241     ncoarse_ml = void_procs;
3242     csin_ds = PETSC_TRUE;
3243     ncoarse_ds = void_procs;
3244     if (!void_procs) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
3245   } else {
3246     csin_ml = PETSC_FALSE;
3247     ncoarse_ml = all_procs;
3248     if (void_procs) {
3249       csin_ds = PETSC_TRUE;
3250       ncoarse_ds = void_procs;
3251       csin_type_simple = PETSC_FALSE;
3252     } else {
3253       csin_ds = PETSC_FALSE;
3254       ncoarse_ds = all_procs;
3255     }
3256   }
3257 
3258   /*
3259     test if we can go multilevel: three conditions must be satisfied:
3260     - we have not exceeded the number of levels requested
3261     - we can actually subassemble the active processes
3262     - we can find a suitable number of MPI processes where we can place the subassembled problem
3263   */
3264   multilevel_allowed = PETSC_FALSE;
3265   multilevel_requested = PETSC_FALSE;
3266   if (pcbddc->current_level < pcbddc->max_levels) {
3267     multilevel_requested = PETSC_TRUE;
3268     if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
3269       multilevel_allowed = PETSC_FALSE;
3270     } else {
3271       multilevel_allowed = PETSC_TRUE;
3272     }
3273   }
3274   /* determine number of process partecipating to coarse solver */
3275   if (multilevel_allowed) {
3276     ncoarse = ncoarse_ml;
3277     csin = csin_ml;
3278   } else {
3279     ncoarse = ncoarse_ds;
3280     csin = csin_ds;
3281   }
3282 
3283   /* creates temporary l2gmap and IS for coarse indexes */
3284   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);CHKERRQ(ierr);
3285   ierr = ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);CHKERRQ(ierr);
3286 
3287   /* creates temporary MATIS object for coarse matrix */
3288   ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_submat_dense);CHKERRQ(ierr);
3289 #if 0
3290   {
3291     PetscViewer viewer;
3292     char filename[256];
3293     sprintf(filename,"local_coarse_mat%d.m",PetscGlobalRank);
3294     ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
3295     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3296     ierr = MatView(coarse_submat_dense,viewer);CHKERRQ(ierr);
3297     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3298   }
3299 #endif
3300   ierr = MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,&t_coarse_mat_is);CHKERRQ(ierr);
3301   ierr = MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);CHKERRQ(ierr);
3302   ierr = MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3303   ierr = MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3304   ierr = MatDestroy(&coarse_submat_dense);CHKERRQ(ierr);
3305 
3306   /* compute dofs splitting and neumann boundaries for coarse dofs */
3307   if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal) ) { /* protects from unneded computations */
3308     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
3309     const PetscInt         *idxs;
3310     ISLocalToGlobalMapping tmap;
3311 
3312     /* create map between primal indices (in local representative ordering) and local primal numbering */
3313     ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);CHKERRQ(ierr);
3314     /* allocate space for temporary storage */
3315     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs);CHKERRQ(ierr);
3316     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs2);CHKERRQ(ierr);
3317     /* allocate for IS array */
3318     nisdofs = pcbddc->n_ISForDofsLocal;
3319     nisneu = !!pcbddc->NeumannBoundariesLocal;
3320     nis = nisdofs + nisneu;
3321     ierr = PetscMalloc(nis*sizeof(IS),&isarray);CHKERRQ(ierr);
3322     /* dofs splitting */
3323     for (i=0;i<nisdofs;i++) {
3324       /* ierr = ISView(pcbddc->ISForDofsLocal[i],0);CHKERRQ(ierr); */
3325       ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);CHKERRQ(ierr);
3326       ierr = ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3327       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3328       ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3329       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3330       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->ISForDofsLocal[i]),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3331       /* ierr = ISView(isarray[i],0);CHKERRQ(ierr); */
3332     }
3333     /* neumann boundaries */
3334     if (pcbddc->NeumannBoundariesLocal) {
3335       /* ierr = ISView(pcbddc->NeumannBoundariesLocal,0);CHKERRQ(ierr); */
3336       ierr = ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);CHKERRQ(ierr);
3337       ierr = ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3338       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3339       ierr = ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3340       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3341       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->NeumannBoundariesLocal),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);CHKERRQ(ierr);
3342       /* ierr = ISView(isarray[nisdofs],0);CHKERRQ(ierr); */
3343     }
3344     /* free memory */
3345     ierr = PetscFree(tidxs);CHKERRQ(ierr);
3346     ierr = PetscFree(tidxs2);CHKERRQ(ierr);
3347     ierr = ISLocalToGlobalMappingDestroy(&tmap);CHKERRQ(ierr);
3348   } else {
3349     nis = 0;
3350     nisdofs = 0;
3351     nisneu = 0;
3352     isarray = NULL;
3353   }
3354   /* destroy no longer needed map */
3355   ierr = ISLocalToGlobalMappingDestroy(&coarse_islg);CHKERRQ(ierr);
3356 
3357   /* restrict on coarse candidates (if needed) */
3358   coarse_mat_is = NULL;
3359   if (csin) {
3360     if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
3361       PetscInt j,tissize,*nisindices;
3362       PetscInt *coarse_candidates;
3363       const PetscInt* tisindices;
3364       /* get coarse candidates' ranks in pc communicator */
3365       ierr = PetscMalloc(all_procs*sizeof(PetscInt),&coarse_candidates);CHKERRQ(ierr);
3366       ierr = MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3367       for (i=0,j=0;i<all_procs;i++) {
3368         if (!coarse_candidates[i]) {
3369           coarse_candidates[j]=i;
3370           j++;
3371         }
3372       }
3373       if (j < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",j,ncoarse);
3374       /* get a suitable subassembling pattern */
3375       if (csin_type_simple) {
3376         PetscMPIInt rank;
3377         PetscInt    issize,isidx;
3378         ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
3379         if (im_active) {
3380           issize = 1;
3381           isidx = (PetscInt)rank;
3382         } else {
3383           issize = 0;
3384           isidx = -1;
3385         }
3386         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3387       } else {
3388         ierr = MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,PETSC_TRUE,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3389       }
3390       if (pcbddc->dbg_flag) {
3391         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3392         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");CHKERRQ(ierr);
3393         ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3394         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");CHKERRQ(ierr);
3395         for (i=0;i<j;i++) {
3396           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);CHKERRQ(ierr);
3397         }
3398         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");CHKERRQ(ierr);
3399         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3400       }
3401       /* shift the pattern on coarse candidates */
3402       ierr = ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);CHKERRQ(ierr);
3403       ierr = ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3404       ierr = PetscMalloc(tissize*sizeof(PetscInt),&nisindices);CHKERRQ(ierr);
3405       for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
3406       ierr = ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3407       ierr = ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);CHKERRQ(ierr);
3408       ierr = PetscFree(coarse_candidates);CHKERRQ(ierr);
3409     }
3410     if (pcbddc->dbg_flag) {
3411       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3412       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");CHKERRQ(ierr);
3413       ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3414       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3415     }
3416     /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
3417     ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
3418   } else {
3419     if (pcbddc->dbg_flag) {
3420       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3421       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");CHKERRQ(ierr);
3422       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3423     }
3424     ierr = PetscObjectReference((PetscObject)t_coarse_mat_is);CHKERRQ(ierr);
3425     coarse_mat_is = t_coarse_mat_is;
3426   }
3427 
3428   /* create local to global scatters for coarse problem */
3429   if (compute_vecs) {
3430     PetscInt lrows;
3431     ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
3432     if (coarse_mat_is) {
3433       ierr = MatGetLocalSize(coarse_mat_is,&lrows,NULL);CHKERRQ(ierr);
3434     } else {
3435       lrows = 0;
3436     }
3437     ierr = VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);CHKERRQ(ierr);
3438     ierr = VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);CHKERRQ(ierr);
3439     ierr = VecSetType(pcbddc->coarse_vec,VECSTANDARD);CHKERRQ(ierr);
3440     ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3441     ierr = VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3442   }
3443   ierr = ISDestroy(&coarse_is);CHKERRQ(ierr);
3444   ierr = MatDestroy(&t_coarse_mat_is);CHKERRQ(ierr);
3445 
3446   /* set defaults for coarse KSP and PC */
3447   if (multilevel_allowed) {
3448     coarse_ksp_type = KSPRICHARDSON;
3449     coarse_pc_type = PCBDDC;
3450   } else {
3451     coarse_ksp_type = KSPPREONLY;
3452     coarse_pc_type = PCREDUNDANT;
3453   }
3454 
3455   /* print some info if requested */
3456   if (pcbddc->dbg_flag) {
3457     if (!multilevel_allowed) {
3458       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3459       if (multilevel_requested) {
3460         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);
3461       } else if (pcbddc->max_levels) {
3462         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);CHKERRQ(ierr);
3463       }
3464       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3465     }
3466   }
3467 
3468   /* create the coarse KSP object only once with defaults */
3469   if (coarse_mat_is) {
3470     MatReuse coarse_mat_reuse;
3471     PetscViewer dbg_viewer;
3472     if (pcbddc->dbg_flag) {
3473       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
3474       ierr = PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3475     }
3476     if (!pcbddc->coarse_ksp) {
3477       char prefix[256],str_level[16];
3478       size_t len;
3479       ierr = KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);CHKERRQ(ierr);
3480       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3481       ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
3482       ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);CHKERRQ(ierr);
3483       ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3484       ierr = KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);CHKERRQ(ierr);
3485       ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3486       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3487       /* prefix */
3488       ierr = PetscStrcpy(prefix,"");CHKERRQ(ierr);
3489       ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
3490       if (!pcbddc->current_level) {
3491         ierr = PetscStrcpy(prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
3492         ierr = PetscStrcat(prefix,"pc_bddc_coarse_");CHKERRQ(ierr);
3493       } else {
3494         ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
3495         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
3496         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
3497         ierr = PetscStrncpy(prefix,((PetscObject)pc)->prefix,len);CHKERRQ(ierr);
3498         *(prefix+len)='\0';
3499         sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
3500         ierr = PetscStrcat(prefix,str_level);CHKERRQ(ierr);
3501       }
3502       ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);CHKERRQ(ierr);
3503       /* allow user customization */
3504       ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3505       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
3506     }
3507 
3508     /* get some info after set from options */
3509     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3510     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);CHKERRQ(ierr);
3511     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);CHKERRQ(ierr);
3512     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);CHKERRQ(ierr);
3513     if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
3514       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3515       isbddc = PETSC_FALSE;
3516     }
3517     if (isredundant) {
3518       KSP inner_ksp;
3519       PC inner_pc;
3520       ierr = PCRedundantGetKSP(pc_temp,&inner_ksp);CHKERRQ(ierr);
3521       ierr = KSPGetPC(inner_ksp,&inner_pc);CHKERRQ(ierr);
3522       ierr = PCFactorSetReuseFill(inner_pc,PETSC_TRUE);CHKERRQ(ierr);
3523     }
3524 
3525     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
3526     ierr = PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);CHKERRQ(ierr);
3527     ierr = PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);CHKERRQ(ierr);
3528     ierr = PCBDDCSetLevels(pc_temp,pcbddc->max_levels);CHKERRQ(ierr);
3529     if (nisdofs) {
3530       ierr = PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);CHKERRQ(ierr);
3531       for (i=0;i<nisdofs;i++) {
3532         ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3533       }
3534     }
3535     if (nisneu) {
3536       ierr = PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);CHKERRQ(ierr);
3537       ierr = ISDestroy(&isarray[nisdofs]);CHKERRQ(ierr);
3538     }
3539 
3540     /* assemble coarse matrix */
3541     if (coarse_reuse) {
3542       ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
3543       ierr = PetscObjectReference((PetscObject)coarse_mat);CHKERRQ(ierr);
3544       coarse_mat_reuse = MAT_REUSE_MATRIX;
3545     } else {
3546       coarse_mat_reuse = MAT_INITIAL_MATRIX;
3547     }
3548     if (isbddc || isnn) {
3549       if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
3550         ierr = MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,PETSC_TRUE,&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3551         if (pcbddc->dbg_flag) {
3552           ierr = PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3553           ierr = PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");CHKERRQ(ierr);
3554           ierr = ISView(pcbddc->coarse_subassembling,dbg_viewer);CHKERRQ(ierr);
3555           ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3556         }
3557       }
3558       ierr = MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);CHKERRQ(ierr);
3559     } else {
3560       ierr = MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);CHKERRQ(ierr);
3561     }
3562     ierr = MatDestroy(&coarse_mat_is);CHKERRQ(ierr);
3563 
3564     /* propagate symmetry info to coarse matrix */
3565     ierr = MatSetOption(coarse_mat,MAT_SYMMETRIC,pcbddc->issym);CHKERRQ(ierr);
3566     ierr = MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
3567 
3568     /* set operators */
3569     ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3570     if (pcbddc->dbg_flag) {
3571       ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3572     }
3573   } else { /* processes non partecipating to coarse solver (if any) */
3574     coarse_mat = 0;
3575   }
3576   ierr = PetscFree(isarray);CHKERRQ(ierr);
3577 #if 0
3578   {
3579     PetscViewer viewer;
3580     char filename[256];
3581     sprintf(filename,"coarse_mat.m");
3582     ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,&viewer);CHKERRQ(ierr);
3583     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3584     ierr = MatView(coarse_mat,viewer);CHKERRQ(ierr);
3585     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3586   }
3587 #endif
3588 
3589   /* Compute coarse null space (special handling by BDDC only) */
3590   if (pcbddc->NullSpace) {
3591     ierr = PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);CHKERRQ(ierr);
3592   }
3593 
3594   if (pcbddc->coarse_ksp) {
3595     Vec crhs,csol;
3596     PetscBool ispreonly;
3597     if (CoarseNullSpace) {
3598       if (isbddc) {
3599         ierr = PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);CHKERRQ(ierr);
3600       } else {
3601         ierr = KSPSetNullSpace(pcbddc->coarse_ksp,CoarseNullSpace);CHKERRQ(ierr);
3602       }
3603     }
3604     /* setup coarse ksp */
3605     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3606     ierr = KSPGetSolution(pcbddc->coarse_ksp,&csol);CHKERRQ(ierr);
3607     ierr = KSPGetRhs(pcbddc->coarse_ksp,&crhs);CHKERRQ(ierr);
3608     /* hack */
3609     if (!csol) {
3610       ierr = MatGetVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);CHKERRQ(ierr);
3611     }
3612     if (!crhs) {
3613       ierr = MatGetVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));CHKERRQ(ierr);
3614     }
3615     /* Check coarse problem if in debug mode or if solving with an iterative method */
3616     ierr = PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);CHKERRQ(ierr);
3617     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
3618       KSP       check_ksp;
3619       KSPType   check_ksp_type;
3620       PC        check_pc;
3621       Vec       check_vec,coarse_vec;
3622       PetscReal abs_infty_error,infty_error,lambda_min,lambda_max;
3623       PetscInt  its;
3624       PetscBool compute_eigs;
3625       PetscReal *eigs_r,*eigs_c;
3626       PetscInt  neigs;
3627       const char *prefix;
3628 
3629       /* Create ksp object suitable for estimation of extreme eigenvalues */
3630       ierr = KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);CHKERRQ(ierr);
3631       ierr = KSPSetOperators(check_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3632       ierr = KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3633       if (ispreonly) {
3634         check_ksp_type = KSPPREONLY;
3635         compute_eigs = PETSC_FALSE;
3636       } else {
3637         check_ksp_type = KSPGMRES;
3638         compute_eigs = PETSC_TRUE;
3639       }
3640       ierr = KSPSetType(check_ksp,check_ksp_type);CHKERRQ(ierr);
3641       ierr = KSPSetComputeSingularValues(check_ksp,compute_eigs);CHKERRQ(ierr);
3642       ierr = KSPSetComputeEigenvalues(check_ksp,compute_eigs);CHKERRQ(ierr);
3643       ierr = KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);CHKERRQ(ierr);
3644       ierr = KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);CHKERRQ(ierr);
3645       ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
3646       ierr = KSPAppendOptionsPrefix(check_ksp,"check_");CHKERRQ(ierr);
3647       ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
3648       ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
3649       ierr = KSPGetPC(pcbddc->coarse_ksp,&check_pc);CHKERRQ(ierr);
3650       ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
3651       /* create random vec */
3652       ierr = KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);CHKERRQ(ierr);
3653       ierr = VecDuplicate(coarse_vec,&check_vec);CHKERRQ(ierr);
3654       ierr = VecSetRandom(check_vec,NULL);CHKERRQ(ierr);
3655       if (CoarseNullSpace) {
3656         ierr = MatNullSpaceRemove(CoarseNullSpace,check_vec);CHKERRQ(ierr);
3657       }
3658       ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3659       /* solve coarse problem */
3660       ierr = KSPSolve(check_ksp,coarse_vec,coarse_vec);CHKERRQ(ierr);
3661       if (CoarseNullSpace) {
3662         ierr = MatNullSpaceRemove(CoarseNullSpace,coarse_vec);CHKERRQ(ierr);
3663       }
3664       /* set eigenvalue estimation if preonly has not been requested */
3665       if (compute_eigs) {
3666         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_r);CHKERRQ(ierr);
3667         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_c);CHKERRQ(ierr);
3668         ierr = KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);CHKERRQ(ierr);
3669         lambda_max = eigs_r[neigs-1];
3670         lambda_min = eigs_r[0];
3671         if (pcbddc->use_coarse_estimates) {
3672           if (lambda_max>lambda_min) {
3673             ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3674             ierr = KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));CHKERRQ(ierr);
3675           }
3676         }
3677       }
3678 
3679       /* check coarse problem residual error */
3680       if (pcbddc->dbg_flag) {
3681         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
3682         ierr = PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3683         ierr = VecAXPY(check_vec,-1.0,coarse_vec);CHKERRQ(ierr);
3684         ierr = VecNorm(check_vec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3685         ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3686         ierr = VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);CHKERRQ(ierr);
3687         ierr = VecDestroy(&check_vec);CHKERRQ(ierr);
3688         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (%d)\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
3689         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);CHKERRQ(ierr);
3690         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);CHKERRQ(ierr);
3691         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);CHKERRQ(ierr);
3692         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);CHKERRQ(ierr);
3693         if (compute_eigs) {
3694           PetscReal lambda_max_s,lambda_min_s;
3695           ierr = KSPGetIterationNumber(check_ksp,&its);CHKERRQ(ierr);
3696           ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);CHKERRQ(ierr);
3697           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);
3698           for (i=0;i<neigs;i++) {
3699             ierr = PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);CHKERRQ(ierr);
3700           }
3701         }
3702         ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3703         ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3704       }
3705       ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
3706       if (compute_eigs) {
3707         ierr = PetscFree(eigs_r);CHKERRQ(ierr);
3708         ierr = PetscFree(eigs_c);CHKERRQ(ierr);
3709       }
3710     }
3711   }
3712   /* print additional info */
3713   if (pcbddc->dbg_flag) {
3714     /* waits until all processes reaches this point */
3715     ierr = PetscBarrier((PetscObject)pc);CHKERRQ(ierr);
3716     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);CHKERRQ(ierr);
3717     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3718   }
3719 
3720   /* free memory */
3721   ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
3722   ierr = MatDestroy(&coarse_mat);CHKERRQ(ierr);
3723   PetscFunctionReturn(0);
3724 }
3725 
3726 #undef __FUNCT__
3727 #define __FUNCT__ "PCBDDCComputePrimalNumbering"
3728 PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
3729 {
3730   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
3731   PC_IS*         pcis = (PC_IS*)pc->data;
3732   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
3733   PetscInt       i,coarse_size;
3734   PetscInt       *local_primal_indices;
3735   PetscErrorCode ierr;
3736 
3737   PetscFunctionBegin;
3738   /* Compute global number of coarse dofs */
3739   if (!pcbddc->primal_indices_local_idxs && pcbddc->local_primal_size) {
3740     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Local primal indices have not been created");
3741   }
3742   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);
3743 
3744   /* check numbering */
3745   if (pcbddc->dbg_flag) {
3746     PetscScalar coarsesum,*array;
3747     PetscBool set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;
3748 
3749     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3750     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3751     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");CHKERRQ(ierr);
3752     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
3753     ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
3754     for (i=0;i<pcbddc->local_primal_size;i++) {
3755       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
3756     }
3757     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
3758     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
3759     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3760     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3761     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3762     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3763     ierr = VecScatterEnd(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3764     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3765     for (i=0;i<pcis->n;i++) {
3766       if (array[i] == 1.0) {
3767         set_error = PETSC_TRUE;
3768         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a single process!\n",PetscGlobalRank,i);CHKERRQ(ierr);
3769       }
3770     }
3771     ierr = MPI_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3772     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3773     for (i=0;i<pcis->n;i++) {
3774       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
3775     }
3776     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3777     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3778     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3779     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3780     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
3781     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));CHKERRQ(ierr);
3782     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
3783       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");CHKERRQ(ierr);
3784       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3785       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
3786       for (i=0;i<pcbddc->local_primal_size;i++) {
3787         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%d]=%d (%d)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i]);
3788       }
3789       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3790     }
3791     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3792     if (set_error_reduced) {
3793       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
3794     }
3795   }
3796   /* get back data */
3797   *coarse_size_n = coarse_size;
3798   *local_primal_indices_n = local_primal_indices;
3799   PetscFunctionReturn(0);
3800 }
3801 
3802 #undef __FUNCT__
3803 #define __FUNCT__ "PCBDDCGlobalToLocal"
3804 PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
3805 {
3806   IS             localis_t;
3807   PetscInt       i,lsize,*idxs,n;
3808   PetscScalar    *vals;
3809   PetscErrorCode ierr;
3810 
3811   PetscFunctionBegin;
3812   /* get indices in local ordering exploiting local to global map */
3813   ierr = ISGetLocalSize(globalis,&lsize);CHKERRQ(ierr);
3814   ierr = PetscMalloc(lsize*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3815   for (i=0;i<lsize;i++) vals[i] = 1.0;
3816   ierr = ISGetIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
3817   ierr = VecSet(gwork,0.0);CHKERRQ(ierr);
3818   ierr = VecSet(lwork,0.0);CHKERRQ(ierr);
3819   if (idxs) { /* multilevel guard */
3820     ierr = VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
3821   }
3822   ierr = VecAssemblyBegin(gwork);CHKERRQ(ierr);
3823   ierr = ISRestoreIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
3824   ierr = PetscFree(vals);CHKERRQ(ierr);
3825   ierr = VecAssemblyEnd(gwork);CHKERRQ(ierr);
3826   /* now compute set in local ordering */
3827   ierr = VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3828   ierr = VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3829   ierr = VecGetArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
3830   ierr = VecGetSize(lwork,&n);CHKERRQ(ierr);
3831   for (i=0,lsize=0;i<n;i++) {
3832     if (PetscRealPart(vals[i]) > 0.5) {
3833       lsize++;
3834     }
3835   }
3836   ierr = PetscMalloc(lsize*sizeof(PetscInt),&idxs);CHKERRQ(ierr);
3837   for (i=0,lsize=0;i<n;i++) {
3838     if (PetscRealPart(vals[i]) > 0.5) {
3839       idxs[lsize++] = i;
3840     }
3841   }
3842   ierr = VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
3843   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);CHKERRQ(ierr);
3844   *localis = localis_t;
3845   PetscFunctionReturn(0);
3846 }
3847