xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision b79f856971bdcd7e5fd5dc3c1062b19885df5cf6)
1 #include <../src/ksp/pc/impls/bddc/bddc.h>
2 #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
3 #include <petscblaslapack.h>
4 
5 static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y);
6 static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y);
7 
8 #undef __FUNCT__
9 #define __FUNCT__ "PCBDDCSetUpSolvers"
10 PetscErrorCode PCBDDCSetUpSolvers(PC pc)
11 {
12   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
13   PetscScalar    *coarse_submat_vals;
14   PetscErrorCode ierr;
15 
16   PetscFunctionBegin;
17   /* Compute matrix after change of basis and extract local submatrices */
18   ierr = PCBDDCSetUpLocalMatrices(pc);CHKERRQ(ierr);
19 
20   /* Setup local scatters R_to_B and (optionally) R_to_D */
21   /* PCBDDCSetUpLocalWorkVectors and PCBDDCSetUpLocalMatrices should be called first! */
22   ierr = PCBDDCSetUpLocalScatters(pc);CHKERRQ(ierr);
23 
24   /* Setup local solvers ksp_D and ksp_R */
25   /* PCBDDCSetUpLocalScatters should be called first! */
26   ierr = PCBDDCSetUpLocalSolvers(pc);CHKERRQ(ierr);
27 
28   /* Change global null space passed in by the user if change of basis has been requested */
29   if (pcbddc->NullSpace && pcbddc->ChangeOfBasisMatrix) {
30     ierr = PCBDDCNullSpaceAdaptGlobal(pc);CHKERRQ(ierr);
31   }
32 
33   /*
34      Setup local correction and local part of coarse basis.
35      Gives back the dense local part of the coarse matrix in column major ordering
36   */
37   ierr = PCBDDCSetUpCorrection(pc,&coarse_submat_vals);CHKERRQ(ierr);
38 
39   /* Compute total number of coarse nodes and setup coarse solver */
40   ierr = PCBDDCSetUpCoarseSolver(pc,coarse_submat_vals);CHKERRQ(ierr);
41 
42   /* free */
43   ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
44   PetscFunctionReturn(0);
45 }
46 
47 #undef __FUNCT__
48 #define __FUNCT__ "PCBDDCResetCustomization"
49 PetscErrorCode PCBDDCResetCustomization(PC pc)
50 {
51   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
52   PetscErrorCode ierr;
53 
54   PetscFunctionBegin;
55   ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
56   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
57   ierr = MatNullSpaceDestroy(&pcbddc->NullSpace);CHKERRQ(ierr);
58   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
59   ierr = ISDestroy(&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
60   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
61   ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
62   ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
63   ierr = ISDestroy(&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
64   ierr = PCBDDCSetDofsSplitting(pc,0,NULL);CHKERRQ(ierr);
65   ierr = PCBDDCSetDofsSplittingLocal(pc,0,NULL);CHKERRQ(ierr);
66   PetscFunctionReturn(0);
67 }
68 
69 #undef __FUNCT__
70 #define __FUNCT__ "PCBDDCResetTopography"
71 PetscErrorCode PCBDDCResetTopography(PC pc)
72 {
73   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
74   PetscErrorCode ierr;
75 
76   PetscFunctionBegin;
77   ierr = MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
78   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
79   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
80   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
81   PetscFunctionReturn(0);
82 }
83 
84 #undef __FUNCT__
85 #define __FUNCT__ "PCBDDCResetSolvers"
86 PetscErrorCode PCBDDCResetSolvers(PC pc)
87 {
88   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
89   PetscErrorCode ierr;
90 
91   PetscFunctionBegin;
92   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
93   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
94   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
95   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
96   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
97   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
98   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
99   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
100   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
101   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
102   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
103   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
104   ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
105   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
106   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
107   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
108   ierr = KSPDestroy(&pcbddc->ksp_D);CHKERRQ(ierr);
109   ierr = KSPDestroy(&pcbddc->ksp_R);CHKERRQ(ierr);
110   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
111   ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
112   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
113   ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
114   ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
115   ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
116   PetscFunctionReturn(0);
117 }
118 
119 #undef __FUNCT__
120 #define __FUNCT__ "PCBDDCSetUpLocalWorkVectors"
121 PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
122 {
123   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
124   PC_IS          *pcis = (PC_IS*)pc->data;
125   VecType        impVecType;
126   PetscInt       n_constraints,n_R,old_size;
127   PetscErrorCode ierr;
128 
129   PetscFunctionBegin;
130   if (!pcbddc->ConstraintMatrix) {
131     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Constraint matrix has not been created");
132   }
133   /* get sizes */
134   n_constraints = pcbddc->local_primal_size - pcbddc->n_actual_vertices;
135   n_R = pcis->n-pcbddc->n_actual_vertices;
136   ierr = VecGetType(pcis->vec1_N,&impVecType);CHKERRQ(ierr);
137   /* local work vectors (try to avoid unneeded work)*/
138   /* R nodes */
139   old_size = -1;
140   if (pcbddc->vec1_R) {
141     ierr = VecGetSize(pcbddc->vec1_R,&old_size);CHKERRQ(ierr);
142   }
143   if (n_R != old_size) {
144     ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
145     ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
146     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);CHKERRQ(ierr);
147     ierr = VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);CHKERRQ(ierr);
148     ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
149     ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
150   }
151   /* local primal dofs */
152   old_size = -1;
153   if (pcbddc->vec1_P) {
154     ierr = VecGetSize(pcbddc->vec1_P,&old_size);CHKERRQ(ierr);
155   }
156   if (pcbddc->local_primal_size != old_size) {
157     ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
158     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);CHKERRQ(ierr);
159     ierr = VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,pcbddc->local_primal_size);CHKERRQ(ierr);
160     ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
161   }
162   /* local explicit constraints */
163   old_size = -1;
164   if (pcbddc->vec1_C) {
165     ierr = VecGetSize(pcbddc->vec1_C,&old_size);CHKERRQ(ierr);
166   }
167   if (n_constraints && n_constraints != old_size) {
168     ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
169     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);CHKERRQ(ierr);
170     ierr = VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);CHKERRQ(ierr);
171     ierr = VecSetType(pcbddc->vec1_C,impVecType);CHKERRQ(ierr);
172   }
173   PetscFunctionReturn(0);
174 }
175 
176 #undef __FUNCT__
177 #define __FUNCT__ "PCBDDCSetUpCorrection"
178 PetscErrorCode PCBDDCSetUpCorrection(PC pc, PetscScalar **coarse_submat_vals_n)
179 {
180   PetscErrorCode         ierr;
181   /* pointers to pcis and pcbddc */
182   PC_IS*                 pcis = (PC_IS*)pc->data;
183   PC_BDDC*               pcbddc = (PC_BDDC*)pc->data;
184   /* submatrices of local problem */
185   Mat                    A_RV,A_VR,A_VV;
186   /* working matrices */
187   Mat                    M1,M2,M3,C_CR;
188   /* working vectors */
189   Vec                    vec1_C,vec2_C,vec1_V,vec2_V;
190   /* additional working stuff */
191   IS                     is_aux;
192   PetscScalar            *coarse_submat_vals; /* TODO: use a PETSc matrix */
193   const PetscScalar      *array,*row_cmat_values;
194   const PetscInt         *row_cmat_indices,*idx_R_local;
195   PetscInt               *idx_V_B,*auxindices;
196   PetscInt               n_vertices,n_constraints,size_of_constraint;
197   PetscInt               i,j,n_R,n_D,n_B;
198   PetscBool              unsymmetric_check;
199   /* matrix type (vector type propagated downstream from vec1_C and local matrix type) */
200   MatType                impMatType;
201   /* some shortcuts to scalars */
202   PetscScalar            zero=0.0,one=1.0,m_one=-1.0;
203   /* for debugging purposes */
204   PetscReal              *coarsefunctions_errors,*constraints_errors;
205 
206   PetscFunctionBegin;
207   /* get number of vertices (corners plus constraints with change of basis)
208      pcbddc->n_actual_vertices stores the actual number of vertices, pcbddc->n_vertices the number of corners computed */
209   n_vertices = pcbddc->n_actual_vertices;
210   n_constraints = pcbddc->local_primal_size-n_vertices;
211   /* Set Non-overlapping dimensions */
212   n_B = pcis->n_B; n_D = pcis->n - n_B;
213   n_R = pcis->n-n_vertices;
214 
215   /* Set types for local objects needed by BDDC precondtioner */
216   impMatType = MATSEQDENSE;
217 
218   /* Allocating some extra storage just to be safe */
219   ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&auxindices);CHKERRQ(ierr);
220   for (i=0;i<pcis->n;i++) auxindices[i]=i;
221 
222   /* vertices in boundary numbering */
223   ierr = PetscMalloc1(n_vertices,&idx_V_B);CHKERRQ(ierr);
224   ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,n_vertices,pcbddc->primal_indices_local_idxs,&i,idx_V_B);CHKERRQ(ierr);
225   if (i != n_vertices) {
226     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for BDDC vertices! %d != %d\n",n_vertices,i);
227   }
228 
229   /* Precompute stuffs needed for preprocessing and application of BDDC*/
230   if (n_constraints) {
231     /* see if we can save some allocations */
232     if (pcbddc->local_auxmat2) {
233       PetscInt on_R,on_constraints;
234       ierr = MatGetSize(pcbddc->local_auxmat2,&on_R,&on_constraints);CHKERRQ(ierr);
235       if (on_R != n_R || on_constraints != n_constraints) {
236         ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
237         ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
238       }
239     }
240     /* work vectors */
241     ierr = VecDuplicate(pcbddc->vec1_C,&vec1_C);CHKERRQ(ierr);
242     ierr = VecDuplicate(pcbddc->vec1_C,&vec2_C);CHKERRQ(ierr);
243     /* auxiliary matrices */
244     if (!pcbddc->local_auxmat2) {
245       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->local_auxmat2);CHKERRQ(ierr);
246       ierr = MatSetSizes(pcbddc->local_auxmat2,n_R,n_constraints,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
247       ierr = MatSetType(pcbddc->local_auxmat2,impMatType);CHKERRQ(ierr);
248       ierr = MatSetUp(pcbddc->local_auxmat2);CHKERRQ(ierr);
249     }
250 
251     /* Extract constraints on R nodes: C_{CR}  */
252     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);CHKERRQ(ierr);
253     ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
254     ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
255 
256     /* Assemble local_auxmat2 = - A_{RR}^{-1} C^T_{CR} needed by BDDC application */
257     for (i=0;i<n_constraints;i++) {
258       ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
259       /* Get row of constraint matrix in R numbering */
260       ierr = MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
261       ierr = VecSetValues(pcbddc->vec1_R,size_of_constraint,row_cmat_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
262       ierr = MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
263       ierr = VecAssemblyBegin(pcbddc->vec1_R);CHKERRQ(ierr);
264       ierr = VecAssemblyEnd(pcbddc->vec1_R);CHKERRQ(ierr);
265       /* Solve for row of constraint matrix in R numbering */
266       ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
267       /* Set values in local_auxmat2 */
268       ierr = VecGetArrayRead(pcbddc->vec2_R,&array);CHKERRQ(ierr);
269       ierr = MatSetValues(pcbddc->local_auxmat2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
270       ierr = VecRestoreArrayRead(pcbddc->vec2_R,&array);CHKERRQ(ierr);
271     }
272     ierr = MatAssemblyBegin(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
273     ierr = MatAssemblyEnd(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
274     ierr = MatScale(pcbddc->local_auxmat2,m_one);CHKERRQ(ierr);
275 
276     /* Assemble explicitly M1 = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} needed in preproc  */
277     ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);CHKERRQ(ierr);
278     ierr = MatLUFactor(M3,NULL,NULL,NULL);CHKERRQ(ierr);
279     ierr = MatCreate(PETSC_COMM_SELF,&M1);CHKERRQ(ierr);
280     ierr = MatSetSizes(M1,n_constraints,n_constraints,n_constraints,n_constraints);CHKERRQ(ierr);
281     ierr = MatSetType(M1,impMatType);CHKERRQ(ierr);
282     ierr = MatSetUp(M1);CHKERRQ(ierr);
283     ierr = MatDuplicate(M1,MAT_DO_NOT_COPY_VALUES,&M2);CHKERRQ(ierr);
284     ierr = MatZeroEntries(M2);CHKERRQ(ierr);
285     ierr = VecSet(vec1_C,m_one);CHKERRQ(ierr);
286     ierr = MatDiagonalSet(M2,vec1_C,INSERT_VALUES);CHKERRQ(ierr);
287     ierr = MatMatSolve(M3,M2,M1);CHKERRQ(ierr);
288     ierr = MatDestroy(&M2);CHKERRQ(ierr);
289     ierr = MatDestroy(&M3);CHKERRQ(ierr);
290     /* Assemble local_auxmat1 = M1*C_{CR} needed by BDDC application in KSP and in preproc */
291     if (!pcbddc->local_auxmat1) {
292       ierr = MatMatMult(M1,C_CR,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
293     } else {
294       ierr = MatMatMult(M1,C_CR,MAT_REUSE_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
295     }
296   }
297 
298   /* Get submatrices from subdomain matrix */
299   if (n_vertices) {
300     PetscInt ibs,mbs;
301     PetscBool issbaij;
302     Mat newmat;
303 
304     ierr = ISComplement(pcbddc->is_R_local,0,pcis->n,&is_aux);CHKERRQ(ierr);
305     ierr = MatGetBlockSize(pcbddc->local_mat,&mbs);CHKERRQ(ierr);
306     ierr = ISGetBlockSize(pcbddc->is_R_local,&ibs);CHKERRQ(ierr);
307     if (ibs != mbs) { /* need to convert to SEQAIJ */
308       ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
309       ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
310       ierr = MatGetSubMatrix(newmat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
311       ierr = MatGetSubMatrix(newmat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
312       ierr = MatDestroy(&newmat);CHKERRQ(ierr);
313     } else {
314       /* this is safe */
315       ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
316       ierr = PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
317       if (issbaij) { /* need to convert to BAIJ to get offdiagonal blocks */
318         ierr = MatConvert(pcbddc->local_mat,MATSEQBAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
319         /* which of the two approaches is faster? */
320         /* ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
321         ierr = MatCreateTranspose(A_RV,&A_VR);CHKERRQ(ierr);*/
322         ierr = MatGetSubMatrix(newmat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
323         ierr = MatCreateTranspose(A_VR,&A_RV);CHKERRQ(ierr);
324         ierr = MatDestroy(&newmat);CHKERRQ(ierr);
325       } else {
326         ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
327         ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
328       }
329     }
330     ierr = MatCreateVecs(A_RV,&vec1_V,NULL);CHKERRQ(ierr);
331     ierr = VecDuplicate(vec1_V,&vec2_V);CHKERRQ(ierr);
332     ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
333   }
334 
335   /* Matrix of coarse basis functions (local) */
336   if (pcbddc->coarse_phi_B) {
337     PetscInt on_B,on_primal;
338     ierr = MatGetSize(pcbddc->coarse_phi_B,&on_B,&on_primal);CHKERRQ(ierr);
339     if (on_B != n_B || on_primal != pcbddc->local_primal_size) {
340       ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
341       ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
342     }
343   }
344   if (pcbddc->coarse_phi_D) {
345     PetscInt on_D,on_primal;
346     ierr = MatGetSize(pcbddc->coarse_phi_D,&on_D,&on_primal);CHKERRQ(ierr);
347     if (on_D != n_D || on_primal != pcbddc->local_primal_size) {
348       ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
349       ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
350     }
351   }
352   if (!pcbddc->coarse_phi_B) {
353     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
354     ierr = MatSetSizes(pcbddc->coarse_phi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
355     ierr = MatSetType(pcbddc->coarse_phi_B,impMatType);CHKERRQ(ierr);
356     ierr = MatSetUp(pcbddc->coarse_phi_B);CHKERRQ(ierr);
357   }
358   if ( (pcbddc->switch_static || pcbddc->dbg_flag) && !pcbddc->coarse_phi_D ) {
359     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
360     ierr = MatSetSizes(pcbddc->coarse_phi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
361     ierr = MatSetType(pcbddc->coarse_phi_D,impMatType);CHKERRQ(ierr);
362     ierr = MatSetUp(pcbddc->coarse_phi_D);CHKERRQ(ierr);
363   }
364 
365   if (pcbddc->dbg_flag) {
366     ierr = ISGetIndices(pcbddc->is_R_local,&idx_R_local);CHKERRQ(ierr);
367     ierr = PetscMalloc1(2*pcbddc->local_primal_size,&coarsefunctions_errors);CHKERRQ(ierr);
368     ierr = PetscMalloc1(2*pcbddc->local_primal_size,&constraints_errors);CHKERRQ(ierr);
369   }
370   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
371   ierr = PetscMalloc1((pcbddc->local_primal_size)*(pcbddc->local_primal_size),&coarse_submat_vals);CHKERRQ(ierr);
372 
373   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
374 
375   /* vertices */
376   for (i=0;i<n_vertices;i++) {
377     /* this should not be needed, but MatMult_BAIJ is broken when using compressed row routines */
378     ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr); /* TODO: REMOVE IT */
379     ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
380     ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
381     ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
382     ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
383     /* simplified solution of saddle point problem with null rhs on constraints multipliers */
384     ierr = MatMult(A_RV,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
385     ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
386     ierr = VecScale(pcbddc->vec1_R,m_one);CHKERRQ(ierr);
387     if (n_constraints) {
388       ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec1_R,vec1_C);CHKERRQ(ierr);
389       ierr = MatMultAdd(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
390       ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
391     }
392     ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
393     ierr = MatMultAdd(A_VV,vec1_V,vec2_V,vec2_V);CHKERRQ(ierr);
394 
395     /* Set values in coarse basis function and subdomain part of coarse_mat */
396     /* coarse basis functions */
397     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
398     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
399     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
400     ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
401     ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
402     ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
403     ierr = MatSetValue(pcbddc->coarse_phi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
404     if (pcbddc->switch_static || pcbddc->dbg_flag) {
405       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
406       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
407       ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
408       ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
409       ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
410     }
411     /* subdomain contribution to coarse matrix. WARNING -> column major ordering */
412     ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
413     ierr = PetscMemcpy(&coarse_submat_vals[i*pcbddc->local_primal_size],array,n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
414     ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
415     if (n_constraints) {
416       ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
417       ierr = PetscMemcpy(&coarse_submat_vals[i*pcbddc->local_primal_size+n_vertices],array,n_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
418       ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
419     }
420 
421     /* check */
422     if (pcbddc->dbg_flag) {
423       /* assemble subdomain vector on local nodes */
424       ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
425       ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
426       if (n_R) {
427         ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
428       }
429       ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
430       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],one,INSERT_VALUES);CHKERRQ(ierr);
431       ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
432       ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
433       /* assemble subdomain vector of lagrange multipliers (i.e. primal nodes) */
434       ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
435       ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
436       ierr = VecSetValues(pcbddc->vec1_P,n_vertices,auxindices,array,INSERT_VALUES);CHKERRQ(ierr);
437       ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
438       if (n_constraints) {
439         ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
440         ierr = VecSetValues(pcbddc->vec1_P,n_constraints,&auxindices[n_vertices],array,INSERT_VALUES);CHKERRQ(ierr);
441         ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
442       }
443       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
444       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
445       ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
446       /* check saddle point solution */
447       ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
448       ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
449       ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i]);CHKERRQ(ierr);
450       ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
451       /* shift by the identity matrix */
452       ierr = VecSetValue(pcbddc->vec1_P,i,m_one,ADD_VALUES);CHKERRQ(ierr);
453       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
454       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
455       ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i]);CHKERRQ(ierr);
456     }
457   }
458 
459   /* constraints */
460   for (i=0;i<n_constraints;i++) {
461     ierr = VecSet(vec2_C,zero);CHKERRQ(ierr);
462     ierr = VecSetValue(vec2_C,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
463     ierr = VecAssemblyBegin(vec2_C);CHKERRQ(ierr);
464     ierr = VecAssemblyEnd(vec2_C);CHKERRQ(ierr);
465     /* simplified solution of saddle point problem with null rhs on vertices multipliers */
466     ierr = MatMult(M1,vec2_C,vec1_C);CHKERRQ(ierr);
467     ierr = MatMult(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
468     ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
469     if (n_vertices) {
470       ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
471     }
472     /* Set values in coarse basis function and subdomain part of coarse_mat */
473     /* coarse basis functions */
474     j = i+n_vertices; /* don't touch this! */
475     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
476     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
477     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
478     ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
479     ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&j,array,INSERT_VALUES);CHKERRQ(ierr);
480     ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
481     if (pcbddc->switch_static || pcbddc->dbg_flag) {
482       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
483       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
484       ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
485       ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&j,array,INSERT_VALUES);CHKERRQ(ierr);
486       ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
487     }
488     /* subdomain contribution to coarse matrix. WARNING -> column major ordering */
489     if (n_vertices) {
490       ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
491       ierr = PetscMemcpy(&coarse_submat_vals[j*pcbddc->local_primal_size],array,n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
492       ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
493     }
494     ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
495     ierr = PetscMemcpy(&coarse_submat_vals[j*pcbddc->local_primal_size+n_vertices],array,n_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
496     ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
497 
498     if (pcbddc->dbg_flag) {
499       /* assemble subdomain vector on nodes */
500       ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
501       ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
502       if (n_R) {
503         ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
504       }
505       ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
506       ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
507       ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
508       /* assemble subdomain vector of lagrange multipliers */
509       ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
510       if (n_vertices) {
511         ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
512         ierr = VecSetValues(pcbddc->vec1_P,n_vertices,auxindices,array,INSERT_VALUES);CHKERRQ(ierr);
513         ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
514       }
515       ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
516       ierr = VecSetValues(pcbddc->vec1_P,n_constraints,&auxindices[n_vertices],array,INSERT_VALUES);CHKERRQ(ierr);
517       ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
518       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
519       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
520       ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
521       /* check saddle point solution */
522       ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
523       ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
524       ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[j]);CHKERRQ(ierr);
525       ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
526       /* shift by the identity matrix */
527       ierr = VecSetValue(pcbddc->vec1_P,j,m_one,ADD_VALUES);CHKERRQ(ierr);
528       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
529       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
530       ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[j]);CHKERRQ(ierr);
531     }
532   }
533   /* call assembling routines for local coarse basis */
534   ierr = MatAssemblyBegin(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
535   ierr = MatAssemblyEnd(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
536   if (pcbddc->switch_static || pcbddc->dbg_flag) {
537     ierr = MatAssemblyBegin(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
538     ierr = MatAssemblyEnd(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
539   }
540 
541   /* compute other basis functions for non-symmetric problems */
542   /*ierr = MatIsSymmetric(pc->pmat,0.,&pcbddc->issym);CHKERRQ(ierr);*/
543   { /* this is a temporary workaround since seqbaij matrices does not have support for symmetry checking */
544     PetscBool setsym;
545     ierr = MatIsSymmetricKnown(pc->pmat,&setsym,&pcbddc->issym);CHKERRQ(ierr);
546     if (!setsym) pcbddc->issym = PETSC_FALSE;
547   }
548 
549   if (!pcbddc->issym) {
550     if (!pcbddc->coarse_psi_B) {
551       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_psi_B);CHKERRQ(ierr);
552       ierr = MatSetSizes(pcbddc->coarse_psi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
553       ierr = MatSetType(pcbddc->coarse_psi_B,impMatType);CHKERRQ(ierr);
554       ierr = MatSetUp(pcbddc->coarse_psi_B);CHKERRQ(ierr);
555     }
556     if ( (pcbddc->switch_static || pcbddc->dbg_flag) && !pcbddc->coarse_psi_D) {
557       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_psi_D);CHKERRQ(ierr);
558       ierr = MatSetSizes(pcbddc->coarse_psi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
559       ierr = MatSetType(pcbddc->coarse_psi_D,impMatType);CHKERRQ(ierr);
560       ierr = MatSetUp(pcbddc->coarse_psi_D);CHKERRQ(ierr);
561     }
562     for (i=0;i<pcbddc->local_primal_size;i++) {
563       if (n_constraints) {
564         ierr = VecSet(vec1_C,zero);CHKERRQ(ierr);
565         for (j=0;j<n_constraints;j++) {
566           ierr = VecSetValue(vec1_C,j,coarse_submat_vals[(j+n_vertices)*pcbddc->local_primal_size+i],INSERT_VALUES);CHKERRQ(ierr);
567         }
568         ierr = VecAssemblyBegin(vec1_C);CHKERRQ(ierr);
569         ierr = VecAssemblyEnd(vec1_C);CHKERRQ(ierr);
570       }
571       if (i<n_vertices) {
572         ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
573         ierr = VecSetValue(vec1_V,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
574         ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
575         ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
576         ierr = MatMultTranspose(A_VR,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
577         if (n_constraints) {
578           ierr = MatMultTransposeAdd(C_CR,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
579         }
580       } else {
581         ierr = MatMultTranspose(C_CR,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
582       }
583       ierr = KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
584       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
585       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
586       ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
587       ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
588       ierr = MatSetValues(pcbddc->coarse_psi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
589       ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
590       if (i<n_vertices) {
591         ierr = MatSetValue(pcbddc->coarse_psi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
592       }
593       if (pcbddc->switch_static || pcbddc->dbg_flag) {
594         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
595         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
596         ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
597         ierr = MatSetValues(pcbddc->coarse_psi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
598         ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
599       }
600 
601       if (pcbddc->dbg_flag) {
602         /* assemble subdomain vector on nodes */
603         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
604         ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
605         if (n_R) {
606           ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
607         }
608         ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
609         if (i<n_vertices) {
610           ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],one,INSERT_VALUES);CHKERRQ(ierr);
611         }
612         ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
613         ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
614         /* assemble subdomain vector of lagrange multipliers */
615         for (j=0;j<pcbddc->local_primal_size;j++) {
616           ierr = VecSetValue(pcbddc->vec1_P,j,-coarse_submat_vals[j*pcbddc->local_primal_size+i],INSERT_VALUES);CHKERRQ(ierr);
617         }
618         ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
619         ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
620         /* check saddle point solution */
621         ierr = MatMultTranspose(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
622         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
623         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i+pcbddc->local_primal_size]);CHKERRQ(ierr);
624         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
625         /* shift by the identity matrix */
626         ierr = VecSetValue(pcbddc->vec1_P,i,m_one,ADD_VALUES);CHKERRQ(ierr);
627         ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
628         ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
629         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i+pcbddc->local_primal_size]);CHKERRQ(ierr);
630       }
631     }
632     ierr = MatAssemblyBegin(pcbddc->coarse_psi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
633     ierr = MatAssemblyEnd(pcbddc->coarse_psi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
634     if (pcbddc->switch_static || pcbddc->dbg_flag) {
635       ierr = MatAssemblyBegin(pcbddc->coarse_psi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
636       ierr = MatAssemblyEnd(pcbddc->coarse_psi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
637     }
638     unsymmetric_check = PETSC_TRUE;
639   } else { /* take references to already computed coarse basis */
640     unsymmetric_check = PETSC_FALSE;
641     ierr = PetscObjectReference((PetscObject)pcbddc->coarse_phi_B);CHKERRQ(ierr);
642     pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
643     if (pcbddc->coarse_phi_D) {
644       ierr = PetscObjectReference((PetscObject)pcbddc->coarse_phi_D);CHKERRQ(ierr);
645       pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
646     }
647   }
648   ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
649   /* Checking coarse_sub_mat and coarse basis functios */
650   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
651   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
652   if (pcbddc->dbg_flag) {
653     Mat         coarse_sub_mat;
654     Mat         AUXMAT,TM1,TM2,TM3,TM4;
655     Mat         coarse_phi_D,coarse_phi_B;
656     Mat         coarse_psi_D,coarse_psi_B;
657     Mat         A_II,A_BB,A_IB,A_BI;
658     MatType     checkmattype=MATSEQAIJ;
659     PetscReal   real_value;
660 
661     ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
662     ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
663     ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
664     ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
665     ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
666     ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
667     if (unsymmetric_check) {
668       ierr = MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);CHKERRQ(ierr);
669       ierr = MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);CHKERRQ(ierr);
670     }
671     ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);
672 
673     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
674     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat and local basis functions\n");CHKERRQ(ierr);
675     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
676     if (unsymmetric_check) {
677       ierr = MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
678       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
679       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
680       ierr = MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
681       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
682       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
683       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
684       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
685       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
686       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
687       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
688       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
689     } else {
690       ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
691       ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
692       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
693       ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
694       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
695       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
696       ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
697       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
698     }
699     ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
700     ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
701     ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
702     ierr = MatConvert(TM1,MATSEQDENSE,MAT_REUSE_MATRIX,&TM1);CHKERRQ(ierr);
703     ierr = MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
704     ierr = MatNorm(TM1,NORM_INFINITY,&real_value);CHKERRQ(ierr);
705     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
706     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"----------------------------------\n");CHKERRQ(ierr);
707     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d \n",PetscGlobalRank);CHKERRQ(ierr);
708     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"matrix error = % 1.14e\n",real_value);CHKERRQ(ierr);
709     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"coarse functions (phi) errors\n");CHKERRQ(ierr);
710     for (i=0;i<pcbddc->local_primal_size;i++) {
711       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i,coarsefunctions_errors[i]);CHKERRQ(ierr);
712     }
713     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"constraints (phi) errors\n");CHKERRQ(ierr);
714     for (i=0;i<pcbddc->local_primal_size;i++) {
715       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i,constraints_errors[i]);CHKERRQ(ierr);
716     }
717     if (unsymmetric_check) {
718       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"coarse functions (psi) errors\n");CHKERRQ(ierr);
719       for (i=pcbddc->local_primal_size;i<2*pcbddc->local_primal_size;i++) {
720         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i-pcbddc->local_primal_size,coarsefunctions_errors[i]);CHKERRQ(ierr);
721       }
722       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"constraints (psi) errors\n");CHKERRQ(ierr);
723       for (i=pcbddc->local_primal_size;i<2*pcbddc->local_primal_size;i++) {
724         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i-pcbddc->local_primal_size,constraints_errors[i]);CHKERRQ(ierr);
725       }
726     }
727     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
728     ierr = MatDestroy(&A_II);CHKERRQ(ierr);
729     ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
730     ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
731     ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
732     ierr = MatDestroy(&TM1);CHKERRQ(ierr);
733     ierr = MatDestroy(&TM2);CHKERRQ(ierr);
734     ierr = MatDestroy(&TM3);CHKERRQ(ierr);
735     ierr = MatDestroy(&TM4);CHKERRQ(ierr);
736     ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
737     ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
738     if (unsymmetric_check) {
739       ierr = MatDestroy(&coarse_psi_D);CHKERRQ(ierr);
740       ierr = MatDestroy(&coarse_psi_B);CHKERRQ(ierr);
741     }
742     ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
743     ierr = ISRestoreIndices(pcbddc->is_R_local,&idx_R_local);CHKERRQ(ierr);
744     ierr = PetscFree(coarsefunctions_errors);CHKERRQ(ierr);
745     ierr = PetscFree(constraints_errors);CHKERRQ(ierr);
746   }
747   /* free memory */
748   if (n_vertices) {
749     ierr = VecDestroy(&vec1_V);CHKERRQ(ierr);
750     ierr = VecDestroy(&vec2_V);CHKERRQ(ierr);
751     ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
752     ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
753     ierr = MatDestroy(&A_VV);CHKERRQ(ierr);
754   }
755   if (n_constraints) {
756     ierr = VecDestroy(&vec1_C);CHKERRQ(ierr);
757     ierr = VecDestroy(&vec2_C);CHKERRQ(ierr);
758     ierr = MatDestroy(&M1);CHKERRQ(ierr);
759     ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
760   }
761   ierr = PetscFree(auxindices);CHKERRQ(ierr);
762   /* get back data */
763   *coarse_submat_vals_n = coarse_submat_vals;
764   PetscFunctionReturn(0);
765 }
766 
767 #undef __FUNCT__
768 #define __FUNCT__ "PCBDDCSetUpLocalMatrices"
769 PetscErrorCode PCBDDCSetUpLocalMatrices(PC pc)
770 {
771   PC_IS*            pcis = (PC_IS*)(pc->data);
772   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
773   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
774   PetscBool         issbaij,isseqaij;
775   /* manage repeated solves */
776   MatReuse          reuse;
777   PetscErrorCode    ierr;
778 
779   PetscFunctionBegin;
780   if ( (pcbddc->use_change_of_basis && !pcbddc->ChangeOfBasisMatrix) || (pcbddc->user_ChangeOfBasisMatrix && !pcbddc->ChangeOfBasisMatrix) ) {
781     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Change of basis matrix has not been created");
782   }
783   /* get mat flags */
784   reuse = MAT_INITIAL_MATRIX;
785   if (pc->setupcalled) {
786     if (pc->flag == SAME_NONZERO_PATTERN) {
787       reuse = MAT_REUSE_MATRIX;
788     } else {
789       reuse = MAT_INITIAL_MATRIX;
790     }
791   }
792   if (reuse == MAT_INITIAL_MATRIX) {
793     ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
794     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
795     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
796     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
797     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
798   }
799 
800   /* transform local matrices if needed */
801   if (pcbddc->ChangeOfBasisMatrix) {
802     Mat       *change_mat_all;
803     IS        is_local,is_global;
804     PetscBool sorted;
805     PetscInt  *idxs_perm;
806 
807     ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n,0,1,&is_local);CHKERRQ(ierr);
808     ierr = ISLocalToGlobalMappingApplyIS(matis->mapping,is_local,&is_global);CHKERRQ(ierr);
809     ierr = ISDestroy(&is_local);CHKERRQ(ierr);
810     ierr = ISSorted(is_global,&sorted);CHKERRQ(ierr);
811     if (!sorted) {
812       const PetscInt *idxs;
813       PetscInt *idxs_sorted,i;
814 
815       ierr = PetscMalloc1(pcis->n,&idxs_perm);CHKERRQ(ierr);
816       ierr = PetscMalloc1(pcis->n,&idxs_sorted);CHKERRQ(ierr);
817       for (i=0;i<pcis->n;i++) {
818         idxs_perm[i] = i;
819       }
820       ierr = ISGetIndices(is_global,&idxs);CHKERRQ(ierr);
821       ierr = PetscSortIntWithPermutation(pcis->n,idxs,idxs_perm);CHKERRQ(ierr);
822       for (i=0;i<pcis->n;i++) {
823         idxs_sorted[i] = idxs[idxs_perm[i]];
824       }
825       ierr = ISRestoreIndices(is_global,&idxs);CHKERRQ(ierr);
826       ierr = ISDestroy(&is_global);CHKERRQ(ierr);
827       ierr = ISCreateGeneral(PETSC_COMM_SELF,pcis->n,idxs_sorted,PETSC_OWN_POINTER,&is_global);CHKERRQ(ierr);
828     }
829 
830     /* get change of basis on the whole set of local dofs */
831     ierr = MatGetSubMatrices(pcbddc->ChangeOfBasisMatrix,1,&is_global,&is_global,MAT_INITIAL_MATRIX,&change_mat_all);CHKERRQ(ierr);
832 
833     if (!sorted) {
834       Mat      new_mat;
835       IS       is_perm;
836       PetscInt *idxs,i;
837 
838       ierr = PetscMalloc1(pcis->n,&idxs);CHKERRQ(ierr);
839       for (i=0;i<pcis->n;i++) {
840         idxs[idxs_perm[i]] = i;
841       }
842       ierr = PetscFree(idxs_perm);CHKERRQ(ierr);
843       ierr = ISCreateGeneral(PETSC_COMM_SELF,pcis->n,idxs,PETSC_OWN_POINTER,&is_perm);CHKERRQ(ierr);
844       ierr = ISSetPermutation(is_perm);CHKERRQ(ierr);
845       ierr = MatPermute(change_mat_all[0],is_perm,is_perm,&new_mat);CHKERRQ(ierr);
846       ierr = MatDestroy(&change_mat_all[0]);CHKERRQ(ierr);
847       change_mat_all[0] = new_mat;
848       ierr = ISDestroy(&is_perm);CHKERRQ(ierr);
849     }
850 
851     /* check */
852     if (pcbddc->dbg_flag) {
853       Vec       x,x_change;
854       PetscReal error;
855 
856       ierr = VecDuplicate(pcis->vec1_global,&x);CHKERRQ(ierr);
857       ierr = VecDuplicate(pcis->vec1_global,&x_change);CHKERRQ(ierr);
858       ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
859       ierr = VecCopy(x,pcis->vec1_global);CHKERRQ(ierr);
860       ierr = VecScatterBegin(matis->ctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
861       ierr = VecScatterEnd(matis->ctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
862       ierr = MatMult(change_mat_all[0],pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
863       ierr = VecScatterBegin(matis->ctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
864       ierr = VecScatterEnd(matis->ctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
865       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);CHKERRQ(ierr);
866       ierr = VecAXPY(x,-1.0,x_change);CHKERRQ(ierr);
867       ierr = VecNorm(x,NORM_INFINITY,&error);CHKERRQ(ierr);
868       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
869       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change on N: %1.6e\n",error);CHKERRQ(ierr);
870       ierr = VecDestroy(&x);CHKERRQ(ierr);
871       ierr = VecDestroy(&x_change);CHKERRQ(ierr);
872     }
873 
874     /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
875     ierr = PetscObjectTypeCompare((PetscObject)matis->A,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
876     if (isseqaij) {
877       ierr = MatPtAP(matis->A,change_mat_all[0],reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
878     } else {
879       Mat work_mat;
880       ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
881       ierr = MatPtAP(work_mat,change_mat_all[0],reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
882       ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
883     }
884     /*
885     ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
886     ierr = MatView(change_mat_all,(PetscViewer)0);CHKERRQ(ierr);
887     */
888     ierr = MatDestroyMatrices(1,&change_mat_all);CHKERRQ(ierr);
889     ierr = ISDestroy(&is_global);CHKERRQ(ierr);
890   } else {
891     /* without change of basis, the local matrix is unchanged */
892     if (!pcbddc->local_mat) {
893       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
894       pcbddc->local_mat = matis->A;
895     }
896   }
897 
898   /* get submatrices */
899   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_I_local,reuse,&pcis->A_II);CHKERRQ(ierr);
900   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,reuse,&pcis->A_BB);CHKERRQ(ierr);
901   ierr = PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
902   if (!issbaij) {
903     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
904     ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
905   } else {
906     Mat newmat;
907     ierr = MatConvert(pcbddc->local_mat,MATSEQBAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
908     ierr = MatGetSubMatrix(newmat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
909     ierr = MatGetSubMatrix(newmat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
910     ierr = MatDestroy(&newmat);CHKERRQ(ierr);
911   }
912   PetscFunctionReturn(0);
913 }
914 
915 #undef __FUNCT__
916 #define __FUNCT__ "PCBDDCSetUpLocalScatters"
917 PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
918 {
919   PC_IS*         pcis = (PC_IS*)(pc->data);
920   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
921   IS             is_aux1,is_aux2;
922   PetscInt       *aux_array1,*aux_array2,*is_indices,*idx_R_local;
923   PetscInt       n_vertices,i,j,n_R,n_D,n_B;
924   PetscInt       vbs,bs;
925   PetscBT        bitmask;
926   PetscErrorCode ierr;
927 
928   PetscFunctionBegin;
929   /*
930     No need to setup local scatters if
931       - primal space is unchanged
932         AND
933       - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
934         AND
935       - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
936   */
937   if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) {
938     PetscFunctionReturn(0);
939   }
940   /* destroy old objects */
941   ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
942   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
943   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
944   /* Set Non-overlapping dimensions */
945   n_B = pcis->n_B; n_D = pcis->n - n_B;
946   n_vertices = pcbddc->n_actual_vertices;
947   /* create auxiliary bitmask */
948   ierr = PetscBTCreate(pcis->n,&bitmask);CHKERRQ(ierr);
949   for (i=0;i<n_vertices;i++) {
950     ierr = PetscBTSet(bitmask,pcbddc->primal_indices_local_idxs[i]);CHKERRQ(ierr);
951   }
952 
953   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
954   ierr = PetscMalloc1((pcis->n-n_vertices),&idx_R_local);CHKERRQ(ierr);
955   for (i=0, n_R=0; i<pcis->n; i++) {
956     if (!PetscBTLookup(bitmask,i)) {
957       idx_R_local[n_R] = i;
958       n_R++;
959     }
960   }
961 
962   /* Block code */
963   vbs = 1;
964   ierr = MatGetBlockSize(pcbddc->local_mat,&bs);CHKERRQ(ierr);
965   if (bs>1 && !(n_vertices%bs)) {
966     PetscBool is_blocked = PETSC_TRUE;
967     PetscInt  *vary;
968     /* Verify if the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
969     ierr = PetscMalloc1(pcis->n/bs,&vary);CHKERRQ(ierr);
970     ierr = PetscMemzero(vary,pcis->n/bs*sizeof(PetscInt));CHKERRQ(ierr);
971     for (i=0; i<n_vertices; i++) vary[pcbddc->primal_indices_local_idxs[i]/bs]++;
972     for (i=0; i<n_vertices; i++) {
973       if (vary[i]!=0 && vary[i]!=bs) {
974         is_blocked = PETSC_FALSE;
975         break;
976       }
977     }
978     if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
979       vbs = bs;
980       for (i=0;i<n_R/vbs;i++) {
981         idx_R_local[i] = idx_R_local[vbs*i]/vbs;
982       }
983     }
984     ierr = PetscFree(vary);CHKERRQ(ierr);
985   }
986   ierr = ISCreateBlock(PETSC_COMM_SELF,vbs,n_R/vbs,idx_R_local,PETSC_COPY_VALUES,&pcbddc->is_R_local);CHKERRQ(ierr);
987   ierr = PetscFree(idx_R_local);CHKERRQ(ierr);
988 
989   /* print some info if requested */
990   if (pcbddc->dbg_flag) {
991     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
992     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
993     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
994     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
995     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
996     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);
997     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
998     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
999   }
1000 
1001   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
1002   ierr = ISGetIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
1003   ierr = PetscMalloc1((pcis->n_B-n_vertices),&aux_array1);CHKERRQ(ierr);
1004   ierr = PetscMalloc1((pcis->n_B-n_vertices),&aux_array2);CHKERRQ(ierr);
1005   ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1006   for (i=0; i<n_D; i++) {
1007     ierr = PetscBTSet(bitmask,is_indices[i]);CHKERRQ(ierr);
1008   }
1009   ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1010   for (i=0, j=0; i<n_R; i++) {
1011     if (!PetscBTLookup(bitmask,idx_R_local[i])) {
1012       aux_array1[j++] = i;
1013     }
1014   }
1015   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
1016   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1017   for (i=0, j=0; i<n_B; i++) {
1018     if (!PetscBTLookup(bitmask,is_indices[i])) {
1019       aux_array2[j++] = i;
1020     }
1021   }
1022   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1023   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);CHKERRQ(ierr);
1024   ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
1025   ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
1026   ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
1027 
1028   if (pcbddc->switch_static || pcbddc->dbg_flag) {
1029     ierr = PetscMalloc1(n_D,&aux_array1);CHKERRQ(ierr);
1030     for (i=0, j=0; i<n_R; i++) {
1031       if (PetscBTLookup(bitmask,idx_R_local[i])) {
1032         aux_array1[j++] = i;
1033       }
1034     }
1035     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
1036     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
1037     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
1038   }
1039   ierr = PetscBTDestroy(&bitmask);CHKERRQ(ierr);
1040   ierr = ISRestoreIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
1041   PetscFunctionReturn(0);
1042 }
1043 
1044 
1045 #undef __FUNCT__
1046 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
1047 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc)
1048 {
1049   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1050   PC_IS          *pcis = (PC_IS*)pc->data;
1051   PC             pc_temp;
1052   Mat            A_RR;
1053   MatReuse       reuse;
1054   PetscScalar    m_one = -1.0;
1055   PetscReal      value;
1056   PetscInt       n_D,n_R,ibs,mbs;
1057   PetscBool      use_exact,use_exact_reduced,issbaij;
1058   PetscErrorCode ierr;
1059   /* prefixes stuff */
1060   char           dir_prefix[256],neu_prefix[256],str_level[16];
1061   size_t         len;
1062 
1063   PetscFunctionBegin;
1064 
1065   /* compute prefixes */
1066   ierr = PetscStrcpy(dir_prefix,"");CHKERRQ(ierr);
1067   ierr = PetscStrcpy(neu_prefix,"");CHKERRQ(ierr);
1068   if (!pcbddc->current_level) {
1069     ierr = PetscStrcpy(dir_prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
1070     ierr = PetscStrcpy(neu_prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
1071     ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
1072     ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
1073   } else {
1074     ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
1075     sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
1076     ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
1077     len -= 15; /* remove "pc_bddc_coarse_" */
1078     if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
1079     if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
1080     ierr = PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
1081     ierr = PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
1082     ierr = PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");CHKERRQ(ierr);
1083     ierr = PetscStrcat(neu_prefix,"pc_bddc_neumann_");CHKERRQ(ierr);
1084     ierr = PetscStrcat(dir_prefix,str_level);CHKERRQ(ierr);
1085     ierr = PetscStrcat(neu_prefix,str_level);CHKERRQ(ierr);
1086   }
1087 
1088   /* DIRICHLET PROBLEM */
1089   /* Matrix for Dirichlet problem is pcis->A_II */
1090   ierr = ISGetSize(pcis->is_I_local,&n_D);CHKERRQ(ierr);
1091   if (!pcbddc->ksp_D) { /* create object if not yet build */
1092     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
1093     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
1094     /* default */
1095     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
1096     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);CHKERRQ(ierr);
1097     ierr = PetscObjectTypeCompare((PetscObject)pcis->A_II,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
1098     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
1099     if (issbaij) {
1100       ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
1101     } else {
1102       ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
1103     }
1104     /* Allow user's customization */
1105     ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
1106     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
1107   }
1108   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II);CHKERRQ(ierr);
1109   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
1110   if (!n_D) {
1111     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
1112     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
1113   }
1114   /* Set Up KSP for Dirichlet problem of BDDC */
1115   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
1116   /* set ksp_D into pcis data */
1117   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
1118   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
1119   pcis->ksp_D = pcbddc->ksp_D;
1120 
1121   /* NEUMANN PROBLEM */
1122   /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
1123   ierr = ISGetSize(pcbddc->is_R_local,&n_R);CHKERRQ(ierr);
1124   if (pcbddc->ksp_R) { /* already created ksp */
1125     PetscInt nn_R;
1126     ierr = KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);CHKERRQ(ierr);
1127     ierr = PetscObjectReference((PetscObject)A_RR);CHKERRQ(ierr);
1128     ierr = MatGetSize(A_RR,&nn_R,NULL);CHKERRQ(ierr);
1129     if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
1130       ierr = KSPReset(pcbddc->ksp_R);CHKERRQ(ierr);
1131       ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1132       reuse = MAT_INITIAL_MATRIX;
1133     } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
1134       if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
1135         ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1136         reuse = MAT_INITIAL_MATRIX;
1137       } else { /* safe to reuse the matrix */
1138         reuse = MAT_REUSE_MATRIX;
1139       }
1140     }
1141     /* last check */
1142     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
1143       ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1144       reuse = MAT_INITIAL_MATRIX;
1145     }
1146   } else { /* first time, so we need to create the matrix */
1147     reuse = MAT_INITIAL_MATRIX;
1148   }
1149   /* extract A_RR */
1150   ierr = MatGetBlockSize(pcbddc->local_mat,&mbs);CHKERRQ(ierr);
1151   ierr = ISGetBlockSize(pcbddc->is_R_local,&ibs);CHKERRQ(ierr);
1152   if (ibs != mbs) {
1153     Mat newmat;
1154     ierr = MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INITIAL_MATRIX,&newmat);CHKERRQ(ierr);
1155     ierr = MatGetSubMatrix(newmat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
1156     ierr = MatDestroy(&newmat);CHKERRQ(ierr);
1157   } else {
1158     ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);CHKERRQ(ierr);
1159   }
1160   if (!pcbddc->ksp_R) { /* create object if not present */
1161     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
1162     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
1163     /* default */
1164     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
1165     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);CHKERRQ(ierr);
1166     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
1167     ierr = PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);CHKERRQ(ierr);
1168     if (issbaij) {
1169       ierr = PCSetType(pc_temp,PCCHOLESKY);CHKERRQ(ierr);
1170     } else {
1171       ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
1172     }
1173     /* Allow user's customization */
1174     ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
1175     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
1176   }
1177   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);CHKERRQ(ierr);
1178   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
1179   if (!n_R) {
1180     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
1181     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
1182   }
1183   /* Set Up KSP for Neumann problem of BDDC */
1184   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
1185 
1186   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
1187   if (pcbddc->NullSpace || pcbddc->dbg_flag) {
1188     /* Dirichlet */
1189     ierr = VecSetRandom(pcis->vec1_D,NULL);CHKERRQ(ierr);
1190     ierr = MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);CHKERRQ(ierr);
1191     ierr = KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);CHKERRQ(ierr);
1192     ierr = VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);CHKERRQ(ierr);
1193     ierr = VecNorm(pcis->vec1_D,NORM_INFINITY,&value);CHKERRQ(ierr);
1194     /* need to be adapted? */
1195     use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
1196     ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1197     ierr = PCBDDCSetUseExactDirichlet(pc,use_exact_reduced);CHKERRQ(ierr);
1198     /* print info */
1199     if (pcbddc->dbg_flag) {
1200       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1201       ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1202       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
1203       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
1204       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);
1205       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1206     }
1207     if (pcbddc->NullSpace && !use_exact_reduced && !pcbddc->switch_static) {
1208       ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcis->is_I_local);CHKERRQ(ierr);
1209     }
1210 
1211     /* Neumann */
1212     ierr = VecSetRandom(pcbddc->vec1_R,NULL);CHKERRQ(ierr);
1213     ierr = MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
1214     ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
1215     ierr = VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);CHKERRQ(ierr);
1216     ierr = VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);CHKERRQ(ierr);
1217     /* need to be adapted? */
1218     use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
1219     ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1220     /* print info */
1221     if (pcbddc->dbg_flag) {
1222       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);
1223       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1224     }
1225     if (pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
1226       ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcbddc->is_R_local);CHKERRQ(ierr);
1227     }
1228   }
1229   /* free Neumann problem's matrix */
1230   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
1231   PetscFunctionReturn(0);
1232 }
1233 
1234 #undef __FUNCT__
1235 #define __FUNCT__ "PCBDDCSolveSubstructureCorrection"
1236 static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec rhs, Vec sol, Vec work, PetscBool applytranspose)
1237 {
1238   PetscErrorCode ierr;
1239   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1240 
1241   PetscFunctionBegin;
1242   if (applytranspose) {
1243     if (pcbddc->local_auxmat1) {
1244       ierr = MatMultTranspose(pcbddc->local_auxmat2,rhs,work);CHKERRQ(ierr);
1245       ierr = MatMultTransposeAdd(pcbddc->local_auxmat1,work,rhs,rhs);CHKERRQ(ierr);
1246     }
1247     ierr = KSPSolveTranspose(pcbddc->ksp_R,rhs,sol);CHKERRQ(ierr);
1248   } else {
1249     ierr = KSPSolve(pcbddc->ksp_R,rhs,sol);CHKERRQ(ierr);
1250     if (pcbddc->local_auxmat1) {
1251       ierr = MatMult(pcbddc->local_auxmat1,sol,work);CHKERRQ(ierr);
1252       ierr = MatMultAdd(pcbddc->local_auxmat2,work,sol,sol);CHKERRQ(ierr);
1253     }
1254   }
1255   PetscFunctionReturn(0);
1256 }
1257 
1258 /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
1259 #undef __FUNCT__
1260 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
1261 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
1262 {
1263   PetscErrorCode ierr;
1264   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
1265   PC_IS*            pcis = (PC_IS*)  (pc->data);
1266   const PetscScalar zero = 0.0;
1267 
1268   PetscFunctionBegin;
1269   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
1270   if (applytranspose) {
1271     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1272     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1273   } else {
1274     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1275     if (pcbddc->switch_static) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1276   }
1277   /* start communications from local primal nodes to rhs of coarse solver */
1278   ierr = VecSet(pcbddc->coarse_vec,zero);CHKERRQ(ierr);
1279   ierr = PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1280   ierr = PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1281 
1282   /* Coarse solution -> rhs and sol updated inside PCBDDCScattarCoarseDataBegin/End */
1283   /* TODO remove null space when doing multilevel */
1284   if (pcbddc->coarse_ksp) {
1285     if (applytranspose) {
1286       ierr = KSPSolveTranspose(pcbddc->coarse_ksp,NULL,NULL);CHKERRQ(ierr);
1287     } else {
1288       ierr = KSPSolve(pcbddc->coarse_ksp,NULL,NULL);CHKERRQ(ierr);
1289     }
1290   }
1291 
1292   /* Local solution on R nodes */
1293   if (pcis->n) {
1294     ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
1295     ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1296     ierr = VecScatterEnd(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1297     if (pcbddc->switch_static) {
1298       ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1299       ierr = VecScatterEnd(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1300     }
1301     ierr = PCBDDCSolveSubstructureCorrection(pc,pcbddc->vec1_R,pcbddc->vec2_R,pcbddc->vec1_C,applytranspose);CHKERRQ(ierr);
1302     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1303     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1304     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1305     if (pcbddc->switch_static) {
1306       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1307       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1308     }
1309   }
1310 
1311   /* communications from coarse sol to local primal nodes */
1312   ierr = PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1313   ierr = PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1314 
1315   /* Sum contributions from two levels */
1316   if (applytranspose) {
1317     ierr = MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1318     if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1319   } else {
1320     ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1321     if (pcbddc->switch_static) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1322   }
1323   PetscFunctionReturn(0);
1324 }
1325 
1326 /* TODO: the following two function can be optimized using VecPlaceArray whenever possible and using overlap flag */
1327 #undef __FUNCT__
1328 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
1329 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
1330 {
1331   PetscErrorCode ierr;
1332   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1333   PetscScalar    *array,*array2;
1334   Vec            from,to;
1335 
1336   PetscFunctionBegin;
1337   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
1338     from = pcbddc->coarse_vec;
1339     to = pcbddc->vec1_P;
1340     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
1341       Vec tvec;
1342       PetscInt lsize;
1343       ierr = KSPGetSolution(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1344       ierr = VecGetLocalSize(tvec,&lsize);CHKERRQ(ierr);
1345       ierr = VecGetArrayRead(tvec,(const PetscScalar**)&array);CHKERRQ(ierr);
1346       ierr = VecGetArray(from,&array2);CHKERRQ(ierr);
1347       ierr = PetscMemcpy(array2,array,lsize*sizeof(PetscScalar));CHKERRQ(ierr);
1348       ierr = VecRestoreArrayRead(tvec,(const PetscScalar**)&array);CHKERRQ(ierr);
1349       ierr = VecRestoreArray(from,&array2);CHKERRQ(ierr);
1350     }
1351   } else { /* from local to global -> put data in coarse right hand side */
1352     from = pcbddc->vec1_P;
1353     to = pcbddc->coarse_vec;
1354   }
1355   ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
1356   PetscFunctionReturn(0);
1357 }
1358 
1359 #undef __FUNCT__
1360 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
1361 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
1362 {
1363   PetscErrorCode ierr;
1364   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1365   PetscScalar    *array,*array2;
1366   Vec            from,to;
1367 
1368   PetscFunctionBegin;
1369   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
1370     from = pcbddc->coarse_vec;
1371     to = pcbddc->vec1_P;
1372   } else { /* from local to global -> put data in coarse right hand side */
1373     from = pcbddc->vec1_P;
1374     to = pcbddc->coarse_vec;
1375   }
1376   ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);CHKERRQ(ierr);
1377   if (smode == SCATTER_FORWARD) {
1378     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
1379       Vec tvec;
1380       PetscInt lsize;
1381       ierr = KSPGetRhs(pcbddc->coarse_ksp,&tvec);CHKERRQ(ierr);
1382       ierr = VecGetLocalSize(tvec,&lsize);CHKERRQ(ierr);
1383       ierr = VecGetArrayRead(to,(const PetscScalar**)&array);CHKERRQ(ierr);
1384       ierr = VecGetArray(tvec,&array2);CHKERRQ(ierr);
1385       ierr = PetscMemcpy(array2,array,lsize*sizeof(PetscScalar));CHKERRQ(ierr);
1386       ierr = VecRestoreArrayRead(to,(const PetscScalar**)&array);CHKERRQ(ierr);
1387       ierr = VecRestoreArray(tvec,&array2);CHKERRQ(ierr);
1388     }
1389   }
1390   PetscFunctionReturn(0);
1391 }
1392 
1393 /* uncomment for testing purposes */
1394 /* #define PETSC_MISSING_LAPACK_GESVD 1 */
1395 #undef __FUNCT__
1396 #define __FUNCT__ "PCBDDCConstraintsSetUp"
1397 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
1398 {
1399   PetscErrorCode    ierr;
1400   PC_IS*            pcis = (PC_IS*)(pc->data);
1401   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
1402   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
1403   /* constraint and (optionally) change of basis matrix implemented as SeqAIJ */
1404   MatType           impMatType=MATSEQAIJ;
1405   /* one and zero */
1406   PetscScalar       one=1.0,zero=0.0;
1407   /* space to store constraints and their local indices */
1408   PetscScalar       *temp_quadrature_constraint;
1409   PetscInt          *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B;
1410   /* iterators */
1411   PetscInt          i,j,k,total_counts,temp_start_ptr;
1412   /* stuff to store connected components stored in pcbddc->mat_graph */
1413   IS                ISForVertices,*ISForFaces,*ISForEdges,*used_IS;
1414   PetscInt          n_ISForFaces,n_ISForEdges;
1415   /* near null space stuff */
1416   MatNullSpace      nearnullsp;
1417   const Vec         *nearnullvecs;
1418   Vec               *localnearnullsp;
1419   PetscBool         nnsp_has_cnst;
1420   PetscInt          nnsp_size;
1421   PetscScalar       *array;
1422   /* BLAS integers */
1423   PetscBLASInt      lwork,lierr;
1424   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
1425   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
1426   /* LAPACK working arrays for SVD or POD */
1427   PetscBool         skip_lapack;
1428   PetscScalar       *work;
1429   PetscReal         *singular_vals;
1430 #if defined(PETSC_USE_COMPLEX)
1431   PetscReal         *rwork;
1432 #endif
1433 #if defined(PETSC_MISSING_LAPACK_GESVD)
1434   PetscBLASInt      Blas_one_2=1;
1435   PetscScalar       *temp_basis,*correlation_mat;
1436 #else
1437   PetscBLASInt      dummy_int_1=1,dummy_int_2=1;
1438   PetscScalar       dummy_scalar_1=0.0,dummy_scalar_2=0.0;
1439 #endif
1440   /* reuse */
1441   PetscInt          olocal_primal_size;
1442   PetscInt          *oprimal_indices_local_idxs;
1443   /* change of basis */
1444   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
1445   PetscBool         boolforchange,qr_needed;
1446   PetscBT           touched,change_basis,qr_needed_idx;
1447   /* auxiliary stuff */
1448   PetscInt          *nnz,*is_indices,*aux_primal_numbering_B;
1449   /* some quantities */
1450   PetscInt          n_vertices,total_primal_vertices,valid_constraints;
1451   PetscInt          size_of_constraint,max_size_of_constraint,max_constraints,temp_constraints;
1452 
1453 
1454   PetscFunctionBegin;
1455   /* Destroy Mat objects computed previously */
1456   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1457   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1458   /* Get index sets for faces, edges and vertices from graph */
1459   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);CHKERRQ(ierr);
1460   /* free unneeded index sets */
1461   if (!pcbddc->use_vertices) {
1462     ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1463   }
1464   if (!pcbddc->use_edges) {
1465     for (i=0;i<n_ISForEdges;i++) {
1466       ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1467     }
1468     ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1469     n_ISForEdges = 0;
1470   }
1471   if (!pcbddc->use_faces) {
1472     for (i=0;i<n_ISForFaces;i++) {
1473       ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1474     }
1475     ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1476     n_ISForFaces = 0;
1477   }
1478   /* HACKS (the following two blocks of code) */
1479   if (!ISForVertices && pcbddc->NullSpace && !pcbddc->user_ChangeOfBasisMatrix) {
1480     pcbddc->use_change_of_basis = PETSC_TRUE;
1481     if (!ISForEdges) {
1482       pcbddc->use_change_on_faces = PETSC_TRUE;
1483     }
1484   }
1485   if (pcbddc->NullSpace) {
1486     /* use_change_of_basis should be consistent among processors */
1487     PetscBool tbool[2],gbool[2];
1488     tbool [0] = pcbddc->use_change_of_basis;
1489     tbool [1] = pcbddc->use_change_on_faces;
1490     ierr = MPI_Allreduce(tbool,gbool,2,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
1491     pcbddc->use_change_of_basis = gbool[0];
1492     pcbddc->use_change_on_faces = gbool[1];
1493   }
1494   /* print some info */
1495   if (pcbddc->dbg_flag) {
1496     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
1497     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1498     i = 0;
1499     if (ISForVertices) {
1500       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
1501     }
1502     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
1503     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
1504     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
1505     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1506   }
1507   /* check if near null space is attached to global mat */
1508   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
1509   if (nearnullsp) {
1510     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1511     /* remove any stored info */
1512     ierr = MatNullSpaceDestroy(&pcbddc->onearnullspace);CHKERRQ(ierr);
1513     ierr = PetscFree(pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1514     /* store information for BDDC solver reuse */
1515     ierr = PetscObjectReference((PetscObject)nearnullsp);CHKERRQ(ierr);
1516     pcbddc->onearnullspace = nearnullsp;
1517     ierr = PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);CHKERRQ(ierr);
1518     for (i=0;i<nnsp_size;i++) {
1519       ierr = PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);CHKERRQ(ierr);
1520     }
1521   } else { /* if near null space is not provided BDDC uses constants by default */
1522     nnsp_size = 0;
1523     nnsp_has_cnst = PETSC_TRUE;
1524   }
1525   /* get max number of constraints on a single cc */
1526   max_constraints = nnsp_size;
1527   if (nnsp_has_cnst) max_constraints++;
1528 
1529   /*
1530        Evaluate maximum storage size needed by the procedure
1531        - temp_indices will contain start index of each constraint stored as follows
1532        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
1533        - 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
1534        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
1535                                                                                                                                                          */
1536   total_counts = n_ISForFaces+n_ISForEdges;
1537   total_counts *= max_constraints;
1538   n_vertices = 0;
1539   if (ISForVertices) {
1540     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
1541   }
1542   total_counts += n_vertices;
1543   ierr = PetscMalloc1((total_counts+1),&temp_indices);CHKERRQ(ierr);
1544   ierr = PetscBTCreate(total_counts,&change_basis);CHKERRQ(ierr);
1545   total_counts = 0;
1546   max_size_of_constraint = 0;
1547   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1548     if (i<n_ISForEdges) {
1549       used_IS = &ISForEdges[i];
1550     } else {
1551       used_IS = &ISForFaces[i-n_ISForEdges];
1552     }
1553     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
1554     total_counts += j;
1555     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
1556   }
1557   total_counts *= max_constraints;
1558   total_counts += n_vertices;
1559   ierr = PetscMalloc3(total_counts,&temp_quadrature_constraint,total_counts,&temp_indices_to_constraint,total_counts,&temp_indices_to_constraint_B);CHKERRQ(ierr);
1560   /* get local part of global near null space vectors */
1561   ierr = PetscMalloc1(nnsp_size,&localnearnullsp);CHKERRQ(ierr);
1562   for (k=0;k<nnsp_size;k++) {
1563     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
1564     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1565     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1566   }
1567 
1568   /* whether or not to skip lapack calls */
1569   skip_lapack = PETSC_TRUE;
1570   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
1571 
1572   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
1573   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1574     PetscScalar temp_work;
1575 #if defined(PETSC_MISSING_LAPACK_GESVD)
1576     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
1577     ierr = PetscMalloc1(max_constraints*max_constraints,&correlation_mat);CHKERRQ(ierr);
1578     ierr = PetscMalloc1(max_constraints,&singular_vals);CHKERRQ(ierr);
1579     ierr = PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);CHKERRQ(ierr);
1580 #if defined(PETSC_USE_COMPLEX)
1581     ierr = PetscMalloc1(3*max_constraints,&rwork);CHKERRQ(ierr);
1582 #endif
1583     /* now we evaluate the optimal workspace using query with lwork=-1 */
1584     ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1585     ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
1586     lwork = -1;
1587     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1588 #if !defined(PETSC_USE_COMPLEX)
1589     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
1590 #else
1591     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
1592 #endif
1593     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1594     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
1595 #else /* on missing GESVD */
1596     /* SVD */
1597     PetscInt max_n,min_n;
1598     max_n = max_size_of_constraint;
1599     min_n = max_constraints;
1600     if (max_size_of_constraint < max_constraints) {
1601       min_n = max_size_of_constraint;
1602       max_n = max_constraints;
1603     }
1604     ierr = PetscMalloc1(min_n,&singular_vals);CHKERRQ(ierr);
1605 #if defined(PETSC_USE_COMPLEX)
1606     ierr = PetscMalloc1(5*min_n,&rwork);CHKERRQ(ierr);
1607 #endif
1608     /* now we evaluate the optimal workspace using query with lwork=-1 */
1609     lwork = -1;
1610     ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
1611     ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
1612     ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
1613     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1614 #if !defined(PETSC_USE_COMPLEX)
1615     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));
1616 #else
1617     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));
1618 #endif
1619     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1620     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
1621 #endif /* on missing GESVD */
1622     /* Allocate optimal workspace */
1623     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
1624     ierr = PetscMalloc1((PetscInt)lwork,&work);CHKERRQ(ierr);
1625   }
1626   /* Now we can loop on constraining sets */
1627   total_counts = 0;
1628   temp_indices[0] = 0;
1629   /* vertices */
1630   if (ISForVertices) {
1631     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1632     if (nnsp_has_cnst) { /* consider all vertices */
1633       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,n_vertices*sizeof(PetscInt));CHKERRQ(ierr);
1634       for (i=0;i<n_vertices;i++) {
1635         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1636         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1637         total_counts++;
1638       }
1639     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
1640       PetscBool used_vertex;
1641       for (i=0;i<n_vertices;i++) {
1642         used_vertex = PETSC_FALSE;
1643         k = 0;
1644         while (!used_vertex && k<nnsp_size) {
1645           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1646           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
1647             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
1648             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1649             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1650             total_counts++;
1651             used_vertex = PETSC_TRUE;
1652           }
1653           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1654           k++;
1655         }
1656       }
1657     }
1658     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1659     n_vertices = total_counts;
1660   }
1661 
1662   /* edges and faces */
1663   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1664     if (i<n_ISForEdges) {
1665       used_IS = &ISForEdges[i];
1666       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
1667     } else {
1668       used_IS = &ISForFaces[i-n_ISForEdges];
1669       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
1670     }
1671     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
1672     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
1673     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
1674     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1675     /* change of basis should not be performed on local periodic nodes */
1676     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
1677     if (nnsp_has_cnst) {
1678       PetscScalar quad_value;
1679       temp_constraints++;
1680       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
1681       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
1682       for (j=0;j<size_of_constraint;j++) {
1683         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
1684       }
1685       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1686       total_counts++;
1687     }
1688     for (k=0;k<nnsp_size;k++) {
1689       PetscReal real_value;
1690       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1691       ierr = PetscMemcpy(&temp_indices_to_constraint[temp_indices[total_counts]],is_indices,size_of_constraint*sizeof(PetscInt));CHKERRQ(ierr);
1692       for (j=0;j<size_of_constraint;j++) {
1693         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
1694       }
1695       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1696       /* check if array is null on the connected component */
1697       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1698       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_one));
1699       if (real_value > 0.0) { /* keep indices and values */
1700         temp_constraints++;
1701         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1702         total_counts++;
1703       }
1704     }
1705     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1706     valid_constraints = temp_constraints;
1707     /* 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 */
1708     if (!pcbddc->use_nnsp_true && temp_constraints) {
1709       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
1710 
1711 #if defined(PETSC_MISSING_LAPACK_GESVD)
1712       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
1713          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
1714          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
1715             the constraints basis will differ (by a complex factor with absolute value equal to 1)
1716             from that computed using LAPACKgesvd
1717          -> This is due to a different computation of eigenvectors in LAPACKheev
1718          -> The quality of the POD-computed basis will be the same */
1719       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
1720       /* Store upper triangular part of correlation matrix */
1721       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1722       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1723       for (j=0;j<temp_constraints;j++) {
1724         for (k=0;k<j+1;k++) {
1725           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));
1726         }
1727       }
1728       /* compute eigenvalues and eigenvectors of correlation matrix */
1729       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1730       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
1731 #if !defined(PETSC_USE_COMPLEX)
1732       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
1733 #else
1734       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
1735 #endif
1736       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1737       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
1738       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
1739       j=0;
1740       while (j < temp_constraints && singular_vals[j] < tol) j++;
1741       total_counts=total_counts-j;
1742       valid_constraints = temp_constraints-j;
1743       /* scale and copy POD basis into used quadrature memory */
1744       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1745       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1746       ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
1747       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1748       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
1749       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1750       if (j<temp_constraints) {
1751         PetscInt ii;
1752         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
1753         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1754         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));
1755         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1756         for (k=0;k<temp_constraints-j;k++) {
1757           for (ii=0;ii<size_of_constraint;ii++) {
1758             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];
1759           }
1760         }
1761       }
1762 #else  /* on missing GESVD */
1763       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1764       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1765       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1766       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1767 #if !defined(PETSC_USE_COMPLEX)
1768       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));
1769 #else
1770       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));
1771 #endif
1772       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
1773       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1774       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
1775       k = temp_constraints;
1776       if (k > size_of_constraint) k = size_of_constraint;
1777       j = 0;
1778       while (j < k && singular_vals[k-j-1] < tol) j++;
1779       total_counts = total_counts-temp_constraints+k-j;
1780       valid_constraints = k-j;
1781 #endif /* on missing GESVD */
1782     }
1783     /* setting change_of_basis flag is safe now */
1784     if (boolforchange) {
1785       for (j=0;j<valid_constraints;j++) {
1786         PetscBTSet(change_basis,total_counts-j-1);
1787       }
1788     }
1789   }
1790   /* free index sets of faces, edges and vertices */
1791   for (i=0;i<n_ISForFaces;i++) {
1792     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1793   }
1794   if (n_ISForFaces) {
1795     ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1796   }
1797   for (i=0;i<n_ISForEdges;i++) {
1798     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1799   }
1800   if (n_ISForEdges) {
1801     ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1802   }
1803   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1804   /* map temp_indices_to_constraint in boundary numbering */
1805   ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,temp_indices[total_counts],temp_indices_to_constraint,&i,temp_indices_to_constraint_B);CHKERRQ(ierr);
1806   if (i != temp_indices[total_counts]) {
1807     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for constraints indices %d != %d\n",temp_indices[total_counts],i);
1808   }
1809 
1810   /* free workspace */
1811   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1812     ierr = PetscFree(work);CHKERRQ(ierr);
1813 #if defined(PETSC_USE_COMPLEX)
1814     ierr = PetscFree(rwork);CHKERRQ(ierr);
1815 #endif
1816     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1817 #if defined(PETSC_MISSING_LAPACK_GESVD)
1818     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1819     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1820 #endif
1821   }
1822   for (k=0;k<nnsp_size;k++) {
1823     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1824   }
1825   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1826 
1827   /* set quantities in pcbddc data structure and store previous primal size */
1828   /* n_vertices defines the number of subdomain corners in the primal space */
1829   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1830   olocal_primal_size = pcbddc->local_primal_size;
1831   pcbddc->local_primal_size = total_counts;
1832   pcbddc->n_vertices = n_vertices;
1833   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
1834 
1835   /* Create constraint matrix */
1836   /* The constraint matrix is used to compute the l2g map of primal dofs */
1837   /* so we need to set it up properly either with or without change of basis */
1838   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1839   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1840   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
1841   /* array to compute a local numbering of constraints : vertices first then constraints */
1842   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_numbering);CHKERRQ(ierr);
1843   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
1844   /* 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 */
1845   ierr = PetscMalloc1(pcbddc->local_primal_size,&aux_primal_minloc);CHKERRQ(ierr);
1846   /* auxiliary stuff for basis change */
1847   ierr = PetscMalloc1(max_size_of_constraint,&global_indices);CHKERRQ(ierr);
1848   ierr = PetscBTCreate(pcis->n_B,&touched);CHKERRQ(ierr);
1849 
1850   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
1851   total_primal_vertices=0;
1852   for (i=0;i<pcbddc->local_primal_size;i++) {
1853     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1854     if (size_of_constraint == 1) {
1855       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]]);CHKERRQ(ierr);
1856       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
1857       aux_primal_minloc[total_primal_vertices]=0;
1858       total_primal_vertices++;
1859     } else if (PetscBTLookup(change_basis,i)) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
1860       PetscInt min_loc,min_index;
1861       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
1862       /* find first untouched local node */
1863       k = 0;
1864       while (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) k++;
1865       min_index = global_indices[k];
1866       min_loc = k;
1867       /* search the minimum among global nodes already untouched on the cc */
1868       for (k=1;k<size_of_constraint;k++) {
1869         /* there can be more than one constraint on a single connected component */
1870         if (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k]) && min_index > global_indices[k]) {
1871           min_index = global_indices[k];
1872           min_loc = k;
1873         }
1874       }
1875       ierr = PetscBTSet(touched,temp_indices_to_constraint_B[temp_indices[i]+min_loc]);CHKERRQ(ierr);
1876       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
1877       aux_primal_minloc[total_primal_vertices]=min_loc;
1878       total_primal_vertices++;
1879     }
1880   }
1881   /* determine if a QR strategy is needed for change of basis */
1882   qr_needed = PETSC_FALSE;
1883   ierr = PetscBTCreate(pcbddc->local_primal_size,&qr_needed_idx);CHKERRQ(ierr);
1884   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1885     if (PetscBTLookup(change_basis,i)) {
1886       size_of_constraint = temp_indices[i+1]-temp_indices[i];
1887       j = 0;
1888       for (k=0;k<size_of_constraint;k++) {
1889         if (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) {
1890           j++;
1891         }
1892       }
1893       /* found more than one primal dof on the cc */
1894       if (j > 1) {
1895         PetscBTSet(qr_needed_idx,i);
1896         qr_needed = PETSC_TRUE;
1897       }
1898     }
1899   }
1900   /* free workspace */
1901   ierr = PetscFree(global_indices);CHKERRQ(ierr);
1902 
1903   /* permute indices in order to have a sorted set of vertices */
1904   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);CHKERRQ(ierr);
1905 
1906   /* nonzero structure of constraint matrix */
1907   ierr = PetscMalloc1(pcbddc->local_primal_size,&nnz);CHKERRQ(ierr);
1908   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
1909   j=total_primal_vertices;
1910   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1911     if (!PetscBTLookup(change_basis,i)) {
1912       nnz[j]=temp_indices[i+1]-temp_indices[i];
1913       j++;
1914     }
1915   }
1916   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1917   ierr = PetscFree(nnz);CHKERRQ(ierr);
1918   /* set values in constraint matrix */
1919   for (i=0;i<total_primal_vertices;i++) {
1920     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
1921   }
1922   total_counts = total_primal_vertices;
1923   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1924     if (!PetscBTLookup(change_basis,i)) {
1925       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1926       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);
1927       total_counts++;
1928     }
1929   }
1930   /* assembling */
1931   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1932   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1933   /*
1934   ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
1935   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
1936   */
1937   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1938   if (pcbddc->use_change_of_basis) {
1939     /* dual and primal dofs on a single cc */
1940     PetscInt     dual_dofs,primal_dofs;
1941     /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
1942     PetscInt     primal_counter;
1943     /* working stuff for GEQRF */
1944     PetscScalar  *qr_basis,*qr_tau = NULL,*qr_work,lqr_work_t;
1945     PetscBLASInt lqr_work;
1946     /* working stuff for UNGQR */
1947     PetscScalar  *gqr_work,lgqr_work_t;
1948     PetscBLASInt lgqr_work;
1949     /* working stuff for TRTRS */
1950     PetscScalar  *trs_rhs;
1951     PetscBLASInt Blas_NRHS;
1952     /* pointers for values insertion into change of basis matrix */
1953     PetscInt     *start_rows,*start_cols;
1954     PetscScalar  *start_vals;
1955     /* working stuff for values insertion */
1956     PetscBT      is_primal;
1957     /* matrix sizes */
1958     PetscInt     global_size,local_size;
1959     /* work array for nonzeros */
1960     PetscScalar  *nnz_array;
1961     /* temporary change of basis */
1962     Mat          localChangeOfBasisMatrix;
1963     /* auxiliary work for global change of basis */
1964     Vec          nnz_vec;
1965     PetscInt     *idxs_I,*idxs_B,*idxs_all;
1966     PetscInt     nvtxs,*xadj,*adjncy,*idxs_mapped;
1967     PetscScalar  *vals;
1968     PetscBool    done;
1969 
1970     /* local temporary change of basis acts on local interfaces -> dimension is n_B x n_B */
1971     ierr = MatCreate(PETSC_COMM_SELF,&localChangeOfBasisMatrix);CHKERRQ(ierr);
1972     ierr = MatSetType(localChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1973     ierr = MatSetSizes(localChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1974 
1975     /* nonzeros for local mat */
1976     ierr = PetscMalloc1(pcis->n_B,&nnz);CHKERRQ(ierr);
1977     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
1978     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1979       if (PetscBTLookup(change_basis,i)) {
1980         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1981         if (PetscBTLookup(qr_needed_idx,i)) {
1982           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1983         } else {
1984           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = 2;
1985           /* get local primal index on the cc */
1986           j = 0;
1987           while (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+j])) j++;
1988           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1989         }
1990       }
1991     }
1992     ierr = MatSeqAIJSetPreallocation(localChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1993     /* Set initial identity in the matrix */
1994     for (i=0;i<pcis->n_B;i++) {
1995       ierr = MatSetValue(localChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1996     }
1997 
1998     if (pcbddc->dbg_flag) {
1999       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
2000       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
2001     }
2002 
2003 
2004     /* Now we loop on the constraints which need a change of basis */
2005     /*
2006        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
2007        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)
2008 
2009        Basic blocks of change of basis matrix T computed
2010 
2011           - Using the following block transformation if there is only a primal dof on the cc
2012             (in the example, primal dof is the last one of the edge in LOCAL ordering
2013              in this code, primal dof is the first one of the edge in GLOBAL ordering)
2014             | 1        0   ...        0     1 |
2015             | 0        1   ...        0     1 |
2016             |              ...                |
2017             | 0        ...            1     1 |
2018             | -s_1/s_n ...    -s_{n-1}/-s_n 1 |
2019 
2020           - via QR decomposition of constraints otherwise
2021     */
2022     if (qr_needed) {
2023       /* space to store Q */
2024       ierr = PetscMalloc1((max_size_of_constraint)*(max_size_of_constraint),&qr_basis);CHKERRQ(ierr);
2025       /* first we issue queries for optimal work */
2026       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
2027       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
2028       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2029       lqr_work = -1;
2030       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
2031       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
2032       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
2033       ierr = PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);CHKERRQ(ierr);
2034       lgqr_work = -1;
2035       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
2036       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
2037       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
2038       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2039       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
2040       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
2041       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
2042       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
2043       ierr = PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);CHKERRQ(ierr);
2044       /* array to store scaling factors for reflectors */
2045       ierr = PetscMalloc1(max_constraints,&qr_tau);CHKERRQ(ierr);
2046       /* array to store rhs and solution of triangular solver */
2047       ierr = PetscMalloc1(max_constraints*max_constraints,&trs_rhs);CHKERRQ(ierr);
2048       /* allocating workspace for check */
2049       if (pcbddc->dbg_flag) {
2050         ierr = PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&work);CHKERRQ(ierr);
2051       }
2052     }
2053     /* array to store whether a node is primal or not */
2054     ierr = PetscBTCreate(pcis->n_B,&is_primal);CHKERRQ(ierr);
2055     ierr = PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);CHKERRQ(ierr);
2056     ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,aux_primal_numbering,&i,aux_primal_numbering_B);CHKERRQ(ierr);
2057     if (i != total_primal_vertices) {
2058       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",total_primal_vertices,i);
2059     }
2060     for (i=0;i<total_primal_vertices;i++) {
2061       ierr = PetscBTSet(is_primal,aux_primal_numbering_B[i]);CHKERRQ(ierr);
2062     }
2063     ierr = PetscFree(aux_primal_numbering_B);CHKERRQ(ierr);
2064 
2065     /* loop on constraints and see whether or not they need a change of basis and compute it */
2066     /* -> using implicit ordering contained in temp_indices data */
2067     total_counts = pcbddc->n_vertices;
2068     primal_counter = total_counts;
2069     while (total_counts<pcbddc->local_primal_size) {
2070       primal_dofs = 1;
2071       if (PetscBTLookup(change_basis,total_counts)) {
2072         /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
2073         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]]) {
2074           primal_dofs++;
2075         }
2076         /* get constraint info */
2077         size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
2078         dual_dofs = size_of_constraint-primal_dofs;
2079 
2080         if (pcbddc->dbg_flag) {
2081           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);
2082         }
2083 
2084         if (primal_dofs > 1) { /* QR */
2085 
2086           /* copy quadrature constraints for change of basis check */
2087           if (pcbddc->dbg_flag) {
2088             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2089           }
2090           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
2091           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2092 
2093           /* compute QR decomposition of constraints */
2094           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2095           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2096           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2097           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2098           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
2099           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
2100           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2101 
2102           /* explictly compute R^-T */
2103           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
2104           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
2105           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2106           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
2107           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2108           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2109           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2110           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
2111           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
2112           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2113 
2114           /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
2115           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2116           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2117           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2118           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2119           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2120           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
2121           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
2122           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2123 
2124           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
2125              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
2126              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
2127           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2128           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2129           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2130           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2131           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2132           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
2133           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2134           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));
2135           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2136           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2137 
2138           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
2139           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
2140           /* insert cols for primal dofs */
2141           for (j=0;j<primal_dofs;j++) {
2142             start_vals = &qr_basis[j*size_of_constraint];
2143             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
2144             ierr = MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2145           }
2146           /* insert cols for dual dofs */
2147           for (j=0,k=0;j<dual_dofs;k++) {
2148             if (!PetscBTLookup(is_primal,temp_indices_to_constraint_B[temp_indices[total_counts]+k])) {
2149               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
2150               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2151               ierr = MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2152               j++;
2153             }
2154           }
2155 
2156           /* check change of basis */
2157           if (pcbddc->dbg_flag) {
2158             PetscInt   ii,jj;
2159             PetscBool valid_qr=PETSC_TRUE;
2160             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
2161             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2162             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
2163             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2164             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
2165             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
2166             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2167             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));
2168             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2169             for (jj=0;jj<size_of_constraint;jj++) {
2170               for (ii=0;ii<primal_dofs;ii++) {
2171                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
2172                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
2173               }
2174             }
2175             if (!valid_qr) {
2176               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");CHKERRQ(ierr);
2177               for (jj=0;jj<size_of_constraint;jj++) {
2178                 for (ii=0;ii<primal_dofs;ii++) {
2179                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
2180                     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]));
2181                   }
2182                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
2183                     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]));
2184                   }
2185                 }
2186               }
2187             } else {
2188               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");CHKERRQ(ierr);
2189             }
2190           }
2191         } else { /* simple transformation block */
2192           PetscInt row,col;
2193           PetscScalar val;
2194           for (j=0;j<size_of_constraint;j++) {
2195             row = temp_indices_to_constraint_B[temp_indices[total_counts]+j];
2196             if (!PetscBTLookup(is_primal,row)) {
2197               col = temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2198               ierr = MatSetValue(localChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);CHKERRQ(ierr);
2199               ierr = MatSetValue(localChangeOfBasisMatrix,row,col,1.0,INSERT_VALUES);CHKERRQ(ierr);
2200             } else {
2201               for (k=0;k<size_of_constraint;k++) {
2202                 col = temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2203                 if (row != col) {
2204                   val = -temp_quadrature_constraint[temp_indices[total_counts]+k]/temp_quadrature_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2205                 } else {
2206                   val = 1.0;
2207                 }
2208                 ierr = MatSetValue(localChangeOfBasisMatrix,row,col,val,INSERT_VALUES);CHKERRQ(ierr);
2209               }
2210             }
2211           }
2212           if (pcbddc->dbg_flag) {
2213             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");CHKERRQ(ierr);
2214           }
2215         }
2216         /* increment primal counter */
2217         primal_counter += primal_dofs;
2218       } else {
2219         if (pcbddc->dbg_flag) {
2220           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);
2221         }
2222       }
2223       /* increment constraint counter total_counts */
2224       total_counts += primal_dofs;
2225     }
2226 
2227     /* free workspace */
2228     if (qr_needed) {
2229       if (pcbddc->dbg_flag) {
2230         ierr = PetscFree(work);CHKERRQ(ierr);
2231       }
2232       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
2233       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
2234       ierr = PetscFree(qr_work);CHKERRQ(ierr);
2235       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
2236       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
2237     }
2238     ierr = PetscBTDestroy(&is_primal);CHKERRQ(ierr);
2239     ierr = MatAssemblyBegin(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2240     ierr = MatAssemblyEnd(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2241 
2242     /* assembling of global change of variable */
2243     ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2244     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,MATAIJ);CHKERRQ(ierr);
2245     ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
2246     ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
2247     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
2248     ierr = MatSetLocalToGlobalMapping(pcbddc->ChangeOfBasisMatrix,matis->mapping,matis->mapping);CHKERRQ(ierr);
2249 
2250     /* nonzeros (overestimated) */
2251     ierr = VecDuplicate(pcis->vec1_global,&nnz_vec);CHKERRQ(ierr);
2252     ierr = VecSetLocalToGlobalMapping(nnz_vec,matis->mapping);CHKERRQ(ierr);
2253     ierr = PetscMalloc2(pcis->n,&nnz_array,pcis->n,&idxs_all);CHKERRQ(ierr);
2254     for (i=0;i<pcis->n;i++) {
2255       nnz_array[i] = 1.0;
2256       idxs_all[i] = i;
2257     }
2258     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&idxs_B);CHKERRQ(ierr);
2259     for (i=0;i<pcis->n_B;i++) {
2260       nnz_array[idxs_B[i]] = nnz[i];
2261     }
2262     if (pcis->n) {
2263       ierr = VecSetValuesLocal(nnz_vec,pcis->n,idxs_all,nnz_array,INSERT_VALUES);CHKERRQ(ierr);
2264     }
2265     ierr = VecAssemblyBegin(nnz_vec);CHKERRQ(ierr);
2266     ierr = VecAssemblyEnd(nnz_vec);CHKERRQ(ierr);
2267     ierr = PetscFree(nnz);CHKERRQ(ierr);
2268     ierr = PetscFree2(nnz_array,idxs_all);CHKERRQ(ierr);
2269     ierr = PetscMalloc1(local_size,&nnz);CHKERRQ(ierr);
2270     ierr = VecGetArray(nnz_vec,&nnz_array);CHKERRQ(ierr);
2271     for (i=0;i<local_size;i++) {
2272       nnz[i] = (PetscInt)(PetscRealPart(nnz_array[i]));
2273     }
2274     ierr = VecRestoreArray(nnz_vec,&nnz_array);CHKERRQ(ierr);
2275     ierr = VecDestroy(&nnz_vec);CHKERRQ(ierr);
2276     ierr = MatMPIAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz,0,nnz);CHKERRQ(ierr);
2277     ierr = PetscFree(nnz);CHKERRQ(ierr);
2278 
2279     /* Set identity on dirichlet dofs */
2280     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&idxs_I);CHKERRQ(ierr);
2281     for (i=0;i<pcis->n-pcis->n_B;i++) {
2282       PetscScalar one=1.0;
2283       ierr = MatSetValuesLocal(pcbddc->ChangeOfBasisMatrix,1,idxs_I+i,1,idxs_I+i,&one,INSERT_VALUES);CHKERRQ(ierr);
2284     }
2285     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&idxs_I);CHKERRQ(ierr);
2286 
2287     /* Set values at interface dofs */
2288     done = PETSC_TRUE;
2289     ierr = MatGetRowIJ(localChangeOfBasisMatrix,0,PETSC_FALSE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&done);CHKERRQ(ierr);
2290     if (!done) {
2291       SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
2292     }
2293     ierr = MatSeqAIJGetArray(localChangeOfBasisMatrix,&vals);CHKERRQ(ierr);
2294     ierr = PetscMalloc1(xadj[nvtxs],&idxs_mapped);CHKERRQ(ierr);
2295     ierr = ISLocalToGlobalMappingApply(pcbddc->BtoNmap,xadj[nvtxs],adjncy,idxs_mapped);CHKERRQ(ierr);
2296     for (i=0;i<nvtxs;i++) {
2297       PetscInt    row,*cols,ncols;
2298       PetscScalar *mat_vals;
2299 
2300       row = idxs_B[i];
2301       ncols = xadj[i+1]-xadj[i];
2302       cols = idxs_mapped+xadj[i];
2303       mat_vals = vals+xadj[i];
2304       ierr = MatSetValuesLocal(pcbddc->ChangeOfBasisMatrix,1,&row,ncols,cols,mat_vals,INSERT_VALUES);CHKERRQ(ierr);
2305     }
2306     ierr = MatRestoreRowIJ(localChangeOfBasisMatrix,0,PETSC_FALSE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&done);CHKERRQ(ierr);
2307     if (!done) {
2308       SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2309     }
2310     ierr = MatSeqAIJRestoreArray(localChangeOfBasisMatrix,&vals);CHKERRQ(ierr);
2311     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&idxs_B);CHKERRQ(ierr);
2312     ierr = PetscFree(idxs_mapped);CHKERRQ(ierr);
2313     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2314     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2315 
2316     /* check */
2317     if (pcbddc->dbg_flag) {
2318       PetscReal error;
2319       Vec       x,x_change;
2320 
2321       ierr = VecDuplicate(pcis->vec1_global,&x);CHKERRQ(ierr);
2322       ierr = VecDuplicate(pcis->vec1_global,&x_change);CHKERRQ(ierr);
2323       ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
2324       ierr = VecCopy(x,pcis->vec1_global);CHKERRQ(ierr);
2325       ierr = VecScatterBegin(pcis->global_to_B,x,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2326       ierr = VecScatterEnd(pcis->global_to_B,x,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2327       ierr = MatMult(localChangeOfBasisMatrix,pcis->vec1_B,pcis->vec2_B);CHKERRQ(ierr);
2328       ierr = VecScatterBegin(pcis->global_to_B,pcis->vec2_B,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2329       ierr = VecScatterEnd(pcis->global_to_B,pcis->vec2_B,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2330       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);CHKERRQ(ierr);
2331       ierr = VecAXPY(x,-1.0,x_change);CHKERRQ(ierr);
2332       ierr = VecNorm(x,NORM_INFINITY,&error);CHKERRQ(ierr);
2333       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2334       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change on B: %1.6e\n",error);CHKERRQ(ierr);
2335       ierr = VecDestroy(&x);CHKERRQ(ierr);
2336       ierr = VecDestroy(&x_change);CHKERRQ(ierr);
2337     }
2338     ierr = MatDestroy(&localChangeOfBasisMatrix);CHKERRQ(ierr);
2339 
2340     /*
2341     ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
2342     ierr = MatView(local_ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
2343     */
2344   } else if (pcbddc->user_ChangeOfBasisMatrix) {
2345     ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2346     pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
2347   }
2348 
2349   /* set up change of basis context */
2350   if (pcbddc->ChangeOfBasisMatrix) {
2351     PCBDDCChange_ctx change_ctx;
2352 
2353     if (!pcbddc->new_global_mat) {
2354       PetscInt global_size,local_size;
2355 
2356       ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
2357       ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
2358       ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->new_global_mat);CHKERRQ(ierr);
2359       ierr = MatSetSizes(pcbddc->new_global_mat,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
2360       ierr = MatSetType(pcbddc->new_global_mat,MATSHELL);CHKERRQ(ierr);
2361       ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT,(void (*)(void))PCBDDCMatMult_Private);CHKERRQ(ierr);
2362       ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCMatMultTranspose_Private);CHKERRQ(ierr);
2363       ierr = PetscNew(&change_ctx);CHKERRQ(ierr);
2364       ierr = MatShellSetContext(pcbddc->new_global_mat,change_ctx);CHKERRQ(ierr);
2365     } else {
2366       ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
2367       ierr = MatDestroy(&change_ctx->global_change);CHKERRQ(ierr);
2368       ierr = VecDestroyVecs(2,&change_ctx->work);CHKERRQ(ierr);
2369     }
2370     if (!pcbddc->user_ChangeOfBasisMatrix) {
2371       ierr = PetscObjectReference((PetscObject)pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2372       change_ctx->global_change = pcbddc->ChangeOfBasisMatrix;
2373     } else {
2374       ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2375       change_ctx->global_change = pcbddc->user_ChangeOfBasisMatrix;
2376     }
2377     ierr = VecDuplicateVecs(pcis->vec1_global,2,&change_ctx->work);CHKERRQ(ierr);
2378     ierr = MatSetUp(pcbddc->new_global_mat);CHKERRQ(ierr);
2379     ierr = MatAssemblyBegin(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2380     ierr = MatAssemblyEnd(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2381   }
2382 
2383   /* get indices in local ordering for vertices and constraints */
2384   if (olocal_primal_size == pcbddc->local_primal_size) { /* if this is true, I need to check if a new primal space has been introduced */
2385     ierr = PetscMalloc1(olocal_primal_size,&oprimal_indices_local_idxs);CHKERRQ(ierr);
2386     ierr = PetscMemcpy(oprimal_indices_local_idxs,pcbddc->primal_indices_local_idxs,olocal_primal_size*sizeof(PetscInt));CHKERRQ(ierr);
2387   }
2388   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2389   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2390   ierr = PetscMalloc1(pcbddc->local_primal_size,&pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2391   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&i,&aux_primal_numbering);CHKERRQ(ierr);
2392   ierr = PetscMemcpy(pcbddc->primal_indices_local_idxs,aux_primal_numbering,i*sizeof(PetscInt));CHKERRQ(ierr);
2393   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2394   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&j,&aux_primal_numbering);CHKERRQ(ierr);
2395   ierr = PetscMemcpy(&pcbddc->primal_indices_local_idxs[i],aux_primal_numbering,j*sizeof(PetscInt));CHKERRQ(ierr);
2396   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2397   /* set quantities in PCBDDC data struct */
2398   pcbddc->n_actual_vertices = i;
2399   /* check if a new primal space has been introduced */
2400   pcbddc->new_primal_space_local = PETSC_TRUE;
2401   if (olocal_primal_size == pcbddc->local_primal_size) {
2402     ierr = PetscMemcmp(pcbddc->primal_indices_local_idxs,oprimal_indices_local_idxs,olocal_primal_size,&pcbddc->new_primal_space_local);CHKERRQ(ierr);
2403     pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
2404     ierr = PetscFree(oprimal_indices_local_idxs);CHKERRQ(ierr);
2405   }
2406   /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
2407   ierr = MPI_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
2408 
2409   /* flush dbg viewer */
2410   if (pcbddc->dbg_flag) {
2411     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2412   }
2413 
2414   /* free workspace */
2415   ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2416   ierr = PetscBTDestroy(&qr_needed_idx);CHKERRQ(ierr);
2417   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
2418   ierr = PetscBTDestroy(&change_basis);CHKERRQ(ierr);
2419   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2420   ierr = PetscFree3(temp_quadrature_constraint,temp_indices_to_constraint,temp_indices_to_constraint_B);CHKERRQ(ierr);
2421   PetscFunctionReturn(0);
2422 }
2423 
2424 #undef __FUNCT__
2425 #define __FUNCT__ "PCBDDCAnalyzeInterface"
2426 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
2427 {
2428   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
2429   PC_IS       *pcis = (PC_IS*)pc->data;
2430   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
2431   PetscInt    ierr,i,vertex_size;
2432   PetscViewer viewer=pcbddc->dbg_viewer;
2433 
2434   PetscFunctionBegin;
2435   /* Reset previously computed graph */
2436   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
2437   /* Init local Graph struct */
2438   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
2439 
2440   /* Check validity of the csr graph passed in by the user */
2441   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
2442     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
2443   }
2444 
2445   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
2446   if (pcbddc->use_local_adj && (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy)) {
2447     Mat mat_adj;
2448     const PetscInt *xadj,*adjncy;
2449     PetscBool flg_row=PETSC_TRUE;
2450 
2451     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
2452     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2453     if (!flg_row) {
2454       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
2455     }
2456     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
2457     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2458     if (!flg_row) {
2459       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2460     }
2461     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
2462     pcbddc->deluxe_compute_rowadj = PETSC_FALSE;
2463   }
2464 
2465   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
2466   vertex_size = 1;
2467   if (pcbddc->user_provided_isfordofs) {
2468     if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
2469       ierr = PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2470       for (i=0;i<pcbddc->n_ISForDofs;i++) {
2471         ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2472         ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
2473       }
2474       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
2475       pcbddc->n_ISForDofs = 0;
2476       ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
2477     }
2478     /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
2479     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
2480   } else {
2481     if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
2482       ierr = MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);CHKERRQ(ierr);
2483       ierr = PetscMalloc(pcbddc->n_ISForDofsLocal*sizeof(IS),&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2484       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
2485         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2486       }
2487     }
2488   }
2489 
2490   /* Setup of Graph */
2491   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
2492     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
2493   }
2494   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
2495     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
2496   }
2497   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices);
2498 
2499   /* Graph's connected components analysis */
2500   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
2501 
2502   /* print some info to stdout */
2503   if (pcbddc->dbg_flag) {
2504     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
2505   }
2506 
2507   /* mark topography has done */
2508   pcbddc->recompute_topography = PETSC_FALSE;
2509   PetscFunctionReturn(0);
2510 }
2511 
2512 #undef __FUNCT__
2513 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
2514 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt **vertices_idx)
2515 {
2516   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2517   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
2518   PetscErrorCode ierr;
2519 
2520   PetscFunctionBegin;
2521   n = 0;
2522   vertices = 0;
2523   if (pcbddc->ConstraintMatrix) {
2524     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
2525     for (i=0;i<local_primal_size;i++) {
2526       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2527       if (size_of_constraint == 1) n++;
2528       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2529     }
2530     if (vertices_idx) {
2531       ierr = PetscMalloc1(n,&vertices);CHKERRQ(ierr);
2532       n = 0;
2533       for (i=0;i<local_primal_size;i++) {
2534         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2535         if (size_of_constraint == 1) {
2536           vertices[n++]=row_cmat_indices[0];
2537         }
2538         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2539       }
2540     }
2541   }
2542   *n_vertices = n;
2543   if (vertices_idx) *vertices_idx = vertices;
2544   PetscFunctionReturn(0);
2545 }
2546 
2547 #undef __FUNCT__
2548 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
2549 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt **constraints_idx)
2550 {
2551   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2552   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
2553   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
2554   PetscBT        touched;
2555   PetscErrorCode ierr;
2556 
2557     /* This function assumes that the number of local constraints per connected component
2558        is not greater than the number of nodes defined for the connected component
2559        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
2560   PetscFunctionBegin;
2561   n = 0;
2562   constraints_index = 0;
2563   if (pcbddc->ConstraintMatrix) {
2564     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
2565     max_size_of_constraint = 0;
2566     for (i=0;i<local_primal_size;i++) {
2567       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2568       if (size_of_constraint > 1) {
2569         n++;
2570       }
2571       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
2572       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2573     }
2574     if (constraints_idx) {
2575       ierr = PetscMalloc1(n,&constraints_index);CHKERRQ(ierr);
2576       ierr = PetscMalloc1(max_size_of_constraint,&row_cmat_global_indices);CHKERRQ(ierr);
2577       ierr = PetscBTCreate(local_size,&touched);CHKERRQ(ierr);
2578       n = 0;
2579       for (i=0;i<local_primal_size;i++) {
2580         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2581         if (size_of_constraint > 1) {
2582           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
2583           /* find first untouched local node */
2584           j = 0;
2585           while (PetscBTLookup(touched,row_cmat_indices[j])) j++;
2586           min_index = row_cmat_global_indices[j];
2587           min_loc = j;
2588           /* search the minimum among nodes not yet touched on the connected component
2589              since there can be more than one constraint on a single cc */
2590           for (j=1;j<size_of_constraint;j++) {
2591             if (!PetscBTLookup(touched,row_cmat_indices[j]) && min_index > row_cmat_global_indices[j]) {
2592               min_index = row_cmat_global_indices[j];
2593               min_loc = j;
2594             }
2595           }
2596           ierr = PetscBTSet(touched,row_cmat_indices[min_loc]);CHKERRQ(ierr);
2597           constraints_index[n++] = row_cmat_indices[min_loc];
2598         }
2599         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2600       }
2601       ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2602       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
2603     }
2604   }
2605   *n_constraints = n;
2606   if (constraints_idx) *constraints_idx = constraints_index;
2607   PetscFunctionReturn(0);
2608 }
2609 
2610 #undef __FUNCT__
2611 #define __FUNCT__ "PCBDDCSubsetNumbering"
2612 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[])
2613 {
2614   Vec            local_vec,global_vec;
2615   IS             seqis,paris;
2616   VecScatter     scatter_ctx;
2617   PetscScalar    *array;
2618   PetscInt       *temp_global_dofs;
2619   PetscScalar    globalsum;
2620   PetscInt       i,j,s;
2621   PetscInt       nlocals,first_index,old_index,max_local;
2622   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
2623   PetscMPIInt    *dof_sizes,*dof_displs;
2624   PetscBool      first_found;
2625   PetscErrorCode ierr;
2626 
2627   PetscFunctionBegin;
2628   /* mpi buffers */
2629   ierr = MPI_Comm_size(comm,&size_prec_comm);CHKERRQ(ierr);
2630   ierr = MPI_Comm_rank(comm,&rank_prec_comm);CHKERRQ(ierr);
2631   j = ( !rank_prec_comm ? size_prec_comm : 0);
2632   ierr = PetscMalloc1(j,&dof_sizes);CHKERRQ(ierr);
2633   ierr = PetscMalloc1(j,&dof_displs);CHKERRQ(ierr);
2634   /* get maximum size of subset */
2635   ierr = PetscMalloc1(n_local_dofs,&temp_global_dofs);CHKERRQ(ierr);
2636   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
2637   max_local = 0;
2638   for (i=0;i<n_local_dofs;i++) {
2639     if (max_local < temp_global_dofs[i] ) {
2640       max_local = temp_global_dofs[i];
2641     }
2642   }
2643   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
2644   max_global++;
2645   max_local = 0;
2646   for (i=0;i<n_local_dofs;i++) {
2647     if (max_local < local_dofs[i] ) {
2648       max_local = local_dofs[i];
2649     }
2650   }
2651   max_local++;
2652   /* allocate workspace */
2653   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
2654   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
2655   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
2656   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
2657   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
2658   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
2659   /* create scatter */
2660   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
2661   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
2662   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
2663   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
2664   ierr = ISDestroy(&paris);CHKERRQ(ierr);
2665   /* init array */
2666   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
2667   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2668   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2669   if (local_dofs_mult) {
2670     for (i=0;i<n_local_dofs;i++) {
2671       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
2672     }
2673   } else {
2674     for (i=0;i<n_local_dofs;i++) {
2675       array[local_dofs[i]]=1.0;
2676     }
2677   }
2678   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2679   /* scatter into global vec and get total number of global dofs */
2680   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2681   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2682   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
2683   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
2684   /* Fill global_vec with cumulative function for global numbering */
2685   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
2686   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
2687   nlocals = 0;
2688   first_index = -1;
2689   first_found = PETSC_FALSE;
2690   for (i=0;i<s;i++) {
2691     if (!first_found && PetscRealPart(array[i]) > 0.1) {
2692       first_found = PETSC_TRUE;
2693       first_index = i;
2694     }
2695     nlocals += (PetscInt)PetscRealPart(array[i]);
2696   }
2697   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2698   if (!rank_prec_comm) {
2699     dof_displs[0]=0;
2700     for (i=1;i<size_prec_comm;i++) {
2701       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
2702     }
2703   }
2704   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2705   if (first_found) {
2706     array[first_index] += (PetscScalar)nlocals;
2707     old_index = first_index;
2708     for (i=first_index+1;i<s;i++) {
2709       if (PetscRealPart(array[i]) > 0.1) {
2710         array[i] += array[old_index];
2711         old_index = i;
2712       }
2713     }
2714   }
2715   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
2716   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2717   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2718   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2719   /* get global ordering of local dofs */
2720   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2721   if (local_dofs_mult) {
2722     for (i=0;i<n_local_dofs;i++) {
2723       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
2724     }
2725   } else {
2726     for (i=0;i<n_local_dofs;i++) {
2727       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
2728     }
2729   }
2730   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2731   /* free workspace */
2732   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
2733   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
2734   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
2735   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
2736   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
2737   /* return pointer to global ordering of local dofs */
2738   *global_numbering_subset = temp_global_dofs;
2739   PetscFunctionReturn(0);
2740 }
2741 
2742 #undef __FUNCT__
2743 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
2744 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
2745 {
2746   PetscInt       i,j;
2747   PetscScalar    *alphas;
2748   PetscErrorCode ierr;
2749 
2750   PetscFunctionBegin;
2751   /* this implements stabilized Gram-Schmidt */
2752   ierr = PetscMalloc1(n,&alphas);CHKERRQ(ierr);
2753   for (i=0;i<n;i++) {
2754     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
2755     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
2756     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
2757   }
2758   ierr = PetscFree(alphas);CHKERRQ(ierr);
2759   PetscFunctionReturn(0);
2760 }
2761 
2762 #undef __FUNCT__
2763 #define __FUNCT__ "MatISGetSubassemblingPattern"
2764 PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscBool contiguous, IS* is_sends)
2765 {
2766   Mat             subdomain_adj;
2767   IS              new_ranks,ranks_send_to;
2768   MatPartitioning partitioner;
2769   Mat_IS          *matis;
2770   PetscInt        n_neighs,*neighs,*n_shared,**shared;
2771   PetscInt        prank;
2772   PetscMPIInt     size,rank,color;
2773   PetscInt        *xadj,*adjncy,*oldranks;
2774   PetscInt        *adjncy_wgt,*v_wgt,*is_indices,*ranks_send_to_idx;
2775   PetscInt        i,j,local_size,threshold=0;
2776   PetscErrorCode  ierr;
2777   PetscBool       use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
2778   PetscSubcomm    subcomm;
2779 
2780   PetscFunctionBegin;
2781   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_square",&use_square,NULL);CHKERRQ(ierr);
2782   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);CHKERRQ(ierr);
2783   ierr = PetscOptionsGetInt(NULL,"-matis_partitioning_threshold",&threshold,NULL);CHKERRQ(ierr);
2784 
2785   /* Get info on mapping */
2786   matis = (Mat_IS*)(mat->data);
2787   ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&local_size);CHKERRQ(ierr);
2788   ierr = ISLocalToGlobalMappingGetInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2789 
2790   /* build local CSR graph of subdomains' connectivity */
2791   ierr = PetscMalloc1(2,&xadj);CHKERRQ(ierr);
2792   xadj[0] = 0;
2793   xadj[1] = PetscMax(n_neighs-1,0);
2794   ierr = PetscMalloc1(xadj[1],&adjncy);CHKERRQ(ierr);
2795   ierr = PetscMalloc1(xadj[1],&adjncy_wgt);CHKERRQ(ierr);
2796 
2797   if (threshold) {
2798     PetscInt* count,min_threshold;
2799     ierr = PetscMalloc1(local_size,&count);CHKERRQ(ierr);
2800     ierr = PetscMemzero(count,local_size*sizeof(PetscInt));CHKERRQ(ierr);
2801     for (i=1;i<n_neighs;i++) {/* i=1 so I don't count myself -> faces nodes counts to 1 */
2802       for (j=0;j<n_shared[i];j++) {
2803         count[shared[i][j]] += 1;
2804       }
2805     }
2806     /* adapt threshold since we dont want to lose significant connections */
2807     min_threshold = n_neighs;
2808     for (i=1;i<n_neighs;i++) {
2809       for (j=0;j<n_shared[i];j++) {
2810         min_threshold = PetscMin(count[shared[i][j]],min_threshold);
2811       }
2812     }
2813     threshold = PetscMax(min_threshold+1,threshold);
2814     xadj[1] = 0;
2815     for (i=1;i<n_neighs;i++) {
2816       for (j=0;j<n_shared[i];j++) {
2817         if (count[shared[i][j]] < threshold) {
2818           adjncy[xadj[1]] = neighs[i];
2819           adjncy_wgt[xadj[1]] = n_shared[i];
2820           xadj[1]++;
2821           break;
2822         }
2823       }
2824     }
2825     ierr = PetscFree(count);CHKERRQ(ierr);
2826   } else {
2827     if (xadj[1]) {
2828       ierr = PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));CHKERRQ(ierr);
2829       ierr = PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));CHKERRQ(ierr);
2830     }
2831   }
2832   ierr = ISLocalToGlobalMappingRestoreInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2833   if (use_square) {
2834     for (i=0;i<xadj[1];i++) {
2835       adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
2836     }
2837   }
2838   ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2839 
2840   ierr = PetscMalloc(sizeof(PetscInt),&ranks_send_to_idx);CHKERRQ(ierr);
2841 
2842   /*
2843     Restrict work on active processes only.
2844   */
2845   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);CHKERRQ(ierr);
2846   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr); /* 2 groups, active process and not active processes */
2847   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
2848   ierr = PetscMPIIntCast(!local_size,&color);CHKERRQ(ierr);
2849   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2850   if (color) {
2851     ierr = PetscFree(xadj);CHKERRQ(ierr);
2852     ierr = PetscFree(adjncy);CHKERRQ(ierr);
2853     ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
2854   } else {
2855     PetscInt coarsening_ratio;
2856     ierr = MPI_Comm_size(subcomm->comm,&size);CHKERRQ(ierr);
2857     ierr = PetscMalloc1(size,&oldranks);CHKERRQ(ierr);
2858     prank = rank;
2859     ierr = MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm->comm);CHKERRQ(ierr);
2860     /*
2861     for (i=0;i<size;i++) {
2862       PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
2863     }
2864     */
2865     for (i=0;i<xadj[1];i++) {
2866       ierr = PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);CHKERRQ(ierr);
2867     }
2868     ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2869     ierr = MatCreateMPIAdj(subcomm->comm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);CHKERRQ(ierr);
2870     /* ierr = MatView(subdomain_adj,0);CHKERRQ(ierr); */
2871 
2872     /* Partition */
2873     ierr = MatPartitioningCreate(subcomm->comm,&partitioner);CHKERRQ(ierr);
2874     ierr = MatPartitioningSetAdjacency(partitioner,subdomain_adj);CHKERRQ(ierr);
2875     if (use_vwgt) {
2876       ierr = PetscMalloc(sizeof(*v_wgt),&v_wgt);CHKERRQ(ierr);
2877       v_wgt[0] = local_size;
2878       ierr = MatPartitioningSetVertexWeights(partitioner,v_wgt);CHKERRQ(ierr);
2879     }
2880     n_subdomains = PetscMin((PetscInt)size,n_subdomains);
2881     coarsening_ratio = size/n_subdomains;
2882     ierr = MatPartitioningSetNParts(partitioner,n_subdomains);CHKERRQ(ierr);
2883     ierr = MatPartitioningSetFromOptions(partitioner);CHKERRQ(ierr);
2884     ierr = MatPartitioningApply(partitioner,&new_ranks);CHKERRQ(ierr);
2885     /* ierr = MatPartitioningView(partitioner,0);CHKERRQ(ierr); */
2886 
2887     ierr = ISGetIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2888     if (contiguous) {
2889       ranks_send_to_idx[0] = oldranks[is_indices[0]]; /* contiguos set of processes */
2890     } else {
2891       ranks_send_to_idx[0] = coarsening_ratio*oldranks[is_indices[0]]; /* scattered set of processes */
2892     }
2893     ierr = ISRestoreIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2894     /* clean up */
2895     ierr = PetscFree(oldranks);CHKERRQ(ierr);
2896     ierr = ISDestroy(&new_ranks);CHKERRQ(ierr);
2897     ierr = MatDestroy(&subdomain_adj);CHKERRQ(ierr);
2898     ierr = MatPartitioningDestroy(&partitioner);CHKERRQ(ierr);
2899   }
2900   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
2901 
2902   /* assemble parallel IS for sends */
2903   i = 1;
2904   if (color) i=0;
2905   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);CHKERRQ(ierr);
2906 
2907   /* get back IS */
2908   *is_sends = ranks_send_to;
2909   PetscFunctionReturn(0);
2910 }
2911 
2912 typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;
2913 
2914 #undef __FUNCT__
2915 #define __FUNCT__ "MatISSubassemble"
2916 PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
2917 {
2918   Mat                    local_mat;
2919   Mat_IS                 *matis;
2920   IS                     is_sends_internal;
2921   PetscInt               rows,cols;
2922   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
2923   PetscBool              ismatis,isdense,destroy_mat;
2924   ISLocalToGlobalMapping l2gmap;
2925   PetscInt*              l2gmap_indices;
2926   const PetscInt*        is_indices;
2927   MatType                new_local_type;
2928   /* buffers */
2929   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
2930   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
2931   PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
2932   /* MPI */
2933   MPI_Comm               comm,comm_n;
2934   PetscSubcomm           subcomm;
2935   PetscMPIInt            n_sends,n_recvs,commsize;
2936   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
2937   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
2938   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
2939   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
2940   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
2941   PetscErrorCode         ierr;
2942 
2943   PetscFunctionBegin;
2944   /* TODO: add missing checks */
2945   PetscValidLogicalCollectiveInt(mat,n_subdomains,3);
2946   PetscValidLogicalCollectiveBool(mat,restrict_comm,4);
2947   PetscValidLogicalCollectiveEnum(mat,reuse,5);
2948   PetscValidLogicalCollectiveInt(mat,nis,7);
2949   ierr = PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);CHKERRQ(ierr);
2950   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
2951   ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
2952   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);CHKERRQ(ierr);
2953   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
2954   ierr = MatGetSize(local_mat,&rows,&cols);CHKERRQ(ierr);
2955   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
2956   if (reuse == MAT_REUSE_MATRIX && *mat_n) {
2957     PetscInt mrows,mcols,mnrows,mncols;
2958     ierr = PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);CHKERRQ(ierr);
2959     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
2960     ierr = MatGetSize(mat,&mrows,&mcols);CHKERRQ(ierr);
2961     ierr = MatGetSize(*mat_n,&mnrows,&mncols);CHKERRQ(ierr);
2962     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
2963     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
2964   }
2965   ierr = MatGetBlockSize(local_mat,&bs);CHKERRQ(ierr);
2966   PetscValidLogicalCollectiveInt(mat,bs,0);
2967   /* prepare IS for sending if not provided */
2968   if (!is_sends) {
2969     PetscBool pcontig = PETSC_TRUE;
2970     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
2971     ierr = MatISGetSubassemblingPattern(mat,n_subdomains,pcontig,&is_sends_internal);CHKERRQ(ierr);
2972   } else {
2973     ierr = PetscObjectReference((PetscObject)is_sends);CHKERRQ(ierr);
2974     is_sends_internal = is_sends;
2975   }
2976 
2977   /* get pointer of MATIS data */
2978   matis = (Mat_IS*)mat->data;
2979 
2980   /* get comm */
2981   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2982 
2983   /* compute number of sends */
2984   ierr = ISGetLocalSize(is_sends_internal,&i);CHKERRQ(ierr);
2985   ierr = PetscMPIIntCast(i,&n_sends);CHKERRQ(ierr);
2986 
2987   /* compute number of receives */
2988   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
2989   ierr = PetscMalloc1(commsize,&iflags);CHKERRQ(ierr);
2990   ierr = PetscMemzero(iflags,commsize*sizeof(*iflags));CHKERRQ(ierr);
2991   ierr = ISGetIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
2992   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
2993   ierr = PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);CHKERRQ(ierr);
2994   ierr = PetscFree(iflags);CHKERRQ(ierr);
2995 
2996   /* restrict comm if requested */
2997   subcomm = 0;
2998   destroy_mat = PETSC_FALSE;
2999   if (restrict_comm) {
3000     PetscMPIInt color,rank,subcommsize;
3001     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3002     color = 0;
3003     if (n_sends && !n_recvs) color = 1; /* sending only processes will not partecipate in new comm */
3004     ierr = MPI_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
3005     subcommsize = commsize - subcommsize;
3006     /* check if reuse has been requested */
3007     if (reuse == MAT_REUSE_MATRIX) {
3008       if (*mat_n) {
3009         PetscMPIInt subcommsize2;
3010         ierr = MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);CHKERRQ(ierr);
3011         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
3012         comm_n = PetscObjectComm((PetscObject)*mat_n);
3013       } else {
3014         comm_n = PETSC_COMM_SELF;
3015       }
3016     } else { /* MAT_INITIAL_MATRIX */
3017       ierr = PetscSubcommCreate(comm,&subcomm);CHKERRQ(ierr);
3018       ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
3019       ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
3020       comm_n = subcomm->comm;
3021     }
3022     /* flag to destroy *mat_n if not significative */
3023     if (color) destroy_mat = PETSC_TRUE;
3024   } else {
3025     comm_n = comm;
3026   }
3027 
3028   /* prepare send/receive buffers */
3029   ierr = PetscMalloc1(commsize,&ilengths_idxs);CHKERRQ(ierr);
3030   ierr = PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));CHKERRQ(ierr);
3031   ierr = PetscMalloc1(commsize,&ilengths_vals);CHKERRQ(ierr);
3032   ierr = PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));CHKERRQ(ierr);
3033   if (nis) {
3034     ierr = PetscMalloc(commsize*sizeof(*ilengths_idxs_is),&ilengths_idxs_is);CHKERRQ(ierr);
3035     ierr = PetscMemzero(ilengths_idxs_is,commsize*sizeof(*ilengths_idxs_is));CHKERRQ(ierr);
3036   }
3037 
3038   /* Get data from local matrices */
3039   if (!isdense) {
3040     SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Subassembling of AIJ local matrices not yet implemented");
3041     /* TODO: See below some guidelines on how to prepare the local buffers */
3042     /*
3043        send_buffer_vals should contain the raw values of the local matrix
3044        send_buffer_idxs should contain:
3045        - MatType_PRIVATE type
3046        - PetscInt        size_of_l2gmap
3047        - PetscInt        global_row_indices[size_of_l2gmap]
3048        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
3049     */
3050   } else {
3051     ierr = MatDenseGetArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3052     ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&i);CHKERRQ(ierr);
3053     ierr = PetscMalloc1((i+2),&send_buffer_idxs);CHKERRQ(ierr);
3054     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
3055     send_buffer_idxs[1] = i;
3056     ierr = ISLocalToGlobalMappingGetIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
3057     ierr = PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));CHKERRQ(ierr);
3058     ierr = ISLocalToGlobalMappingRestoreIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
3059     ierr = PetscMPIIntCast(i,&len);CHKERRQ(ierr);
3060     for (i=0;i<n_sends;i++) {
3061       ilengths_vals[is_indices[i]] = len*len;
3062       ilengths_idxs[is_indices[i]] = len+2;
3063     }
3064   }
3065   ierr = PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);CHKERRQ(ierr);
3066   /* additional is (if any) */
3067   if (nis) {
3068     PetscMPIInt psum;
3069     PetscInt j;
3070     for (j=0,psum=0;j<nis;j++) {
3071       PetscInt plen;
3072       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
3073       ierr = PetscMPIIntCast(plen,&len);CHKERRQ(ierr);
3074       psum += len+1; /* indices + lenght */
3075     }
3076     ierr = PetscMalloc(psum*sizeof(PetscInt),&send_buffer_idxs_is);CHKERRQ(ierr);
3077     for (j=0,psum=0;j<nis;j++) {
3078       PetscInt plen;
3079       const PetscInt *is_array_idxs;
3080       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
3081       send_buffer_idxs_is[psum] = plen;
3082       ierr = ISGetIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
3083       ierr = PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));CHKERRQ(ierr);
3084       ierr = ISRestoreIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
3085       psum += plen+1; /* indices + lenght */
3086     }
3087     for (i=0;i<n_sends;i++) {
3088       ilengths_idxs_is[is_indices[i]] = psum;
3089     }
3090     ierr = PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);CHKERRQ(ierr);
3091   }
3092 
3093   buf_size_idxs = 0;
3094   buf_size_vals = 0;
3095   buf_size_idxs_is = 0;
3096   for (i=0;i<n_recvs;i++) {
3097     buf_size_idxs += (PetscInt)olengths_idxs[i];
3098     buf_size_vals += (PetscInt)olengths_vals[i];
3099     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
3100   }
3101   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);CHKERRQ(ierr);
3102   ierr = PetscMalloc1(buf_size_vals,&recv_buffer_vals);CHKERRQ(ierr);
3103   ierr = PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);CHKERRQ(ierr);
3104 
3105   /* get new tags for clean communications */
3106   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);CHKERRQ(ierr);
3107   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_vals);CHKERRQ(ierr);
3108   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);CHKERRQ(ierr);
3109 
3110   /* allocate for requests */
3111   ierr = PetscMalloc1(n_sends,&send_req_idxs);CHKERRQ(ierr);
3112   ierr = PetscMalloc1(n_sends,&send_req_vals);CHKERRQ(ierr);
3113   ierr = PetscMalloc1(n_sends,&send_req_idxs_is);CHKERRQ(ierr);
3114   ierr = PetscMalloc1(n_recvs,&recv_req_idxs);CHKERRQ(ierr);
3115   ierr = PetscMalloc1(n_recvs,&recv_req_vals);CHKERRQ(ierr);
3116   ierr = PetscMalloc1(n_recvs,&recv_req_idxs_is);CHKERRQ(ierr);
3117 
3118   /* communications */
3119   ptr_idxs = recv_buffer_idxs;
3120   ptr_vals = recv_buffer_vals;
3121   ptr_idxs_is = recv_buffer_idxs_is;
3122   for (i=0;i<n_recvs;i++) {
3123     source_dest = onodes[i];
3124     ierr = MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);CHKERRQ(ierr);
3125     ierr = MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);CHKERRQ(ierr);
3126     ptr_idxs += olengths_idxs[i];
3127     ptr_vals += olengths_vals[i];
3128     if (nis) {
3129       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);
3130       ptr_idxs_is += olengths_idxs_is[i];
3131     }
3132   }
3133   for (i=0;i<n_sends;i++) {
3134     ierr = PetscMPIIntCast(is_indices[i],&source_dest);CHKERRQ(ierr);
3135     ierr = MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);CHKERRQ(ierr);
3136     ierr = MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);CHKERRQ(ierr);
3137     if (nis) {
3138       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);
3139     }
3140   }
3141   ierr = ISRestoreIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
3142   ierr = ISDestroy(&is_sends_internal);CHKERRQ(ierr);
3143 
3144   /* assemble new l2g map */
3145   ierr = MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3146   ptr_idxs = recv_buffer_idxs;
3147   buf_size_idxs = 0;
3148   for (i=0;i<n_recvs;i++) {
3149     buf_size_idxs += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3150     ptr_idxs += olengths_idxs[i];
3151   }
3152   ierr = PetscMalloc1(buf_size_idxs,&l2gmap_indices);CHKERRQ(ierr);
3153   ptr_idxs = recv_buffer_idxs;
3154   buf_size_idxs = 0;
3155   for (i=0;i<n_recvs;i++) {
3156     ierr = PetscMemcpy(&l2gmap_indices[buf_size_idxs],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));CHKERRQ(ierr);
3157     buf_size_idxs += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3158     ptr_idxs += olengths_idxs[i];
3159   }
3160   ierr = PetscSortRemoveDupsInt(&buf_size_idxs,l2gmap_indices);CHKERRQ(ierr);
3161   ierr = ISLocalToGlobalMappingCreate(comm_n,1,buf_size_idxs,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);CHKERRQ(ierr);
3162   ierr = PetscFree(l2gmap_indices);CHKERRQ(ierr);
3163 
3164   /* infer new local matrix type from received local matrices type */
3165   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
3166   /* 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) */
3167   if (n_recvs) {
3168     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
3169     ptr_idxs = recv_buffer_idxs;
3170     for (i=0;i<n_recvs;i++) {
3171       if ((PetscInt)new_local_type_private != *ptr_idxs) {
3172         new_local_type_private = MATAIJ_PRIVATE;
3173         break;
3174       }
3175       ptr_idxs += olengths_idxs[i];
3176     }
3177     switch (new_local_type_private) {
3178       case MATDENSE_PRIVATE:
3179         if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
3180           new_local_type = MATSEQAIJ;
3181           bs = 1;
3182         } else { /* if I receive only 1 dense matrix */
3183           new_local_type = MATSEQDENSE;
3184           bs = 1;
3185         }
3186         break;
3187       case MATAIJ_PRIVATE:
3188         new_local_type = MATSEQAIJ;
3189         bs = 1;
3190         break;
3191       case MATBAIJ_PRIVATE:
3192         new_local_type = MATSEQBAIJ;
3193         break;
3194       case MATSBAIJ_PRIVATE:
3195         new_local_type = MATSEQSBAIJ;
3196         break;
3197       default:
3198         SETERRQ2(comm,PETSC_ERR_PLIB,"Unkwown private type %d in %s",new_local_type_private,__FUNCT__);
3199         break;
3200     }
3201   } else { /* by default, new_local_type is seqdense */
3202     new_local_type = MATSEQDENSE;
3203     bs = 1;
3204   }
3205 
3206   /* create MATIS object if needed */
3207   if (reuse == MAT_INITIAL_MATRIX) {
3208     ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
3209     ierr = MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,mat_n);CHKERRQ(ierr);
3210   } else {
3211     /* it also destroys the local matrices */
3212     ierr = MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);CHKERRQ(ierr);
3213   }
3214   ierr = ISLocalToGlobalMappingDestroy(&l2gmap);CHKERRQ(ierr);
3215   ierr = MatISGetLocalMat(*mat_n,&local_mat);CHKERRQ(ierr);
3216   ierr = MatSetType(local_mat,new_local_type);CHKERRQ(ierr);
3217   ierr = MatSetUp(local_mat);CHKERRQ(ierr); /* WARNING -> no preallocation yet */
3218 
3219   /* set values */
3220   ierr = MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3221   ptr_vals = recv_buffer_vals;
3222   ptr_idxs = recv_buffer_idxs;
3223   for (i=0;i<n_recvs;i++) {
3224     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
3225       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
3226       ierr = MatSetValues(*mat_n,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);CHKERRQ(ierr);
3227       ierr = MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3228       ierr = MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3229       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
3230     } else {
3231       /* TODO */
3232     }
3233     ptr_idxs += olengths_idxs[i];
3234     ptr_vals += olengths_vals[i];
3235   }
3236   ierr = MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3237   ierr = MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3238   ierr = MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3239   ierr = MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3240 
3241 #if 0
3242   if (!restrict_comm) { /* check */
3243     Vec       lvec,rvec;
3244     PetscReal infty_error;
3245 
3246     ierr = MatCreateVecs(mat,&rvec,&lvec);CHKERRQ(ierr);
3247     ierr = VecSetRandom(rvec,NULL);CHKERRQ(ierr);
3248     ierr = MatMult(mat,rvec,lvec);CHKERRQ(ierr);
3249     ierr = VecScale(lvec,-1.0);CHKERRQ(ierr);
3250     ierr = MatMultAdd(*mat_n,rvec,lvec,lvec);CHKERRQ(ierr);
3251     ierr = VecNorm(lvec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3252     ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
3253     ierr = VecDestroy(&rvec);CHKERRQ(ierr);
3254     ierr = VecDestroy(&lvec);CHKERRQ(ierr);
3255   }
3256 #endif
3257 
3258   /* assemble new additional is (if any) */
3259   if (nis) {
3260     PetscInt **temp_idxs,*count_is,j,psum;
3261 
3262     ierr = MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3263     ierr = PetscMalloc(nis*sizeof(PetscInt),&count_is);CHKERRQ(ierr);
3264     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3265     ptr_idxs = recv_buffer_idxs_is;
3266     psum = 0;
3267     for (i=0;i<n_recvs;i++) {
3268       for (j=0;j<nis;j++) {
3269         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3270         count_is[j] += plen; /* increment counting of buffer for j-th IS */
3271         psum += plen;
3272         ptr_idxs += plen+1; /* shift pointer to received data */
3273       }
3274     }
3275     ierr = PetscMalloc(nis*sizeof(PetscInt*),&temp_idxs);CHKERRQ(ierr);
3276     ierr = PetscMalloc(psum*sizeof(PetscInt),&temp_idxs[0]);CHKERRQ(ierr);
3277     for (i=1;i<nis;i++) {
3278       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
3279     }
3280     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3281     ptr_idxs = recv_buffer_idxs_is;
3282     for (i=0;i<n_recvs;i++) {
3283       for (j=0;j<nis;j++) {
3284         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3285         ierr = PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));CHKERRQ(ierr);
3286         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
3287         ptr_idxs += plen+1; /* shift pointer to received data */
3288       }
3289     }
3290     for (i=0;i<nis;i++) {
3291       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3292       ierr = PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);CHKERRQ(ierr);CHKERRQ(ierr);
3293       ierr = ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3294     }
3295     ierr = PetscFree(count_is);CHKERRQ(ierr);
3296     ierr = PetscFree(temp_idxs[0]);CHKERRQ(ierr);
3297     ierr = PetscFree(temp_idxs);CHKERRQ(ierr);
3298   }
3299   /* free workspace */
3300   ierr = PetscFree(recv_buffer_idxs);CHKERRQ(ierr);
3301   ierr = PetscFree(recv_buffer_vals);CHKERRQ(ierr);
3302   ierr = PetscFree(recv_buffer_idxs_is);CHKERRQ(ierr);
3303   ierr = MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3304   ierr = PetscFree(send_buffer_idxs);CHKERRQ(ierr);
3305   ierr = MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3306   if (isdense) {
3307     ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
3308     ierr = MatDenseRestoreArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3309   } else {
3310     /* ierr = PetscFree(send_buffer_vals);CHKERRQ(ierr); */
3311   }
3312   if (nis) {
3313     ierr = MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3314     ierr = PetscFree(send_buffer_idxs_is);CHKERRQ(ierr);
3315   }
3316   ierr = PetscFree(recv_req_idxs);CHKERRQ(ierr);
3317   ierr = PetscFree(recv_req_vals);CHKERRQ(ierr);
3318   ierr = PetscFree(recv_req_idxs_is);CHKERRQ(ierr);
3319   ierr = PetscFree(send_req_idxs);CHKERRQ(ierr);
3320   ierr = PetscFree(send_req_vals);CHKERRQ(ierr);
3321   ierr = PetscFree(send_req_idxs_is);CHKERRQ(ierr);
3322   ierr = PetscFree(ilengths_vals);CHKERRQ(ierr);
3323   ierr = PetscFree(ilengths_idxs);CHKERRQ(ierr);
3324   ierr = PetscFree(olengths_vals);CHKERRQ(ierr);
3325   ierr = PetscFree(olengths_idxs);CHKERRQ(ierr);
3326   ierr = PetscFree(onodes);CHKERRQ(ierr);
3327   if (nis) {
3328     ierr = PetscFree(ilengths_idxs_is);CHKERRQ(ierr);
3329     ierr = PetscFree(olengths_idxs_is);CHKERRQ(ierr);
3330     ierr = PetscFree(onodes_is);CHKERRQ(ierr);
3331   }
3332   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
3333   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
3334     ierr = MatDestroy(mat_n);CHKERRQ(ierr);
3335     for (i=0;i<nis;i++) {
3336       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3337     }
3338   }
3339   PetscFunctionReturn(0);
3340 }
3341 
3342 /* temporary hack into ksp private data structure */
3343 #include <petsc-private/kspimpl.h>
3344 
3345 #undef __FUNCT__
3346 #define __FUNCT__ "PCBDDCSetUpCoarseSolver"
3347 PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
3348 {
3349   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
3350   PC_IS                  *pcis = (PC_IS*)pc->data;
3351   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
3352   MatNullSpace           CoarseNullSpace=NULL;
3353   ISLocalToGlobalMapping coarse_islg;
3354   IS                     coarse_is,*isarray;
3355   PetscInt               i,im_active=-1,active_procs=-1;
3356   PetscInt               nis,nisdofs,nisneu;
3357   PC                     pc_temp;
3358   PCType                 coarse_pc_type;
3359   KSPType                coarse_ksp_type;
3360   PetscBool              multilevel_requested,multilevel_allowed;
3361   PetscBool              isredundant,isbddc,isnn,coarse_reuse;
3362   Mat                    t_coarse_mat_is;
3363   PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
3364   PetscMPIInt            all_procs;
3365   PetscBool              csin_ml,csin_ds,csin,csin_type_simple;
3366   PetscBool              compute_vecs = PETSC_FALSE;
3367   PetscErrorCode         ierr;
3368 
3369   PetscFunctionBegin;
3370   /* Assign global numbering to coarse dofs */
3371   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 */
3372     compute_vecs = PETSC_TRUE;
3373     PetscInt ocoarse_size;
3374     ocoarse_size = pcbddc->coarse_size;
3375     ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
3376     ierr = PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);CHKERRQ(ierr);
3377     /* see if we can avoid some work */
3378     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
3379       if (ocoarse_size != pcbddc->coarse_size) { /* ...but with different size, so reset it and set reuse flag to false */
3380         ierr = KSPReset(pcbddc->coarse_ksp);CHKERRQ(ierr);
3381         coarse_reuse = PETSC_FALSE;
3382       } else { /* we can safely reuse already computed coarse matrix */
3383         coarse_reuse = PETSC_TRUE;
3384       }
3385     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
3386       coarse_reuse = PETSC_FALSE;
3387     }
3388     /* reset any subassembling information */
3389     ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3390     ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3391   } else { /* primal space is unchanged, so we can reuse coarse matrix */
3392     coarse_reuse = PETSC_TRUE;
3393   }
3394 
3395   /* count "active" (i.e. with positive local size) and "void" processes */
3396   im_active = !!(pcis->n);
3397   ierr = MPI_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3398   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);CHKERRQ(ierr);
3399   void_procs = all_procs-active_procs;
3400   csin_type_simple = PETSC_TRUE;
3401   if (pcbddc->current_level) {
3402     csin_ml = PETSC_TRUE;
3403     ncoarse_ml = void_procs;
3404     csin_ds = PETSC_TRUE;
3405     ncoarse_ds = void_procs;
3406     if (!void_procs) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
3407   } else {
3408     csin_ml = PETSC_FALSE;
3409     ncoarse_ml = all_procs;
3410     if (void_procs) {
3411       csin_ds = PETSC_TRUE;
3412       ncoarse_ds = void_procs;
3413       csin_type_simple = PETSC_FALSE;
3414     } else {
3415       csin_ds = PETSC_FALSE;
3416       ncoarse_ds = all_procs;
3417     }
3418   }
3419 
3420   /*
3421     test if we can go multilevel: three conditions must be satisfied:
3422     - we have not exceeded the number of levels requested
3423     - we can actually subassemble the active processes
3424     - we can find a suitable number of MPI processes where we can place the subassembled problem
3425   */
3426   multilevel_allowed = PETSC_FALSE;
3427   multilevel_requested = PETSC_FALSE;
3428   if (pcbddc->current_level < pcbddc->max_levels) {
3429     multilevel_requested = PETSC_TRUE;
3430     if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
3431       multilevel_allowed = PETSC_FALSE;
3432     } else {
3433       multilevel_allowed = PETSC_TRUE;
3434     }
3435   }
3436   /* determine number of process partecipating to coarse solver */
3437   if (multilevel_allowed) {
3438     ncoarse = ncoarse_ml;
3439     csin = csin_ml;
3440   } else {
3441     ncoarse = ncoarse_ds;
3442     csin = csin_ds;
3443   }
3444 
3445   /* creates temporary l2gmap and IS for coarse indexes */
3446   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);CHKERRQ(ierr);
3447   ierr = ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);CHKERRQ(ierr);
3448 
3449   /* creates temporary MATIS object for coarse matrix */
3450   ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_submat_dense);CHKERRQ(ierr);
3451 #if 0
3452   {
3453     PetscViewer viewer;
3454     char filename[256];
3455     sprintf(filename,"local_coarse_mat%d.m",PetscGlobalRank);
3456     ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
3457     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3458     ierr = MatView(coarse_submat_dense,viewer);CHKERRQ(ierr);
3459     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3460   }
3461 #endif
3462   ierr = MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,&t_coarse_mat_is);CHKERRQ(ierr);
3463   ierr = MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);CHKERRQ(ierr);
3464   ierr = MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3465   ierr = MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3466   ierr = MatDestroy(&coarse_submat_dense);CHKERRQ(ierr);
3467 
3468   /* compute dofs splitting and neumann boundaries for coarse dofs */
3469   if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal) ) { /* protects from unneded computations */
3470     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
3471     const PetscInt         *idxs;
3472     ISLocalToGlobalMapping tmap;
3473 
3474     /* create map between primal indices (in local representative ordering) and local primal numbering */
3475     ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);CHKERRQ(ierr);
3476     /* allocate space for temporary storage */
3477     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs);CHKERRQ(ierr);
3478     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs2);CHKERRQ(ierr);
3479     /* allocate for IS array */
3480     nisdofs = pcbddc->n_ISForDofsLocal;
3481     nisneu = !!pcbddc->NeumannBoundariesLocal;
3482     nis = nisdofs + nisneu;
3483     ierr = PetscMalloc(nis*sizeof(IS),&isarray);CHKERRQ(ierr);
3484     /* dofs splitting */
3485     for (i=0;i<nisdofs;i++) {
3486       /* ierr = ISView(pcbddc->ISForDofsLocal[i],0);CHKERRQ(ierr); */
3487       ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);CHKERRQ(ierr);
3488       ierr = ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3489       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3490       ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3491       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3492       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->ISForDofsLocal[i]),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3493       /* ierr = ISView(isarray[i],0);CHKERRQ(ierr); */
3494     }
3495     /* neumann boundaries */
3496     if (pcbddc->NeumannBoundariesLocal) {
3497       /* ierr = ISView(pcbddc->NeumannBoundariesLocal,0);CHKERRQ(ierr); */
3498       ierr = ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);CHKERRQ(ierr);
3499       ierr = ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3500       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3501       ierr = ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3502       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3503       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->NeumannBoundariesLocal),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);CHKERRQ(ierr);
3504       /* ierr = ISView(isarray[nisdofs],0);CHKERRQ(ierr); */
3505     }
3506     /* free memory */
3507     ierr = PetscFree(tidxs);CHKERRQ(ierr);
3508     ierr = PetscFree(tidxs2);CHKERRQ(ierr);
3509     ierr = ISLocalToGlobalMappingDestroy(&tmap);CHKERRQ(ierr);
3510   } else {
3511     nis = 0;
3512     nisdofs = 0;
3513     nisneu = 0;
3514     isarray = NULL;
3515   }
3516   /* destroy no longer needed map */
3517   ierr = ISLocalToGlobalMappingDestroy(&coarse_islg);CHKERRQ(ierr);
3518 
3519   /* restrict on coarse candidates (if needed) */
3520   coarse_mat_is = NULL;
3521   if (csin) {
3522     if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
3523       PetscInt j,tissize,*nisindices;
3524       PetscInt *coarse_candidates;
3525       const PetscInt* tisindices;
3526       /* get coarse candidates' ranks in pc communicator */
3527       ierr = PetscMalloc(all_procs*sizeof(PetscInt),&coarse_candidates);CHKERRQ(ierr);
3528       ierr = MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3529       for (i=0,j=0;i<all_procs;i++) {
3530         if (!coarse_candidates[i]) {
3531           coarse_candidates[j]=i;
3532           j++;
3533         }
3534       }
3535       if (j < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",j,ncoarse);
3536       /* get a suitable subassembling pattern */
3537       if (csin_type_simple) {
3538         PetscMPIInt rank;
3539         PetscInt    issize,isidx;
3540         ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
3541         if (im_active) {
3542           issize = 1;
3543           isidx = (PetscInt)rank;
3544         } else {
3545           issize = 0;
3546           isidx = -1;
3547         }
3548         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3549       } else {
3550         ierr = MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,PETSC_TRUE,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3551       }
3552       if (pcbddc->dbg_flag) {
3553         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3554         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");CHKERRQ(ierr);
3555         ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3556         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");CHKERRQ(ierr);
3557         for (i=0;i<j;i++) {
3558           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);CHKERRQ(ierr);
3559         }
3560         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");CHKERRQ(ierr);
3561         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3562       }
3563       /* shift the pattern on coarse candidates */
3564       ierr = ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);CHKERRQ(ierr);
3565       ierr = ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3566       ierr = PetscMalloc(tissize*sizeof(PetscInt),&nisindices);CHKERRQ(ierr);
3567       for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
3568       ierr = ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3569       ierr = ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);CHKERRQ(ierr);
3570       ierr = PetscFree(coarse_candidates);CHKERRQ(ierr);
3571     }
3572     if (pcbddc->dbg_flag) {
3573       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3574       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");CHKERRQ(ierr);
3575       ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3576       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3577     }
3578     /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
3579     ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
3580   } else {
3581     if (pcbddc->dbg_flag) {
3582       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3583       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");CHKERRQ(ierr);
3584       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3585     }
3586     ierr = PetscObjectReference((PetscObject)t_coarse_mat_is);CHKERRQ(ierr);
3587     coarse_mat_is = t_coarse_mat_is;
3588   }
3589 
3590   /* create local to global scatters for coarse problem */
3591   if (compute_vecs) {
3592     PetscInt lrows;
3593     ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
3594     if (coarse_mat_is) {
3595       ierr = MatGetLocalSize(coarse_mat_is,&lrows,NULL);CHKERRQ(ierr);
3596     } else {
3597       lrows = 0;
3598     }
3599     ierr = VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);CHKERRQ(ierr);
3600     ierr = VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);CHKERRQ(ierr);
3601     ierr = VecSetType(pcbddc->coarse_vec,VECSTANDARD);CHKERRQ(ierr);
3602     ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3603     ierr = VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3604   }
3605   ierr = ISDestroy(&coarse_is);CHKERRQ(ierr);
3606   ierr = MatDestroy(&t_coarse_mat_is);CHKERRQ(ierr);
3607 
3608   /* set defaults for coarse KSP and PC */
3609   if (multilevel_allowed) {
3610     coarse_ksp_type = KSPRICHARDSON;
3611     coarse_pc_type = PCBDDC;
3612   } else {
3613     coarse_ksp_type = KSPPREONLY;
3614     coarse_pc_type = PCREDUNDANT;
3615   }
3616 
3617   /* print some info if requested */
3618   if (pcbddc->dbg_flag) {
3619     if (!multilevel_allowed) {
3620       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3621       if (multilevel_requested) {
3622         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);
3623       } else if (pcbddc->max_levels) {
3624         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);CHKERRQ(ierr);
3625       }
3626       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3627     }
3628   }
3629 
3630   /* create the coarse KSP object only once with defaults */
3631   if (coarse_mat_is) {
3632     MatReuse coarse_mat_reuse;
3633     PetscViewer dbg_viewer = NULL;
3634     if (pcbddc->dbg_flag) {
3635       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
3636       ierr = PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3637     }
3638     if (!pcbddc->coarse_ksp) {
3639       char prefix[256],str_level[16];
3640       size_t len;
3641       ierr = KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);CHKERRQ(ierr);
3642       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3643       ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
3644       ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);CHKERRQ(ierr);
3645       ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3646       ierr = KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);CHKERRQ(ierr);
3647       ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3648       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3649       /* prefix */
3650       ierr = PetscStrcpy(prefix,"");CHKERRQ(ierr);
3651       ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
3652       if (!pcbddc->current_level) {
3653         ierr = PetscStrcpy(prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
3654         ierr = PetscStrcat(prefix,"pc_bddc_coarse_");CHKERRQ(ierr);
3655       } else {
3656         ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
3657         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
3658         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
3659         ierr = PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
3660         sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
3661         ierr = PetscStrcat(prefix,str_level);CHKERRQ(ierr);
3662       }
3663       ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);CHKERRQ(ierr);
3664       /* allow user customization */
3665       ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3666       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
3667     }
3668 
3669     /* get some info after set from options */
3670     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3671     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);CHKERRQ(ierr);
3672     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);CHKERRQ(ierr);
3673     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);CHKERRQ(ierr);
3674     if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
3675       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3676       isbddc = PETSC_FALSE;
3677     }
3678     if (isredundant) {
3679       KSP inner_ksp;
3680       PC inner_pc;
3681       ierr = PCRedundantGetKSP(pc_temp,&inner_ksp);CHKERRQ(ierr);
3682       ierr = KSPGetPC(inner_ksp,&inner_pc);CHKERRQ(ierr);
3683       ierr = PCFactorSetReuseFill(inner_pc,PETSC_TRUE);CHKERRQ(ierr);
3684     }
3685 
3686     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
3687     ierr = PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);CHKERRQ(ierr);
3688     ierr = PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);CHKERRQ(ierr);
3689     ierr = PCBDDCSetLevels(pc_temp,pcbddc->max_levels);CHKERRQ(ierr);
3690     if (nisdofs) {
3691       ierr = PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);CHKERRQ(ierr);
3692       for (i=0;i<nisdofs;i++) {
3693         ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3694       }
3695     }
3696     if (nisneu) {
3697       ierr = PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);CHKERRQ(ierr);
3698       ierr = ISDestroy(&isarray[nisdofs]);CHKERRQ(ierr);
3699     }
3700 
3701     /* assemble coarse matrix */
3702     if (coarse_reuse) {
3703       ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
3704       ierr = PetscObjectReference((PetscObject)coarse_mat);CHKERRQ(ierr);
3705       coarse_mat_reuse = MAT_REUSE_MATRIX;
3706     } else {
3707       coarse_mat_reuse = MAT_INITIAL_MATRIX;
3708     }
3709     if (isbddc || isnn) {
3710       if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
3711         ierr = MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,PETSC_TRUE,&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3712         if (pcbddc->dbg_flag) {
3713           ierr = PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3714           ierr = PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");CHKERRQ(ierr);
3715           ierr = ISView(pcbddc->coarse_subassembling,dbg_viewer);CHKERRQ(ierr);
3716           ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3717         }
3718       }
3719       ierr = MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);CHKERRQ(ierr);
3720     } else {
3721       ierr = MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);CHKERRQ(ierr);
3722     }
3723     ierr = MatDestroy(&coarse_mat_is);CHKERRQ(ierr);
3724 
3725     /* propagate symmetry info to coarse matrix */
3726     ierr = MatSetOption(coarse_mat,MAT_SYMMETRIC,pcbddc->issym);CHKERRQ(ierr);
3727     ierr = MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
3728 
3729     /* set operators */
3730     ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3731     if (pcbddc->dbg_flag) {
3732       ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3733     }
3734   } else { /* processes non partecipating to coarse solver (if any) */
3735     coarse_mat = 0;
3736   }
3737   ierr = PetscFree(isarray);CHKERRQ(ierr);
3738 #if 0
3739   {
3740     PetscViewer viewer;
3741     char filename[256];
3742     sprintf(filename,"coarse_mat.m");
3743     ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,&viewer);CHKERRQ(ierr);
3744     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3745     ierr = MatView(coarse_mat,viewer);CHKERRQ(ierr);
3746     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3747   }
3748 #endif
3749 
3750   /* Compute coarse null space (special handling by BDDC only) */
3751   if (pcbddc->NullSpace) {
3752     ierr = PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);CHKERRQ(ierr);
3753   }
3754 
3755   if (pcbddc->coarse_ksp) {
3756     Vec crhs,csol;
3757     PetscBool ispreonly;
3758     if (CoarseNullSpace) {
3759       if (isbddc) {
3760         ierr = PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);CHKERRQ(ierr);
3761       } else {
3762         ierr = KSPSetNullSpace(pcbddc->coarse_ksp,CoarseNullSpace);CHKERRQ(ierr);
3763       }
3764     }
3765     /* setup coarse ksp */
3766     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3767     ierr = KSPGetSolution(pcbddc->coarse_ksp,&csol);CHKERRQ(ierr);
3768     ierr = KSPGetRhs(pcbddc->coarse_ksp,&crhs);CHKERRQ(ierr);
3769     /* hack */
3770     if (!csol) {
3771       ierr = MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);CHKERRQ(ierr);
3772     }
3773     if (!crhs) {
3774       ierr = MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));CHKERRQ(ierr);
3775     }
3776     /* Check coarse problem if in debug mode or if solving with an iterative method */
3777     ierr = PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);CHKERRQ(ierr);
3778     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
3779       KSP       check_ksp;
3780       KSPType   check_ksp_type;
3781       PC        check_pc;
3782       Vec       check_vec,coarse_vec;
3783       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
3784       PetscInt  its;
3785       PetscBool compute_eigs;
3786       PetscReal *eigs_r,*eigs_c;
3787       PetscInt  neigs;
3788       const char *prefix;
3789 
3790       /* Create ksp object suitable for estimation of extreme eigenvalues */
3791       ierr = KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);CHKERRQ(ierr);
3792       ierr = KSPSetOperators(check_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3793       ierr = KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3794       if (ispreonly) {
3795         check_ksp_type = KSPPREONLY;
3796         compute_eigs = PETSC_FALSE;
3797       } else {
3798         check_ksp_type = KSPGMRES;
3799         compute_eigs = PETSC_TRUE;
3800       }
3801       ierr = KSPSetType(check_ksp,check_ksp_type);CHKERRQ(ierr);
3802       ierr = KSPSetComputeSingularValues(check_ksp,compute_eigs);CHKERRQ(ierr);
3803       ierr = KSPSetComputeEigenvalues(check_ksp,compute_eigs);CHKERRQ(ierr);
3804       ierr = KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);CHKERRQ(ierr);
3805       ierr = KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);CHKERRQ(ierr);
3806       ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
3807       ierr = KSPAppendOptionsPrefix(check_ksp,"check_");CHKERRQ(ierr);
3808       ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
3809       ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
3810       ierr = KSPGetPC(pcbddc->coarse_ksp,&check_pc);CHKERRQ(ierr);
3811       ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
3812       /* create random vec */
3813       ierr = KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);CHKERRQ(ierr);
3814       ierr = VecDuplicate(coarse_vec,&check_vec);CHKERRQ(ierr);
3815       ierr = VecSetRandom(check_vec,NULL);CHKERRQ(ierr);
3816       if (CoarseNullSpace) {
3817         ierr = MatNullSpaceRemove(CoarseNullSpace,check_vec);CHKERRQ(ierr);
3818       }
3819       ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3820       /* solve coarse problem */
3821       ierr = KSPSolve(check_ksp,coarse_vec,coarse_vec);CHKERRQ(ierr);
3822       if (CoarseNullSpace) {
3823         ierr = MatNullSpaceRemove(CoarseNullSpace,coarse_vec);CHKERRQ(ierr);
3824       }
3825       /* set eigenvalue estimation if preonly has not been requested */
3826       if (compute_eigs) {
3827         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_r);CHKERRQ(ierr);
3828         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_c);CHKERRQ(ierr);
3829         ierr = KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);CHKERRQ(ierr);
3830         lambda_max = eigs_r[neigs-1];
3831         lambda_min = eigs_r[0];
3832         if (pcbddc->use_coarse_estimates) {
3833           if (lambda_max>lambda_min) {
3834             ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3835             ierr = KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));CHKERRQ(ierr);
3836           }
3837         }
3838       }
3839 
3840       /* check coarse problem residual error */
3841       if (pcbddc->dbg_flag) {
3842         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
3843         ierr = PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3844         ierr = VecAXPY(check_vec,-1.0,coarse_vec);CHKERRQ(ierr);
3845         ierr = VecNorm(check_vec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3846         ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3847         ierr = VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);CHKERRQ(ierr);
3848         ierr = VecDestroy(&check_vec);CHKERRQ(ierr);
3849         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (%d)\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
3850         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);CHKERRQ(ierr);
3851         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);CHKERRQ(ierr);
3852         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);CHKERRQ(ierr);
3853         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);CHKERRQ(ierr);
3854         if (compute_eigs) {
3855           PetscReal lambda_max_s,lambda_min_s;
3856           ierr = KSPGetType(check_ksp,&check_ksp_type);CHKERRQ(ierr);
3857           ierr = KSPGetIterationNumber(check_ksp,&its);CHKERRQ(ierr);
3858           ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);CHKERRQ(ierr);
3859           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);
3860           for (i=0;i<neigs;i++) {
3861             ierr = PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);CHKERRQ(ierr);
3862           }
3863         }
3864         ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3865         ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3866       }
3867       ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
3868       if (compute_eigs) {
3869         ierr = PetscFree(eigs_r);CHKERRQ(ierr);
3870         ierr = PetscFree(eigs_c);CHKERRQ(ierr);
3871       }
3872     }
3873   }
3874   /* print additional info */
3875   if (pcbddc->dbg_flag) {
3876     /* waits until all processes reaches this point */
3877     ierr = PetscBarrier((PetscObject)pc);CHKERRQ(ierr);
3878     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);CHKERRQ(ierr);
3879     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3880   }
3881 
3882   /* free memory */
3883   ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
3884   ierr = MatDestroy(&coarse_mat);CHKERRQ(ierr);
3885   PetscFunctionReturn(0);
3886 }
3887 
3888 #undef __FUNCT__
3889 #define __FUNCT__ "PCBDDCComputePrimalNumbering"
3890 PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
3891 {
3892   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
3893   PC_IS*         pcis = (PC_IS*)pc->data;
3894   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
3895   PetscInt       i,coarse_size;
3896   PetscInt       *local_primal_indices;
3897   PetscErrorCode ierr;
3898 
3899   PetscFunctionBegin;
3900   /* Compute global number of coarse dofs */
3901   if (!pcbddc->primal_indices_local_idxs && pcbddc->local_primal_size) {
3902     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Local primal indices have not been created");
3903   }
3904   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);
3905 
3906   /* check numbering */
3907   if (pcbddc->dbg_flag) {
3908     PetscScalar coarsesum,*array;
3909     PetscBool set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;
3910 
3911     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3912     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3913     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");CHKERRQ(ierr);
3914     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
3915     ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
3916     for (i=0;i<pcbddc->local_primal_size;i++) {
3917       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
3918     }
3919     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
3920     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
3921     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3922     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3923     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3924     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3925     ierr = VecScatterEnd(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3926     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3927     for (i=0;i<pcis->n;i++) {
3928       if (array[i] == 1.0) {
3929         set_error = PETSC_TRUE;
3930         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a single process!\n",PetscGlobalRank,i);CHKERRQ(ierr);
3931       }
3932     }
3933     ierr = MPI_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3934     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3935     for (i=0;i<pcis->n;i++) {
3936       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
3937     }
3938     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3939     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3940     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3941     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3942     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
3943     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));CHKERRQ(ierr);
3944     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
3945       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");CHKERRQ(ierr);
3946       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3947       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
3948       for (i=0;i<pcbddc->local_primal_size;i++) {
3949         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%d]=%d (%d)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i]);
3950       }
3951       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3952     }
3953     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3954     if (set_error_reduced) {
3955       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
3956     }
3957   }
3958   /* get back data */
3959   *coarse_size_n = coarse_size;
3960   *local_primal_indices_n = local_primal_indices;
3961   PetscFunctionReturn(0);
3962 }
3963 
3964 #undef __FUNCT__
3965 #define __FUNCT__ "PCBDDCGlobalToLocal"
3966 PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
3967 {
3968   IS             localis_t;
3969   PetscInt       i,lsize,*idxs,n;
3970   PetscScalar    *vals;
3971   PetscErrorCode ierr;
3972 
3973   PetscFunctionBegin;
3974   /* get indices in local ordering exploiting local to global map */
3975   ierr = ISGetLocalSize(globalis,&lsize);CHKERRQ(ierr);
3976   ierr = PetscMalloc(lsize*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
3977   for (i=0;i<lsize;i++) vals[i] = 1.0;
3978   ierr = ISGetIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
3979   ierr = VecSet(gwork,0.0);CHKERRQ(ierr);
3980   ierr = VecSet(lwork,0.0);CHKERRQ(ierr);
3981   if (idxs) { /* multilevel guard */
3982     ierr = VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
3983   }
3984   ierr = VecAssemblyBegin(gwork);CHKERRQ(ierr);
3985   ierr = ISRestoreIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
3986   ierr = PetscFree(vals);CHKERRQ(ierr);
3987   ierr = VecAssemblyEnd(gwork);CHKERRQ(ierr);
3988   /* now compute set in local ordering */
3989   ierr = VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3990   ierr = VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3991   ierr = VecGetArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
3992   ierr = VecGetSize(lwork,&n);CHKERRQ(ierr);
3993   for (i=0,lsize=0;i<n;i++) {
3994     if (PetscRealPart(vals[i]) > 0.5) {
3995       lsize++;
3996     }
3997   }
3998   ierr = PetscMalloc(lsize*sizeof(PetscInt),&idxs);CHKERRQ(ierr);
3999   for (i=0,lsize=0;i<n;i++) {
4000     if (PetscRealPart(vals[i]) > 0.5) {
4001       idxs[lsize++] = i;
4002     }
4003   }
4004   ierr = VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
4005   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);CHKERRQ(ierr);
4006   *localis = localis_t;
4007   PetscFunctionReturn(0);
4008 }
4009 
4010 /* the next two functions will be called in KSPMatMult if a change of basis has been requested */
4011 #undef __FUNCT__
4012 #define __FUNCT__ "PCBDDCMatMult_Private"
4013 static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y)
4014 {
4015   PCBDDCChange_ctx change_ctx;
4016   PetscErrorCode   ierr;
4017 
4018   PetscFunctionBegin;
4019   ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
4020   ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
4021   ierr = MatMult(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
4022   ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
4023   PetscFunctionReturn(0);
4024 }
4025 
4026 #undef __FUNCT__
4027 #define __FUNCT__ "PCBDDCMatMultTranspose_Private"
4028 static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y)
4029 {
4030   PCBDDCChange_ctx change_ctx;
4031   PetscErrorCode   ierr;
4032 
4033   PetscFunctionBegin;
4034   ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
4035   ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
4036   ierr = MatMultTranspose(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
4037   ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
4038   PetscFunctionReturn(0);
4039 }
4040