xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision fa4347430b1c47e767b475a4523ef660315dd0ce)
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       if (!pcbddc->use_qr_single) {
1887         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1888         j = 0;
1889         for (k=0;k<size_of_constraint;k++) {
1890           if (PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+k])) {
1891             j++;
1892           }
1893         }
1894         /* found more than one primal dof on the cc */
1895         if (j > 1) {
1896           PetscBTSet(qr_needed_idx,i);
1897           qr_needed = PETSC_TRUE;
1898         }
1899       } else {
1900         PetscBTSet(qr_needed_idx,i);
1901         qr_needed = PETSC_TRUE;
1902       }
1903     }
1904   }
1905   /* free workspace */
1906   ierr = PetscFree(global_indices);CHKERRQ(ierr);
1907 
1908   /* permute indices in order to have a sorted set of vertices */
1909   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);CHKERRQ(ierr);
1910 
1911   /* nonzero structure of constraint matrix */
1912   ierr = PetscMalloc1(pcbddc->local_primal_size,&nnz);CHKERRQ(ierr);
1913   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
1914   j=total_primal_vertices;
1915   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1916     if (!PetscBTLookup(change_basis,i)) {
1917       nnz[j]=temp_indices[i+1]-temp_indices[i];
1918       j++;
1919     }
1920   }
1921   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1922   ierr = PetscFree(nnz);CHKERRQ(ierr);
1923   /* set values in constraint matrix */
1924   for (i=0;i<total_primal_vertices;i++) {
1925     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
1926   }
1927   total_counts = total_primal_vertices;
1928   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1929     if (!PetscBTLookup(change_basis,i)) {
1930       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1931       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);
1932       total_counts++;
1933     }
1934   }
1935   /* assembling */
1936   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1937   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1938   /*
1939   ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
1940   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
1941   */
1942   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1943   if (pcbddc->use_change_of_basis) {
1944     /* dual and primal dofs on a single cc */
1945     PetscInt     dual_dofs,primal_dofs;
1946     /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
1947     PetscInt     primal_counter;
1948     /* working stuff for GEQRF */
1949     PetscScalar  *qr_basis,*qr_tau = NULL,*qr_work,lqr_work_t;
1950     PetscBLASInt lqr_work;
1951     /* working stuff for UNGQR */
1952     PetscScalar  *gqr_work,lgqr_work_t;
1953     PetscBLASInt lgqr_work;
1954     /* working stuff for TRTRS */
1955     PetscScalar  *trs_rhs;
1956     PetscBLASInt Blas_NRHS;
1957     /* pointers for values insertion into change of basis matrix */
1958     PetscInt     *start_rows,*start_cols;
1959     PetscScalar  *start_vals;
1960     /* working stuff for values insertion */
1961     PetscBT      is_primal;
1962     /* matrix sizes */
1963     PetscInt     global_size,local_size;
1964     /* work array for nonzeros */
1965     PetscScalar  *nnz_array;
1966     /* temporary change of basis */
1967     Mat          localChangeOfBasisMatrix;
1968     /* auxiliary work for global change of basis */
1969     Vec          nnz_vec;
1970     PetscInt     *idxs_I,*idxs_B,*idxs_all,*d_nnz,*o_nnz;
1971     PetscInt     nvtxs,*xadj,*adjncy,*idxs_mapped;
1972     PetscScalar  *vals;
1973     PetscBool    done;
1974 
1975     /* local temporary change of basis acts on local interfaces -> dimension is n_B x n_B */
1976     ierr = MatCreate(PETSC_COMM_SELF,&localChangeOfBasisMatrix);CHKERRQ(ierr);
1977     ierr = MatSetType(localChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1978     ierr = MatSetSizes(localChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1979 
1980     /* nonzeros for local mat */
1981     ierr = PetscMalloc1(pcis->n_B,&nnz);CHKERRQ(ierr);
1982     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
1983     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1984       if (PetscBTLookup(change_basis,i)) {
1985         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1986         if (PetscBTLookup(qr_needed_idx,i)) {
1987           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1988         } else {
1989           for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = 2;
1990           /* get local primal index on the cc */
1991           j = 0;
1992           while (!PetscBTLookup(touched,temp_indices_to_constraint_B[temp_indices[i]+j])) j++;
1993           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1994         }
1995       }
1996     }
1997     ierr = MatSeqAIJSetPreallocation(localChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1998     /* Set initial identity in the matrix */
1999     for (i=0;i<pcis->n_B;i++) {
2000       ierr = MatSetValue(localChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
2001     }
2002 
2003     if (pcbddc->dbg_flag) {
2004       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
2005       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
2006     }
2007 
2008 
2009     /* Now we loop on the constraints which need a change of basis */
2010     /*
2011        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
2012        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)
2013 
2014        Basic blocks of change of basis matrix T computed
2015 
2016           - Using the following block transformation if there is only a primal dof on the cc
2017             (in the example, primal dof is the last one of the edge in LOCAL ordering
2018              in this code, primal dof is the first one of the edge in GLOBAL ordering)
2019             | 1        0   ...        0     1 |
2020             | 0        1   ...        0     1 |
2021             |              ...                |
2022             | 0        ...            1     1 |
2023             | -s_1/s_n ...    -s_{n-1}/-s_n 1 |
2024 
2025           - via QR decomposition of constraints otherwise
2026     */
2027     if (qr_needed) {
2028       /* space to store Q */
2029       ierr = PetscMalloc1((max_size_of_constraint)*(max_size_of_constraint),&qr_basis);CHKERRQ(ierr);
2030       /* first we issue queries for optimal work */
2031       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
2032       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
2033       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2034       lqr_work = -1;
2035       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
2036       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
2037       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
2038       ierr = PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);CHKERRQ(ierr);
2039       lgqr_work = -1;
2040       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
2041       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
2042       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
2043       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2044       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
2045       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
2046       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
2047       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
2048       ierr = PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);CHKERRQ(ierr);
2049       /* array to store scaling factors for reflectors */
2050       ierr = PetscMalloc1(max_constraints,&qr_tau);CHKERRQ(ierr);
2051       /* array to store rhs and solution of triangular solver */
2052       ierr = PetscMalloc1(max_constraints*max_constraints,&trs_rhs);CHKERRQ(ierr);
2053       /* allocating workspace for check */
2054       if (pcbddc->dbg_flag) {
2055         ierr = PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&work);CHKERRQ(ierr);
2056       }
2057     }
2058     /* array to store whether a node is primal or not */
2059     ierr = PetscBTCreate(pcis->n_B,&is_primal);CHKERRQ(ierr);
2060     ierr = PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);CHKERRQ(ierr);
2061     ierr = ISGlobalToLocalMappingApply(pcbddc->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,aux_primal_numbering,&i,aux_primal_numbering_B);CHKERRQ(ierr);
2062     if (i != total_primal_vertices) {
2063       SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",total_primal_vertices,i);
2064     }
2065     for (i=0;i<total_primal_vertices;i++) {
2066       ierr = PetscBTSet(is_primal,aux_primal_numbering_B[i]);CHKERRQ(ierr);
2067     }
2068     ierr = PetscFree(aux_primal_numbering_B);CHKERRQ(ierr);
2069 
2070     /* loop on constraints and see whether or not they need a change of basis and compute it */
2071     /* -> using implicit ordering contained in temp_indices data */
2072     total_counts = pcbddc->n_vertices;
2073     primal_counter = total_counts;
2074     while (total_counts<pcbddc->local_primal_size) {
2075       primal_dofs = 1;
2076       if (PetscBTLookup(change_basis,total_counts)) {
2077         /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
2078         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]]) {
2079           primal_dofs++;
2080         }
2081         /* get constraint info */
2082         size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
2083         dual_dofs = size_of_constraint-primal_dofs;
2084 
2085         if (pcbddc->dbg_flag) {
2086           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);
2087         }
2088 
2089         if (PetscBTLookup(qr_needed_idx,total_counts)) { /* QR */
2090 
2091           /* copy quadrature constraints for change of basis check */
2092           if (pcbddc->dbg_flag) {
2093             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2094           }
2095           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
2096           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2097 
2098           /* compute QR decomposition of constraints */
2099           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2100           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2101           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2102           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2103           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
2104           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
2105           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2106 
2107           /* explictly compute R^-T */
2108           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
2109           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
2110           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2111           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
2112           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2113           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2114           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2115           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
2116           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
2117           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2118 
2119           /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
2120           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2121           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2122           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2123           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2124           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2125           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
2126           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
2127           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2128 
2129           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
2130              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
2131              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
2132           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
2133           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
2134           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
2135           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2136           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
2137           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
2138           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2139           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));
2140           ierr = PetscFPTrapPop();CHKERRQ(ierr);
2141           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
2142 
2143           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
2144           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
2145           /* insert cols for primal dofs */
2146           for (j=0;j<primal_dofs;j++) {
2147             start_vals = &qr_basis[j*size_of_constraint];
2148             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
2149             ierr = MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2150           }
2151           /* insert cols for dual dofs */
2152           for (j=0,k=0;j<dual_dofs;k++) {
2153             if (!PetscBTLookup(is_primal,temp_indices_to_constraint_B[temp_indices[total_counts]+k])) {
2154               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
2155               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2156               ierr = MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
2157               j++;
2158             }
2159           }
2160 
2161           /* check change of basis */
2162           if (pcbddc->dbg_flag) {
2163             PetscInt   ii,jj;
2164             PetscBool valid_qr=PETSC_TRUE;
2165             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
2166             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
2167             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
2168             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
2169             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
2170             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
2171             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
2172             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));
2173             ierr = PetscFPTrapPop();CHKERRQ(ierr);
2174             for (jj=0;jj<size_of_constraint;jj++) {
2175               for (ii=0;ii<primal_dofs;ii++) {
2176                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
2177                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
2178               }
2179             }
2180             if (!valid_qr) {
2181               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");CHKERRQ(ierr);
2182               for (jj=0;jj<size_of_constraint;jj++) {
2183                 for (ii=0;ii<primal_dofs;ii++) {
2184                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
2185                     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]));
2186                   }
2187                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
2188                     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]));
2189                   }
2190                 }
2191               }
2192             } else {
2193               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");CHKERRQ(ierr);
2194             }
2195           }
2196         } else { /* simple transformation block */
2197           PetscInt row,col;
2198           PetscScalar val;
2199           for (j=0;j<size_of_constraint;j++) {
2200             row = temp_indices_to_constraint_B[temp_indices[total_counts]+j];
2201             if (!PetscBTLookup(is_primal,row)) {
2202               col = temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2203               ierr = MatSetValue(localChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);CHKERRQ(ierr);
2204               ierr = MatSetValue(localChangeOfBasisMatrix,row,col,1.0,INSERT_VALUES);CHKERRQ(ierr);
2205             } else {
2206               for (k=0;k<size_of_constraint;k++) {
2207                 col = temp_indices_to_constraint_B[temp_indices[total_counts]+k];
2208                 if (row != col) {
2209                   val = -temp_quadrature_constraint[temp_indices[total_counts]+k]/temp_quadrature_constraint[temp_indices[total_counts]+aux_primal_minloc[primal_counter]];
2210                 } else {
2211                   val = 1.0;
2212                 }
2213                 ierr = MatSetValue(localChangeOfBasisMatrix,row,col,val,INSERT_VALUES);CHKERRQ(ierr);
2214               }
2215             }
2216           }
2217           if (pcbddc->dbg_flag) {
2218             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");CHKERRQ(ierr);
2219           }
2220         }
2221         /* increment primal counter */
2222         primal_counter += primal_dofs;
2223       } else {
2224         if (pcbddc->dbg_flag) {
2225           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);
2226         }
2227       }
2228       /* increment constraint counter total_counts */
2229       total_counts += primal_dofs;
2230     }
2231 
2232     /* free workspace */
2233     if (qr_needed) {
2234       if (pcbddc->dbg_flag) {
2235         ierr = PetscFree(work);CHKERRQ(ierr);
2236       }
2237       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
2238       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
2239       ierr = PetscFree(qr_work);CHKERRQ(ierr);
2240       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
2241       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
2242     }
2243     ierr = PetscBTDestroy(&is_primal);CHKERRQ(ierr);
2244     ierr = MatAssemblyBegin(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2245     ierr = MatAssemblyEnd(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2246 
2247     /* assembling of global change of variable */
2248     ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2249     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,MATAIJ);CHKERRQ(ierr);
2250     ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
2251     ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
2252     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
2253     ierr = MatSetLocalToGlobalMapping(pcbddc->ChangeOfBasisMatrix,matis->mapping,matis->mapping);CHKERRQ(ierr);
2254 
2255     /* nonzeros (overestimated) */
2256     ierr = VecDuplicate(pcis->vec1_global,&nnz_vec);CHKERRQ(ierr);
2257     ierr = VecSetLocalToGlobalMapping(nnz_vec,matis->mapping);CHKERRQ(ierr);
2258     ierr = PetscMalloc2(pcis->n,&nnz_array,pcis->n,&idxs_all);CHKERRQ(ierr);
2259     for (i=0;i<pcis->n;i++) {
2260       nnz_array[i] = 1.0;
2261       idxs_all[i] = i;
2262     }
2263     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&idxs_B);CHKERRQ(ierr);
2264     for (i=0;i<pcis->n_B;i++) {
2265       nnz_array[idxs_B[i]] = nnz[i];
2266     }
2267     if (pcis->n) {
2268       ierr = VecSetValuesLocal(nnz_vec,pcis->n,idxs_all,nnz_array,INSERT_VALUES);CHKERRQ(ierr);
2269     }
2270     ierr = VecAssemblyBegin(nnz_vec);CHKERRQ(ierr);
2271     ierr = VecAssemblyEnd(nnz_vec);CHKERRQ(ierr);
2272     ierr = PetscFree(nnz);CHKERRQ(ierr);
2273     ierr = PetscFree2(nnz_array,idxs_all);CHKERRQ(ierr);
2274     ierr = PetscMalloc2(local_size,&d_nnz,local_size,&o_nnz);CHKERRQ(ierr);
2275     ierr = VecGetArray(nnz_vec,&nnz_array);CHKERRQ(ierr);
2276     for (i=0;i<local_size;i++) {
2277       d_nnz[i] = PetscMin((PetscInt)(PetscRealPart(nnz_array[i])),local_size);
2278       o_nnz[i] = PetscMin((PetscInt)(PetscRealPart(nnz_array[i])),global_size-local_size);
2279     }
2280     ierr = VecRestoreArray(nnz_vec,&nnz_array);CHKERRQ(ierr);
2281     ierr = VecDestroy(&nnz_vec);CHKERRQ(ierr);
2282     ierr = MatMPIAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
2283     ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
2284 
2285     /* Set identity on dirichlet dofs */
2286     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&idxs_I);CHKERRQ(ierr);
2287     for (i=0;i<pcis->n-pcis->n_B;i++) {
2288       PetscScalar one=1.0;
2289       ierr = MatSetValuesLocal(pcbddc->ChangeOfBasisMatrix,1,idxs_I+i,1,idxs_I+i,&one,INSERT_VALUES);CHKERRQ(ierr);
2290     }
2291     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&idxs_I);CHKERRQ(ierr);
2292 
2293     /* Set values at interface dofs */
2294     done = PETSC_TRUE;
2295     ierr = MatGetRowIJ(localChangeOfBasisMatrix,0,PETSC_FALSE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&done);CHKERRQ(ierr);
2296     if (!done) {
2297       SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
2298     }
2299     ierr = MatSeqAIJGetArray(localChangeOfBasisMatrix,&vals);CHKERRQ(ierr);
2300     ierr = PetscMalloc1(xadj[nvtxs],&idxs_mapped);CHKERRQ(ierr);
2301     ierr = ISLocalToGlobalMappingApply(pcbddc->BtoNmap,xadj[nvtxs],adjncy,idxs_mapped);CHKERRQ(ierr);
2302     for (i=0;i<nvtxs;i++) {
2303       PetscInt    row,*cols,ncols;
2304       PetscScalar *mat_vals;
2305 
2306       row = idxs_B[i];
2307       ncols = xadj[i+1]-xadj[i];
2308       cols = idxs_mapped+xadj[i];
2309       mat_vals = vals+xadj[i];
2310       ierr = MatSetValuesLocal(pcbddc->ChangeOfBasisMatrix,1,&row,ncols,cols,mat_vals,INSERT_VALUES);CHKERRQ(ierr);
2311     }
2312     ierr = MatRestoreRowIJ(localChangeOfBasisMatrix,0,PETSC_FALSE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&done);CHKERRQ(ierr);
2313     if (!done) {
2314       SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2315     }
2316     ierr = MatSeqAIJRestoreArray(localChangeOfBasisMatrix,&vals);CHKERRQ(ierr);
2317     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&idxs_B);CHKERRQ(ierr);
2318     ierr = PetscFree(idxs_mapped);CHKERRQ(ierr);
2319     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2320     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2321 
2322     /* check */
2323     if (pcbddc->dbg_flag) {
2324       PetscReal error;
2325       Vec       x,x_change;
2326 
2327       ierr = VecDuplicate(pcis->vec1_global,&x);CHKERRQ(ierr);
2328       ierr = VecDuplicate(pcis->vec1_global,&x_change);CHKERRQ(ierr);
2329       ierr = VecSetRandom(x,NULL);CHKERRQ(ierr);
2330       ierr = VecCopy(x,pcis->vec1_global);CHKERRQ(ierr);
2331       ierr = VecScatterBegin(pcis->global_to_B,x,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2332       ierr = VecScatterEnd(pcis->global_to_B,x,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2333       ierr = MatMult(localChangeOfBasisMatrix,pcis->vec1_B,pcis->vec2_B);CHKERRQ(ierr);
2334       ierr = VecScatterBegin(pcis->global_to_B,pcis->vec2_B,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2335       ierr = VecScatterEnd(pcis->global_to_B,pcis->vec2_B,x,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2336       ierr = MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);CHKERRQ(ierr);
2337       ierr = VecAXPY(x,-1.0,x_change);CHKERRQ(ierr);
2338       ierr = VecNorm(x,NORM_INFINITY,&error);CHKERRQ(ierr);
2339       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2340       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change on B: %1.6e\n",error);CHKERRQ(ierr);
2341       ierr = VecDestroy(&x);CHKERRQ(ierr);
2342       ierr = VecDestroy(&x_change);CHKERRQ(ierr);
2343     }
2344     ierr = MatDestroy(&localChangeOfBasisMatrix);CHKERRQ(ierr);
2345 
2346     /*
2347     ierr = PetscViewerSetFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
2348     ierr = MatView(local_ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
2349     */
2350   } else if (pcbddc->user_ChangeOfBasisMatrix) {
2351     ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2352     pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
2353   }
2354 
2355   /* set up change of basis context */
2356   if (pcbddc->ChangeOfBasisMatrix) {
2357     PCBDDCChange_ctx change_ctx;
2358 
2359     if (!pcbddc->new_global_mat) {
2360       PetscInt global_size,local_size;
2361 
2362       ierr = VecGetSize(pcis->vec1_global,&global_size);CHKERRQ(ierr);
2363       ierr = VecGetLocalSize(pcis->vec1_global,&local_size);CHKERRQ(ierr);
2364       ierr = MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->new_global_mat);CHKERRQ(ierr);
2365       ierr = MatSetSizes(pcbddc->new_global_mat,local_size,local_size,global_size,global_size);CHKERRQ(ierr);
2366       ierr = MatSetType(pcbddc->new_global_mat,MATSHELL);CHKERRQ(ierr);
2367       ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT,(void (*)(void))PCBDDCMatMult_Private);CHKERRQ(ierr);
2368       ierr = MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCMatMultTranspose_Private);CHKERRQ(ierr);
2369       ierr = PetscNew(&change_ctx);CHKERRQ(ierr);
2370       ierr = MatShellSetContext(pcbddc->new_global_mat,change_ctx);CHKERRQ(ierr);
2371     } else {
2372       ierr = MatShellGetContext(pcbddc->new_global_mat,&change_ctx);CHKERRQ(ierr);
2373       ierr = MatDestroy(&change_ctx->global_change);CHKERRQ(ierr);
2374       ierr = VecDestroyVecs(2,&change_ctx->work);CHKERRQ(ierr);
2375     }
2376     if (!pcbddc->user_ChangeOfBasisMatrix) {
2377       ierr = PetscObjectReference((PetscObject)pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
2378       change_ctx->global_change = pcbddc->ChangeOfBasisMatrix;
2379     } else {
2380       ierr = PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);CHKERRQ(ierr);
2381       change_ctx->global_change = pcbddc->user_ChangeOfBasisMatrix;
2382     }
2383     ierr = VecDuplicateVecs(pcis->vec1_global,2,&change_ctx->work);CHKERRQ(ierr);
2384     ierr = MatSetUp(pcbddc->new_global_mat);CHKERRQ(ierr);
2385     ierr = MatAssemblyBegin(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2386     ierr = MatAssemblyEnd(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2387   }
2388 
2389   /* get indices in local ordering for vertices and constraints */
2390   if (olocal_primal_size == pcbddc->local_primal_size) { /* if this is true, I need to check if a new primal space has been introduced */
2391     ierr = PetscMalloc1(olocal_primal_size,&oprimal_indices_local_idxs);CHKERRQ(ierr);
2392     ierr = PetscMemcpy(oprimal_indices_local_idxs,pcbddc->primal_indices_local_idxs,olocal_primal_size*sizeof(PetscInt));CHKERRQ(ierr);
2393   }
2394   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2395   ierr = PetscFree(pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2396   ierr = PetscMalloc1(pcbddc->local_primal_size,&pcbddc->primal_indices_local_idxs);CHKERRQ(ierr);
2397   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&i,&aux_primal_numbering);CHKERRQ(ierr);
2398   ierr = PetscMemcpy(pcbddc->primal_indices_local_idxs,aux_primal_numbering,i*sizeof(PetscInt));CHKERRQ(ierr);
2399   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2400   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&j,&aux_primal_numbering);CHKERRQ(ierr);
2401   ierr = PetscMemcpy(&pcbddc->primal_indices_local_idxs[i],aux_primal_numbering,j*sizeof(PetscInt));CHKERRQ(ierr);
2402   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
2403   /* set quantities in PCBDDC data struct */
2404   pcbddc->n_actual_vertices = i;
2405   /* check if a new primal space has been introduced */
2406   pcbddc->new_primal_space_local = PETSC_TRUE;
2407   if (olocal_primal_size == pcbddc->local_primal_size) {
2408     ierr = PetscMemcmp(pcbddc->primal_indices_local_idxs,oprimal_indices_local_idxs,olocal_primal_size,&pcbddc->new_primal_space_local);CHKERRQ(ierr);
2409     pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
2410     ierr = PetscFree(oprimal_indices_local_idxs);CHKERRQ(ierr);
2411   }
2412   /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
2413   ierr = MPI_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
2414 
2415   /* flush dbg viewer */
2416   if (pcbddc->dbg_flag) {
2417     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
2418   }
2419 
2420   /* free workspace */
2421   ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2422   ierr = PetscBTDestroy(&qr_needed_idx);CHKERRQ(ierr);
2423   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
2424   ierr = PetscBTDestroy(&change_basis);CHKERRQ(ierr);
2425   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
2426   ierr = PetscFree3(temp_quadrature_constraint,temp_indices_to_constraint,temp_indices_to_constraint_B);CHKERRQ(ierr);
2427   PetscFunctionReturn(0);
2428 }
2429 
2430 #undef __FUNCT__
2431 #define __FUNCT__ "PCBDDCAnalyzeInterface"
2432 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
2433 {
2434   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
2435   PC_IS       *pcis = (PC_IS*)pc->data;
2436   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
2437   PetscInt    ierr,i,vertex_size;
2438   PetscViewer viewer=pcbddc->dbg_viewer;
2439 
2440   PetscFunctionBegin;
2441   /* Reset previously computed graph */
2442   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
2443   /* Init local Graph struct */
2444   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
2445 
2446   /* Check validity of the csr graph passed in by the user */
2447   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
2448     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
2449   }
2450 
2451   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
2452   if (pcbddc->use_local_adj && (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy)) {
2453     Mat mat_adj;
2454     const PetscInt *xadj,*adjncy;
2455     PetscBool flg_row=PETSC_TRUE;
2456 
2457     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
2458     ierr = MatGetRowIJ(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 MatGetRowIJ called in %s\n",__FUNCT__);
2461     }
2462     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
2463     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
2464     if (!flg_row) {
2465       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
2466     }
2467     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
2468     pcbddc->deluxe_compute_rowadj = PETSC_FALSE;
2469   }
2470 
2471   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
2472   vertex_size = 1;
2473   if (pcbddc->user_provided_isfordofs) {
2474     if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
2475       ierr = PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2476       for (i=0;i<pcbddc->n_ISForDofs;i++) {
2477         ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2478         ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
2479       }
2480       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
2481       pcbddc->n_ISForDofs = 0;
2482       ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
2483     }
2484     /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
2485     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
2486   } else {
2487     if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
2488       ierr = MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);CHKERRQ(ierr);
2489       ierr = PetscMalloc(pcbddc->n_ISForDofsLocal*sizeof(IS),&pcbddc->ISForDofsLocal);CHKERRQ(ierr);
2490       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
2491         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);CHKERRQ(ierr);
2492       }
2493     }
2494   }
2495 
2496   /* Setup of Graph */
2497   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
2498     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);CHKERRQ(ierr);
2499   }
2500   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
2501     ierr = PCBDDCGlobalToLocal(matis->ctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);CHKERRQ(ierr);
2502   }
2503   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices);
2504 
2505   /* Graph's connected components analysis */
2506   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
2507 
2508   /* print some info to stdout */
2509   if (pcbddc->dbg_flag) {
2510     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
2511   }
2512 
2513   /* mark topography has done */
2514   pcbddc->recompute_topography = PETSC_FALSE;
2515   PetscFunctionReturn(0);
2516 }
2517 
2518 #undef __FUNCT__
2519 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
2520 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt **vertices_idx)
2521 {
2522   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2523   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
2524   PetscErrorCode ierr;
2525 
2526   PetscFunctionBegin;
2527   n = 0;
2528   vertices = 0;
2529   if (pcbddc->ConstraintMatrix) {
2530     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
2531     for (i=0;i<local_primal_size;i++) {
2532       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2533       if (size_of_constraint == 1) n++;
2534       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2535     }
2536     if (vertices_idx) {
2537       ierr = PetscMalloc1(n,&vertices);CHKERRQ(ierr);
2538       n = 0;
2539       for (i=0;i<local_primal_size;i++) {
2540         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2541         if (size_of_constraint == 1) {
2542           vertices[n++]=row_cmat_indices[0];
2543         }
2544         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2545       }
2546     }
2547   }
2548   *n_vertices = n;
2549   if (vertices_idx) *vertices_idx = vertices;
2550   PetscFunctionReturn(0);
2551 }
2552 
2553 #undef __FUNCT__
2554 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
2555 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt **constraints_idx)
2556 {
2557   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2558   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
2559   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
2560   PetscBT        touched;
2561   PetscErrorCode ierr;
2562 
2563     /* This function assumes that the number of local constraints per connected component
2564        is not greater than the number of nodes defined for the connected component
2565        (otherwise we will surely have linear dependence between constraints and thus a singular coarse problem) */
2566   PetscFunctionBegin;
2567   n = 0;
2568   constraints_index = 0;
2569   if (pcbddc->ConstraintMatrix) {
2570     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
2571     max_size_of_constraint = 0;
2572     for (i=0;i<local_primal_size;i++) {
2573       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2574       if (size_of_constraint > 1) {
2575         n++;
2576       }
2577       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
2578       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2579     }
2580     if (constraints_idx) {
2581       ierr = PetscMalloc1(n,&constraints_index);CHKERRQ(ierr);
2582       ierr = PetscMalloc1(max_size_of_constraint,&row_cmat_global_indices);CHKERRQ(ierr);
2583       ierr = PetscBTCreate(local_size,&touched);CHKERRQ(ierr);
2584       n = 0;
2585       for (i=0;i<local_primal_size;i++) {
2586         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2587         if (size_of_constraint > 1) {
2588           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
2589           /* find first untouched local node */
2590           j = 0;
2591           while (PetscBTLookup(touched,row_cmat_indices[j])) j++;
2592           min_index = row_cmat_global_indices[j];
2593           min_loc = j;
2594           /* search the minimum among nodes not yet touched on the connected component
2595              since there can be more than one constraint on a single cc */
2596           for (j=1;j<size_of_constraint;j++) {
2597             if (!PetscBTLookup(touched,row_cmat_indices[j]) && min_index > row_cmat_global_indices[j]) {
2598               min_index = row_cmat_global_indices[j];
2599               min_loc = j;
2600             }
2601           }
2602           ierr = PetscBTSet(touched,row_cmat_indices[min_loc]);CHKERRQ(ierr);
2603           constraints_index[n++] = row_cmat_indices[min_loc];
2604         }
2605         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2606       }
2607       ierr = PetscBTDestroy(&touched);CHKERRQ(ierr);
2608       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
2609     }
2610   }
2611   *n_constraints = n;
2612   if (constraints_idx) *constraints_idx = constraints_index;
2613   PetscFunctionReturn(0);
2614 }
2615 
2616 #undef __FUNCT__
2617 #define __FUNCT__ "PCBDDCSubsetNumbering"
2618 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[])
2619 {
2620   Vec            local_vec,global_vec;
2621   IS             seqis,paris;
2622   VecScatter     scatter_ctx;
2623   PetscScalar    *array;
2624   PetscInt       *temp_global_dofs;
2625   PetscScalar    globalsum;
2626   PetscInt       i,j,s;
2627   PetscInt       nlocals,first_index,old_index,max_local;
2628   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
2629   PetscMPIInt    *dof_sizes,*dof_displs;
2630   PetscBool      first_found;
2631   PetscErrorCode ierr;
2632 
2633   PetscFunctionBegin;
2634   /* mpi buffers */
2635   ierr = MPI_Comm_size(comm,&size_prec_comm);CHKERRQ(ierr);
2636   ierr = MPI_Comm_rank(comm,&rank_prec_comm);CHKERRQ(ierr);
2637   j = ( !rank_prec_comm ? size_prec_comm : 0);
2638   ierr = PetscMalloc1(j,&dof_sizes);CHKERRQ(ierr);
2639   ierr = PetscMalloc1(j,&dof_displs);CHKERRQ(ierr);
2640   /* get maximum size of subset */
2641   ierr = PetscMalloc1(n_local_dofs,&temp_global_dofs);CHKERRQ(ierr);
2642   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
2643   max_local = 0;
2644   for (i=0;i<n_local_dofs;i++) {
2645     if (max_local < temp_global_dofs[i] ) {
2646       max_local = temp_global_dofs[i];
2647     }
2648   }
2649   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);CHKERRQ(ierr);
2650   max_global++;
2651   max_local = 0;
2652   for (i=0;i<n_local_dofs;i++) {
2653     if (max_local < local_dofs[i] ) {
2654       max_local = local_dofs[i];
2655     }
2656   }
2657   max_local++;
2658   /* allocate workspace */
2659   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
2660   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
2661   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
2662   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
2663   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
2664   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
2665   /* create scatter */
2666   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
2667   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
2668   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
2669   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
2670   ierr = ISDestroy(&paris);CHKERRQ(ierr);
2671   /* init array */
2672   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
2673   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2674   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2675   if (local_dofs_mult) {
2676     for (i=0;i<n_local_dofs;i++) {
2677       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
2678     }
2679   } else {
2680     for (i=0;i<n_local_dofs;i++) {
2681       array[local_dofs[i]]=1.0;
2682     }
2683   }
2684   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2685   /* scatter into global vec and get total number of global dofs */
2686   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2687   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2688   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
2689   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
2690   /* Fill global_vec with cumulative function for global numbering */
2691   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
2692   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
2693   nlocals = 0;
2694   first_index = -1;
2695   first_found = PETSC_FALSE;
2696   for (i=0;i<s;i++) {
2697     if (!first_found && PetscRealPart(array[i]) > 0.1) {
2698       first_found = PETSC_TRUE;
2699       first_index = i;
2700     }
2701     nlocals += (PetscInt)PetscRealPart(array[i]);
2702   }
2703   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2704   if (!rank_prec_comm) {
2705     dof_displs[0]=0;
2706     for (i=1;i<size_prec_comm;i++) {
2707       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
2708     }
2709   }
2710   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2711   if (first_found) {
2712     array[first_index] += (PetscScalar)nlocals;
2713     old_index = first_index;
2714     for (i=first_index+1;i<s;i++) {
2715       if (PetscRealPart(array[i]) > 0.1) {
2716         array[i] += array[old_index];
2717         old_index = i;
2718       }
2719     }
2720   }
2721   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
2722   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2723   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2724   ierr = VecScatterEnd(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2725   /* get global ordering of local dofs */
2726   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2727   if (local_dofs_mult) {
2728     for (i=0;i<n_local_dofs;i++) {
2729       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
2730     }
2731   } else {
2732     for (i=0;i<n_local_dofs;i++) {
2733       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
2734     }
2735   }
2736   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2737   /* free workspace */
2738   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
2739   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
2740   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
2741   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
2742   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
2743   /* return pointer to global ordering of local dofs */
2744   *global_numbering_subset = temp_global_dofs;
2745   PetscFunctionReturn(0);
2746 }
2747 
2748 #undef __FUNCT__
2749 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
2750 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
2751 {
2752   PetscInt       i,j;
2753   PetscScalar    *alphas;
2754   PetscErrorCode ierr;
2755 
2756   PetscFunctionBegin;
2757   /* this implements stabilized Gram-Schmidt */
2758   ierr = PetscMalloc1(n,&alphas);CHKERRQ(ierr);
2759   for (i=0;i<n;i++) {
2760     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
2761     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
2762     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
2763   }
2764   ierr = PetscFree(alphas);CHKERRQ(ierr);
2765   PetscFunctionReturn(0);
2766 }
2767 
2768 #undef __FUNCT__
2769 #define __FUNCT__ "MatISGetSubassemblingPattern"
2770 PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscBool contiguous, IS* is_sends)
2771 {
2772   Mat             subdomain_adj;
2773   IS              new_ranks,ranks_send_to;
2774   MatPartitioning partitioner;
2775   Mat_IS          *matis;
2776   PetscInt        n_neighs,*neighs,*n_shared,**shared;
2777   PetscInt        prank;
2778   PetscMPIInt     size,rank,color;
2779   PetscInt        *xadj,*adjncy,*oldranks;
2780   PetscInt        *adjncy_wgt,*v_wgt,*is_indices,*ranks_send_to_idx;
2781   PetscInt        i,local_size,threshold=0;
2782   PetscErrorCode  ierr;
2783   PetscBool       use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
2784   PetscSubcomm    subcomm;
2785 
2786   PetscFunctionBegin;
2787   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_square",&use_square,NULL);CHKERRQ(ierr);
2788   ierr = PetscOptionsGetBool(NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);CHKERRQ(ierr);
2789   ierr = PetscOptionsGetInt(NULL,"-matis_partitioning_threshold",&threshold,NULL);CHKERRQ(ierr);
2790 
2791   /* Get info on mapping */
2792   matis = (Mat_IS*)(mat->data);
2793   ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&local_size);CHKERRQ(ierr);
2794   ierr = ISLocalToGlobalMappingGetInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2795 
2796   /* build local CSR graph of subdomains' connectivity */
2797   ierr = PetscMalloc1(2,&xadj);CHKERRQ(ierr);
2798   xadj[0] = 0;
2799   xadj[1] = PetscMax(n_neighs-1,0);
2800   ierr = PetscMalloc1(xadj[1],&adjncy);CHKERRQ(ierr);
2801   ierr = PetscMalloc1(xadj[1],&adjncy_wgt);CHKERRQ(ierr);
2802 
2803   if (threshold) {
2804     PetscInt xadj_count = 0;
2805     for (i=1;i<n_neighs;i++) {
2806       if (n_shared[i] > threshold) {
2807         adjncy[xadj_count] = neighs[i];
2808         adjncy_wgt[xadj_count] = n_shared[i];
2809         xadj_count++;
2810       }
2811     }
2812     xadj[1] = xadj_count;
2813   } else {
2814     if (xadj[1]) {
2815       ierr = PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));CHKERRQ(ierr);
2816       ierr = PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));CHKERRQ(ierr);
2817     }
2818   }
2819   ierr = ISLocalToGlobalMappingRestoreInfo(matis->mapping,&n_neighs,&neighs,&n_shared,&shared);CHKERRQ(ierr);
2820   if (use_square) {
2821     for (i=0;i<xadj[1];i++) {
2822       adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
2823     }
2824   }
2825   ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2826 
2827   ierr = PetscMalloc1(1,&ranks_send_to_idx);CHKERRQ(ierr);
2828 
2829   /*
2830     Restrict work on active processes only.
2831   */
2832   ierr = PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);CHKERRQ(ierr);
2833   ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr); /* 2 groups, active process and not active processes */
2834   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
2835   ierr = PetscMPIIntCast(!local_size,&color);CHKERRQ(ierr);
2836   ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
2837   if (color) {
2838     ierr = PetscFree(xadj);CHKERRQ(ierr);
2839     ierr = PetscFree(adjncy);CHKERRQ(ierr);
2840     ierr = PetscFree(adjncy_wgt);CHKERRQ(ierr);
2841   } else {
2842     PetscInt coarsening_ratio;
2843     ierr = MPI_Comm_size(subcomm->comm,&size);CHKERRQ(ierr);
2844     ierr = PetscMalloc1(size,&oldranks);CHKERRQ(ierr);
2845     prank = rank;
2846     ierr = MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm->comm);CHKERRQ(ierr);
2847     /*
2848     for (i=0;i<size;i++) {
2849       PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
2850     }
2851     */
2852     for (i=0;i<xadj[1];i++) {
2853       ierr = PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);CHKERRQ(ierr);
2854     }
2855     ierr = PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);CHKERRQ(ierr);
2856     ierr = MatCreateMPIAdj(subcomm->comm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);CHKERRQ(ierr);
2857     /* ierr = MatView(subdomain_adj,0);CHKERRQ(ierr); */
2858 
2859     /* Partition */
2860     ierr = MatPartitioningCreate(subcomm->comm,&partitioner);CHKERRQ(ierr);
2861     ierr = MatPartitioningSetAdjacency(partitioner,subdomain_adj);CHKERRQ(ierr);
2862     if (use_vwgt) {
2863       ierr = PetscMalloc1(1,&v_wgt);CHKERRQ(ierr);
2864       v_wgt[0] = local_size;
2865       ierr = MatPartitioningSetVertexWeights(partitioner,v_wgt);CHKERRQ(ierr);
2866     }
2867     n_subdomains = PetscMin((PetscInt)size,n_subdomains);
2868     coarsening_ratio = size/n_subdomains;
2869     ierr = MatPartitioningSetNParts(partitioner,n_subdomains);CHKERRQ(ierr);
2870     ierr = MatPartitioningSetFromOptions(partitioner);CHKERRQ(ierr);
2871     ierr = MatPartitioningApply(partitioner,&new_ranks);CHKERRQ(ierr);
2872     /* ierr = MatPartitioningView(partitioner,0);CHKERRQ(ierr); */
2873 
2874     ierr = ISGetIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2875     if (contiguous) {
2876       ranks_send_to_idx[0] = oldranks[is_indices[0]]; /* contiguos set of processes */
2877     } else {
2878       ranks_send_to_idx[0] = coarsening_ratio*oldranks[is_indices[0]]; /* scattered set of processes */
2879     }
2880     ierr = ISRestoreIndices(new_ranks,(const PetscInt**)&is_indices);CHKERRQ(ierr);
2881     /* clean up */
2882     ierr = PetscFree(oldranks);CHKERRQ(ierr);
2883     ierr = ISDestroy(&new_ranks);CHKERRQ(ierr);
2884     ierr = MatDestroy(&subdomain_adj);CHKERRQ(ierr);
2885     ierr = MatPartitioningDestroy(&partitioner);CHKERRQ(ierr);
2886   }
2887   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
2888 
2889   /* assemble parallel IS for sends */
2890   i = 1;
2891   if (color) i=0;
2892   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);CHKERRQ(ierr);
2893 
2894   /* get back IS */
2895   *is_sends = ranks_send_to;
2896   PetscFunctionReturn(0);
2897 }
2898 
2899 typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;
2900 
2901 #undef __FUNCT__
2902 #define __FUNCT__ "MatISSubassemble"
2903 PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
2904 {
2905   Mat                    local_mat;
2906   Mat_IS                 *matis;
2907   IS                     is_sends_internal;
2908   PetscInt               rows,cols,new_local_rows;
2909   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
2910   PetscBool              ismatis,isdense,newisdense,destroy_mat;
2911   ISLocalToGlobalMapping l2gmap;
2912   PetscInt*              l2gmap_indices;
2913   const PetscInt*        is_indices;
2914   MatType                new_local_type;
2915   /* buffers */
2916   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
2917   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
2918   PetscInt               *recv_buffer_idxs_local;
2919   PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
2920   /* MPI */
2921   MPI_Comm               comm,comm_n;
2922   PetscSubcomm           subcomm;
2923   PetscMPIInt            n_sends,n_recvs,commsize;
2924   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
2925   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
2926   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
2927   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
2928   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
2929   PetscErrorCode         ierr;
2930 
2931   PetscFunctionBegin;
2932   /* TODO: add missing checks */
2933   PetscValidLogicalCollectiveInt(mat,n_subdomains,3);
2934   PetscValidLogicalCollectiveBool(mat,restrict_comm,4);
2935   PetscValidLogicalCollectiveEnum(mat,reuse,5);
2936   PetscValidLogicalCollectiveInt(mat,nis,7);
2937   ierr = PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);CHKERRQ(ierr);
2938   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
2939   ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
2940   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);CHKERRQ(ierr);
2941   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
2942   ierr = MatGetSize(local_mat,&rows,&cols);CHKERRQ(ierr);
2943   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
2944   if (reuse == MAT_REUSE_MATRIX && *mat_n) {
2945     PetscInt mrows,mcols,mnrows,mncols;
2946     ierr = PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);CHKERRQ(ierr);
2947     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
2948     ierr = MatGetSize(mat,&mrows,&mcols);CHKERRQ(ierr);
2949     ierr = MatGetSize(*mat_n,&mnrows,&mncols);CHKERRQ(ierr);
2950     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
2951     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
2952   }
2953   ierr = MatGetBlockSize(local_mat,&bs);CHKERRQ(ierr);
2954   PetscValidLogicalCollectiveInt(mat,bs,0);
2955   /* prepare IS for sending if not provided */
2956   if (!is_sends) {
2957     PetscBool pcontig = PETSC_TRUE;
2958     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
2959     ierr = MatISGetSubassemblingPattern(mat,n_subdomains,pcontig,&is_sends_internal);CHKERRQ(ierr);
2960   } else {
2961     ierr = PetscObjectReference((PetscObject)is_sends);CHKERRQ(ierr);
2962     is_sends_internal = is_sends;
2963   }
2964 
2965   /* get pointer of MATIS data */
2966   matis = (Mat_IS*)mat->data;
2967 
2968   /* get comm */
2969   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
2970 
2971   /* compute number of sends */
2972   ierr = ISGetLocalSize(is_sends_internal,&i);CHKERRQ(ierr);
2973   ierr = PetscMPIIntCast(i,&n_sends);CHKERRQ(ierr);
2974 
2975   /* compute number of receives */
2976   ierr = MPI_Comm_size(comm,&commsize);CHKERRQ(ierr);
2977   ierr = PetscMalloc1(commsize,&iflags);CHKERRQ(ierr);
2978   ierr = PetscMemzero(iflags,commsize*sizeof(*iflags));CHKERRQ(ierr);
2979   ierr = ISGetIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
2980   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
2981   ierr = PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);CHKERRQ(ierr);
2982   ierr = PetscFree(iflags);CHKERRQ(ierr);
2983 
2984   /* restrict comm if requested */
2985   subcomm = 0;
2986   destroy_mat = PETSC_FALSE;
2987   if (restrict_comm) {
2988     PetscMPIInt color,rank,subcommsize;
2989     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2990     color = 0;
2991     if (n_sends && !n_recvs) color = 1; /* sending only processes will not partecipate in new comm */
2992     ierr = MPI_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);CHKERRQ(ierr);
2993     subcommsize = commsize - subcommsize;
2994     /* check if reuse has been requested */
2995     if (reuse == MAT_REUSE_MATRIX) {
2996       if (*mat_n) {
2997         PetscMPIInt subcommsize2;
2998         ierr = MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);CHKERRQ(ierr);
2999         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
3000         comm_n = PetscObjectComm((PetscObject)*mat_n);
3001       } else {
3002         comm_n = PETSC_COMM_SELF;
3003       }
3004     } else { /* MAT_INITIAL_MATRIX */
3005       ierr = PetscSubcommCreate(comm,&subcomm);CHKERRQ(ierr);
3006       ierr = PetscSubcommSetNumber(subcomm,2);CHKERRQ(ierr);
3007       ierr = PetscSubcommSetTypeGeneral(subcomm,color,rank);CHKERRQ(ierr);
3008       comm_n = subcomm->comm;
3009     }
3010     /* flag to destroy *mat_n if not significative */
3011     if (color) destroy_mat = PETSC_TRUE;
3012   } else {
3013     comm_n = comm;
3014   }
3015 
3016   /* prepare send/receive buffers */
3017   ierr = PetscMalloc1(commsize,&ilengths_idxs);CHKERRQ(ierr);
3018   ierr = PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));CHKERRQ(ierr);
3019   ierr = PetscMalloc1(commsize,&ilengths_vals);CHKERRQ(ierr);
3020   ierr = PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));CHKERRQ(ierr);
3021   if (nis) {
3022     ierr = PetscMalloc(commsize*sizeof(*ilengths_idxs_is),&ilengths_idxs_is);CHKERRQ(ierr);
3023     ierr = PetscMemzero(ilengths_idxs_is,commsize*sizeof(*ilengths_idxs_is));CHKERRQ(ierr);
3024   }
3025 
3026   /* Get data from local matrices */
3027   if (!isdense) {
3028     SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Subassembling of AIJ local matrices not yet implemented");
3029     /* TODO: See below some guidelines on how to prepare the local buffers */
3030     /*
3031        send_buffer_vals should contain the raw values of the local matrix
3032        send_buffer_idxs should contain:
3033        - MatType_PRIVATE type
3034        - PetscInt        size_of_l2gmap
3035        - PetscInt        global_row_indices[size_of_l2gmap]
3036        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
3037     */
3038   } else {
3039     ierr = MatDenseGetArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3040     ierr = ISLocalToGlobalMappingGetSize(matis->mapping,&i);CHKERRQ(ierr);
3041     ierr = PetscMalloc1((i+2),&send_buffer_idxs);CHKERRQ(ierr);
3042     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
3043     send_buffer_idxs[1] = i;
3044     ierr = ISLocalToGlobalMappingGetIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
3045     ierr = PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));CHKERRQ(ierr);
3046     ierr = ISLocalToGlobalMappingRestoreIndices(matis->mapping,(const PetscInt**)&ptr_idxs);CHKERRQ(ierr);
3047     ierr = PetscMPIIntCast(i,&len);CHKERRQ(ierr);
3048     for (i=0;i<n_sends;i++) {
3049       ilengths_vals[is_indices[i]] = len*len;
3050       ilengths_idxs[is_indices[i]] = len+2;
3051     }
3052   }
3053   ierr = PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);CHKERRQ(ierr);
3054   /* additional is (if any) */
3055   if (nis) {
3056     PetscMPIInt psum;
3057     PetscInt j;
3058     for (j=0,psum=0;j<nis;j++) {
3059       PetscInt plen;
3060       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
3061       ierr = PetscMPIIntCast(plen,&len);CHKERRQ(ierr);
3062       psum += len+1; /* indices + lenght */
3063     }
3064     ierr = PetscMalloc(psum*sizeof(PetscInt),&send_buffer_idxs_is);CHKERRQ(ierr);
3065     for (j=0,psum=0;j<nis;j++) {
3066       PetscInt plen;
3067       const PetscInt *is_array_idxs;
3068       ierr = ISGetLocalSize(isarray[j],&plen);CHKERRQ(ierr);
3069       send_buffer_idxs_is[psum] = plen;
3070       ierr = ISGetIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
3071       ierr = PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));CHKERRQ(ierr);
3072       ierr = ISRestoreIndices(isarray[j],&is_array_idxs);CHKERRQ(ierr);
3073       psum += plen+1; /* indices + lenght */
3074     }
3075     for (i=0;i<n_sends;i++) {
3076       ilengths_idxs_is[is_indices[i]] = psum;
3077     }
3078     ierr = PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);CHKERRQ(ierr);
3079   }
3080 
3081   buf_size_idxs = 0;
3082   buf_size_vals = 0;
3083   buf_size_idxs_is = 0;
3084   for (i=0;i<n_recvs;i++) {
3085     buf_size_idxs += (PetscInt)olengths_idxs[i];
3086     buf_size_vals += (PetscInt)olengths_vals[i];
3087     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
3088   }
3089   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);CHKERRQ(ierr);
3090   ierr = PetscMalloc1(buf_size_vals,&recv_buffer_vals);CHKERRQ(ierr);
3091   ierr = PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);CHKERRQ(ierr);
3092 
3093   /* get new tags for clean communications */
3094   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);CHKERRQ(ierr);
3095   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_vals);CHKERRQ(ierr);
3096   ierr = PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);CHKERRQ(ierr);
3097 
3098   /* allocate for requests */
3099   ierr = PetscMalloc1(n_sends,&send_req_idxs);CHKERRQ(ierr);
3100   ierr = PetscMalloc1(n_sends,&send_req_vals);CHKERRQ(ierr);
3101   ierr = PetscMalloc1(n_sends,&send_req_idxs_is);CHKERRQ(ierr);
3102   ierr = PetscMalloc1(n_recvs,&recv_req_idxs);CHKERRQ(ierr);
3103   ierr = PetscMalloc1(n_recvs,&recv_req_vals);CHKERRQ(ierr);
3104   ierr = PetscMalloc1(n_recvs,&recv_req_idxs_is);CHKERRQ(ierr);
3105 
3106   /* communications */
3107   ptr_idxs = recv_buffer_idxs;
3108   ptr_vals = recv_buffer_vals;
3109   ptr_idxs_is = recv_buffer_idxs_is;
3110   for (i=0;i<n_recvs;i++) {
3111     source_dest = onodes[i];
3112     ierr = MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);CHKERRQ(ierr);
3113     ierr = MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);CHKERRQ(ierr);
3114     ptr_idxs += olengths_idxs[i];
3115     ptr_vals += olengths_vals[i];
3116     if (nis) {
3117       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);
3118       ptr_idxs_is += olengths_idxs_is[i];
3119     }
3120   }
3121   for (i=0;i<n_sends;i++) {
3122     ierr = PetscMPIIntCast(is_indices[i],&source_dest);CHKERRQ(ierr);
3123     ierr = MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);CHKERRQ(ierr);
3124     ierr = MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);CHKERRQ(ierr);
3125     if (nis) {
3126       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);
3127     }
3128   }
3129   ierr = ISRestoreIndices(is_sends_internal,&is_indices);CHKERRQ(ierr);
3130   ierr = ISDestroy(&is_sends_internal);CHKERRQ(ierr);
3131 
3132   /* assemble new l2g map */
3133   ierr = MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3134   ptr_idxs = recv_buffer_idxs;
3135   new_local_rows = 0;
3136   for (i=0;i<n_recvs;i++) {
3137     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3138     ptr_idxs += olengths_idxs[i];
3139   }
3140   ierr = PetscMalloc1(new_local_rows,&l2gmap_indices);CHKERRQ(ierr);
3141   ptr_idxs = recv_buffer_idxs;
3142   new_local_rows = 0;
3143   for (i=0;i<n_recvs;i++) {
3144     ierr = PetscMemcpy(&l2gmap_indices[new_local_rows],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));CHKERRQ(ierr);
3145     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
3146     ptr_idxs += olengths_idxs[i];
3147   }
3148   ierr = PetscSortRemoveDupsInt(&new_local_rows,l2gmap_indices);CHKERRQ(ierr);
3149   ierr = ISLocalToGlobalMappingCreate(comm_n,1,new_local_rows,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);CHKERRQ(ierr);
3150   ierr = PetscFree(l2gmap_indices);CHKERRQ(ierr);
3151 
3152   /* infer new local matrix type from received local matrices type */
3153   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
3154   /* 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) */
3155   if (n_recvs) {
3156     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
3157     ptr_idxs = recv_buffer_idxs;
3158     for (i=0;i<n_recvs;i++) {
3159       if ((PetscInt)new_local_type_private != *ptr_idxs) {
3160         new_local_type_private = MATAIJ_PRIVATE;
3161         break;
3162       }
3163       ptr_idxs += olengths_idxs[i];
3164     }
3165     switch (new_local_type_private) {
3166       case MATDENSE_PRIVATE:
3167         if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
3168           new_local_type = MATSEQAIJ;
3169           bs = 1;
3170         } else { /* if I receive only 1 dense matrix */
3171           new_local_type = MATSEQDENSE;
3172           bs = 1;
3173         }
3174         break;
3175       case MATAIJ_PRIVATE:
3176         new_local_type = MATSEQAIJ;
3177         bs = 1;
3178         break;
3179       case MATBAIJ_PRIVATE:
3180         new_local_type = MATSEQBAIJ;
3181         break;
3182       case MATSBAIJ_PRIVATE:
3183         new_local_type = MATSEQSBAIJ;
3184         break;
3185       default:
3186         SETERRQ2(comm,PETSC_ERR_SUP,"Unsupported private type %d in %s",new_local_type_private,__FUNCT__);
3187         break;
3188     }
3189   } else { /* by default, new_local_type is seqdense */
3190     new_local_type = MATSEQDENSE;
3191     bs = 1;
3192   }
3193 
3194   /* create MATIS object if needed */
3195   if (reuse == MAT_INITIAL_MATRIX) {
3196     ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
3197     ierr = MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,mat_n);CHKERRQ(ierr);
3198   } else {
3199     /* it also destroys the local matrices */
3200     ierr = MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);CHKERRQ(ierr);
3201   }
3202   ierr = MatISGetLocalMat(*mat_n,&local_mat);CHKERRQ(ierr);
3203   ierr = MatSetType(local_mat,new_local_type);CHKERRQ(ierr);
3204 
3205   ierr = MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3206 
3207   /* Global to local map of received indices */
3208   ierr = PetscMalloc1(buf_size_idxs,&recv_buffer_idxs_local);CHKERRQ(ierr); /* needed for values insertion */
3209   ierr = ISGlobalToLocalMappingApply(l2gmap,IS_GTOLM_MASK,buf_size_idxs,recv_buffer_idxs,&i,recv_buffer_idxs_local);CHKERRQ(ierr);
3210   ierr = ISLocalToGlobalMappingDestroy(&l2gmap);CHKERRQ(ierr);
3211 
3212   /* restore attributes -> type of incoming data and its size */
3213   buf_size_idxs = 0;
3214   for (i=0;i<n_recvs;i++) {
3215     recv_buffer_idxs_local[buf_size_idxs] = recv_buffer_idxs[buf_size_idxs];
3216     recv_buffer_idxs_local[buf_size_idxs+1] = recv_buffer_idxs[buf_size_idxs+1];
3217     buf_size_idxs += (PetscInt)olengths_idxs[i];
3218   }
3219   ierr = PetscFree(recv_buffer_idxs);CHKERRQ(ierr);
3220 
3221   /* set preallocation */
3222   ierr = PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&newisdense);CHKERRQ(ierr);
3223   if (!newisdense) {
3224     PetscInt *new_local_nnz=0;
3225 
3226     ptr_vals = recv_buffer_vals;
3227     ptr_idxs = recv_buffer_idxs_local;
3228     if (n_recvs) {
3229       ierr = PetscCalloc1(new_local_rows,&new_local_nnz);CHKERRQ(ierr);
3230     }
3231     for (i=0;i<n_recvs;i++) {
3232       PetscInt j;
3233       if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
3234         for (j=0;j<*(ptr_idxs+1);j++) {
3235           new_local_nnz[*(ptr_idxs+2+j)] += *(ptr_idxs+1);
3236         }
3237       } else {
3238         /* TODO */
3239       }
3240       ptr_idxs += olengths_idxs[i];
3241     }
3242     if (new_local_nnz) {
3243       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMin(new_local_nnz[i],new_local_rows);
3244       ierr = MatSeqAIJSetPreallocation(local_mat,0,new_local_nnz);CHKERRQ(ierr);
3245       for (i=0;i<new_local_rows;i++) new_local_nnz[i] /= bs;
3246       ierr = MatSeqBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);CHKERRQ(ierr);
3247       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMax(new_local_nnz[i]-i,0);
3248       ierr = MatSeqSBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);CHKERRQ(ierr);
3249     } else {
3250       ierr = MatSetUp(local_mat);CHKERRQ(ierr);
3251     }
3252     ierr = PetscFree(new_local_nnz);CHKERRQ(ierr);
3253   } else {
3254     ierr = MatSetUp(local_mat);CHKERRQ(ierr);
3255   }
3256 
3257   /* set values */
3258   ptr_vals = recv_buffer_vals;
3259   ptr_idxs = recv_buffer_idxs_local;
3260   for (i=0;i<n_recvs;i++) {
3261     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
3262       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);CHKERRQ(ierr);
3263       ierr = MatSetValues(local_mat,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);CHKERRQ(ierr);
3264       ierr = MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3265       ierr = MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr);
3266       ierr = MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);CHKERRQ(ierr);
3267     } else {
3268       /* TODO */
3269     }
3270     ptr_idxs += olengths_idxs[i];
3271     ptr_vals += olengths_vals[i];
3272   }
3273   ierr = MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3274   ierr = MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3275   ierr = MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3276   ierr = MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3277   ierr = PetscFree(recv_buffer_vals);CHKERRQ(ierr);
3278   ierr = PetscFree(recv_buffer_idxs_local);CHKERRQ(ierr);
3279 
3280 #if 0
3281   if (!restrict_comm) { /* check */
3282     Vec       lvec,rvec;
3283     PetscReal infty_error;
3284 
3285     ierr = MatCreateVecs(mat,&rvec,&lvec);CHKERRQ(ierr);
3286     ierr = VecSetRandom(rvec,NULL);CHKERRQ(ierr);
3287     ierr = MatMult(mat,rvec,lvec);CHKERRQ(ierr);
3288     ierr = VecScale(lvec,-1.0);CHKERRQ(ierr);
3289     ierr = MatMultAdd(*mat_n,rvec,lvec,lvec);CHKERRQ(ierr);
3290     ierr = VecNorm(lvec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3291     ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
3292     ierr = VecDestroy(&rvec);CHKERRQ(ierr);
3293     ierr = VecDestroy(&lvec);CHKERRQ(ierr);
3294   }
3295 #endif
3296 
3297   /* assemble new additional is (if any) */
3298   if (nis) {
3299     PetscInt **temp_idxs,*count_is,j,psum;
3300 
3301     ierr = MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3302     ierr = PetscMalloc(nis*sizeof(PetscInt),&count_is);CHKERRQ(ierr);
3303     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3304     ptr_idxs = recv_buffer_idxs_is;
3305     psum = 0;
3306     for (i=0;i<n_recvs;i++) {
3307       for (j=0;j<nis;j++) {
3308         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3309         count_is[j] += plen; /* increment counting of buffer for j-th IS */
3310         psum += plen;
3311         ptr_idxs += plen+1; /* shift pointer to received data */
3312       }
3313     }
3314     ierr = PetscMalloc(nis*sizeof(PetscInt*),&temp_idxs);CHKERRQ(ierr);
3315     ierr = PetscMalloc(psum*sizeof(PetscInt),&temp_idxs[0]);CHKERRQ(ierr);
3316     for (i=1;i<nis;i++) {
3317       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
3318     }
3319     ierr = PetscMemzero(count_is,nis*sizeof(PetscInt));CHKERRQ(ierr);
3320     ptr_idxs = recv_buffer_idxs_is;
3321     for (i=0;i<n_recvs;i++) {
3322       for (j=0;j<nis;j++) {
3323         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
3324         ierr = PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));CHKERRQ(ierr);
3325         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
3326         ptr_idxs += plen+1; /* shift pointer to received data */
3327       }
3328     }
3329     for (i=0;i<nis;i++) {
3330       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3331       ierr = PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);CHKERRQ(ierr);CHKERRQ(ierr);
3332       ierr = ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3333     }
3334     ierr = PetscFree(count_is);CHKERRQ(ierr);
3335     ierr = PetscFree(temp_idxs[0]);CHKERRQ(ierr);
3336     ierr = PetscFree(temp_idxs);CHKERRQ(ierr);
3337   }
3338   /* free workspace */
3339   ierr = PetscFree(recv_buffer_idxs_is);CHKERRQ(ierr);
3340   ierr = MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3341   ierr = PetscFree(send_buffer_idxs);CHKERRQ(ierr);
3342   ierr = MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3343   if (isdense) {
3344     ierr = MatISGetLocalMat(mat,&local_mat);CHKERRQ(ierr);
3345     ierr = MatDenseRestoreArray(local_mat,&send_buffer_vals);CHKERRQ(ierr);
3346   } else {
3347     /* ierr = PetscFree(send_buffer_vals);CHKERRQ(ierr); */
3348   }
3349   if (nis) {
3350     ierr = MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);CHKERRQ(ierr);
3351     ierr = PetscFree(send_buffer_idxs_is);CHKERRQ(ierr);
3352   }
3353   ierr = PetscFree(recv_req_idxs);CHKERRQ(ierr);
3354   ierr = PetscFree(recv_req_vals);CHKERRQ(ierr);
3355   ierr = PetscFree(recv_req_idxs_is);CHKERRQ(ierr);
3356   ierr = PetscFree(send_req_idxs);CHKERRQ(ierr);
3357   ierr = PetscFree(send_req_vals);CHKERRQ(ierr);
3358   ierr = PetscFree(send_req_idxs_is);CHKERRQ(ierr);
3359   ierr = PetscFree(ilengths_vals);CHKERRQ(ierr);
3360   ierr = PetscFree(ilengths_idxs);CHKERRQ(ierr);
3361   ierr = PetscFree(olengths_vals);CHKERRQ(ierr);
3362   ierr = PetscFree(olengths_idxs);CHKERRQ(ierr);
3363   ierr = PetscFree(onodes);CHKERRQ(ierr);
3364   if (nis) {
3365     ierr = PetscFree(ilengths_idxs_is);CHKERRQ(ierr);
3366     ierr = PetscFree(olengths_idxs_is);CHKERRQ(ierr);
3367     ierr = PetscFree(onodes_is);CHKERRQ(ierr);
3368   }
3369   ierr = PetscSubcommDestroy(&subcomm);CHKERRQ(ierr);
3370   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
3371     ierr = MatDestroy(mat_n);CHKERRQ(ierr);
3372     for (i=0;i<nis;i++) {
3373       ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3374     }
3375   }
3376   PetscFunctionReturn(0);
3377 }
3378 
3379 /* temporary hack into ksp private data structure */
3380 #include <petsc-private/kspimpl.h>
3381 
3382 #undef __FUNCT__
3383 #define __FUNCT__ "PCBDDCSetUpCoarseSolver"
3384 PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
3385 {
3386   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
3387   PC_IS                  *pcis = (PC_IS*)pc->data;
3388   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
3389   MatNullSpace           CoarseNullSpace=NULL;
3390   ISLocalToGlobalMapping coarse_islg;
3391   IS                     coarse_is,*isarray;
3392   PetscInt               i,im_active=-1,active_procs=-1;
3393   PetscInt               nis,nisdofs,nisneu;
3394   PC                     pc_temp;
3395   PCType                 coarse_pc_type;
3396   KSPType                coarse_ksp_type;
3397   PetscBool              multilevel_requested,multilevel_allowed;
3398   PetscBool              isredundant,isbddc,isnn,coarse_reuse;
3399   Mat                    t_coarse_mat_is;
3400   PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
3401   PetscMPIInt            all_procs;
3402   PetscBool              csin_ml,csin_ds,csin,csin_type_simple,redist;
3403   PetscBool              compute_vecs = PETSC_FALSE;
3404   PetscScalar            *array;
3405   PetscErrorCode         ierr;
3406 
3407   PetscFunctionBegin;
3408   /* Assign global numbering to coarse dofs */
3409   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 */
3410     compute_vecs = PETSC_TRUE;
3411     PetscInt ocoarse_size;
3412     ocoarse_size = pcbddc->coarse_size;
3413     ierr = PetscFree(pcbddc->global_primal_indices);CHKERRQ(ierr);
3414     ierr = PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);CHKERRQ(ierr);
3415     /* see if we can avoid some work */
3416     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
3417       if (ocoarse_size != pcbddc->coarse_size) { /* ...but with different size, so reset it and set reuse flag to false */
3418         ierr = KSPReset(pcbddc->coarse_ksp);CHKERRQ(ierr);
3419         coarse_reuse = PETSC_FALSE;
3420       } else { /* we can safely reuse already computed coarse matrix */
3421         coarse_reuse = PETSC_TRUE;
3422       }
3423     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
3424       coarse_reuse = PETSC_FALSE;
3425     }
3426     /* reset any subassembling information */
3427     ierr = ISDestroy(&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3428     ierr = ISDestroy(&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3429   } else { /* primal space is unchanged, so we can reuse coarse matrix */
3430     coarse_reuse = PETSC_TRUE;
3431   }
3432 
3433   /* count "active" (i.e. with positive local size) and "void" processes */
3434   im_active = !!(pcis->n);
3435   ierr = MPI_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3436   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);CHKERRQ(ierr);
3437   void_procs = all_procs-active_procs;
3438   csin_type_simple = PETSC_TRUE;
3439   redist = PETSC_FALSE;
3440   if (pcbddc->current_level && void_procs) {
3441     csin_ml = PETSC_TRUE;
3442     ncoarse_ml = void_procs;
3443     csin_ds = PETSC_TRUE;
3444     ncoarse_ds = void_procs;
3445   } else {
3446     csin_ml = PETSC_FALSE;
3447     ncoarse_ml = all_procs;
3448     if (void_procs) {
3449       csin_ds = PETSC_TRUE;
3450       ncoarse_ds = void_procs;
3451       csin_type_simple = PETSC_FALSE;
3452     } else {
3453       if (pcbddc->redistribute_coarse && pcbddc->redistribute_coarse < all_procs) {
3454         csin_ds = PETSC_TRUE;
3455         ncoarse_ds = pcbddc->redistribute_coarse;
3456         redist = PETSC_TRUE;
3457       } else {
3458         csin_ds = PETSC_FALSE;
3459         ncoarse_ds = all_procs;
3460       }
3461     }
3462   }
3463 
3464   /*
3465     test if we can go multilevel: three conditions must be satisfied:
3466     - we have not exceeded the number of levels requested
3467     - we can actually subassemble the active processes
3468     - we can find a suitable number of MPI processes where we can place the subassembled problem
3469   */
3470   multilevel_allowed = PETSC_FALSE;
3471   multilevel_requested = PETSC_FALSE;
3472   if (pcbddc->current_level < pcbddc->max_levels) {
3473     multilevel_requested = PETSC_TRUE;
3474     if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
3475       multilevel_allowed = PETSC_FALSE;
3476     } else {
3477       multilevel_allowed = PETSC_TRUE;
3478     }
3479   }
3480   /* determine number of process partecipating to coarse solver */
3481   if (multilevel_allowed) {
3482     ncoarse = ncoarse_ml;
3483     csin = csin_ml;
3484   } else {
3485     ncoarse = ncoarse_ds;
3486     csin = csin_ds;
3487   }
3488 
3489   /* creates temporary l2gmap and IS for coarse indexes */
3490   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);CHKERRQ(ierr);
3491   ierr = ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);CHKERRQ(ierr);
3492 
3493   /* creates temporary MATIS object for coarse matrix */
3494   ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,NULL,&coarse_submat_dense);CHKERRQ(ierr);
3495   ierr = MatDenseGetArray(coarse_submat_dense,&array);CHKERRQ(ierr);
3496   ierr = PetscMemcpy(array,coarse_submat_vals,sizeof(*coarse_submat_vals)*pcbddc->local_primal_size*pcbddc->local_primal_size);CHKERRQ(ierr);
3497   ierr = MatDenseRestoreArray(coarse_submat_dense,&array);CHKERRQ(ierr);
3498 #if 0
3499   {
3500     PetscViewer viewer;
3501     char filename[256];
3502     sprintf(filename,"local_coarse_mat%d.m",PetscGlobalRank);
3503     ierr = PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);CHKERRQ(ierr);
3504     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3505     ierr = MatView(coarse_submat_dense,viewer);CHKERRQ(ierr);
3506     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3507   }
3508 #endif
3509   ierr = MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,&t_coarse_mat_is);CHKERRQ(ierr);
3510   ierr = MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);CHKERRQ(ierr);
3511   ierr = MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3512   ierr = MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3513   ierr = MatDestroy(&coarse_submat_dense);CHKERRQ(ierr);
3514 
3515   /* compute dofs splitting and neumann boundaries for coarse dofs */
3516   if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal) ) { /* protects from unneded computations */
3517     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
3518     const PetscInt         *idxs;
3519     ISLocalToGlobalMapping tmap;
3520 
3521     /* create map between primal indices (in local representative ordering) and local primal numbering */
3522     ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);CHKERRQ(ierr);
3523     /* allocate space for temporary storage */
3524     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs);CHKERRQ(ierr);
3525     ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&tidxs2);CHKERRQ(ierr);
3526     /* allocate for IS array */
3527     nisdofs = pcbddc->n_ISForDofsLocal;
3528     nisneu = !!pcbddc->NeumannBoundariesLocal;
3529     nis = nisdofs + nisneu;
3530     ierr = PetscMalloc(nis*sizeof(IS),&isarray);CHKERRQ(ierr);
3531     /* dofs splitting */
3532     for (i=0;i<nisdofs;i++) {
3533       /* ierr = ISView(pcbddc->ISForDofsLocal[i],0);CHKERRQ(ierr); */
3534       ierr = ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);CHKERRQ(ierr);
3535       ierr = ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3536       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3537       ierr = ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);CHKERRQ(ierr);
3538       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3539       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->ISForDofsLocal[i]),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);CHKERRQ(ierr);
3540       /* ierr = ISView(isarray[i],0);CHKERRQ(ierr); */
3541     }
3542     /* neumann boundaries */
3543     if (pcbddc->NeumannBoundariesLocal) {
3544       /* ierr = ISView(pcbddc->NeumannBoundariesLocal,0);CHKERRQ(ierr); */
3545       ierr = ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);CHKERRQ(ierr);
3546       ierr = ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3547       ierr = ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);CHKERRQ(ierr);
3548       ierr = ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);CHKERRQ(ierr);
3549       ierr = ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);CHKERRQ(ierr);
3550       ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->NeumannBoundariesLocal),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);CHKERRQ(ierr);
3551       /* ierr = ISView(isarray[nisdofs],0);CHKERRQ(ierr); */
3552     }
3553     /* free memory */
3554     ierr = PetscFree(tidxs);CHKERRQ(ierr);
3555     ierr = PetscFree(tidxs2);CHKERRQ(ierr);
3556     ierr = ISLocalToGlobalMappingDestroy(&tmap);CHKERRQ(ierr);
3557   } else {
3558     nis = 0;
3559     nisdofs = 0;
3560     nisneu = 0;
3561     isarray = NULL;
3562   }
3563   /* destroy no longer needed map */
3564   ierr = ISLocalToGlobalMappingDestroy(&coarse_islg);CHKERRQ(ierr);
3565 
3566   /* restrict on coarse candidates (if needed) */
3567   coarse_mat_is = NULL;
3568   if (csin) {
3569     if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
3570       if (redist) {
3571         PetscMPIInt rank;
3572         PetscInt spc,n_spc_p1,dest[1];
3573 
3574         ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
3575         spc = all_procs/pcbddc->redistribute_coarse;
3576         n_spc_p1 = all_procs%pcbddc->redistribute_coarse;
3577         if (rank > n_spc_p1*(spc+1)-1) {
3578           dest[0] = n_spc_p1+(rank-(n_spc_p1*(spc+1)))/spc;
3579         } else {
3580           dest[0] = rank/(spc+1);
3581         }
3582         ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),1,dest,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3583         ierr = ISView(pcbddc->coarse_subassembling_init,NULL);CHKERRQ(ierr);
3584       } else {
3585         PetscInt j,tissize,*nisindices;
3586         PetscInt *coarse_candidates;
3587         const PetscInt* tisindices;
3588         /* get coarse candidates' ranks in pc communicator */
3589         ierr = PetscMalloc(all_procs*sizeof(PetscInt),&coarse_candidates);CHKERRQ(ierr);
3590         ierr = MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
3591         for (i=0,j=0;i<all_procs;i++) {
3592           if (!coarse_candidates[i]) {
3593             coarse_candidates[j]=i;
3594             j++;
3595           }
3596         }
3597         if (j < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",j,ncoarse);
3598         /* get a suitable subassembling pattern */
3599         if (csin_type_simple) {
3600           PetscMPIInt rank;
3601           PetscInt    issize,isidx;
3602           ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);CHKERRQ(ierr);
3603           if (im_active) {
3604             issize = 1;
3605             isidx = (PetscInt)rank;
3606           } else {
3607             issize = 0;
3608             isidx = -1;
3609           }
3610           ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3611         } else {
3612           ierr = MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,PETSC_TRUE,&pcbddc->coarse_subassembling_init);CHKERRQ(ierr);
3613         }
3614         if (pcbddc->dbg_flag) {
3615           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3616           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");CHKERRQ(ierr);
3617           ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3618           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");CHKERRQ(ierr);
3619           for (i=0;i<j;i++) {
3620             ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);CHKERRQ(ierr);
3621           }
3622           ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");CHKERRQ(ierr);
3623           ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3624         }
3625         /* shift the pattern on coarse candidates */
3626         ierr = ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);CHKERRQ(ierr);
3627         ierr = ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3628         ierr = PetscMalloc(tissize*sizeof(PetscInt),&nisindices);CHKERRQ(ierr);
3629         for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
3630         ierr = ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);CHKERRQ(ierr);
3631         ierr = ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);CHKERRQ(ierr);
3632         ierr = PetscFree(coarse_candidates);CHKERRQ(ierr);
3633       }
3634     }
3635     if (pcbddc->dbg_flag) {
3636       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3637       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");CHKERRQ(ierr);
3638       ierr = ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);CHKERRQ(ierr);
3639       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3640     }
3641     /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
3642     ierr = MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);CHKERRQ(ierr);
3643   } else {
3644     if (pcbddc->dbg_flag) {
3645       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3646       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");CHKERRQ(ierr);
3647       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3648     }
3649     ierr = PetscObjectReference((PetscObject)t_coarse_mat_is);CHKERRQ(ierr);
3650     coarse_mat_is = t_coarse_mat_is;
3651   }
3652 
3653   /* create local to global scatters for coarse problem */
3654   if (compute_vecs) {
3655     PetscInt lrows;
3656     ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
3657     if (coarse_mat_is) {
3658       ierr = MatGetLocalSize(coarse_mat_is,&lrows,NULL);CHKERRQ(ierr);
3659     } else {
3660       lrows = 0;
3661     }
3662     ierr = VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);CHKERRQ(ierr);
3663     ierr = VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);CHKERRQ(ierr);
3664     ierr = VecSetType(pcbddc->coarse_vec,VECSTANDARD);CHKERRQ(ierr);
3665     ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3666     ierr = VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
3667   }
3668   ierr = ISDestroy(&coarse_is);CHKERRQ(ierr);
3669   ierr = MatDestroy(&t_coarse_mat_is);CHKERRQ(ierr);
3670 
3671   /* set defaults for coarse KSP and PC */
3672   if (multilevel_allowed) {
3673     coarse_ksp_type = KSPRICHARDSON;
3674     coarse_pc_type = PCBDDC;
3675   } else {
3676     coarse_ksp_type = KSPPREONLY;
3677     coarse_pc_type = PCREDUNDANT;
3678   }
3679 
3680   /* print some info if requested */
3681   if (pcbddc->dbg_flag) {
3682     if (!multilevel_allowed) {
3683       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3684       if (multilevel_requested) {
3685         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);
3686       } else if (pcbddc->max_levels) {
3687         ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);CHKERRQ(ierr);
3688       }
3689       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3690     }
3691   }
3692 
3693   /* create the coarse KSP object only once with defaults */
3694   if (coarse_mat_is) {
3695     MatReuse coarse_mat_reuse;
3696     PetscViewer dbg_viewer = NULL;
3697     if (pcbddc->dbg_flag) {
3698       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
3699       ierr = PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3700     }
3701     if (!pcbddc->coarse_ksp) {
3702       char prefix[256],str_level[16];
3703       size_t len;
3704       ierr = KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);CHKERRQ(ierr);
3705       ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);CHKERRQ(ierr);
3706       ierr = KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);CHKERRQ(ierr);
3707       ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);CHKERRQ(ierr);
3708       ierr = KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);CHKERRQ(ierr);
3709       ierr = KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);CHKERRQ(ierr);
3710       ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3711       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3712       /* prefix */
3713       ierr = PetscStrcpy(prefix,"");CHKERRQ(ierr);
3714       ierr = PetscStrcpy(str_level,"");CHKERRQ(ierr);
3715       if (!pcbddc->current_level) {
3716         ierr = PetscStrcpy(prefix,((PetscObject)pc)->prefix);CHKERRQ(ierr);
3717         ierr = PetscStrcat(prefix,"pc_bddc_coarse_");CHKERRQ(ierr);
3718       } else {
3719         ierr = PetscStrlen(((PetscObject)pc)->prefix,&len);CHKERRQ(ierr);
3720         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
3721         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
3722         ierr = PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);CHKERRQ(ierr);
3723         sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
3724         ierr = PetscStrcat(prefix,str_level);CHKERRQ(ierr);
3725       }
3726       ierr = KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);CHKERRQ(ierr);
3727       /* allow user customization */
3728       ierr = KSPSetFromOptions(pcbddc->coarse_ksp);CHKERRQ(ierr);
3729       ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
3730     }
3731 
3732     /* get some info after set from options */
3733     ierr = KSPGetPC(pcbddc->coarse_ksp,&pc_temp);CHKERRQ(ierr);
3734     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);CHKERRQ(ierr);
3735     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);CHKERRQ(ierr);
3736     ierr = PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);CHKERRQ(ierr);
3737     if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
3738       ierr = PCSetType(pc_temp,coarse_pc_type);CHKERRQ(ierr);
3739       isbddc = PETSC_FALSE;
3740     }
3741     if (isredundant) {
3742       KSP inner_ksp;
3743       PC inner_pc;
3744       ierr = PCRedundantGetKSP(pc_temp,&inner_ksp);CHKERRQ(ierr);
3745       ierr = KSPGetPC(inner_ksp,&inner_pc);CHKERRQ(ierr);
3746       ierr = PCFactorSetReuseFill(inner_pc,PETSC_TRUE);CHKERRQ(ierr);
3747     }
3748 
3749     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
3750     ierr = PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);CHKERRQ(ierr);
3751     ierr = PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);CHKERRQ(ierr);
3752     ierr = PCBDDCSetLevels(pc_temp,pcbddc->max_levels);CHKERRQ(ierr);
3753     if (nisdofs) {
3754       ierr = PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);CHKERRQ(ierr);
3755       for (i=0;i<nisdofs;i++) {
3756         ierr = ISDestroy(&isarray[i]);CHKERRQ(ierr);
3757       }
3758     }
3759     if (nisneu) {
3760       ierr = PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);CHKERRQ(ierr);
3761       ierr = ISDestroy(&isarray[nisdofs]);CHKERRQ(ierr);
3762     }
3763 
3764     /* assemble coarse matrix */
3765     if (coarse_reuse) {
3766       ierr = KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);CHKERRQ(ierr);
3767       ierr = PetscObjectReference((PetscObject)coarse_mat);CHKERRQ(ierr);
3768       coarse_mat_reuse = MAT_REUSE_MATRIX;
3769     } else {
3770       coarse_mat_reuse = MAT_INITIAL_MATRIX;
3771     }
3772     if (isbddc || isnn) {
3773       if (pcbddc->coarsening_ratio > 1) {
3774         if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
3775           ierr = MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,PETSC_TRUE,&pcbddc->coarse_subassembling);CHKERRQ(ierr);
3776           if (pcbddc->dbg_flag) {
3777             ierr = PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3778             ierr = PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");CHKERRQ(ierr);
3779             ierr = ISView(pcbddc->coarse_subassembling,dbg_viewer);CHKERRQ(ierr);
3780             ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3781           }
3782         }
3783         ierr = MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);CHKERRQ(ierr);
3784       } else {
3785         ierr = PetscObjectReference((PetscObject)coarse_mat_is);CHKERRQ(ierr);
3786         coarse_mat = coarse_mat_is;
3787       }
3788     } else {
3789       ierr = MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);CHKERRQ(ierr);
3790     }
3791     ierr = MatDestroy(&coarse_mat_is);CHKERRQ(ierr);
3792 
3793     /* propagate symmetry info to coarse matrix */
3794     ierr = MatSetOption(coarse_mat,MAT_SYMMETRIC,pcbddc->issym);CHKERRQ(ierr);
3795     ierr = MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
3796 
3797     /* set operators */
3798     ierr = KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3799     if (pcbddc->dbg_flag) {
3800       ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);CHKERRQ(ierr);
3801     }
3802   } else { /* processes non partecipating to coarse solver (if any) */
3803     coarse_mat = 0;
3804   }
3805   ierr = PetscFree(isarray);CHKERRQ(ierr);
3806 #if 0
3807   {
3808     PetscViewer viewer;
3809     char filename[256];
3810     sprintf(filename,"coarse_mat.m");
3811     ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,&viewer);CHKERRQ(ierr);
3812     ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
3813     ierr = MatView(coarse_mat,viewer);CHKERRQ(ierr);
3814     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3815   }
3816 #endif
3817 
3818   /* Compute coarse null space (special handling by BDDC only) */
3819   if (pcbddc->NullSpace) {
3820     ierr = PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);CHKERRQ(ierr);
3821   }
3822 
3823   if (pcbddc->coarse_ksp) {
3824     Vec crhs,csol;
3825     PetscBool ispreonly;
3826     if (CoarseNullSpace) {
3827       if (isbddc) {
3828         ierr = PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);CHKERRQ(ierr);
3829       } else {
3830         ierr = KSPSetNullSpace(pcbddc->coarse_ksp,CoarseNullSpace);CHKERRQ(ierr);
3831       }
3832     }
3833     /* setup coarse ksp */
3834     ierr = KSPSetUp(pcbddc->coarse_ksp);CHKERRQ(ierr);
3835     ierr = KSPGetSolution(pcbddc->coarse_ksp,&csol);CHKERRQ(ierr);
3836     ierr = KSPGetRhs(pcbddc->coarse_ksp,&crhs);CHKERRQ(ierr);
3837     /* hack */
3838     if (!csol) {
3839       ierr = MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);CHKERRQ(ierr);
3840     }
3841     if (!crhs) {
3842       ierr = MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));CHKERRQ(ierr);
3843     }
3844     /* Check coarse problem if in debug mode or if solving with an iterative method */
3845     ierr = PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);CHKERRQ(ierr);
3846     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
3847       KSP       check_ksp;
3848       KSPType   check_ksp_type;
3849       PC        check_pc;
3850       Vec       check_vec,coarse_vec;
3851       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
3852       PetscInt  its;
3853       PetscBool compute_eigs;
3854       PetscReal *eigs_r,*eigs_c;
3855       PetscInt  neigs;
3856       const char *prefix;
3857 
3858       /* Create ksp object suitable for estimation of extreme eigenvalues */
3859       ierr = KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);CHKERRQ(ierr);
3860       ierr = KSPSetOperators(check_ksp,coarse_mat,coarse_mat);CHKERRQ(ierr);
3861       ierr = KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);CHKERRQ(ierr);
3862       if (ispreonly) {
3863         check_ksp_type = KSPPREONLY;
3864         compute_eigs = PETSC_FALSE;
3865       } else {
3866         check_ksp_type = KSPGMRES;
3867         compute_eigs = PETSC_TRUE;
3868       }
3869       ierr = KSPSetType(check_ksp,check_ksp_type);CHKERRQ(ierr);
3870       ierr = KSPSetComputeSingularValues(check_ksp,compute_eigs);CHKERRQ(ierr);
3871       ierr = KSPSetComputeEigenvalues(check_ksp,compute_eigs);CHKERRQ(ierr);
3872       ierr = KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);CHKERRQ(ierr);
3873       ierr = KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);CHKERRQ(ierr);
3874       ierr = KSPSetOptionsPrefix(check_ksp,prefix);CHKERRQ(ierr);
3875       ierr = KSPAppendOptionsPrefix(check_ksp,"check_");CHKERRQ(ierr);
3876       ierr = KSPSetFromOptions(check_ksp);CHKERRQ(ierr);
3877       ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
3878       ierr = KSPGetPC(pcbddc->coarse_ksp,&check_pc);CHKERRQ(ierr);
3879       ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
3880       /* create random vec */
3881       ierr = KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);CHKERRQ(ierr);
3882       ierr = VecDuplicate(coarse_vec,&check_vec);CHKERRQ(ierr);
3883       ierr = VecSetRandom(check_vec,NULL);CHKERRQ(ierr);
3884       if (CoarseNullSpace) {
3885         ierr = MatNullSpaceRemove(CoarseNullSpace,check_vec);CHKERRQ(ierr);
3886       }
3887       ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3888       /* solve coarse problem */
3889       ierr = KSPSolve(check_ksp,coarse_vec,coarse_vec);CHKERRQ(ierr);
3890       if (CoarseNullSpace) {
3891         ierr = MatNullSpaceRemove(CoarseNullSpace,coarse_vec);CHKERRQ(ierr);
3892       }
3893       /* set eigenvalue estimation if preonly has not been requested */
3894       if (compute_eigs) {
3895         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_r);CHKERRQ(ierr);
3896         ierr = PetscMalloc((pcbddc->coarse_size+1)*sizeof(PetscReal),&eigs_c);CHKERRQ(ierr);
3897         ierr = KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);CHKERRQ(ierr);
3898         lambda_max = eigs_r[neigs-1];
3899         lambda_min = eigs_r[0];
3900         if (pcbddc->use_coarse_estimates) {
3901           if (lambda_max>lambda_min) {
3902             ierr = KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);CHKERRQ(ierr);
3903             ierr = KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));CHKERRQ(ierr);
3904           }
3905         }
3906       }
3907 
3908       /* check coarse problem residual error */
3909       if (pcbddc->dbg_flag) {
3910         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
3911         ierr = PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3912         ierr = VecAXPY(check_vec,-1.0,coarse_vec);CHKERRQ(ierr);
3913         ierr = VecNorm(check_vec,NORM_INFINITY,&infty_error);CHKERRQ(ierr);
3914         ierr = MatMult(coarse_mat,check_vec,coarse_vec);CHKERRQ(ierr);
3915         ierr = VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);CHKERRQ(ierr);
3916         ierr = VecDestroy(&check_vec);CHKERRQ(ierr);
3917         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (%d)\n",pcbddc->use_coarse_estimates);CHKERRQ(ierr);
3918         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);CHKERRQ(ierr);
3919         ierr = PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);CHKERRQ(ierr);
3920         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);CHKERRQ(ierr);
3921         ierr = PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);CHKERRQ(ierr);
3922         if (compute_eigs) {
3923           PetscReal lambda_max_s,lambda_min_s;
3924           ierr = KSPGetType(check_ksp,&check_ksp_type);CHKERRQ(ierr);
3925           ierr = KSPGetIterationNumber(check_ksp,&its);CHKERRQ(ierr);
3926           ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);CHKERRQ(ierr);
3927           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);
3928           for (i=0;i<neigs;i++) {
3929             ierr = PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);CHKERRQ(ierr);
3930           }
3931         }
3932         ierr = PetscViewerFlush(dbg_viewer);CHKERRQ(ierr);
3933         ierr = PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));CHKERRQ(ierr);
3934       }
3935       ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
3936       if (compute_eigs) {
3937         ierr = PetscFree(eigs_r);CHKERRQ(ierr);
3938         ierr = PetscFree(eigs_c);CHKERRQ(ierr);
3939       }
3940     }
3941   }
3942   /* print additional info */
3943   if (pcbddc->dbg_flag) {
3944     /* waits until all processes reaches this point */
3945     ierr = PetscBarrier((PetscObject)pc);CHKERRQ(ierr);
3946     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);CHKERRQ(ierr);
3947     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3948   }
3949 
3950   /* free memory */
3951   ierr = MatNullSpaceDestroy(&CoarseNullSpace);CHKERRQ(ierr);
3952   ierr = MatDestroy(&coarse_mat);CHKERRQ(ierr);
3953   PetscFunctionReturn(0);
3954 }
3955 
3956 #undef __FUNCT__
3957 #define __FUNCT__ "PCBDDCComputePrimalNumbering"
3958 PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
3959 {
3960   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
3961   PC_IS*         pcis = (PC_IS*)pc->data;
3962   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
3963   PetscInt       i,coarse_size;
3964   PetscInt       *local_primal_indices;
3965   PetscErrorCode ierr;
3966 
3967   PetscFunctionBegin;
3968   /* Compute global number of coarse dofs */
3969   if (!pcbddc->primal_indices_local_idxs && pcbddc->local_primal_size) {
3970     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Local primal indices have not been created");
3971   }
3972   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);
3973 
3974   /* check numbering */
3975   if (pcbddc->dbg_flag) {
3976     PetscScalar coarsesum,*array;
3977     PetscBool set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;
3978 
3979     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
3980     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
3981     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");CHKERRQ(ierr);
3982     ierr = PetscViewerASCIISynchronizedAllow(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
3983     ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
3984     for (i=0;i<pcbddc->local_primal_size;i++) {
3985       ierr = VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
3986     }
3987     ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
3988     ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
3989     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
3990     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3991     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
3992     ierr = VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3993     ierr = VecScatterEnd(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
3994     ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
3995     for (i=0;i<pcis->n;i++) {
3996       if (array[i] == 1.0) {
3997         set_error = PETSC_TRUE;
3998         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a single process!\n",PetscGlobalRank,i);CHKERRQ(ierr);
3999       }
4000     }
4001     ierr = MPI_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
4002     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4003     for (i=0;i<pcis->n;i++) {
4004       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
4005     }
4006     ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
4007     ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
4008     ierr = VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4009     ierr = VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
4010     ierr = VecSum(pcis->vec1_global,&coarsesum);CHKERRQ(ierr);
4011     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));CHKERRQ(ierr);
4012     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
4013       ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");CHKERRQ(ierr);
4014       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4015       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
4016       for (i=0;i<pcbddc->local_primal_size;i++) {
4017         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%d]=%d (%d)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i]);
4018       }
4019       ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4020     }
4021     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
4022     if (set_error_reduced) {
4023       SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
4024     }
4025   }
4026   /* get back data */
4027   *coarse_size_n = coarse_size;
4028   *local_primal_indices_n = local_primal_indices;
4029   PetscFunctionReturn(0);
4030 }
4031 
4032 #undef __FUNCT__
4033 #define __FUNCT__ "PCBDDCGlobalToLocal"
4034 PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
4035 {
4036   IS             localis_t;
4037   PetscInt       i,lsize,*idxs,n;
4038   PetscScalar    *vals;
4039   PetscErrorCode ierr;
4040 
4041   PetscFunctionBegin;
4042   /* get indices in local ordering exploiting local to global map */
4043   ierr = ISGetLocalSize(globalis,&lsize);CHKERRQ(ierr);
4044   ierr = PetscMalloc(lsize*sizeof(PetscScalar),&vals);CHKERRQ(ierr);
4045   for (i=0;i<lsize;i++) vals[i] = 1.0;
4046   ierr = ISGetIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
4047   ierr = VecSet(gwork,0.0);CHKERRQ(ierr);
4048   ierr = VecSet(lwork,0.0);CHKERRQ(ierr);
4049   if (idxs) { /* multilevel guard */
4050     ierr = VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);CHKERRQ(ierr);
4051   }
4052   ierr = VecAssemblyBegin(gwork);CHKERRQ(ierr);
4053   ierr = ISRestoreIndices(globalis,(const PetscInt**)&idxs);CHKERRQ(ierr);
4054   ierr = PetscFree(vals);CHKERRQ(ierr);
4055   ierr = VecAssemblyEnd(gwork);CHKERRQ(ierr);
4056   /* now compute set in local ordering */
4057   ierr = VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4058   ierr = VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
4059   ierr = VecGetArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
4060   ierr = VecGetSize(lwork,&n);CHKERRQ(ierr);
4061   for (i=0,lsize=0;i<n;i++) {
4062     if (PetscRealPart(vals[i]) > 0.5) {
4063       lsize++;
4064     }
4065   }
4066   ierr = PetscMalloc(lsize*sizeof(PetscInt),&idxs);CHKERRQ(ierr);
4067   for (i=0,lsize=0;i<n;i++) {
4068     if (PetscRealPart(vals[i]) > 0.5) {
4069       idxs[lsize++] = i;
4070     }
4071   }
4072   ierr = VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);CHKERRQ(ierr);
4073   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);CHKERRQ(ierr);
4074   *localis = localis_t;
4075   PetscFunctionReturn(0);
4076 }
4077 
4078 /* the next two functions will be called in KSPMatMult if a change of basis has been requested */
4079 #undef __FUNCT__
4080 #define __FUNCT__ "PCBDDCMatMult_Private"
4081 static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y)
4082 {
4083   PCBDDCChange_ctx change_ctx;
4084   PetscErrorCode   ierr;
4085 
4086   PetscFunctionBegin;
4087   ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
4088   ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
4089   ierr = MatMult(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
4090   ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
4091   PetscFunctionReturn(0);
4092 }
4093 
4094 #undef __FUNCT__
4095 #define __FUNCT__ "PCBDDCMatMultTranspose_Private"
4096 static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y)
4097 {
4098   PCBDDCChange_ctx change_ctx;
4099   PetscErrorCode   ierr;
4100 
4101   PetscFunctionBegin;
4102   ierr = MatShellGetContext(A,&change_ctx);CHKERRQ(ierr);
4103   ierr = MatMult(change_ctx->global_change,x,change_ctx->work[0]);CHKERRQ(ierr);
4104   ierr = MatMultTranspose(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);CHKERRQ(ierr);
4105   ierr = MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);CHKERRQ(ierr);
4106   PetscFunctionReturn(0);
4107 }
4108