xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision bcab024551cbaaaa7f49e357634a3584f91cb6d5)
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,*d_nnz,*o_nnz;
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 = PetscMalloc2(local_size,&d_nnz,local_size,&o_nnz);CHKERRQ(ierr);
2270     ierr = VecGetArray(nnz_vec,&nnz_array);CHKERRQ(ierr);
2271     for (i=0;i<local_size;i++) {
2272       d_nnz[i] = PetscMin((PetscInt)(PetscRealPart(nnz_array[i])),local_size);
2273       o_nnz[i] = PetscMin((PetscInt)(PetscRealPart(nnz_array[i])),global_size-local_size);
2274     }
2275     ierr = VecRestoreArray(nnz_vec,&nnz_array);CHKERRQ(ierr);
2276     ierr = VecDestroy(&nnz_vec);CHKERRQ(ierr);
2277     ierr = MatMPIAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2278     ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
2279 
2280     /* Set identity on dirichlet dofs */
2281     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&idxs_I);CHKERRQ(ierr);
2282     for (i=0;i<pcis->n-pcis->n_B;i++) {
2283       PetscScalar one=1.0;
2284       ierr = MatSetValuesLocal(pcbddc->ChangeOfBasisMatrix,1,idxs_I+i,1,idxs_I+i,&one,INSERT_VALUES);CHKERRQ(ierr);
2285     }
2286     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&idxs_I);CHKERRQ(ierr);
2287 
2288     /* Set values at interface dofs */
2289     done = PETSC_TRUE;
2290     ierr = MatGetRowIJ(localChangeOfBasisMatrix,0,PETSC_FALSE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&done);CHKERRQ(ierr);
2291     if (!done) {
2292       SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
2293     }
2294     ierr = MatSeqAIJGetArray(localChangeOfBasisMatrix,&vals);CHKERRQ(ierr);
2295     ierr = PetscMalloc1(xadj[nvtxs],&idxs_mapped);CHKERRQ(ierr);
2296     ierr = ISLocalToGlobalMappingApply(pcbddc->BtoNmap,xadj[nvtxs],adjncy,idxs_mapped);CHKERRQ(ierr);
2297     for (i=0;i<nvtxs;i++) {
2298       PetscInt    row,*cols,ncols;
2299       PetscScalar *mat_vals;
2300 
2301       row = idxs_B[i];
2302       ncols = xadj[i+1]-xadj[i];
2303       cols = idxs_mapped+xadj[i];
2304       mat_vals = vals+xadj[i];
2305       ierr = MatSetValuesLocal(pcbddc->ChangeOfBasisMatrix,1,&row,ncols,cols,mat_vals,INSERT_VALUES);CHKERRQ(ierr);
2306     }
2307     ierr = MatRestoreRowIJ(localChangeOfBasisMatrix,0,PETSC_FALSE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&done);CHKERRQ(ierr);
2308     if (!done) {
2309       SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2310     }
2311     ierr = MatSeqAIJRestoreArray(localChangeOfBasisMatrix,&vals);CHKERRQ(ierr);
2312     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&idxs_B);CHKERRQ(ierr);
2313     ierr = PetscFree(idxs_mapped);CHKERRQ(ierr);
2314     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2315     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2316 
2317     /* check */
2318     if (pcbddc->dbg_flag) {
2319       PetscReal error;
2320       Vec       x,x_change;
2321 
2322       ierr = VecDuplicate(pcis->vec1_global,&x);CHKERRQ(ierr);
2323       ierr = VecDuplicate(pcis->vec1_global,&x_change);CHKERRQ(ierr);
2324       ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
2325       ierr = VecCopy(x,pcis->vec1_global);CHKERRQ(ierr);
2326       ierr = VecScatterBegin(pcis->global_to_B,x,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2327       ierr = VecScatterEnd(pcis->global_to_B,x,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2328       ierr = MatMult(localChangeOfBasisMatrix,pcis->vec1_B,pcis->vec2_B);CHKERRQ(ierr);
2329       ierr = VecScatterBegin(pcis->global_to_B,pcis->vec2_B,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2330       ierr = VecScatterEnd(pcis->global_to_B,pcis->vec2_B,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2331       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);CHKERRQ(ierr);
2332       ierr = VecAXPY(x,-1.0,x_change);CHKERRQ(ierr);
2333       ierr = VecNorm(x,NORM_INFINITY,&error);CHKERRQ(ierr);
2334       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2335       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change on B: %1.6e\n",error);CHKERRQ(ierr);
2336       ierr = VecDestroy(&x);CHKERRQ(ierr);
2337       ierr = VecDestroy(&x_change);CHKERRQ(ierr);
2338     }
2339     ierr = MatDestroy(&localChangeOfBasisMatrix);CHKERRQ(ierr);
2340 
2341     /*
2342     ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
2343     ierr = MatView(local_ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
2344     */
2345   } else if (pcbddc->user_ChangeOfBasisMatrix) {
2346     ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2347     pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
2348   }
2349 
2350   /* set up change of basis context */
2351   if (pcbddc->ChangeOfBasisMatrix) {
2352     PCBDDCChange_ctx change_ctx;
2353 
2354     if (!pcbddc->new_global_mat) {
2355       PetscInt global_size,local_size;
2356 
2357       ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
2358       ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
2359       ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->new_global_mat);CHKERRQ(ierr);
2360       ierr = MatSetSizes(pcbddc->new_global_mat,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
2361       ierr = MatSetType(pcbddc->new_global_mat,MATSHELL);CHKERRQ(ierr);
2362       ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT,(void (*)(void))PCBDDCMatMult_Private);CHKERRQ(ierr);
2363       ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCMatMultTranspose_Private);CHKERRQ(ierr);
2364       ierr = PetscNew(&change_ctx);CHKERRQ(ierr);
2365       ierr = MatShellSetContext(pcbddc->new_global_mat,change_ctx);CHKERRQ(ierr);
2366     } else {
2367       ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
2368       ierr = MatDestroy(&change_ctx->global_change);CHKERRQ(ierr);
2369       ierr = VecDestroyVecs(2,&change_ctx->work);CHKERRQ(ierr);
2370     }
2371     if (!pcbddc->user_ChangeOfBasisMatrix) {
2372       ierr = PetscObjectReference((PetscObject)pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2373       change_ctx->global_change = pcbddc->ChangeOfBasisMatrix;
2374     } else {
2375       ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2376       change_ctx->global_change = pcbddc->user_ChangeOfBasisMatrix;
2377     }
2378     ierr = VecDuplicateVecs(pcis->vec1_global,2,&change_ctx->work);CHKERRQ(ierr);
2379     ierr = MatSetUp(pcbddc->new_global_mat);CHKERRQ(ierr);
2380     ierr = MatAssemblyBegin(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2381     ierr = MatAssemblyEnd(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2382   }
2383 
2384   /* get indices in local ordering for vertices and constraints */
2385   if (olocal_primal_size == pcbddc->local_primal_size) { /* if this is true, I need to check if a new primal space has been introduced */
2386     ierr = PetscMalloc1(olocal_primal_size,&oprimal_indices_local_idxs);CHKERRQ(ierr);
2387     ierr = PetscMemcpy(oprimal_indices_local_idxs,pcbddc->primal_indices_local_idxs,olocal_primal_size*sizeof(PetscInt));CHKERRQ(ierr);
2388   }
2389   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2390   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2391   ierr = PetscMalloc1(pcbddc->local_primal_size,&pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2392   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&i,&aux_primal_numbering);CHKERRQ(ierr);
2393   ierr = PetscMemcpy(pcbddc->primal_indices_local_idxs,aux_primal_numbering,i*sizeof(PetscInt));CHKERRQ(ierr);
2394   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2395   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&j,&aux_primal_numbering);CHKERRQ(ierr);
2396   ierr = PetscMemcpy(&pcbddc->primal_indices_local_idxs[i],aux_primal_numbering,j*sizeof(PetscInt));CHKERRQ(ierr);
2397   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2398   /* set quantities in PCBDDC data struct */
2399   pcbddc->n_actual_vertices = i;
2400   /* check if a new primal space has been introduced */
2401   pcbddc->new_primal_space_local = PETSC_TRUE;
2402   if (olocal_primal_size == pcbddc->local_primal_size) {
2403     ierr = PetscMemcmp(pcbddc->primal_indices_local_idxs,oprimal_indices_local_idxs,olocal_primal_size,&pcbddc->new_primal_space_local);CHKERRQ(ierr);
2404     pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
2405     ierr = PetscFree(oprimal_indices_local_idxs);CHKERRQ(ierr);
2406   }
2407   /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
2408   ierr = MPI_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
2409 
2410   /* flush dbg viewer */
2411   if (pcbddc->dbg_flag) {
2412     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2413   }
2414 
2415   /* free workspace */
2416   ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2417   ierr = PetscBTDestroy(&qr_needed_idx);CHKERRQ(ierr);
2418   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
2419   ierr = PetscBTDestroy(&change_basis);CHKERRQ(ierr);
2420   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2421   ierr = PetscFree3(temp_quadrature_constraint,temp_indices_to_constraint,temp_indices_to_constraint_B);CHKERRQ(ierr);
2422   PetscFunctionReturn(0);
2423 }
2424 
2425 #undef __FUNCT__
2426 #define __FUNCT__ "PCBDDCAnalyzeInterface"
2427 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
2428 {
2429   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
2430   PC_IS       *pcis = (PC_IS*)pc->data;
2431   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
2432   PetscInt    ierr,i,vertex_size;
2433   PetscViewer viewer=pcbddc->dbg_viewer;
2434 
2435   PetscFunctionBegin;
2436   /* Reset previously computed graph */
2437   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
2438   /* Init local Graph struct */
2439   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
2440 
2441   /* Check validity of the csr graph passed in by the user */
2442   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
2443     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
2444   }
2445 
2446   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
2447   if (pcbddc->use_local_adj && (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy)) {
2448     Mat mat_adj;
2449     const PetscInt *xadj,*adjncy;
2450     PetscBool flg_row=PETSC_TRUE;
2451 
2452     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
2453     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2454     if (!flg_row) {
2455       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
2456     }
2457     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
2458     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2459     if (!flg_row) {
2460       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2461     }
2462     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
2463     pcbddc->deluxe_compute_rowadj = PETSC_FALSE;
2464   }
2465 
2466   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
2467   vertex_size = 1;
2468   if (pcbddc->user_provided_isfordofs) {
2469     if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
2470       ierr = PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2471       for (i=0;i<pcbddc->n_ISForDofs;i++) {
2472         ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2473         ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
2474       }
2475       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
2476       pcbddc->n_ISForDofs = 0;
2477       ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
2478     }
2479     /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
2480     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
2481   } else {
2482     if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
2483       ierr = MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);CHKERRQ(ierr);
2484       ierr = PetscMalloc(pcbddc->n_ISForDofsLocal*sizeof(IS),&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2485       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
2486         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2487       }
2488     }
2489   }
2490 
2491   /* Setup of Graph */
2492   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
2493     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
2494   }
2495   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
2496     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
2497   }
2498   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices);
2499 
2500   /* Graph's connected components analysis */
2501   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
2502 
2503   /* print some info to stdout */
2504   if (pcbddc->dbg_flag) {
2505     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
2506   }
2507 
2508   /* mark topography has done */
2509   pcbddc->recompute_topography = PETSC_FALSE;
2510   PetscFunctionReturn(0);
2511 }
2512 
2513 #undef __FUNCT__
2514 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
2515 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt **vertices_idx)
2516 {
2517   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2518   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
2519   PetscErrorCode ierr;
2520 
2521   PetscFunctionBegin;
2522   n = 0;
2523   vertices = 0;
2524   if (pcbddc->ConstraintMatrix) {
2525     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
2526     for (i=0;i<local_primal_size;i++) {
2527       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2528       if (size_of_constraint == 1) n++;
2529       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2530     }
2531     if (vertices_idx) {
2532       ierr = PetscMalloc1(n,&vertices);CHKERRQ(ierr);
2533       n = 0;
2534       for (i=0;i<local_primal_size;i++) {
2535         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2536         if (size_of_constraint == 1) {
2537           vertices[n++]=row_cmat_indices[0];
2538         }
2539         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2540       }
2541     }
2542   }
2543   *n_vertices = n;
2544   if (vertices_idx) *vertices_idx = vertices;
2545   PetscFunctionReturn(0);
2546 }
2547 
2548 #undef __FUNCT__
2549 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
2550 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt **constraints_idx)
2551 {
2552   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2553   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
2554   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
2555   PetscBT        touched;
2556   PetscErrorCode ierr;
2557 
2558     /* This function assumes that the number of local constraints per connected component
2559        is not greater than the number of nodes defined for the connected component
2560        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
2561   PetscFunctionBegin;
2562   n = 0;
2563   constraints_index = 0;
2564   if (pcbddc->ConstraintMatrix) {
2565     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
2566     max_size_of_constraint = 0;
2567     for (i=0;i<local_primal_size;i++) {
2568       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2569       if (size_of_constraint > 1) {
2570         n++;
2571       }
2572       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
2573       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2574     }
2575     if (constraints_idx) {
2576       ierr = PetscMalloc1(n,&constraints_index);CHKERRQ(ierr);
2577       ierr = PetscMalloc1(max_size_of_constraint,&row_cmat_global_indices);CHKERRQ(ierr);
2578       ierr = PetscBTCreate(local_size,&touched);CHKERRQ(ierr);
2579       n = 0;
2580       for (i=0;i<local_primal_size;i++) {
2581         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2582         if (size_of_constraint > 1) {
2583           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
2584           /* find first untouched local node */
2585           j = 0;
2586           while (PetscBTLookup(touched,row_cmat_indices[j])) j++;
2587           min_index = row_cmat_global_indices[j];
2588           min_loc = j;
2589           /* search the minimum among nodes not yet touched on the connected component
2590              since there can be more than one constraint on a single cc */
2591           for (j=1;j<size_of_constraint;j++) {
2592             if (!PetscBTLookup(touched,row_cmat_indices[j]) && min_index > row_cmat_global_indices[j]) {
2593               min_index = row_cmat_global_indices[j];
2594               min_loc = j;
2595             }
2596           }
2597           ierr = PetscBTSet(touched,row_cmat_indices[min_loc]);CHKERRQ(ierr);
2598           constraints_index[n++] = row_cmat_indices[min_loc];
2599         }
2600         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2601       }
2602       ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2603       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
2604     }
2605   }
2606   *n_constraints = n;
2607   if (constraints_idx) *constraints_idx = constraints_index;
2608   PetscFunctionReturn(0);
2609 }
2610 
2611 #undef __FUNCT__
2612 #define __FUNCT__ "PCBDDCSubsetNumbering"
2613 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[])
2614 {
2615   Vec            local_vec,global_vec;
2616   IS             seqis,paris;
2617   VecScatter     scatter_ctx;
2618   PetscScalar    *array;
2619   PetscInt       *temp_global_dofs;
2620   PetscScalar    globalsum;
2621   PetscInt       i,j,s;
2622   PetscInt       nlocals,first_index,old_index,max_local;
2623   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
2624   PetscMPIInt    *dof_sizes,*dof_displs;
2625   PetscBool      first_found;
2626   PetscErrorCode ierr;
2627 
2628   PetscFunctionBegin;
2629   /* mpi buffers */
2630   ierr = MPI_Comm_size(comm,&size_prec_comm);CHKERRQ(ierr);
2631   ierr = MPI_Comm_rank(comm,&rank_prec_comm);CHKERRQ(ierr);
2632   j = ( !rank_prec_comm ? size_prec_comm : 0);
2633   ierr = PetscMalloc1(j,&dof_sizes);CHKERRQ(ierr);
2634   ierr = PetscMalloc1(j,&dof_displs);CHKERRQ(ierr);
2635   /* get maximum size of subset */
2636   ierr = PetscMalloc1(n_local_dofs,&temp_global_dofs);CHKERRQ(ierr);
2637   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
2638   max_local = 0;
2639   for (i=0;i<n_local_dofs;i++) {
2640     if (max_local < temp_global_dofs[i] ) {
2641       max_local = temp_global_dofs[i];
2642     }
2643   }
2644   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
2645   max_global++;
2646   max_local = 0;
2647   for (i=0;i<n_local_dofs;i++) {
2648     if (max_local < local_dofs[i] ) {
2649       max_local = local_dofs[i];
2650     }
2651   }
2652   max_local++;
2653   /* allocate workspace */
2654   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
2655   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
2656   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
2657   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
2658   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
2659   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
2660   /* create scatter */
2661   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
2662   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
2663   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
2664   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
2665   ierr = ISDestroy(&paris);CHKERRQ(ierr);
2666   /* init array */
2667   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
2668   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2669   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2670   if (local_dofs_mult) {
2671     for (i=0;i<n_local_dofs;i++) {
2672       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
2673     }
2674   } else {
2675     for (i=0;i<n_local_dofs;i++) {
2676       array[local_dofs[i]]=1.0;
2677     }
2678   }
2679   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2680   /* scatter into global vec and get total number of global dofs */
2681   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2682   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2683   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
2684   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
2685   /* Fill global_vec with cumulative function for global numbering */
2686   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
2687   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
2688   nlocals = 0;
2689   first_index = -1;
2690   first_found = PETSC_FALSE;
2691   for (i=0;i<s;i++) {
2692     if (!first_found && PetscRealPart(array[i]) > 0.1) {
2693       first_found = PETSC_TRUE;
2694       first_index = i;
2695     }
2696     nlocals += (PetscInt)PetscRealPart(array[i]);
2697   }
2698   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2699   if (!rank_prec_comm) {
2700     dof_displs[0]=0;
2701     for (i=1;i<size_prec_comm;i++) {
2702       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
2703     }
2704   }
2705   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2706   if (first_found) {
2707     array[first_index] += (PetscScalar)nlocals;
2708     old_index = first_index;
2709     for (i=first_index+1;i<s;i++) {
2710       if (PetscRealPart(array[i]) > 0.1) {
2711         array[i] += array[old_index];
2712         old_index = i;
2713       }
2714     }
2715   }
2716   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
2717   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2718   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2719   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2720   /* get global ordering of local dofs */
2721   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2722   if (local_dofs_mult) {
2723     for (i=0;i<n_local_dofs;i++) {
2724       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
2725     }
2726   } else {
2727     for (i=0;i<n_local_dofs;i++) {
2728       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
2729     }
2730   }
2731   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2732   /* free workspace */
2733   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
2734   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
2735   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
2736   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
2737   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
2738   /* return pointer to global ordering of local dofs */
2739   *global_numbering_subset = temp_global_dofs;
2740   PetscFunctionReturn(0);
2741 }
2742 
2743 #undef __FUNCT__
2744 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
2745 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
2746 {
2747   PetscInt       i,j;
2748   PetscScalar    *alphas;
2749   PetscErrorCode ierr;
2750 
2751   PetscFunctionBegin;
2752   /* this implements stabilized Gram-Schmidt */
2753   ierr = PetscMalloc1(n,&alphas);CHKERRQ(ierr);
2754   for (i=0;i<n;i++) {
2755     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
2756     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
2757     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
2758   }
2759   ierr = PetscFree(alphas);CHKERRQ(ierr);
2760   PetscFunctionReturn(0);
2761 }
2762 
2763 #undef __FUNCT__
2764 #define __FUNCT__ "MatISGetSubassemblingPattern"
2765 PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscBool contiguous, IS* is_sends)
2766 {
2767   Mat             subdomain_adj;
2768   IS              new_ranks,ranks_send_to;
2769   MatPartitioning partitioner;
2770   Mat_IS          *matis;
2771   PetscInt        n_neighs,*neighs,*n_shared,**shared;
2772   PetscInt        prank;
2773   PetscMPIInt     size,rank,color;
2774   PetscInt        *xadj,*adjncy,*oldranks;
2775   PetscInt        *adjncy_wgt,*v_wgt,*is_indices,*ranks_send_to_idx;
2776   PetscInt        i,local_size,threshold=0;
2777   PetscErrorCode  ierr;
2778   PetscBool       use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
2779   PetscSubcomm    subcomm;
2780 
2781   PetscFunctionBegin;
2782   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_square",&use_square,NULL);CHKERRQ(ierr);
2783   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);CHKERRQ(ierr);
2784   ierr = PetscOptionsGetInt(NULL,"-matis_partitioning_threshold",&threshold,NULL);CHKERRQ(ierr);
2785 
2786   /* Get info on mapping */
2787   matis = (Mat_IS*)(mat->data);
2788   ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&local_size);CHKERRQ(ierr);
2789   ierr = ISLocalToGlobalMappingGetInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2790 
2791   /* build local CSR graph of subdomains' connectivity */
2792   ierr = PetscMalloc1(2,&xadj);CHKERRQ(ierr);
2793   xadj[0] = 0;
2794   xadj[1] = PetscMax(n_neighs-1,0);
2795   ierr = PetscMalloc1(xadj[1],&adjncy);CHKERRQ(ierr);
2796   ierr = PetscMalloc1(xadj[1],&adjncy_wgt);CHKERRQ(ierr);
2797 
2798   if (threshold) {
2799     PetscInt xadj_count = 0;
2800     for (i=1;i<n_neighs;i++) {
2801       if (n_shared[i] > threshold) {
2802         adjncy[xadj_count] = neighs[i];
2803         adjncy_wgt[xadj_count] = n_shared[i];
2804         xadj_count++;
2805       }
2806     }
2807     xadj[1] = xadj_count;
2808   } else {
2809     if (xadj[1]) {
2810       ierr = PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));CHKERRQ(ierr);
2811       ierr = PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));CHKERRQ(ierr);
2812     }
2813   }
2814   ierr = ISLocalToGlobalMappingRestoreInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2815   if (use_square) {
2816     for (i=0;i<xadj[1];i++) {
2817       adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
2818     }
2819   }
2820   ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2821 
2822   ierr = PetscMalloc1(1,&ranks_send_to_idx);CHKERRQ(ierr);
2823 
2824   /*
2825     Restrict work on active processes only.
2826   */
2827   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);CHKERRQ(ierr);
2828   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr); /* 2 groups, active process and not active processes */
2829   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
2830   ierr = PetscMPIIntCast(!local_size,&color);CHKERRQ(ierr);
2831   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2832   if (color) {
2833     ierr = PetscFree(xadj);CHKERRQ(ierr);
2834     ierr = PetscFree(adjncy);CHKERRQ(ierr);
2835     ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
2836   } else {
2837     PetscInt coarsening_ratio;
2838     ierr = MPI_Comm_size(subcomm->comm,&size);CHKERRQ(ierr);
2839     ierr = PetscMalloc1(size,&oldranks);CHKERRQ(ierr);
2840     prank = rank;
2841     ierr = MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm->comm);CHKERRQ(ierr);
2842     /*
2843     for (i=0;i<size;i++) {
2844       PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
2845     }
2846     */
2847     for (i=0;i<xadj[1];i++) {
2848       ierr = PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);CHKERRQ(ierr);
2849     }
2850     ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2851     ierr = MatCreateMPIAdj(subcomm->comm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);CHKERRQ(ierr);
2852     /* ierr = MatView(subdomain_adj,0);CHKERRQ(ierr); */
2853 
2854     /* Partition */
2855     ierr = MatPartitioningCreate(subcomm->comm,&partitioner);CHKERRQ(ierr);
2856     ierr = MatPartitioningSetAdjacency(partitioner,subdomain_adj);CHKERRQ(ierr);
2857     if (use_vwgt) {
2858       ierr = PetscMalloc1(1,&v_wgt);CHKERRQ(ierr);
2859       v_wgt[0] = local_size;
2860       ierr = MatPartitioningSetVertexWeights(partitioner,v_wgt);CHKERRQ(ierr);
2861     }
2862     n_subdomains = PetscMin((PetscInt)size,n_subdomains);
2863     coarsening_ratio = size/n_subdomains;
2864     ierr = MatPartitioningSetNParts(partitioner,n_subdomains);CHKERRQ(ierr);
2865     ierr = MatPartitioningSetFromOptions(partitioner);CHKERRQ(ierr);
2866     ierr = MatPartitioningApply(partitioner,&new_ranks);CHKERRQ(ierr);
2867     /* ierr = MatPartitioningView(partitioner,0);CHKERRQ(ierr); */
2868 
2869     ierr = ISGetIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2870     if (contiguous) {
2871       ranks_send_to_idx[0] = oldranks[is_indices[0]]; /* contiguos set of processes */
2872     } else {
2873       ranks_send_to_idx[0] = coarsening_ratio*oldranks[is_indices[0]]; /* scattered set of processes */
2874     }
2875     ierr = ISRestoreIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2876     /* clean up */
2877     ierr = PetscFree(oldranks);CHKERRQ(ierr);
2878     ierr = ISDestroy(&new_ranks);CHKERRQ(ierr);
2879     ierr = MatDestroy(&subdomain_adj);CHKERRQ(ierr);
2880     ierr = MatPartitioningDestroy(&partitioner);CHKERRQ(ierr);
2881   }
2882   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
2883 
2884   /* assemble parallel IS for sends */
2885   i = 1;
2886   if (color) i=0;
2887   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);CHKERRQ(ierr);
2888 
2889   /* get back IS */
2890   *is_sends = ranks_send_to;
2891   PetscFunctionReturn(0);
2892 }
2893 
2894 typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;
2895 
2896 #undef __FUNCT__
2897 #define __FUNCT__ "MatISSubassemble"
2898 PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
2899 {
2900   Mat                    local_mat;
2901   Mat_IS                 *matis;
2902   IS                     is_sends_internal;
2903   PetscInt               rows,cols,new_local_rows;
2904   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
2905   PetscBool              ismatis,isdense,newisdense,destroy_mat;
2906   ISLocalToGlobalMapping l2gmap;
2907   PetscInt*              l2gmap_indices;
2908   const PetscInt*        is_indices;
2909   MatType                new_local_type;
2910   /* buffers */
2911   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
2912   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
2913   PetscInt               *recv_buffer_idxs_local;
2914   PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
2915   /* MPI */
2916   MPI_Comm               comm,comm_n;
2917   PetscSubcomm           subcomm;
2918   PetscMPIInt            n_sends,n_recvs,commsize;
2919   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
2920   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
2921   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
2922   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
2923   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
2924   PetscErrorCode         ierr;
2925 
2926   PetscFunctionBegin;
2927   /* TODO: add missing checks */
2928   PetscValidLogicalCollectiveInt(mat,n_subdomains,3);
2929   PetscValidLogicalCollectiveBool(mat,restrict_comm,4);
2930   PetscValidLogicalCollectiveEnum(mat,reuse,5);
2931   PetscValidLogicalCollectiveInt(mat,nis,7);
2932   ierr = PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);CHKERRQ(ierr);
2933   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
2934   ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
2935   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);CHKERRQ(ierr);
2936   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
2937   ierr = MatGetSize(local_mat,&rows,&cols);CHKERRQ(ierr);
2938   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
2939   if (reuse == MAT_REUSE_MATRIX && *mat_n) {
2940     PetscInt mrows,mcols,mnrows,mncols;
2941     ierr = PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);CHKERRQ(ierr);
2942     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
2943     ierr = MatGetSize(mat,&mrows,&mcols);CHKERRQ(ierr);
2944     ierr = MatGetSize(*mat_n,&mnrows,&mncols);CHKERRQ(ierr);
2945     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
2946     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
2947   }
2948   ierr = MatGetBlockSize(local_mat,&bs);CHKERRQ(ierr);
2949   PetscValidLogicalCollectiveInt(mat,bs,0);
2950   /* prepare IS for sending if not provided */
2951   if (!is_sends) {
2952     PetscBool pcontig = PETSC_TRUE;
2953     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
2954     ierr = MatISGetSubassemblingPattern(mat,n_subdomains,pcontig,&is_sends_internal);CHKERRQ(ierr);
2955   } else {
2956     ierr = PetscObjectReference((PetscObject)is_sends);CHKERRQ(ierr);
2957     is_sends_internal = is_sends;
2958   }
2959 
2960   /* get pointer of MATIS data */
2961   matis = (Mat_IS*)mat->data;
2962 
2963   /* get comm */
2964   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2965 
2966   /* compute number of sends */
2967   ierr = ISGetLocalSize(is_sends_internal,&i);CHKERRQ(ierr);
2968   ierr = PetscMPIIntCast(i,&n_sends);CHKERRQ(ierr);
2969 
2970   /* compute number of receives */
2971   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
2972   ierr = PetscMalloc1(commsize,&iflags);CHKERRQ(ierr);
2973   ierr = PetscMemzero(iflags,commsize*sizeof(*iflags));CHKERRQ(ierr);
2974   ierr = ISGetIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
2975   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
2976   ierr = PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);CHKERRQ(ierr);
2977   ierr = PetscFree(iflags);CHKERRQ(ierr);
2978 
2979   /* restrict comm if requested */
2980   subcomm = 0;
2981   destroy_mat = PETSC_FALSE;
2982   if (restrict_comm) {
2983     PetscMPIInt color,rank,subcommsize;
2984     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2985     color = 0;
2986     if (n_sends && !n_recvs) color = 1; /* sending only processes will not partecipate in new comm */
2987     ierr = MPI_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
2988     subcommsize = commsize - subcommsize;
2989     /* check if reuse has been requested */
2990     if (reuse == MAT_REUSE_MATRIX) {
2991       if (*mat_n) {
2992         PetscMPIInt subcommsize2;
2993         ierr = MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);CHKERRQ(ierr);
2994         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
2995         comm_n = PetscObjectComm((PetscObject)*mat_n);
2996       } else {
2997         comm_n = PETSC_COMM_SELF;
2998       }
2999     } else { /* MAT_INITIAL_MATRIX */
3000       ierr = PetscSubcommCreate(comm,&subcomm);CHKERRQ(ierr);
3001       ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
3002       ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
3003       comm_n = subcomm->comm;
3004     }
3005     /* flag to destroy *mat_n if not significative */
3006     if (color) destroy_mat = PETSC_TRUE;
3007   } else {
3008     comm_n = comm;
3009   }
3010 
3011   /* prepare send/receive buffers */
3012   ierr = PetscMalloc1(commsize,&ilengths_idxs);CHKERRQ(ierr);
3013   ierr = PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));CHKERRQ(ierr);
3014   ierr = PetscMalloc1(commsize,&ilengths_vals);CHKERRQ(ierr);
3015   ierr = PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));CHKERRQ(ierr);
3016   if (nis) {
3017     ierr = PetscMalloc(commsize*sizeof(*ilengths_idxs_is),&ilengths_idxs_is);CHKERRQ(ierr);
3018     ierr = PetscMemzero(ilengths_idxs_is,commsize*sizeof(*ilengths_idxs_is));CHKERRQ(ierr);
3019   }
3020 
3021   /* Get data from local matrices */
3022   if (!isdense) {
3023     SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Subassembling of AIJ local matrices not yet implemented");
3024     /* TODO: See below some guidelines on how to prepare the local buffers */
3025     /*
3026        send_buffer_vals should contain the raw values of the local matrix
3027        send_buffer_idxs should contain:
3028        - MatType_PRIVATE type
3029        - PetscInt        size_of_l2gmap
3030        - PetscInt        global_row_indices[size_of_l2gmap]
3031        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
3032     */
3033   } else {
3034     ierr = MatDenseGetArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3035     ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&i);CHKERRQ(ierr);
3036     ierr = PetscMalloc1((i+2),&send_buffer_idxs);CHKERRQ(ierr);
3037     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
3038     send_buffer_idxs[1] = i;
3039     ierr = ISLocalToGlobalMappingGetIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
3040     ierr = PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));CHKERRQ(ierr);
3041     ierr = ISLocalToGlobalMappingRestoreIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
3042     ierr = PetscMPIIntCast(i,&len);CHKERRQ(ierr);
3043     for (i=0;i<n_sends;i++) {
3044       ilengths_vals[is_indices[i]] = len*len;
3045       ilengths_idxs[is_indices[i]] = len+2;
3046     }
3047   }
3048   ierr = PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);CHKERRQ(ierr);
3049   /* additional is (if any) */
3050   if (nis) {
3051     PetscMPIInt psum;
3052     PetscInt j;
3053     for (j=0,psum=0;j<nis;j++) {
3054       PetscInt plen;
3055       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
3056       ierr = PetscMPIIntCast(plen,&len);CHKERRQ(ierr);
3057       psum += len+1; /* indices + lenght */
3058     }
3059     ierr = PetscMalloc(psum*sizeof(PetscInt),&send_buffer_idxs_is);CHKERRQ(ierr);
3060     for (j=0,psum=0;j<nis;j++) {
3061       PetscInt plen;
3062       const PetscInt *is_array_idxs;
3063       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
3064       send_buffer_idxs_is[psum] = plen;
3065       ierr = ISGetIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
3066       ierr = PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));CHKERRQ(ierr);
3067       ierr = ISRestoreIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
3068       psum += plen+1; /* indices + lenght */
3069     }
3070     for (i=0;i<n_sends;i++) {
3071       ilengths_idxs_is[is_indices[i]] = psum;
3072     }
3073     ierr = PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);CHKERRQ(ierr);
3074   }
3075 
3076   buf_size_idxs = 0;
3077   buf_size_vals = 0;
3078   buf_size_idxs_is = 0;
3079   for (i=0;i<n_recvs;i++) {
3080     buf_size_idxs += (PetscInt)olengths_idxs[i];
3081     buf_size_vals += (PetscInt)olengths_vals[i];
3082     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
3083   }
3084   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);CHKERRQ(ierr);
3085   ierr = PetscMalloc1(buf_size_vals,&recv_buffer_vals);CHKERRQ(ierr);
3086   ierr = PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);CHKERRQ(ierr);
3087 
3088   /* get new tags for clean communications */
3089   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);CHKERRQ(ierr);
3090   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_vals);CHKERRQ(ierr);
3091   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);CHKERRQ(ierr);
3092 
3093   /* allocate for requests */
3094   ierr = PetscMalloc1(n_sends,&send_req_idxs);CHKERRQ(ierr);
3095   ierr = PetscMalloc1(n_sends,&send_req_vals);CHKERRQ(ierr);
3096   ierr = PetscMalloc1(n_sends,&send_req_idxs_is);CHKERRQ(ierr);
3097   ierr = PetscMalloc1(n_recvs,&recv_req_idxs);CHKERRQ(ierr);
3098   ierr = PetscMalloc1(n_recvs,&recv_req_vals);CHKERRQ(ierr);
3099   ierr = PetscMalloc1(n_recvs,&recv_req_idxs_is);CHKERRQ(ierr);
3100 
3101   /* communications */
3102   ptr_idxs = recv_buffer_idxs;
3103   ptr_vals = recv_buffer_vals;
3104   ptr_idxs_is = recv_buffer_idxs_is;
3105   for (i=0;i<n_recvs;i++) {
3106     source_dest = onodes[i];
3107     ierr = MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);CHKERRQ(ierr);
3108     ierr = MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);CHKERRQ(ierr);
3109     ptr_idxs += olengths_idxs[i];
3110     ptr_vals += olengths_vals[i];
3111     if (nis) {
3112       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);
3113       ptr_idxs_is += olengths_idxs_is[i];
3114     }
3115   }
3116   for (i=0;i<n_sends;i++) {
3117     ierr = PetscMPIIntCast(is_indices[i],&source_dest);CHKERRQ(ierr);
3118     ierr = MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);CHKERRQ(ierr);
3119     ierr = MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);CHKERRQ(ierr);
3120     if (nis) {
3121       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);
3122     }
3123   }
3124   ierr = ISRestoreIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
3125   ierr = ISDestroy(&is_sends_internal);CHKERRQ(ierr);
3126 
3127   /* assemble new l2g map */
3128   ierr = MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3129   ptr_idxs = recv_buffer_idxs;
3130   new_local_rows = 0;
3131   for (i=0;i<n_recvs;i++) {
3132     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3133     ptr_idxs += olengths_idxs[i];
3134   }
3135   ierr = PetscMalloc1(new_local_rows,&l2gmap_indices);CHKERRQ(ierr);
3136   ptr_idxs = recv_buffer_idxs;
3137   new_local_rows = 0;
3138   for (i=0;i<n_recvs;i++) {
3139     ierr = PetscMemcpy(&l2gmap_indices[new_local_rows],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));CHKERRQ(ierr);
3140     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3141     ptr_idxs += olengths_idxs[i];
3142   }
3143   ierr = PetscSortRemoveDupsInt(&new_local_rows,l2gmap_indices);CHKERRQ(ierr);
3144   ierr = ISLocalToGlobalMappingCreate(comm_n,1,new_local_rows,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);CHKERRQ(ierr);
3145   ierr = PetscFree(l2gmap_indices);CHKERRQ(ierr);
3146 
3147   /* infer new local matrix type from received local matrices type */
3148   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
3149   /* 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) */
3150   if (n_recvs) {
3151     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
3152     ptr_idxs = recv_buffer_idxs;
3153     for (i=0;i<n_recvs;i++) {
3154       if ((PetscInt)new_local_type_private != *ptr_idxs) {
3155         new_local_type_private = MATAIJ_PRIVATE;
3156         break;
3157       }
3158       ptr_idxs += olengths_idxs[i];
3159     }
3160     switch (new_local_type_private) {
3161       case MATDENSE_PRIVATE:
3162         if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
3163           new_local_type = MATSEQAIJ;
3164           bs = 1;
3165         } else { /* if I receive only 1 dense matrix */
3166           new_local_type = MATSEQDENSE;
3167           bs = 1;
3168         }
3169         break;
3170       case MATAIJ_PRIVATE:
3171         new_local_type = MATSEQAIJ;
3172         bs = 1;
3173         break;
3174       case MATBAIJ_PRIVATE:
3175         new_local_type = MATSEQBAIJ;
3176         break;
3177       case MATSBAIJ_PRIVATE:
3178         new_local_type = MATSEQSBAIJ;
3179         break;
3180       default:
3181         SETERRQ2(comm,PETSC_ERR_SUP,"Unsupported private type %d in %s",new_local_type_private,__FUNCT__);
3182         break;
3183     }
3184   } else { /* by default, new_local_type is seqdense */
3185     new_local_type = MATSEQDENSE;
3186     bs = 1;
3187   }
3188 
3189   /* create MATIS object if needed */
3190   if (reuse == MAT_INITIAL_MATRIX) {
3191     ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
3192     ierr = MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,mat_n);CHKERRQ(ierr);
3193   } else {
3194     /* it also destroys the local matrices */
3195     ierr = MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);CHKERRQ(ierr);
3196   }
3197   ierr = MatISGetLocalMat(*mat_n,&local_mat);CHKERRQ(ierr);
3198   ierr = MatSetType(local_mat,new_local_type);CHKERRQ(ierr);
3199 
3200   ierr = MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3201 
3202   /* Global to local map of received indices */
3203   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs_local);CHKERRQ(ierr); /* needed for values insertion */
3204   ierr = ISGlobalToLocalMappingApply(l2gmap,IS_GTOLM_MASK,buf_size_idxs,recv_buffer_idxs,&i,recv_buffer_idxs_local);CHKERRQ(ierr);
3205   ierr = ISLocalToGlobalMappingDestroy(&l2gmap);CHKERRQ(ierr);
3206 
3207   /* restore attributes -> type of incoming data and its size */
3208   buf_size_idxs = 0;
3209   for (i=0;i<n_recvs;i++) {
3210     recv_buffer_idxs_local[buf_size_idxs] = recv_buffer_idxs[buf_size_idxs];
3211     recv_buffer_idxs_local[buf_size_idxs+1] = recv_buffer_idxs[buf_size_idxs+1];
3212     buf_size_idxs += (PetscInt)olengths_idxs[i];
3213   }
3214   ierr = PetscFree(recv_buffer_idxs);CHKERRQ(ierr);
3215 
3216   /* set preallocation */
3217   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&newisdense);CHKERRQ(ierr);
3218   if (!newisdense) {
3219     PetscInt *new_local_nnz=0;
3220 
3221     ptr_vals = recv_buffer_vals;
3222     ptr_idxs = recv_buffer_idxs_local;
3223     if (n_recvs) {
3224       ierr = PetscCalloc1(new_local_rows,&new_local_nnz);CHKERRQ(ierr);
3225     }
3226     for (i=0;i<n_recvs;i++) {
3227       PetscInt j;
3228       if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
3229         for (j=0;j<*(ptr_idxs+1);j++) {
3230           new_local_nnz[*(ptr_idxs+2+j)] += *(ptr_idxs+1);
3231         }
3232       } else {
3233         /* TODO */
3234       }
3235       ptr_idxs += olengths_idxs[i];
3236     }
3237     if (new_local_nnz) {
3238       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMin(new_local_nnz[i],new_local_rows);
3239       ierr = MatSeqAIJSetPreallocation(local_mat,0,new_local_nnz);CHKERRQ(ierr);
3240       for (i=0;i<new_local_rows;i++) new_local_nnz[i] /= bs;
3241       ierr = MatSeqBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);CHKERRQ(ierr);
3242       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMax(new_local_nnz[i]-i,0);
3243       ierr = MatSeqSBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);CHKERRQ(ierr);
3244     } else {
3245       ierr = MatSetUp(local_mat);CHKERRQ(ierr);
3246     }
3247     ierr = PetscFree(new_local_nnz);CHKERRQ(ierr);
3248   } else {
3249     ierr = MatSetUp(local_mat);CHKERRQ(ierr);
3250   }
3251 
3252   /* set values */
3253   ptr_vals = recv_buffer_vals;
3254   ptr_idxs = recv_buffer_idxs_local;
3255   for (i=0;i<n_recvs;i++) {
3256     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
3257       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
3258       ierr = MatSetValues(local_mat,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);CHKERRQ(ierr);
3259       ierr = MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3260       ierr = MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3261       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
3262     } else {
3263       /* TODO */
3264     }
3265     ptr_idxs += olengths_idxs[i];
3266     ptr_vals += olengths_vals[i];
3267   }
3268   ierr = MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3269   ierr = MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3270   ierr = MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3271   ierr = MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3272   ierr = PetscFree(recv_buffer_vals);CHKERRQ(ierr);
3273   ierr = PetscFree(recv_buffer_idxs_local);CHKERRQ(ierr);
3274 
3275 #if 0
3276   if (!restrict_comm) { /* check */
3277     Vec       lvec,rvec;
3278     PetscReal infty_error;
3279 
3280     ierr = MatCreateVecs(mat,&rvec,&lvec);CHKERRQ(ierr);
3281     ierr = VecSetRandom(rvec,NULL);CHKERRQ(ierr);
3282     ierr = MatMult(mat,rvec,lvec);CHKERRQ(ierr);
3283     ierr = VecScale(lvec,-1.0);CHKERRQ(ierr);
3284     ierr = MatMultAdd(*mat_n,rvec,lvec,lvec);CHKERRQ(ierr);
3285     ierr = VecNorm(lvec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3286     ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
3287     ierr = VecDestroy(&rvec);CHKERRQ(ierr);
3288     ierr = VecDestroy(&lvec);CHKERRQ(ierr);
3289   }
3290 #endif
3291 
3292   /* assemble new additional is (if any) */
3293   if (nis) {
3294     PetscInt **temp_idxs,*count_is,j,psum;
3295 
3296     ierr = MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3297     ierr = PetscMalloc(nis*sizeof(PetscInt),&count_is);CHKERRQ(ierr);
3298     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3299     ptr_idxs = recv_buffer_idxs_is;
3300     psum = 0;
3301     for (i=0;i<n_recvs;i++) {
3302       for (j=0;j<nis;j++) {
3303         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3304         count_is[j] += plen; /* increment counting of buffer for j-th IS */
3305         psum += plen;
3306         ptr_idxs += plen+1; /* shift pointer to received data */
3307       }
3308     }
3309     ierr = PetscMalloc(nis*sizeof(PetscInt*),&temp_idxs);CHKERRQ(ierr);
3310     ierr = PetscMalloc(psum*sizeof(PetscInt),&temp_idxs[0]);CHKERRQ(ierr);
3311     for (i=1;i<nis;i++) {
3312       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
3313     }
3314     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3315     ptr_idxs = recv_buffer_idxs_is;
3316     for (i=0;i<n_recvs;i++) {
3317       for (j=0;j<nis;j++) {
3318         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3319         ierr = PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));CHKERRQ(ierr);
3320         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
3321         ptr_idxs += plen+1; /* shift pointer to received data */
3322       }
3323     }
3324     for (i=0;i<nis;i++) {
3325       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3326       ierr = PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);CHKERRQ(ierr);CHKERRQ(ierr);
3327       ierr = ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3328     }
3329     ierr = PetscFree(count_is);CHKERRQ(ierr);
3330     ierr = PetscFree(temp_idxs[0]);CHKERRQ(ierr);
3331     ierr = PetscFree(temp_idxs);CHKERRQ(ierr);
3332   }
3333   /* free workspace */
3334   ierr = PetscFree(recv_buffer_idxs_is);CHKERRQ(ierr);
3335   ierr = MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3336   ierr = PetscFree(send_buffer_idxs);CHKERRQ(ierr);
3337   ierr = MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3338   if (isdense) {
3339     ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
3340     ierr = MatDenseRestoreArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3341   } else {
3342     /* ierr = PetscFree(send_buffer_vals);CHKERRQ(ierr); */
3343   }
3344   if (nis) {
3345     ierr = MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3346     ierr = PetscFree(send_buffer_idxs_is);CHKERRQ(ierr);
3347   }
3348   ierr = PetscFree(recv_req_idxs);CHKERRQ(ierr);
3349   ierr = PetscFree(recv_req_vals);CHKERRQ(ierr);
3350   ierr = PetscFree(recv_req_idxs_is);CHKERRQ(ierr);
3351   ierr = PetscFree(send_req_idxs);CHKERRQ(ierr);
3352   ierr = PetscFree(send_req_vals);CHKERRQ(ierr);
3353   ierr = PetscFree(send_req_idxs_is);CHKERRQ(ierr);
3354   ierr = PetscFree(ilengths_vals);CHKERRQ(ierr);
3355   ierr = PetscFree(ilengths_idxs);CHKERRQ(ierr);
3356   ierr = PetscFree(olengths_vals);CHKERRQ(ierr);
3357   ierr = PetscFree(olengths_idxs);CHKERRQ(ierr);
3358   ierr = PetscFree(onodes);CHKERRQ(ierr);
3359   if (nis) {
3360     ierr = PetscFree(ilengths_idxs_is);CHKERRQ(ierr);
3361     ierr = PetscFree(olengths_idxs_is);CHKERRQ(ierr);
3362     ierr = PetscFree(onodes_is);CHKERRQ(ierr);
3363   }
3364   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
3365   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
3366     ierr = MatDestroy(mat_n);CHKERRQ(ierr);
3367     for (i=0;i<nis;i++) {
3368       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3369     }
3370   }
3371   PetscFunctionReturn(0);
3372 }
3373 
3374 /* temporary hack into ksp private data structure */
3375 #include <petsc-private/kspimpl.h>
3376 
3377 #undef __FUNCT__
3378 #define __FUNCT__ "PCBDDCSetUpCoarseSolver"
3379 PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
3380 {
3381   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
3382   PC_IS                  *pcis = (PC_IS*)pc->data;
3383   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
3384   MatNullSpace           CoarseNullSpace=NULL;
3385   ISLocalToGlobalMapping coarse_islg;
3386   IS                     coarse_is,*isarray;
3387   PetscInt               i,im_active=-1,active_procs=-1;
3388   PetscInt               nis,nisdofs,nisneu;
3389   PC                     pc_temp;
3390   PCType                 coarse_pc_type;
3391   KSPType                coarse_ksp_type;
3392   PetscBool              multilevel_requested,multilevel_allowed;
3393   PetscBool              isredundant,isbddc,isnn,coarse_reuse;
3394   Mat                    t_coarse_mat_is;
3395   PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
3396   PetscMPIInt            all_procs;
3397   PetscBool              csin_ml,csin_ds,csin,csin_type_simple,redist;
3398   PetscBool              compute_vecs = PETSC_FALSE;
3399   PetscScalar            *array;
3400   PetscErrorCode         ierr;
3401 
3402   PetscFunctionBegin;
3403   /* Assign global numbering to coarse dofs */
3404   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 */
3405     compute_vecs = PETSC_TRUE;
3406     PetscInt ocoarse_size;
3407     ocoarse_size = pcbddc->coarse_size;
3408     ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
3409     ierr = PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);CHKERRQ(ierr);
3410     /* see if we can avoid some work */
3411     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
3412       if (ocoarse_size != pcbddc->coarse_size) { /* ...but with different size, so reset it and set reuse flag to false */
3413         ierr = KSPReset(pcbddc->coarse_ksp);CHKERRQ(ierr);
3414         coarse_reuse = PETSC_FALSE;
3415       } else { /* we can safely reuse already computed coarse matrix */
3416         coarse_reuse = PETSC_TRUE;
3417       }
3418     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
3419       coarse_reuse = PETSC_FALSE;
3420     }
3421     /* reset any subassembling information */
3422     ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3423     ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3424   } else { /* primal space is unchanged, so we can reuse coarse matrix */
3425     coarse_reuse = PETSC_TRUE;
3426   }
3427 
3428   /* count "active" (i.e. with positive local size) and "void" processes */
3429   im_active = !!(pcis->n);
3430   ierr = MPI_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3431   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);CHKERRQ(ierr);
3432   void_procs = all_procs-active_procs;
3433   csin_type_simple = PETSC_TRUE;
3434   redist = PETSC_FALSE;
3435   if (pcbddc->current_level && void_procs) {
3436     csin_ml = PETSC_TRUE;
3437     ncoarse_ml = void_procs;
3438     csin_ds = PETSC_TRUE;
3439     ncoarse_ds = void_procs;
3440   } else {
3441     csin_ml = PETSC_FALSE;
3442     ncoarse_ml = all_procs;
3443     if (void_procs) {
3444       csin_ds = PETSC_TRUE;
3445       ncoarse_ds = void_procs;
3446       csin_type_simple = PETSC_FALSE;
3447     } else {
3448       if (pcbddc->redistribute_coarse && pcbddc->redistribute_coarse < all_procs) {
3449         csin_ds = PETSC_TRUE;
3450         ncoarse_ds = pcbddc->redistribute_coarse;
3451         redist = PETSC_TRUE;
3452       } else {
3453         csin_ds = PETSC_FALSE;
3454         ncoarse_ds = all_procs;
3455       }
3456     }
3457   }
3458 
3459   /*
3460     test if we can go multilevel: three conditions must be satisfied:
3461     - we have not exceeded the number of levels requested
3462     - we can actually subassemble the active processes
3463     - we can find a suitable number of MPI processes where we can place the subassembled problem
3464   */
3465   multilevel_allowed = PETSC_FALSE;
3466   multilevel_requested = PETSC_FALSE;
3467   if (pcbddc->current_level < pcbddc->max_levels) {
3468     multilevel_requested = PETSC_TRUE;
3469     if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
3470       multilevel_allowed = PETSC_FALSE;
3471     } else {
3472       multilevel_allowed = PETSC_TRUE;
3473     }
3474   }
3475   /* determine number of process partecipating to coarse solver */
3476   if (multilevel_allowed) {
3477     ncoarse = ncoarse_ml;
3478     csin = csin_ml;
3479   } else {
3480     ncoarse = ncoarse_ds;
3481     csin = csin_ds;
3482   }
3483 
3484   /* creates temporary l2gmap and IS for coarse indexes */
3485   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);CHKERRQ(ierr);
3486   ierr = ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);CHKERRQ(ierr);
3487 
3488   /* creates temporary MATIS object for coarse matrix */
3489   ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,NULL,&coarse_submat_dense);CHKERRQ(ierr);
3490   ierr = MatDenseGetArray(coarse_submat_dense,&array);CHKERRQ(ierr);
3491   ierr = PetscMemcpy(array,coarse_submat_vals,sizeof(*coarse_submat_vals)*pcbddc->local_primal_size*pcbddc->local_primal_size);CHKERRQ(ierr);
3492   ierr = MatDenseRestoreArray(coarse_submat_dense,&array);CHKERRQ(ierr);
3493 #if 0
3494   {
3495     PetscViewer viewer;
3496     char filename[256];
3497     sprintf(filename,"local_coarse_mat%d.m",PetscGlobalRank);
3498     ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
3499     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3500     ierr = MatView(coarse_submat_dense,viewer);CHKERRQ(ierr);
3501     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3502   }
3503 #endif
3504   ierr = MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,&t_coarse_mat_is);CHKERRQ(ierr);
3505   ierr = MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);CHKERRQ(ierr);
3506   ierr = MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3507   ierr = MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3508   ierr = MatDestroy(&coarse_submat_dense);CHKERRQ(ierr);
3509 
3510   /* compute dofs splitting and neumann boundaries for coarse dofs */
3511   if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal) ) { /* protects from unneded computations */
3512     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
3513     const PetscInt         *idxs;
3514     ISLocalToGlobalMapping tmap;
3515 
3516     /* create map between primal indices (in local representative ordering) and local primal numbering */
3517     ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);CHKERRQ(ierr);
3518     /* allocate space for temporary storage */
3519     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs);CHKERRQ(ierr);
3520     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs2);CHKERRQ(ierr);
3521     /* allocate for IS array */
3522     nisdofs = pcbddc->n_ISForDofsLocal;
3523     nisneu = !!pcbddc->NeumannBoundariesLocal;
3524     nis = nisdofs + nisneu;
3525     ierr = PetscMalloc(nis*sizeof(IS),&isarray);CHKERRQ(ierr);
3526     /* dofs splitting */
3527     for (i=0;i<nisdofs;i++) {
3528       /* ierr = ISView(pcbddc->ISForDofsLocal[i],0);CHKERRQ(ierr); */
3529       ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);CHKERRQ(ierr);
3530       ierr = ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3531       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3532       ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3533       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3534       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->ISForDofsLocal[i]),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3535       /* ierr = ISView(isarray[i],0);CHKERRQ(ierr); */
3536     }
3537     /* neumann boundaries */
3538     if (pcbddc->NeumannBoundariesLocal) {
3539       /* ierr = ISView(pcbddc->NeumannBoundariesLocal,0);CHKERRQ(ierr); */
3540       ierr = ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);CHKERRQ(ierr);
3541       ierr = ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3542       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3543       ierr = ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3544       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3545       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->NeumannBoundariesLocal),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);CHKERRQ(ierr);
3546       /* ierr = ISView(isarray[nisdofs],0);CHKERRQ(ierr); */
3547     }
3548     /* free memory */
3549     ierr = PetscFree(tidxs);CHKERRQ(ierr);
3550     ierr = PetscFree(tidxs2);CHKERRQ(ierr);
3551     ierr = ISLocalToGlobalMappingDestroy(&tmap);CHKERRQ(ierr);
3552   } else {
3553     nis = 0;
3554     nisdofs = 0;
3555     nisneu = 0;
3556     isarray = NULL;
3557   }
3558   /* destroy no longer needed map */
3559   ierr = ISLocalToGlobalMappingDestroy(&coarse_islg);CHKERRQ(ierr);
3560 
3561   /* restrict on coarse candidates (if needed) */
3562   coarse_mat_is = NULL;
3563   if (csin) {
3564     if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
3565       if (redist) {
3566         PetscMPIInt rank;
3567         PetscInt spc,n_spc_p1,dest[1];
3568 
3569         ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
3570         spc = all_procs/pcbddc->redistribute_coarse;
3571         n_spc_p1 = all_procs%pcbddc->redistribute_coarse;
3572         if (rank > n_spc_p1*(spc+1)-1) {
3573           dest[0] = n_spc_p1+(rank-(n_spc_p1*(spc+1)))/spc;
3574         } else {
3575           dest[0] = rank/(spc+1);
3576         }
3577         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),1,dest,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3578         ierr = ISView(pcbddc->coarse_subassembling_init,NULL);CHKERRQ(ierr);
3579       } else {
3580         PetscInt j,tissize,*nisindices;
3581         PetscInt *coarse_candidates;
3582         const PetscInt* tisindices;
3583         /* get coarse candidates' ranks in pc communicator */
3584         ierr = PetscMalloc(all_procs*sizeof(PetscInt),&coarse_candidates);CHKERRQ(ierr);
3585         ierr = MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3586         for (i=0,j=0;i<all_procs;i++) {
3587           if (!coarse_candidates[i]) {
3588             coarse_candidates[j]=i;
3589             j++;
3590           }
3591         }
3592         if (j < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",j,ncoarse);
3593         /* get a suitable subassembling pattern */
3594         if (csin_type_simple) {
3595           PetscMPIInt rank;
3596           PetscInt    issize,isidx;
3597           ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
3598           if (im_active) {
3599             issize = 1;
3600             isidx = (PetscInt)rank;
3601           } else {
3602             issize = 0;
3603             isidx = -1;
3604           }
3605           ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3606         } else {
3607           ierr = MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,PETSC_TRUE,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3608         }
3609         if (pcbddc->dbg_flag) {
3610           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3611           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");CHKERRQ(ierr);
3612           ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3613           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");CHKERRQ(ierr);
3614           for (i=0;i<j;i++) {
3615             ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);CHKERRQ(ierr);
3616           }
3617           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");CHKERRQ(ierr);
3618           ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3619         }
3620         /* shift the pattern on coarse candidates */
3621         ierr = ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);CHKERRQ(ierr);
3622         ierr = ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3623         ierr = PetscMalloc(tissize*sizeof(PetscInt),&nisindices);CHKERRQ(ierr);
3624         for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
3625         ierr = ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3626         ierr = ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);CHKERRQ(ierr);
3627         ierr = PetscFree(coarse_candidates);CHKERRQ(ierr);
3628       }
3629     }
3630     if (pcbddc->dbg_flag) {
3631       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3632       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");CHKERRQ(ierr);
3633       ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3634       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3635     }
3636     /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
3637     ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
3638   } else {
3639     if (pcbddc->dbg_flag) {
3640       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3641       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");CHKERRQ(ierr);
3642       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3643     }
3644     ierr = PetscObjectReference((PetscObject)t_coarse_mat_is);CHKERRQ(ierr);
3645     coarse_mat_is = t_coarse_mat_is;
3646   }
3647 
3648   /* create local to global scatters for coarse problem */
3649   if (compute_vecs) {
3650     PetscInt lrows;
3651     ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
3652     if (coarse_mat_is) {
3653       ierr = MatGetLocalSize(coarse_mat_is,&lrows,NULL);CHKERRQ(ierr);
3654     } else {
3655       lrows = 0;
3656     }
3657     ierr = VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);CHKERRQ(ierr);
3658     ierr = VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);CHKERRQ(ierr);
3659     ierr = VecSetType(pcbddc->coarse_vec,VECSTANDARD);CHKERRQ(ierr);
3660     ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3661     ierr = VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3662   }
3663   ierr = ISDestroy(&coarse_is);CHKERRQ(ierr);
3664   ierr = MatDestroy(&t_coarse_mat_is);CHKERRQ(ierr);
3665 
3666   /* set defaults for coarse KSP and PC */
3667   if (multilevel_allowed) {
3668     coarse_ksp_type = KSPRICHARDSON;
3669     coarse_pc_type = PCBDDC;
3670   } else {
3671     coarse_ksp_type = KSPPREONLY;
3672     coarse_pc_type = PCREDUNDANT;
3673   }
3674 
3675   /* print some info if requested */
3676   if (pcbddc->dbg_flag) {
3677     if (!multilevel_allowed) {
3678       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3679       if (multilevel_requested) {
3680         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);
3681       } else if (pcbddc->max_levels) {
3682         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);CHKERRQ(ierr);
3683       }
3684       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3685     }
3686   }
3687 
3688   /* create the coarse KSP object only once with defaults */
3689   if (coarse_mat_is) {
3690     MatReuse coarse_mat_reuse;
3691     PetscViewer dbg_viewer = NULL;
3692     if (pcbddc->dbg_flag) {
3693       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
3694       ierr = PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3695     }
3696     if (!pcbddc->coarse_ksp) {
3697       char prefix[256],str_level[16];
3698       size_t len;
3699       ierr = KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);CHKERRQ(ierr);
3700       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3701       ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
3702       ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);CHKERRQ(ierr);
3703       ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3704       ierr = KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);CHKERRQ(ierr);
3705       ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3706       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3707       /* prefix */
3708       ierr = PetscStrcpy(prefix,"");CHKERRQ(ierr);
3709       ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
3710       if (!pcbddc->current_level) {
3711         ierr = PetscStrcpy(prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
3712         ierr = PetscStrcat(prefix,"pc_bddc_coarse_");CHKERRQ(ierr);
3713       } else {
3714         ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
3715         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
3716         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
3717         ierr = PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
3718         sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
3719         ierr = PetscStrcat(prefix,str_level);CHKERRQ(ierr);
3720       }
3721       ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);CHKERRQ(ierr);
3722       /* allow user customization */
3723       ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3724       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
3725     }
3726 
3727     /* get some info after set from options */
3728     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3729     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);CHKERRQ(ierr);
3730     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);CHKERRQ(ierr);
3731     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);CHKERRQ(ierr);
3732     if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
3733       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3734       isbddc = PETSC_FALSE;
3735     }
3736     if (isredundant) {
3737       KSP inner_ksp;
3738       PC inner_pc;
3739       ierr = PCRedundantGetKSP(pc_temp,&inner_ksp);CHKERRQ(ierr);
3740       ierr = KSPGetPC(inner_ksp,&inner_pc);CHKERRQ(ierr);
3741       ierr = PCFactorSetReuseFill(inner_pc,PETSC_TRUE);CHKERRQ(ierr);
3742     }
3743 
3744     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
3745     ierr = PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);CHKERRQ(ierr);
3746     ierr = PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);CHKERRQ(ierr);
3747     ierr = PCBDDCSetLevels(pc_temp,pcbddc->max_levels);CHKERRQ(ierr);
3748     if (nisdofs) {
3749       ierr = PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);CHKERRQ(ierr);
3750       for (i=0;i<nisdofs;i++) {
3751         ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3752       }
3753     }
3754     if (nisneu) {
3755       ierr = PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);CHKERRQ(ierr);
3756       ierr = ISDestroy(&isarray[nisdofs]);CHKERRQ(ierr);
3757     }
3758 
3759     /* assemble coarse matrix */
3760     if (coarse_reuse) {
3761       ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
3762       ierr = PetscObjectReference((PetscObject)coarse_mat);CHKERRQ(ierr);
3763       coarse_mat_reuse = MAT_REUSE_MATRIX;
3764     } else {
3765       coarse_mat_reuse = MAT_INITIAL_MATRIX;
3766     }
3767     if (isbddc || isnn) {
3768       if (pcbddc->coarsening_ratio > 1) {
3769         if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
3770           ierr = MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,PETSC_TRUE,&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3771           if (pcbddc->dbg_flag) {
3772             ierr = PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3773             ierr = PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");CHKERRQ(ierr);
3774             ierr = ISView(pcbddc->coarse_subassembling,dbg_viewer);CHKERRQ(ierr);
3775             ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3776           }
3777         }
3778         ierr = MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);CHKERRQ(ierr);
3779       } else {
3780         ierr = PetscObjectReference((PetscObject)coarse_mat_is);CHKERRQ(ierr);
3781         coarse_mat = coarse_mat_is;
3782       }
3783     } else {
3784       ierr = MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);CHKERRQ(ierr);
3785     }
3786     ierr = MatDestroy(&coarse_mat_is);CHKERRQ(ierr);
3787 
3788     /* propagate symmetry info to coarse matrix */
3789     ierr = MatSetOption(coarse_mat,MAT_SYMMETRIC,pcbddc->issym);CHKERRQ(ierr);
3790     ierr = MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
3791 
3792     /* set operators */
3793     ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3794     if (pcbddc->dbg_flag) {
3795       ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3796     }
3797   } else { /* processes non partecipating to coarse solver (if any) */
3798     coarse_mat = 0;
3799   }
3800   ierr = PetscFree(isarray);CHKERRQ(ierr);
3801 #if 0
3802   {
3803     PetscViewer viewer;
3804     char filename[256];
3805     sprintf(filename,"coarse_mat.m");
3806     ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,&viewer);CHKERRQ(ierr);
3807     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3808     ierr = MatView(coarse_mat,viewer);CHKERRQ(ierr);
3809     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3810   }
3811 #endif
3812 
3813   /* Compute coarse null space (special handling by BDDC only) */
3814   if (pcbddc->NullSpace) {
3815     ierr = PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);CHKERRQ(ierr);
3816   }
3817 
3818   if (pcbddc->coarse_ksp) {
3819     Vec crhs,csol;
3820     PetscBool ispreonly;
3821     if (CoarseNullSpace) {
3822       if (isbddc) {
3823         ierr = PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);CHKERRQ(ierr);
3824       } else {
3825         ierr = KSPSetNullSpace(pcbddc->coarse_ksp,CoarseNullSpace);CHKERRQ(ierr);
3826       }
3827     }
3828     /* setup coarse ksp */
3829     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3830     ierr = KSPGetSolution(pcbddc->coarse_ksp,&csol);CHKERRQ(ierr);
3831     ierr = KSPGetRhs(pcbddc->coarse_ksp,&crhs);CHKERRQ(ierr);
3832     /* hack */
3833     if (!csol) {
3834       ierr = MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);CHKERRQ(ierr);
3835     }
3836     if (!crhs) {
3837       ierr = MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));CHKERRQ(ierr);
3838     }
3839     /* Check coarse problem if in debug mode or if solving with an iterative method */
3840     ierr = PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);CHKERRQ(ierr);
3841     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
3842       KSP       check_ksp;
3843       KSPType   check_ksp_type;
3844       PC        check_pc;
3845       Vec       check_vec,coarse_vec;
3846       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
3847       PetscInt  its;
3848       PetscBool compute_eigs;
3849       PetscReal *eigs_r,*eigs_c;
3850       PetscInt  neigs;
3851       const char *prefix;
3852 
3853       /* Create ksp object suitable for estimation of extreme eigenvalues */
3854       ierr = KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);CHKERRQ(ierr);
3855       ierr = KSPSetOperators(check_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3856       ierr = KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3857       if (ispreonly) {
3858         check_ksp_type = KSPPREONLY;
3859         compute_eigs = PETSC_FALSE;
3860       } else {
3861         check_ksp_type = KSPGMRES;
3862         compute_eigs = PETSC_TRUE;
3863       }
3864       ierr = KSPSetType(check_ksp,check_ksp_type);CHKERRQ(ierr);
3865       ierr = KSPSetComputeSingularValues(check_ksp,compute_eigs);CHKERRQ(ierr);
3866       ierr = KSPSetComputeEigenvalues(check_ksp,compute_eigs);CHKERRQ(ierr);
3867       ierr = KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);CHKERRQ(ierr);
3868       ierr = KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);CHKERRQ(ierr);
3869       ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
3870       ierr = KSPAppendOptionsPrefix(check_ksp,"check_");CHKERRQ(ierr);
3871       ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
3872       ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
3873       ierr = KSPGetPC(pcbddc->coarse_ksp,&check_pc);CHKERRQ(ierr);
3874       ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
3875       /* create random vec */
3876       ierr = KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);CHKERRQ(ierr);
3877       ierr = VecDuplicate(coarse_vec,&check_vec);CHKERRQ(ierr);
3878       ierr = VecSetRandom(check_vec,NULL);CHKERRQ(ierr);
3879       if (CoarseNullSpace) {
3880         ierr = MatNullSpaceRemove(CoarseNullSpace,check_vec);CHKERRQ(ierr);
3881       }
3882       ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3883       /* solve coarse problem */
3884       ierr = KSPSolve(check_ksp,coarse_vec,coarse_vec);CHKERRQ(ierr);
3885       if (CoarseNullSpace) {
3886         ierr = MatNullSpaceRemove(CoarseNullSpace,coarse_vec);CHKERRQ(ierr);
3887       }
3888       /* set eigenvalue estimation if preonly has not been requested */
3889       if (compute_eigs) {
3890         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_r);CHKERRQ(ierr);
3891         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_c);CHKERRQ(ierr);
3892         ierr = KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);CHKERRQ(ierr);
3893         lambda_max = eigs_r[neigs-1];
3894         lambda_min = eigs_r[0];
3895         if (pcbddc->use_coarse_estimates) {
3896           if (lambda_max>lambda_min) {
3897             ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3898             ierr = KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));CHKERRQ(ierr);
3899           }
3900         }
3901       }
3902 
3903       /* check coarse problem residual error */
3904       if (pcbddc->dbg_flag) {
3905         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
3906         ierr = PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3907         ierr = VecAXPY(check_vec,-1.0,coarse_vec);CHKERRQ(ierr);
3908         ierr = VecNorm(check_vec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3909         ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3910         ierr = VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);CHKERRQ(ierr);
3911         ierr = VecDestroy(&check_vec);CHKERRQ(ierr);
3912         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (%d)\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
3913         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);CHKERRQ(ierr);
3914         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);CHKERRQ(ierr);
3915         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);CHKERRQ(ierr);
3916         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);CHKERRQ(ierr);
3917         if (compute_eigs) {
3918           PetscReal lambda_max_s,lambda_min_s;
3919           ierr = KSPGetType(check_ksp,&check_ksp_type);CHKERRQ(ierr);
3920           ierr = KSPGetIterationNumber(check_ksp,&its);CHKERRQ(ierr);
3921           ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);CHKERRQ(ierr);
3922           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);
3923           for (i=0;i<neigs;i++) {
3924             ierr = PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);CHKERRQ(ierr);
3925           }
3926         }
3927         ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3928         ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3929       }
3930       ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
3931       if (compute_eigs) {
3932         ierr = PetscFree(eigs_r);CHKERRQ(ierr);
3933         ierr = PetscFree(eigs_c);CHKERRQ(ierr);
3934       }
3935     }
3936   }
3937   /* print additional info */
3938   if (pcbddc->dbg_flag) {
3939     /* waits until all processes reaches this point */
3940     ierr = PetscBarrier((PetscObject)pc);CHKERRQ(ierr);
3941     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);CHKERRQ(ierr);
3942     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3943   }
3944 
3945   /* free memory */
3946   ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
3947   ierr = MatDestroy(&coarse_mat);CHKERRQ(ierr);
3948   PetscFunctionReturn(0);
3949 }
3950 
3951 #undef __FUNCT__
3952 #define __FUNCT__ "PCBDDCComputePrimalNumbering"
3953 PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
3954 {
3955   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
3956   PC_IS*         pcis = (PC_IS*)pc->data;
3957   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
3958   PetscInt       i,coarse_size;
3959   PetscInt       *local_primal_indices;
3960   PetscErrorCode ierr;
3961 
3962   PetscFunctionBegin;
3963   /* Compute global number of coarse dofs */
3964   if (!pcbddc->primal_indices_local_idxs && pcbddc->local_primal_size) {
3965     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Local primal indices have not been created");
3966   }
3967   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);
3968 
3969   /* check numbering */
3970   if (pcbddc->dbg_flag) {
3971     PetscScalar coarsesum,*array;
3972     PetscBool set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;
3973 
3974     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3975     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3976     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");CHKERRQ(ierr);
3977     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
3978     ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
3979     for (i=0;i<pcbddc->local_primal_size;i++) {
3980       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
3981     }
3982     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
3983     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
3984     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3985     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3986     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3987     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3988     ierr = VecScatterEnd(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3989     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3990     for (i=0;i<pcis->n;i++) {
3991       if (array[i] == 1.0) {
3992         set_error = PETSC_TRUE;
3993         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a single process!\n",PetscGlobalRank,i);CHKERRQ(ierr);
3994       }
3995     }
3996     ierr = MPI_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3997     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3998     for (i=0;i<pcis->n;i++) {
3999       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
4000     }
4001     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4002     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4003     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4004     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4005     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
4006     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));CHKERRQ(ierr);
4007     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
4008       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");CHKERRQ(ierr);
4009       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4010       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
4011       for (i=0;i<pcbddc->local_primal_size;i++) {
4012         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%d]=%d (%d)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i]);
4013       }
4014       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4015     }
4016     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4017     if (set_error_reduced) {
4018       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
4019     }
4020   }
4021   /* get back data */
4022   *coarse_size_n = coarse_size;
4023   *local_primal_indices_n = local_primal_indices;
4024   PetscFunctionReturn(0);
4025 }
4026 
4027 #undef __FUNCT__
4028 #define __FUNCT__ "PCBDDCGlobalToLocal"
4029 PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
4030 {
4031   IS             localis_t;
4032   PetscInt       i,lsize,*idxs,n;
4033   PetscScalar    *vals;
4034   PetscErrorCode ierr;
4035 
4036   PetscFunctionBegin;
4037   /* get indices in local ordering exploiting local to global map */
4038   ierr = ISGetLocalSize(globalis,&lsize);CHKERRQ(ierr);
4039   ierr = PetscMalloc(lsize*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
4040   for (i=0;i<lsize;i++) vals[i] = 1.0;
4041   ierr = ISGetIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
4042   ierr = VecSet(gwork,0.0);CHKERRQ(ierr);
4043   ierr = VecSet(lwork,0.0);CHKERRQ(ierr);
4044   if (idxs) { /* multilevel guard */
4045     ierr = VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
4046   }
4047   ierr = VecAssemblyBegin(gwork);CHKERRQ(ierr);
4048   ierr = ISRestoreIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
4049   ierr = PetscFree(vals);CHKERRQ(ierr);
4050   ierr = VecAssemblyEnd(gwork);CHKERRQ(ierr);
4051   /* now compute set in local ordering */
4052   ierr = VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4053   ierr = VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4054   ierr = VecGetArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
4055   ierr = VecGetSize(lwork,&n);CHKERRQ(ierr);
4056   for (i=0,lsize=0;i<n;i++) {
4057     if (PetscRealPart(vals[i]) > 0.5) {
4058       lsize++;
4059     }
4060   }
4061   ierr = PetscMalloc(lsize*sizeof(PetscInt),&idxs);CHKERRQ(ierr);
4062   for (i=0,lsize=0;i<n;i++) {
4063     if (PetscRealPart(vals[i]) > 0.5) {
4064       idxs[lsize++] = i;
4065     }
4066   }
4067   ierr = VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
4068   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);CHKERRQ(ierr);
4069   *localis = localis_t;
4070   PetscFunctionReturn(0);
4071 }
4072 
4073 /* the next two functions will be called in KSPMatMult if a change of basis has been requested */
4074 #undef __FUNCT__
4075 #define __FUNCT__ "PCBDDCMatMult_Private"
4076 static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y)
4077 {
4078   PCBDDCChange_ctx change_ctx;
4079   PetscErrorCode   ierr;
4080 
4081   PetscFunctionBegin;
4082   ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
4083   ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
4084   ierr = MatMult(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
4085   ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
4086   PetscFunctionReturn(0);
4087 }
4088 
4089 #undef __FUNCT__
4090 #define __FUNCT__ "PCBDDCMatMultTranspose_Private"
4091 static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y)
4092 {
4093   PCBDDCChange_ctx change_ctx;
4094   PetscErrorCode   ierr;
4095 
4096   PetscFunctionBegin;
4097   ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
4098   ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
4099   ierr = MatMultTranspose(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
4100   ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
4101   PetscFunctionReturn(0);
4102 }
4103