xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision a401a8b6f7bc823ba5fc6d107d6739773b0b4d41)
1 #include "bddc.h"
2 #include "bddcprivate.h"
3 #include <petscblaslapack.h>
4 
5 #undef __FUNCT__
6 #define __FUNCT__ "PCBDDCSetLevel"
7 PetscErrorCode PCBDDCSetLevel(PC pc,PetscInt level)
8 {
9   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
10 
11   PetscFunctionBegin;
12   pcbddc->current_level=level;
13   PetscFunctionReturn(0);
14 }
15 
16 #undef __FUNCT__
17 #define __FUNCT__ "PCBDDCResetCustomization"
18 PetscErrorCode PCBDDCResetCustomization(PC pc)
19 {
20   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
21   PetscInt       i;
22   PetscErrorCode ierr;
23 
24   PetscFunctionBegin;
25   ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
26   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
27   ierr = MatNullSpaceDestroy(&pcbddc->NullSpace);CHKERRQ(ierr);
28   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
29   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
30   for (i=0;i<pcbddc->n_ISForDofs;i++) {
31     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
32   }
33   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
34   PetscFunctionReturn(0);
35 }
36 
37 #undef __FUNCT__
38 #define __FUNCT__ "PCBDDCResetTopography"
39 PetscErrorCode PCBDDCResetTopography(PC pc)
40 {
41   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
42   PetscErrorCode ierr;
43 
44   PetscFunctionBegin;
45   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
46   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
47   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
48   PetscFunctionReturn(0);
49 }
50 
51 #undef __FUNCT__
52 #define __FUNCT__ "PCBDDCResetSolvers"
53 PetscErrorCode PCBDDCResetSolvers(PC pc)
54 {
55   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
56   PetscErrorCode ierr;
57 
58   PetscFunctionBegin;
59   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
60   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
61   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
62   ierr = MatDestroy(&pcbddc->coarse_mat);CHKERRQ(ierr);
63   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
64   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
65   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
66   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
67   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
68   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
69   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
70   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
71   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
72   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
73   ierr = VecDestroy(&pcbddc->vec4_D);CHKERRQ(ierr);
74   ierr = ISDestroy(&pcbddc->is_R_local);CHKERRQ(ierr);
75   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
76   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
77   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
78   ierr = PetscFree(pcbddc->local_primal_indices);CHKERRQ(ierr);
79   ierr = PetscFree(pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
80   ierr = PetscFree(pcbddc->replicated_local_primal_values);CHKERRQ(ierr);
81   ierr = PetscFree(pcbddc->local_primal_displacements);CHKERRQ(ierr);
82   ierr = PetscFree(pcbddc->local_primal_sizes);CHKERRQ(ierr);
83   PetscFunctionReturn(0);
84 }
85 
86 #undef __FUNCT__
87 #define __FUNCT__ "PCBDDCCreateWorkVectors"
88 PetscErrorCode PCBDDCCreateWorkVectors(PC pc)
89 {
90   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
91   PC_IS          *pcis = (PC_IS*)pc->data;
92   VecType        impVecType;
93   PetscInt       n_vertices,n_constraints,local_primal_size,n_R;
94   PetscErrorCode ierr;
95 
96   PetscFunctionBegin;
97   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,NULL);CHKERRQ(ierr);
98   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&n_constraints,NULL);CHKERRQ(ierr);
99   local_primal_size = n_constraints+n_vertices;
100   n_R = pcis->n-n_vertices;
101   /* local work vectors */
102   ierr = VecGetType(pcis->vec1_N,&impVecType);CHKERRQ(ierr);
103   ierr = VecDuplicate(pcis->vec1_D,&pcbddc->vec4_D);CHKERRQ(ierr);
104   ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);CHKERRQ(ierr);
105   ierr = VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);CHKERRQ(ierr);
106   ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
107   ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
108   ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);CHKERRQ(ierr);
109   ierr = VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,local_primal_size);CHKERRQ(ierr);
110   ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
111   if (n_constraints) {
112     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);CHKERRQ(ierr);
113     ierr = VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);CHKERRQ(ierr);
114     ierr = VecSetType(pcbddc->vec1_C,impVecType);CHKERRQ(ierr);
115   }
116   PetscFunctionReturn(0);
117 }
118 
119 #undef __FUNCT__
120 #define __FUNCT__ "PCBDDCSetUpCoarseLocal"
121 PetscErrorCode PCBDDCSetUpCoarseLocal(PC pc)
122 {
123   PetscErrorCode         ierr;
124   /* pointers to pcis and pcbddc */
125   PC_IS*                 pcis = (PC_IS*)pc->data;
126   PC_BDDC*               pcbddc = (PC_BDDC*)pc->data;
127   /* submatrices of local problem */
128   Mat                    A_RV,A_VR,A_VV;
129   /* working matrices */
130   Mat                    M1,M2,M3,C_CR;
131   /* working vectors */
132   Vec                    vec1_C,vec2_C,vec1_V,vec2_V;
133   /* additional working stuff */
134   IS                     is_aux;
135   ISLocalToGlobalMapping BtoNmap;
136   PetscScalar            *coarse_submat_vals; /* TODO: use a PETSc matrix */
137   const PetscScalar      *array,*row_cmat_values;
138   const PetscInt         *row_cmat_indices,*idx_R_local;
139   PetscInt               *vertices,*idx_V_B,*auxindices;
140   PetscInt               n_vertices,n_constraints,size_of_constraint;
141   PetscInt               i,j,n_R,n_D,n_B;
142   PetscBool              setsym=PETSC_FALSE,issym=PETSC_FALSE;
143   /* Vector and matrix types */
144   VecType                impVecType;
145   MatType                impMatType;
146   /* some shortcuts to scalars */
147   PetscScalar            zero=0.0,one=1.0,m_one=-1.0;
148   /* for debugging purposes */
149   PetscReal              *coarsefunctions_errors,*constraints_errors;
150 
151   PetscFunctionBegin;
152   /* get number of vertices and their local indices */
153   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,&vertices);CHKERRQ(ierr);
154   n_constraints = pcbddc->local_primal_size-n_vertices;
155   /* Set Non-overlapping dimensions */
156   n_B = pcis->n_B; n_D = pcis->n - n_B;
157   n_R = pcis->n-n_vertices;
158 
159   /* Set types for local objects needed by BDDC precondtioner */
160   impMatType = MATSEQDENSE;
161   ierr = VecGetType(pcis->vec1_N,&impVecType);CHKERRQ(ierr);
162 
163   /* Allocating some extra storage just to be safe */
164   ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&auxindices);CHKERRQ(ierr);
165   for (i=0;i<pcis->n;i++) auxindices[i]=i;
166 
167   /* vertices in boundary numbering */
168   ierr = PetscMalloc(n_vertices*sizeof(PetscInt),&idx_V_B);CHKERRQ(ierr);
169   ierr = ISLocalToGlobalMappingCreateIS(pcis->is_B_local,&BtoNmap);CHKERRQ(ierr);
170   ierr = ISGlobalToLocalMappingApply(BtoNmap,IS_GTOLM_DROP,n_vertices,vertices,&i,idx_V_B);CHKERRQ(ierr);
171   ierr = ISLocalToGlobalMappingDestroy(&BtoNmap);CHKERRQ(ierr);
172   if (i != n_vertices) {
173     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",n_vertices,i);
174   }
175 
176   /* some work vectors on vertices and/or constraints */
177   if (n_vertices) {
178     ierr = VecCreate(PETSC_COMM_SELF,&vec1_V);CHKERRQ(ierr);
179     ierr = VecSetSizes(vec1_V,n_vertices,n_vertices);CHKERRQ(ierr);
180     ierr = VecSetType(vec1_V,impVecType);CHKERRQ(ierr);
181     ierr = VecDuplicate(vec1_V,&vec2_V);CHKERRQ(ierr);
182   }
183   if (n_constraints) {
184     ierr = VecDuplicate(pcbddc->vec1_C,&vec1_C);CHKERRQ(ierr);
185     ierr = VecDuplicate(pcbddc->vec1_C,&vec2_C);CHKERRQ(ierr);
186   }
187 
188   /* Precompute stuffs needed for preprocessing and application of BDDC*/
189   if (n_constraints) {
190     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->local_auxmat2);CHKERRQ(ierr);
191     ierr = MatSetSizes(pcbddc->local_auxmat2,n_R,n_constraints,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
192     ierr = MatSetType(pcbddc->local_auxmat2,impMatType);CHKERRQ(ierr);
193     ierr = MatSetUp(pcbddc->local_auxmat2);CHKERRQ(ierr);
194 
195     /* Extract constraints on R nodes: C_{CR}  */
196     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);CHKERRQ(ierr);
197     ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
198     ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
199 
200     /* Assemble local_auxmat2 = - A_{RR}^{-1} C^T_{CR} needed by BDDC application */
201     for (i=0;i<n_constraints;i++) {
202       ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
203       /* Get row of constraint matrix in R numbering */
204       ierr = MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
205       ierr = VecSetValues(pcbddc->vec1_R,size_of_constraint,row_cmat_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
206       ierr = MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);CHKERRQ(ierr);
207       ierr = VecAssemblyBegin(pcbddc->vec1_R);CHKERRQ(ierr);
208       ierr = VecAssemblyEnd(pcbddc->vec1_R);CHKERRQ(ierr);
209       /* Solve for row of constraint matrix in R numbering */
210       ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
211       /* Set values in local_auxmat2 */
212       ierr = VecGetArrayRead(pcbddc->vec2_R,&array);CHKERRQ(ierr);
213       ierr = MatSetValues(pcbddc->local_auxmat2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
214       ierr = VecRestoreArrayRead(pcbddc->vec2_R,&array);CHKERRQ(ierr);
215     }
216     ierr = MatAssemblyBegin(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
217     ierr = MatAssemblyEnd(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
218     ierr = MatScale(pcbddc->local_auxmat2,m_one);CHKERRQ(ierr);
219 
220     /* Assemble explicitly M1 = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} needed in preproc  */
221     ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);CHKERRQ(ierr);
222     ierr = MatLUFactor(M3,NULL,NULL,NULL);CHKERRQ(ierr);
223     ierr = MatCreate(PETSC_COMM_SELF,&M1);CHKERRQ(ierr);
224     ierr = MatSetSizes(M1,n_constraints,n_constraints,n_constraints,n_constraints);CHKERRQ(ierr);
225     ierr = MatSetType(M1,impMatType);CHKERRQ(ierr);
226     ierr = MatSetUp(M1);CHKERRQ(ierr);
227     ierr = MatDuplicate(M1,MAT_DO_NOT_COPY_VALUES,&M2);CHKERRQ(ierr);
228     ierr = MatZeroEntries(M2);CHKERRQ(ierr);
229     ierr = VecSet(vec1_C,m_one);CHKERRQ(ierr);
230     ierr = MatDiagonalSet(M2,vec1_C,INSERT_VALUES);CHKERRQ(ierr);
231     ierr = MatMatSolve(M3,M2,M1);CHKERRQ(ierr);
232     ierr = MatDestroy(&M2);CHKERRQ(ierr);
233     ierr = MatDestroy(&M3);CHKERRQ(ierr);
234     /* Assemble local_auxmat1 = M1*C_{CR} needed by BDDC application in KSP and in preproc */
235     ierr = MatMatMult(M1,C_CR,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
236   }
237 
238   /* Get submatrices from subdomain matrix */
239   if (n_vertices) {
240     ierr = ISCreateGeneral(PETSC_COMM_SELF,n_vertices,vertices,PETSC_COPY_VALUES,&is_aux);CHKERRQ(ierr);
241     ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
242     ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
243     ierr = MatGetSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
244     ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
245   }
246 
247   /* Matrix of coarse basis functions (local) */
248   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
249   ierr = MatSetSizes(pcbddc->coarse_phi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
250   ierr = MatSetType(pcbddc->coarse_phi_B,impMatType);CHKERRQ(ierr);
251   ierr = MatSetUp(pcbddc->coarse_phi_B);CHKERRQ(ierr);
252   if (pcbddc->inexact_prec_type || pcbddc->dbg_flag) {
253     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
254     ierr = MatSetSizes(pcbddc->coarse_phi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
255     ierr = MatSetType(pcbddc->coarse_phi_D,impMatType);CHKERRQ(ierr);
256     ierr = MatSetUp(pcbddc->coarse_phi_D);CHKERRQ(ierr);
257   }
258 
259   if (pcbddc->dbg_flag) {
260     ierr = ISGetIndices(pcbddc->is_R_local,&idx_R_local);CHKERRQ(ierr);
261     ierr = PetscMalloc(2*pcbddc->local_primal_size*sizeof(*coarsefunctions_errors),&coarsefunctions_errors);CHKERRQ(ierr);
262     ierr = PetscMalloc(2*pcbddc->local_primal_size*sizeof(*constraints_errors),&constraints_errors);CHKERRQ(ierr);
263   }
264   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
265   ierr = PetscMalloc((pcbddc->local_primal_size)*(pcbddc->local_primal_size)*sizeof(PetscScalar),&coarse_submat_vals);CHKERRQ(ierr);
266 
267   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
268 
269   /* vertices */
270   for (i=0;i<n_vertices;i++) {
271     ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
272     ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
273     ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
274     ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
275     /* simplified solution of saddle point problem with null rhs on constraints multipliers */
276     ierr = MatMult(A_RV,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
277     ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
278     ierr = VecScale(pcbddc->vec1_R,m_one);CHKERRQ(ierr);
279     if (n_constraints) {
280       ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec1_R,vec1_C);CHKERRQ(ierr);
281       ierr = MatMultAdd(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
282       ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
283     }
284     ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
285     ierr = MatMultAdd(A_VV,vec1_V,vec2_V,vec2_V);CHKERRQ(ierr);
286 
287     /* Set values in coarse basis function and subdomain part of coarse_mat */
288     /* coarse basis functions */
289     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
290     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
291     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
292     ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
293     ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
294     ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
295     ierr = MatSetValue(pcbddc->coarse_phi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
296     if (pcbddc->inexact_prec_type || pcbddc->dbg_flag) {
297       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
298       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
299       ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
300       ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
301       ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
302     }
303     /* subdomain contribution to coarse matrix. WARNING -> column major ordering */
304     ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
305     ierr = PetscMemcpy(&coarse_submat_vals[i*pcbddc->local_primal_size],array,n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
306     ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
307     if (n_constraints) {
308       ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
309       ierr = PetscMemcpy(&coarse_submat_vals[i*pcbddc->local_primal_size+n_vertices],array,n_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
310       ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
311     }
312 
313     /* check */
314     if (pcbddc->dbg_flag) {
315       /* assemble subdomain vector on local nodes */
316       ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
317       ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
318       ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
319       ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
320       ierr = VecSetValue(pcis->vec1_N,vertices[i],one,INSERT_VALUES);CHKERRQ(ierr);
321       ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
322       ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
323       /* assemble subdomain vector of lagrange multipliers (i.e. primal nodes) */
324       ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
325       ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
326       ierr = VecSetValues(pcbddc->vec1_P,n_vertices,auxindices,array,INSERT_VALUES);CHKERRQ(ierr);
327       ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
328       if (n_constraints) {
329         ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
330         ierr = VecSetValues(pcbddc->vec1_P,n_constraints,&auxindices[n_vertices],array,INSERT_VALUES);CHKERRQ(ierr);
331         ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
332       }
333       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
334       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
335       ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
336       /* check saddle point solution */
337       ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
338       ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
339       ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i]);CHKERRQ(ierr);
340       ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
341       /* shift by the identity matrix */
342       ierr = VecSetValue(pcbddc->vec1_P,i,m_one,ADD_VALUES);CHKERRQ(ierr);
343       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
344       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
345       ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i]);CHKERRQ(ierr);
346     }
347   }
348 
349   /* constraints */
350   for (i=0;i<n_constraints;i++) {
351     ierr = VecSet(vec2_C,zero);CHKERRQ(ierr);
352     ierr = VecSetValue(vec2_C,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
353     ierr = VecAssemblyBegin(vec2_C);CHKERRQ(ierr);
354     ierr = VecAssemblyEnd(vec2_C);CHKERRQ(ierr);
355     /* simplified solution of saddle point problem with null rhs on vertices multipliers */
356     ierr = MatMult(M1,vec2_C,vec1_C);CHKERRQ(ierr);
357     ierr = MatMult(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
358     ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
359     if (n_vertices) {
360       ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
361     }
362     /* Set values in coarse basis function and subdomain part of coarse_mat */
363     /* coarse basis functions */
364     j = i+n_vertices; /* don't touch this! */
365     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
366     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
367     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
368     ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
369     ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&j,array,INSERT_VALUES);CHKERRQ(ierr);
370     ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
371     if (pcbddc->inexact_prec_type || pcbddc->dbg_flag) {
372       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
373       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
374       ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
375       ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&j,array,INSERT_VALUES);CHKERRQ(ierr);
376       ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
377     }
378     /* subdomain contribution to coarse matrix. WARNING -> column major ordering */
379     if (n_vertices) {
380       ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
381       ierr = PetscMemcpy(&coarse_submat_vals[j*pcbddc->local_primal_size],array,n_vertices*sizeof(PetscScalar));CHKERRQ(ierr);
382       ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
383     }
384     ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
385     ierr = PetscMemcpy(&coarse_submat_vals[j*pcbddc->local_primal_size+n_vertices],array,n_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
386     ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
387 
388     if (pcbddc->dbg_flag) {
389       /* assemble subdomain vector on nodes */
390       ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
391       ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
392       ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
393       ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
394       ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
395       ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
396       /* assemble subdomain vector of lagrange multipliers */
397       ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
398       if (n_vertices) {
399         ierr = VecGetArrayRead(vec2_V,&array);CHKERRQ(ierr);
400         ierr = VecSetValues(pcbddc->vec1_P,n_vertices,auxindices,array,INSERT_VALUES);CHKERRQ(ierr);
401         ierr = VecRestoreArrayRead(vec2_V,&array);CHKERRQ(ierr);
402       }
403       ierr = VecGetArrayRead(vec1_C,&array);CHKERRQ(ierr);
404       ierr = VecSetValues(pcbddc->vec1_P,n_constraints,&auxindices[n_vertices],array,INSERT_VALUES);CHKERRQ(ierr);
405       ierr = VecRestoreArrayRead(vec1_C,&array);CHKERRQ(ierr);
406       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
407       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
408       ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
409       /* check saddle point solution */
410       ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
411       ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
412       ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[j]);CHKERRQ(ierr);
413       ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
414       /* shift by the identity matrix */
415       ierr = VecSetValue(pcbddc->vec1_P,j,m_one,ADD_VALUES);CHKERRQ(ierr);
416       ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
417       ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
418       ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[j]);CHKERRQ(ierr);
419     }
420   }
421   /* call assembling routines for local coarse basis */
422   ierr = MatAssemblyBegin(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
423   ierr = MatAssemblyEnd(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
424   if (pcbddc->inexact_prec_type || pcbddc->dbg_flag) {
425     ierr = MatAssemblyBegin(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
426     ierr = MatAssemblyEnd(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
427   }
428 
429   /* compute other basis functions for non-symmetric problems */
430   ierr = MatIsSymmetricKnown(pc->pmat,&setsym,&issym);CHKERRQ(ierr);
431   if (!setsym || (setsym && !issym)) {
432     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_psi_B);CHKERRQ(ierr);
433     ierr = MatSetSizes(pcbddc->coarse_psi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
434     ierr = MatSetType(pcbddc->coarse_psi_B,impMatType);CHKERRQ(ierr);
435     ierr = MatSetUp(pcbddc->coarse_psi_B);CHKERRQ(ierr);
436     if (pcbddc->inexact_prec_type || pcbddc->dbg_flag ) {
437       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_psi_D);CHKERRQ(ierr);
438       ierr = MatSetSizes(pcbddc->coarse_psi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
439       ierr = MatSetType(pcbddc->coarse_psi_D,impMatType);CHKERRQ(ierr);
440       ierr = MatSetUp(pcbddc->coarse_psi_D);CHKERRQ(ierr);
441     }
442     for (i=0;i<pcbddc->local_primal_size;i++) {
443       if (n_constraints) {
444         ierr = VecSet(vec1_C,zero);CHKERRQ(ierr);
445         for (j=0;j<n_constraints;j++) {
446           ierr = VecSetValue(vec1_C,j,coarse_submat_vals[(j+n_vertices)*pcbddc->local_primal_size+i],INSERT_VALUES);CHKERRQ(ierr);
447         }
448         ierr = VecAssemblyBegin(vec1_C);CHKERRQ(ierr);
449         ierr = VecAssemblyEnd(vec1_C);CHKERRQ(ierr);
450       }
451       if (i<n_vertices) {
452         ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
453         ierr = VecSetValue(vec1_V,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
454         ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
455         ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
456         ierr = MatMultTranspose(A_VR,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
457         if (n_constraints) {
458           ierr = MatMultTransposeAdd(C_CR,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
459         }
460       } else {
461         ierr = MatMultTranspose(C_CR,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
462       }
463       ierr = KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
464       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
465       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
466       ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
467       ierr = VecGetArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
468       ierr = MatSetValues(pcbddc->coarse_psi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
469       ierr = VecRestoreArrayRead(pcis->vec1_B,&array);CHKERRQ(ierr);
470       if (i<n_vertices) {
471         ierr = MatSetValue(pcbddc->coarse_psi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
472       }
473       if (pcbddc->inexact_prec_type || pcbddc->dbg_flag) {
474         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
475         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
476         ierr = VecGetArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
477         ierr = MatSetValues(pcbddc->coarse_psi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
478         ierr = VecRestoreArrayRead(pcis->vec1_D,&array);CHKERRQ(ierr);
479       }
480 
481       if (pcbddc->dbg_flag) {
482         /* assemble subdomain vector on nodes */
483         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
484         ierr = VecGetArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
485         ierr = VecSetValues(pcis->vec1_N,n_R,idx_R_local,array,INSERT_VALUES);CHKERRQ(ierr);
486         ierr = VecRestoreArrayRead(pcbddc->vec1_R,&array);CHKERRQ(ierr);
487         if (i<n_vertices) {
488           ierr = VecSetValue(pcis->vec1_N,vertices[i],one,INSERT_VALUES);CHKERRQ(ierr);
489         }
490         ierr = VecAssemblyBegin(pcis->vec1_N);CHKERRQ(ierr);
491         ierr = VecAssemblyEnd(pcis->vec1_N);CHKERRQ(ierr);
492         /* assemble subdomain vector of lagrange multipliers */
493         for (j=0;j<pcbddc->local_primal_size;j++) {
494           ierr = VecSetValue(pcbddc->vec1_P,j,-coarse_submat_vals[j*pcbddc->local_primal_size+i],INSERT_VALUES);CHKERRQ(ierr);
495         }
496         ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
497         ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
498         /* check saddle point solution */
499         ierr = MatMultTranspose(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
500         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
501         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i+pcbddc->local_primal_size]);CHKERRQ(ierr);
502         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
503         /* shift by the identity matrix */
504         ierr = VecSetValue(pcbddc->vec1_P,i,m_one,ADD_VALUES);CHKERRQ(ierr);
505         ierr = VecAssemblyBegin(pcbddc->vec1_P);CHKERRQ(ierr);
506         ierr = VecAssemblyEnd(pcbddc->vec1_P);CHKERRQ(ierr);
507         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i+pcbddc->local_primal_size]);CHKERRQ(ierr);
508       }
509     }
510     ierr = MatAssemblyBegin(pcbddc->coarse_psi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
511     ierr = MatAssemblyEnd(pcbddc->coarse_psi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
512     if ( pcbddc->inexact_prec_type || pcbddc->dbg_flag ) {
513       ierr = MatAssemblyBegin(pcbddc->coarse_psi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
514       ierr = MatAssemblyEnd(pcbddc->coarse_psi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
515     }
516   }
517   ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
518   /* Checking coarse_sub_mat and coarse basis functios */
519   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
520   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
521   if (pcbddc->dbg_flag) {
522     Mat         coarse_sub_mat;
523     Mat         AUXMAT,TM1,TM2,TM3,TM4;
524     Mat         coarse_phi_D,coarse_phi_B;
525     Mat         coarse_psi_D,coarse_psi_B;
526     Mat         A_II,A_BB,A_IB,A_BI;
527     MatType     checkmattype=MATSEQAIJ;
528     PetscReal   real_value;
529 
530     ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
531     ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
532     ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
533     ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
534     ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
535     ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
536     if (pcbddc->coarse_psi_B) {
537       ierr = MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);CHKERRQ(ierr);
538       ierr = MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);CHKERRQ(ierr);
539     }
540     ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);
541 
542     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
543     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat and local basis functions\n");CHKERRQ(ierr);
544     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
545     if (pcbddc->coarse_psi_B) {
546       ierr = MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
547       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
548       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
549       ierr = MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
550       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
551       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
552       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
553       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
554       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
555       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
556       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
557       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
558     } else {
559       ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
560       ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
561       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
562       ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
563       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
564       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
565       ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
566       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
567     }
568     ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
569     ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
570     ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
571     ierr = MatConvert(TM1,MATSEQDENSE,MAT_REUSE_MATRIX,&TM1);CHKERRQ(ierr);
572     ierr = MatAXPY(TM1,m_one,coarse_sub_mat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
573     ierr = MatNorm(TM1,NORM_INFINITY,&real_value);CHKERRQ(ierr);
574     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"----------------------------------\n");CHKERRQ(ierr);
575     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d \n",PetscGlobalRank);CHKERRQ(ierr);
576     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"matrix error = % 1.14e\n",real_value);CHKERRQ(ierr);
577     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"coarse functions (phi) errors\n");CHKERRQ(ierr);
578     for (i=0;i<pcbddc->local_primal_size;i++) {
579       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i,coarsefunctions_errors[i]);CHKERRQ(ierr);
580     }
581     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"constraints (phi) errors\n");CHKERRQ(ierr);
582     for (i=0;i<pcbddc->local_primal_size;i++) {
583       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i,constraints_errors[i]);CHKERRQ(ierr);
584     }
585     if (pcbddc->coarse_psi_B) {
586       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"coarse functions (psi) errors\n");CHKERRQ(ierr);
587       for (i=pcbddc->local_primal_size;i<2*pcbddc->local_primal_size;i++) {
588         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i-pcbddc->local_primal_size,coarsefunctions_errors[i]);CHKERRQ(ierr);
589       }
590       ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"constraints (psi) errors\n");CHKERRQ(ierr);
591       for (i=pcbddc->local_primal_size;i<2*pcbddc->local_primal_size;i++) {
592         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local %02d-th function error = % 1.14e\n",i-pcbddc->local_primal_size,constraints_errors[i]);CHKERRQ(ierr);
593       }
594     }
595     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
596     ierr = MatDestroy(&A_II);CHKERRQ(ierr);
597     ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
598     ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
599     ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
600     ierr = MatDestroy(&TM1);CHKERRQ(ierr);
601     ierr = MatDestroy(&TM2);CHKERRQ(ierr);
602     ierr = MatDestroy(&TM3);CHKERRQ(ierr);
603     ierr = MatDestroy(&TM4);CHKERRQ(ierr);
604     ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
605     ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
606     if (pcbddc->coarse_psi_B) {
607       ierr = MatDestroy(&coarse_psi_D);CHKERRQ(ierr);
608       ierr = MatDestroy(&coarse_psi_B);CHKERRQ(ierr);
609     }
610     ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
611     ierr = ISRestoreIndices(pcbddc->is_R_local,&idx_R_local);CHKERRQ(ierr);
612     ierr = PetscFree(coarsefunctions_errors);CHKERRQ(ierr);
613     ierr = PetscFree(constraints_errors);CHKERRQ(ierr);
614   }
615   /* free memory */
616   if (n_vertices) {
617     ierr = PetscFree(vertices);CHKERRQ(ierr);
618     ierr = VecDestroy(&vec1_V);CHKERRQ(ierr);
619     ierr = VecDestroy(&vec2_V);CHKERRQ(ierr);
620     ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
621     ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
622     ierr = MatDestroy(&A_VV);CHKERRQ(ierr);
623   }
624   if (n_constraints) {
625     ierr = VecDestroy(&vec1_C);CHKERRQ(ierr);
626     ierr = VecDestroy(&vec2_C);CHKERRQ(ierr);
627     ierr = MatDestroy(&M1);CHKERRQ(ierr);
628     ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
629   }
630   ierr = PetscFree(auxindices);CHKERRQ(ierr);
631   /* create coarse matrix and data structures for message passing associated actual choice of coarse problem type */
632   ierr = PCBDDCSetUpCoarseEnvironment(pc,coarse_submat_vals);CHKERRQ(ierr);
633   ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
634   PetscFunctionReturn(0);
635 }
636 
637 #undef __FUNCT__
638 #define __FUNCT__ "PCBDDCSetUpLocalMatrices"
639 PetscErrorCode PCBDDCSetUpLocalMatrices(PC pc)
640 {
641   PC_IS*            pcis = (PC_IS*)(pc->data);
642   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
643   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
644   /* manage repeated solves */
645   MatReuse          reuse;
646   MatStructure      matstruct;
647   PetscErrorCode    ierr;
648 
649   PetscFunctionBegin;
650   /* get mat flags */
651   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
652   reuse = MAT_INITIAL_MATRIX;
653   if (pc->setupcalled) {
654     /* when matstruct is SAME_PRECONDITIONER, we shouldn't be here */
655     if (matstruct == SAME_PRECONDITIONER) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
656     if (matstruct == SAME_NONZERO_PATTERN) {
657       reuse = MAT_REUSE_MATRIX;
658     } else {
659       reuse = MAT_INITIAL_MATRIX;
660     }
661   }
662   if (reuse == MAT_INITIAL_MATRIX) {
663     ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
664     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
665     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
666     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
667     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
668   }
669 
670   /* transform local matrices if needed */
671   if (pcbddc->use_change_of_basis) {
672     Mat         change_mat_all;
673     PetscScalar *row_cmat_values;
674     PetscInt    *row_cmat_indices;
675     PetscInt    *nnz,*is_indices,*temp_indices;
676     PetscInt    i,j,k,n_D,n_B;
677 
678     /* Get Non-overlapping dimensions */
679     n_B = pcis->n_B;
680     n_D = pcis->n-n_B;
681 
682     /* compute nonzero structure of change of basis on all local nodes */
683     ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
684     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
685     for (i=0;i<n_D;i++) nnz[is_indices[i]] = 1;
686     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
687     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
688     k=1;
689     for (i=0;i<n_B;i++) {
690       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
691       nnz[is_indices[i]]=j;
692       if (k < j) k = j;
693       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
694     }
695     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
696     /* assemble change of basis matrix on the whole set of local dofs */
697     ierr = PetscMalloc(k*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
698     ierr = MatCreate(PETSC_COMM_SELF,&change_mat_all);CHKERRQ(ierr);
699     ierr = MatSetSizes(change_mat_all,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
700     ierr = MatSetType(change_mat_all,MATSEQAIJ);CHKERRQ(ierr);
701     ierr = MatSeqAIJSetPreallocation(change_mat_all,0,nnz);CHKERRQ(ierr);
702     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
703     for (i=0;i<n_D;i++) {
704       ierr = MatSetValue(change_mat_all,is_indices[i],is_indices[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
705     }
706     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
707     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
708     for (i=0;i<n_B;i++) {
709       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
710       for (k=0; k<j; k++) temp_indices[k]=is_indices[row_cmat_indices[k]];
711       ierr = MatSetValues(change_mat_all,1,&is_indices[i],j,temp_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
712       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
713     }
714     ierr = MatAssemblyBegin(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
715     ierr = MatAssemblyEnd(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
716     /* TODO: HOW TO WORK WITH BAIJ? PtAP not provided */
717     ierr = MatGetBlockSize(matis->A,&i);CHKERRQ(ierr);
718     if (i==1) {
719       ierr = MatPtAP(matis->A,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
720     } else {
721       Mat work_mat;
722       ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
723       ierr = MatPtAP(work_mat,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
724       ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
725     }
726     ierr = MatDestroy(&change_mat_all);CHKERRQ(ierr);
727     ierr = PetscFree(nnz);CHKERRQ(ierr);
728     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
729   } else {
730     /* without change of basis, the local matrix is unchanged */
731     if (!pcbddc->local_mat) {
732       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
733       pcbddc->local_mat = matis->A;
734     }
735   }
736 
737   /* get submatrices */
738   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_I_local,reuse,&pcis->A_II);CHKERRQ(ierr);
739   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
740   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
741   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,reuse,&pcis->A_BB);CHKERRQ(ierr);
742   PetscFunctionReturn(0);
743 }
744 
745 #undef __FUNCT__
746 #define __FUNCT__ "PCBDDCSetUpLocalScatters"
747 PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
748 {
749   PC_IS*         pcis = (PC_IS*)(pc->data);
750   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
751   IS             is_aux1,is_aux2;
752   PetscInt       *vertices,*aux_array1,*aux_array2,*is_indices,*idx_R_local;
753   PetscInt       n_vertices,n_constraints,i,j,n_R,n_D,n_B;
754   PetscBool      *array_bool;
755   PetscErrorCode ierr;
756 
757   PetscFunctionBegin;
758   /* Set Non-overlapping dimensions */
759   n_B = pcis->n_B; n_D = pcis->n - n_B;
760   /* get vertex indices from constraint matrix */
761   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,&vertices);CHKERRQ(ierr);
762   /* Set number of constraints */
763   n_constraints = pcbddc->local_primal_size-n_vertices;
764   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
765   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&array_bool);CHKERRQ(ierr);
766   for (i=0;i<pcis->n;i++) array_bool[i] = PETSC_TRUE;
767   for (i=0;i<n_vertices;i++) array_bool[vertices[i]] = PETSC_FALSE;
768   ierr = PetscMalloc((pcis->n-n_vertices)*sizeof(PetscInt),&idx_R_local);CHKERRQ(ierr);
769   for (i=0, n_R=0; i<pcis->n; i++) {
770     if (array_bool[i]) {
771       idx_R_local[n_R] = i;
772       n_R++;
773     }
774   }
775   ierr = PetscFree(vertices);CHKERRQ(ierr);
776   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_R,idx_R_local,PETSC_OWN_POINTER,&pcbddc->is_R_local);CHKERRQ(ierr);
777 
778   /* print some info if requested */
779   if (pcbddc->dbg_flag) {
780     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
781     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
782     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
783     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
784     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"r_size = %d, v_size = %d, constraints = %d, local_primal_size = %d\n",n_R,n_vertices,n_constraints,pcbddc->local_primal_size);CHKERRQ(ierr);
785     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
786     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
787   }
788 
789   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
790   ierr = PetscMalloc((pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
791   ierr = PetscMalloc((pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array2);CHKERRQ(ierr);
792   ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
793   for (i=0; i<n_D; i++) array_bool[is_indices[i]] = PETSC_FALSE;
794   ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
795   for (i=0, j=0; i<n_R; i++) {
796     if (array_bool[idx_R_local[i]]) {
797       aux_array1[j] = i;
798       j++;
799     }
800   }
801   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
802   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
803   for (i=0, j=0; i<n_B; i++) {
804     if (array_bool[is_indices[i]]) {
805       aux_array2[j] = i; j++;
806     }
807   }
808   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
809   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);CHKERRQ(ierr);
810   ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
811   ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
812   ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
813 
814   if (pcbddc->inexact_prec_type || pcbddc->dbg_flag ) {
815     ierr = PetscMalloc(n_D*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
816     for (i=0, j=0; i<n_R; i++) {
817       if (!array_bool[idx_R_local[i]]) {
818         aux_array1[j] = i;
819         j++;
820       }
821     }
822     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
823     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
824     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
825   }
826   ierr = PetscFree(array_bool);CHKERRQ(ierr);
827   PetscFunctionReturn(0);
828 }
829 
830 #undef __FUNCT__
831 #define __FUNCT__ "PCBDDCSetUseExactDirichlet"
832 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool use)
833 {
834   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
835 
836   PetscFunctionBegin;
837   pcbddc->use_exact_dirichlet=use;
838   PetscFunctionReturn(0);
839 }
840 
841 #undef __FUNCT__
842 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
843 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc)
844 {
845   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
846   PC_IS          *pcis = (PC_IS*)pc->data;
847   PC             pc_temp;
848   Mat            A_RR;
849   Vec            vec1,vec2,vec3;
850   MatStructure   matstruct;
851   PetscScalar    m_one = -1.0;
852   PetscReal      value;
853   PetscInt       n_D,n_R,use_exact,use_exact_reduced;
854   PetscErrorCode ierr;
855 
856   PetscFunctionBegin;
857   /* Creating PC contexts for local Dirichlet and Neumann problems */
858   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
859 
860   /* DIRICHLET PROBLEM */
861   /* Matrix for Dirichlet problem is pcis->A_II */
862   ierr = ISGetSize(pcis->is_I_local,&n_D);CHKERRQ(ierr);
863   if (!pcbddc->ksp_D) { /* create object if not yet build */
864     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
865     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
866     /* default */
867     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
868     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
869     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
870     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
871     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
872   }
873   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,matstruct);CHKERRQ(ierr);
874   /* Allow user's customization */
875   ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
876   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
877   if (!n_D) {
878     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
879     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
880   }
881   /* Set Up KSP for Dirichlet problem of BDDC */
882   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
883   /* set ksp_D into pcis data */
884   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
885   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
886   pcis->ksp_D = pcbddc->ksp_D;
887 
888   /* NEUMANN PROBLEM */
889   /* Matrix for Neumann problem is A_RR -> we need to create it */
890   ierr = ISGetSize(pcbddc->is_R_local,&n_R);CHKERRQ(ierr);
891   ierr = MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
892   if (!pcbddc->ksp_R) { /* create object if not yet build */
893     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
894     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
895     /* default */
896     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
897     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
898     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
899     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
900     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
901   }
902   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,matstruct);CHKERRQ(ierr);
903   /* Allow user's customization */
904   ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
905   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
906   if (!n_R) {
907     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
908     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
909   }
910   /* Set Up KSP for Neumann problem of BDDC */
911   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
912 
913   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
914 
915   /* Dirichlet */
916   ierr = MatGetVecs(pcis->A_II,&vec1,&vec2);CHKERRQ(ierr);
917   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
918   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
919   ierr = MatMult(pcis->A_II,vec1,vec2);CHKERRQ(ierr);
920   ierr = KSPSolve(pcbddc->ksp_D,vec2,vec3);CHKERRQ(ierr);
921   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
922   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
923   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
924   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
925   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
926   /* need to be adapted? */
927   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
928   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
929   ierr = PCBDDCSetUseExactDirichlet(pc,(PetscBool)use_exact_reduced);CHKERRQ(ierr);
930   /* print info */
931   if (pcbddc->dbg_flag) {
932     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
933     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
934     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
935     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
936     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
937   }
938   if (n_D && pcbddc->NullSpace && !use_exact_reduced && !pcbddc->inexact_prec_type) {
939     ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcis->is_I_local);CHKERRQ(ierr);
940   }
941 
942   /* Neumann */
943   ierr = MatGetVecs(A_RR,&vec1,&vec2);CHKERRQ(ierr);
944   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
945   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
946   ierr = MatMult(A_RR,vec1,vec2);CHKERRQ(ierr);
947   ierr = KSPSolve(pcbddc->ksp_R,vec2,vec3);CHKERRQ(ierr);
948   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
949   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
950   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
951   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
952   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
953   /* need to be adapted? */
954   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
955   if (PetscAbsReal(value) > 1.e-4) use_exact = 0;
956   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
957   /* print info */
958   if (pcbddc->dbg_flag) {
959     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
960     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
961   }
962   if (n_R && pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
963     ierr = PCBDDCNullSpaceAssembleCorrection(pc,pcbddc->is_R_local);CHKERRQ(ierr);
964   }
965 
966   /* free Neumann problem's matrix */
967   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
968   PetscFunctionReturn(0);
969 }
970 
971 #undef __FUNCT__
972 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
973 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
974 {
975   PetscErrorCode ierr;
976   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
977 
978   PetscFunctionBegin;
979   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
980   if (pcbddc->local_auxmat1) {
981     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
982     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
983   }
984   PetscFunctionReturn(0);
985 }
986 
987 #undef __FUNCT__
988 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
989 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
990 {
991   PetscErrorCode ierr;
992   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
993   PC_IS*            pcis = (PC_IS*)  (pc->data);
994   const PetscScalar zero = 0.0;
995 
996   PetscFunctionBegin;
997   /* Application of PHI^T (or PSI^T)  */
998   if (pcbddc->coarse_psi_B) {
999     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1000     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1001   } else {
1002     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1003     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1004   }
1005   /* Scatter data of coarse_rhs */
1006   if (pcbddc->coarse_rhs) { ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr); }
1007   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1008 
1009   /* Local solution on R nodes */
1010   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
1011   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1012   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1013   if (pcbddc->inexact_prec_type) {
1014     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1015     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1016   }
1017   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
1018   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1019   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1020   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1021   if (pcbddc->inexact_prec_type) {
1022     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1023     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1024   }
1025 
1026   /* Coarse solution */
1027   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1028   if (pcbddc->coarse_rhs) { /* TODO remove null space when doing multilevel */
1029     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
1030   }
1031   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1032   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1033 
1034   /* Sum contributions from two levels */
1035   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1036   if (pcbddc->inexact_prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1037   PetscFunctionReturn(0);
1038 }
1039 
1040 #undef __FUNCT__
1041 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
1042 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
1043 {
1044   PetscErrorCode ierr;
1045   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1046 
1047   PetscFunctionBegin;
1048   switch (pcbddc->coarse_communications_type) {
1049     case SCATTERS_BDDC:
1050       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
1051       break;
1052     case GATHERS_BDDC:
1053       break;
1054   }
1055   PetscFunctionReturn(0);
1056 }
1057 
1058 #undef __FUNCT__
1059 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
1060 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
1061 {
1062   PetscErrorCode ierr;
1063   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1064   PetscScalar*   array_to;
1065   PetscScalar*   array_from;
1066   MPI_Comm       comm;
1067   PetscInt       i;
1068 
1069   PetscFunctionBegin;
1070   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
1071   switch (pcbddc->coarse_communications_type) {
1072     case SCATTERS_BDDC:
1073       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
1074       break;
1075     case GATHERS_BDDC:
1076       if (vec_from) {
1077         ierr = VecGetArray(vec_from,&array_from);CHKERRQ(ierr);
1078       }
1079       if (vec_to) {
1080         ierr = VecGetArray(vec_to,&array_to);CHKERRQ(ierr);
1081       }
1082       switch(pcbddc->coarse_problem_type){
1083         case SEQUENTIAL_BDDC:
1084           if (smode == SCATTER_FORWARD) {
1085             ierr = MPI_Gatherv(&array_from[0],pcbddc->local_primal_size,MPIU_SCALAR,&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,0,comm);CHKERRQ(ierr);
1086             if (vec_to) {
1087               if (imode == ADD_VALUES) {
1088                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
1089                   array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
1090                 }
1091               } else {
1092                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
1093                   array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
1094                 }
1095               }
1096             }
1097           } else {
1098             if (vec_from) {
1099               if (imode == ADD_VALUES) {
1100                 MPI_Comm vec_from_comm;
1101                 ierr = PetscObjectGetComm((PetscObject)(vec_from),&vec_from_comm);CHKERRQ(ierr);
1102                 SETERRQ2(vec_from_comm,PETSC_ERR_SUP,"Unsupported insert mode ADD_VALUES for SCATTER_REVERSE in %s for case %d\n",__FUNCT__,pcbddc->coarse_problem_type);
1103               }
1104               for (i=0;i<pcbddc->replicated_primal_size;i++) {
1105                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
1106               }
1107             }
1108             ierr = MPI_Scatterv(&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,&array_to[0],pcbddc->local_primal_size,MPIU_SCALAR,0,comm);CHKERRQ(ierr);
1109           }
1110           break;
1111         case REPLICATED_BDDC:
1112           if (smode == SCATTER_FORWARD) {
1113             ierr = MPI_Allgatherv(&array_from[0],pcbddc->local_primal_size,MPIU_SCALAR,&pcbddc->replicated_local_primal_values[0],pcbddc->local_primal_sizes,pcbddc->local_primal_displacements,MPIU_SCALAR,comm);CHKERRQ(ierr);
1114             if (imode == ADD_VALUES) {
1115               for (i=0;i<pcbddc->replicated_primal_size;i++) {
1116                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
1117               }
1118             } else {
1119               for (i=0;i<pcbddc->replicated_primal_size;i++) {
1120                 array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
1121               }
1122             }
1123           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
1124             if (imode == ADD_VALUES) {
1125               for (i=0;i<pcbddc->local_primal_size;i++) {
1126                 array_to[i]+=array_from[pcbddc->local_primal_indices[i]];
1127               }
1128             } else {
1129               for (i=0;i<pcbddc->local_primal_size;i++) {
1130                 array_to[i]=array_from[pcbddc->local_primal_indices[i]];
1131               }
1132             }
1133           }
1134           break;
1135         case MULTILEVEL_BDDC:
1136           break;
1137         case PARALLEL_BDDC:
1138           break;
1139       }
1140       if (vec_from) {
1141         ierr = VecRestoreArray(vec_from,&array_from);CHKERRQ(ierr);
1142       }
1143       if (vec_to) {
1144         ierr = VecRestoreArray(vec_to,&array_to);CHKERRQ(ierr);
1145       }
1146       break;
1147   }
1148   PetscFunctionReturn(0);
1149 }
1150 
1151 /* uncomment for testing purposes */
1152 /* #define PETSC_MISSING_LAPACK_GESVD 1 */
1153 #undef __FUNCT__
1154 #define __FUNCT__ "PCBDDCConstraintsSetUp"
1155 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
1156 {
1157   PetscErrorCode    ierr;
1158   PC_IS*            pcis = (PC_IS*)(pc->data);
1159   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
1160   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
1161   /* constraint and (optionally) change of basis matrix implemented as SeqAIJ */
1162   MatType           impMatType=MATSEQAIJ;
1163   /* one and zero */
1164   PetscScalar       one=1.0,zero=0.0;
1165   /* space to store constraints and their local indices */
1166   PetscScalar       *temp_quadrature_constraint;
1167   PetscInt          *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B;
1168   /* iterators */
1169   PetscInt          i,j,k,total_counts,temp_start_ptr;
1170   /* stuff to store connected components stored in pcbddc->mat_graph */
1171   IS                ISForVertices,*ISForFaces,*ISForEdges,*used_IS;
1172   PetscInt          n_ISForFaces,n_ISForEdges;
1173   PetscBool         get_faces,get_edges,get_vertices;
1174   /* near null space stuff */
1175   MatNullSpace      nearnullsp;
1176   const Vec         *nearnullvecs;
1177   Vec               *localnearnullsp;
1178   PetscBool         nnsp_has_cnst;
1179   PetscInt          nnsp_size;
1180   PetscScalar       *array;
1181   /* BLAS integers */
1182   PetscBLASInt      lwork,lierr;
1183   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
1184   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
1185   /* LAPACK working arrays for SVD or POD */
1186   PetscBool         skip_lapack;
1187   PetscScalar       *work;
1188   PetscReal         *singular_vals;
1189 #if defined(PETSC_USE_COMPLEX)
1190   PetscReal         *rwork;
1191 #endif
1192 #if defined(PETSC_MISSING_LAPACK_GESVD)
1193   PetscBLASInt      Blas_one_2=1;
1194   PetscScalar       *temp_basis,*correlation_mat;
1195 #else
1196   PetscBLASInt      dummy_int_1=1,dummy_int_2=1;
1197   PetscScalar       dummy_scalar_1=0.0,dummy_scalar_2=0.0;
1198 #endif
1199   /* change of basis */
1200   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
1201   PetscBool         boolforchange,*change_basis,*touched;
1202   /* auxiliary stuff */
1203   PetscInt          *nnz,*is_indices,*local_to_B;
1204   /* some quantities */
1205   PetscInt          n_vertices,total_primal_vertices;
1206   PetscInt          size_of_constraint,max_size_of_constraint,max_constraints,temp_constraints;
1207 
1208 
1209   PetscFunctionBegin;
1210   /* Get index sets for faces, edges and vertices from graph */
1211   get_faces = PETSC_TRUE;
1212   get_edges = PETSC_TRUE;
1213   get_vertices = PETSC_TRUE;
1214   if (pcbddc->vertices_flag) {
1215     get_faces = PETSC_FALSE;
1216     get_edges = PETSC_FALSE;
1217   }
1218   if (pcbddc->constraints_flag) {
1219     get_vertices = PETSC_FALSE;
1220   }
1221   if (pcbddc->faces_flag) {
1222     get_edges = PETSC_FALSE;
1223   }
1224   if (pcbddc->edges_flag) {
1225     get_faces = PETSC_FALSE;
1226   }
1227   /* default */
1228   if (!get_faces && !get_edges && !get_vertices) {
1229     get_vertices = PETSC_TRUE;
1230   }
1231   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
1232   /* print some info */
1233   if (pcbddc->dbg_flag) {
1234     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1235     i = 0;
1236     if (ISForVertices) {
1237       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
1238     }
1239     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
1240     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
1241     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
1242     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1243   }
1244   /* check if near null space is attached to global mat */
1245   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
1246   if (nearnullsp) {
1247     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1248   } else { /* if near null space is not provided BDDC uses constants by default */
1249     nnsp_size = 0;
1250     nnsp_has_cnst = PETSC_TRUE;
1251   }
1252   /* get max number of constraints on a single cc */
1253   max_constraints = nnsp_size;
1254   if (nnsp_has_cnst) max_constraints++;
1255 
1256   /*
1257        Evaluate maximum storage size needed by the procedure
1258        - temp_indices will contain start index of each constraint stored as follows
1259        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
1260        - 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
1261        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
1262                                                                                                                                                          */
1263   total_counts = n_ISForFaces+n_ISForEdges;
1264   total_counts *= max_constraints;
1265   n_vertices = 0;
1266   if (ISForVertices) {
1267     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
1268   }
1269   total_counts += n_vertices;
1270   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
1271   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
1272   total_counts = 0;
1273   max_size_of_constraint = 0;
1274   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1275     if (i<n_ISForEdges) {
1276       used_IS = &ISForEdges[i];
1277     } else {
1278       used_IS = &ISForFaces[i-n_ISForEdges];
1279     }
1280     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
1281     total_counts += j;
1282     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
1283   }
1284   total_counts *= max_constraints;
1285   total_counts += n_vertices;
1286   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
1287   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
1288   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
1289   /* local to boundary numbering */
1290   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
1291   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1292   for (i=0;i<pcis->n;i++) local_to_B[i]=-1;
1293   for (i=0;i<pcis->n_B;i++) local_to_B[is_indices[i]]=i;
1294   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1295   /* get local part of global near null space vectors */
1296   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
1297   for (k=0;k<nnsp_size;k++) {
1298     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
1299     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1300     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1301   }
1302 
1303   /* whether or not to skip lapack calls */
1304   skip_lapack = PETSC_TRUE;
1305   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
1306 
1307   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
1308   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1309     PetscScalar temp_work;
1310 #if defined(PETSC_MISSING_LAPACK_GESVD)
1311     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
1312     ierr = PetscMalloc(max_constraints*max_constraints*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
1313     ierr = PetscMalloc(max_constraints*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
1314     ierr = PetscMalloc(max_size_of_constraint*max_constraints*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
1315 #if defined(PETSC_USE_COMPLEX)
1316     ierr = PetscMalloc(3*max_constraints*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
1317 #endif
1318     /* now we evaluate the optimal workspace using query with lwork=-1 */
1319     ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1320     ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
1321     lwork = -1;
1322     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1323 #if !defined(PETSC_USE_COMPLEX)
1324     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
1325 #else
1326     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
1327 #endif
1328     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1329     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
1330 #else /* on missing GESVD */
1331     /* SVD */
1332     PetscInt max_n,min_n;
1333     max_n = max_size_of_constraint;
1334     min_n = max_constraints;
1335     if (max_size_of_constraint < max_constraints) {
1336       min_n = max_size_of_constraint;
1337       max_n = max_constraints;
1338     }
1339     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
1340 #if defined(PETSC_USE_COMPLEX)
1341     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
1342 #endif
1343     /* now we evaluate the optimal workspace using query with lwork=-1 */
1344     lwork = -1;
1345     ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
1346     ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
1347     ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
1348     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1349 #if !defined(PETSC_USE_COMPLEX)
1350     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));
1351 #else
1352     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));
1353 #endif
1354     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1355     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
1356 #endif /* on missing GESVD */
1357     /* Allocate optimal workspace */
1358     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
1359     ierr = PetscMalloc((PetscInt)lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
1360   }
1361   /* Now we can loop on constraining sets */
1362   total_counts = 0;
1363   temp_indices[0] = 0;
1364   /* vertices */
1365   if (ISForVertices) {
1366     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1367     if (nnsp_has_cnst) { /* consider all vertices */
1368       for (i=0;i<n_vertices;i++) {
1369         temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
1370         temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
1371         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1372         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1373         change_basis[total_counts]=PETSC_FALSE;
1374         total_counts++;
1375       }
1376     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
1377       PetscBool used_vertex;
1378       for (i=0;i<n_vertices;i++) {
1379         used_vertex = PETSC_FALSE;
1380         k = 0;
1381         while (!used_vertex && k<nnsp_size) {
1382           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1383           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
1384             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
1385             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
1386             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1387             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1388             change_basis[total_counts]=PETSC_FALSE;
1389             total_counts++;
1390             used_vertex = PETSC_TRUE;
1391           }
1392           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1393           k++;
1394         }
1395       }
1396     }
1397     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1398     n_vertices = total_counts;
1399   }
1400 
1401   /* edges and faces */
1402   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1403     if (i<n_ISForEdges) {
1404       used_IS = &ISForEdges[i];
1405       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
1406     } else {
1407       used_IS = &ISForFaces[i-n_ISForEdges];
1408       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
1409     }
1410     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
1411     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
1412     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
1413     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1414     /* change of basis should not be performed on local periodic nodes */
1415     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
1416     if (nnsp_has_cnst) {
1417       PetscScalar quad_value;
1418       temp_constraints++;
1419       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
1420       for (j=0;j<size_of_constraint;j++) {
1421         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
1422         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
1423         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
1424       }
1425       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1426       change_basis[total_counts]=boolforchange;
1427       total_counts++;
1428     }
1429     for (k=0;k<nnsp_size;k++) {
1430       PetscReal real_value;
1431       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1432       for (j=0;j<size_of_constraint;j++) {
1433         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
1434         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
1435         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
1436       }
1437       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1438       /* check if array is null on the connected component */
1439       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1440       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_one));
1441       if (real_value > 0.0) { /* keep indices and values */
1442         temp_constraints++;
1443         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1444         change_basis[total_counts]=boolforchange;
1445         total_counts++;
1446       }
1447     }
1448     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1449     /* perform SVD on the constraints if use_nnsp_true has not be requested by the user */
1450     if (!pcbddc->use_nnsp_true) {
1451       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
1452 
1453 #if defined(PETSC_MISSING_LAPACK_GESVD)
1454       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
1455          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
1456          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
1457             the constraints basis will differ (by a complex factor with absolute value equal to 1)
1458             from that computed using LAPACKgesvd
1459          -> This is due to a different computation of eigenvectors in LAPACKheev
1460          -> The quality of the POD-computed basis will be the same */
1461       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
1462       /* Store upper triangular part of correlation matrix */
1463       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1464       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1465       for (j=0;j<temp_constraints;j++) {
1466         for (k=0;k<j+1;k++) {
1467           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));
1468         }
1469       }
1470       /* compute eigenvalues and eigenvectors of correlation matrix */
1471       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1472       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
1473 #if !defined(PETSC_USE_COMPLEX)
1474       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
1475 #else
1476       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
1477 #endif
1478       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1479       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
1480       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
1481       j=0;
1482       while (j < temp_constraints && singular_vals[j] < tol) j++;
1483       total_counts=total_counts-j;
1484       /* scale and copy POD basis into used quadrature memory */
1485       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1486       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1487       ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
1488       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1489       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
1490       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1491       if (j<temp_constraints) {
1492         PetscInt ii;
1493         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
1494         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1495         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));
1496         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1497         for (k=0;k<temp_constraints-j;k++) {
1498           for (ii=0;ii<size_of_constraint;ii++) {
1499             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];
1500           }
1501         }
1502       }
1503 #else  /* on missing GESVD */
1504       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1505       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1506       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1507       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1508 #if !defined(PETSC_USE_COMPLEX)
1509       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));
1510 #else
1511       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));
1512 #endif
1513       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
1514       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1515       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
1516       k = temp_constraints;
1517       if (k > size_of_constraint) k = size_of_constraint;
1518       j = 0;
1519       while (j < k && singular_vals[k-j-1] < tol) j++;
1520       total_counts = total_counts-temp_constraints+k-j;
1521 #endif /* on missing GESVD */
1522     }
1523   }
1524   /* free index sets of faces, edges and vertices */
1525   for (i=0;i<n_ISForFaces;i++) {
1526     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1527   }
1528   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1529   for (i=0;i<n_ISForEdges;i++) {
1530     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1531   }
1532   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1533   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1534 
1535   /* free workspace */
1536   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1537     ierr = PetscFree(work);CHKERRQ(ierr);
1538 #if defined(PETSC_USE_COMPLEX)
1539     ierr = PetscFree(rwork);CHKERRQ(ierr);
1540 #endif
1541     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1542 #if defined(PETSC_MISSING_LAPACK_GESVD)
1543     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1544     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1545 #endif
1546   }
1547   for (k=0;k<nnsp_size;k++) {
1548     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1549   }
1550   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1551 
1552   /* set quantities in pcbddc data structure */
1553   /* n_vertices defines the number of subdomain corners in the primal space */
1554   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1555   pcbddc->local_primal_size = total_counts;
1556   pcbddc->n_vertices = n_vertices;
1557   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
1558 
1559   /* Create constraint matrix */
1560   /* The constraint matrix is used to compute the l2g map of primal dofs */
1561   /* so we need to set it up properly either with or without change of basis */
1562   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1563   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1564   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
1565   /* array to compute a local numbering of constraints : vertices first then constraints */
1566   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
1567   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
1568   /* 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 */
1569   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_minloc);CHKERRQ(ierr);
1570   /* auxiliary stuff for basis change */
1571   ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&global_indices);CHKERRQ(ierr);
1572   ierr = PetscMalloc(pcis->n_B*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1573   ierr = PetscMemzero(touched,pcis->n_B*sizeof(PetscBool));CHKERRQ(ierr);
1574 
1575   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
1576   total_primal_vertices=0;
1577   for (i=0;i<pcbddc->local_primal_size;i++) {
1578     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1579     if (size_of_constraint == 1) {
1580       touched[temp_indices_to_constraint_B[temp_indices[i]]]=PETSC_TRUE;
1581       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
1582       aux_primal_minloc[total_primal_vertices]=0;
1583       total_primal_vertices++;
1584     } else if (change_basis[i]) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
1585       PetscInt min_loc,min_index;
1586       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
1587       /* find first untouched local node */
1588       k = 0;
1589       while (touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) k++;
1590       min_index = global_indices[k];
1591       min_loc = k;
1592       /* search the minimum among global nodes already untouched on the cc */
1593       for (k=1;k<size_of_constraint;k++) {
1594         /* there can be more than one constraint on a single connected component */
1595         if (min_index > global_indices[k] && !touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) {
1596           min_index = global_indices[k];
1597           min_loc = k;
1598         }
1599       }
1600       touched[temp_indices_to_constraint_B[temp_indices[i]+min_loc]] = PETSC_TRUE;
1601       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
1602       aux_primal_minloc[total_primal_vertices]=min_loc;
1603       total_primal_vertices++;
1604     }
1605   }
1606   /* free workspace */
1607   ierr = PetscFree(global_indices);CHKERRQ(ierr);
1608   ierr = PetscFree(touched);CHKERRQ(ierr);
1609   /* permute indices in order to have a sorted set of vertices */
1610   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);
1611 
1612   /* nonzero structure of constraint matrix */
1613   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1614   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
1615   j=total_primal_vertices;
1616   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1617     if (!change_basis[i]) {
1618       nnz[j]=temp_indices[i+1]-temp_indices[i];
1619       j++;
1620     }
1621   }
1622   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1623   ierr = PetscFree(nnz);CHKERRQ(ierr);
1624   /* set values in constraint matrix */
1625   for (i=0;i<total_primal_vertices;i++) {
1626     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
1627   }
1628   total_counts = total_primal_vertices;
1629   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1630     if (!change_basis[i]) {
1631       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1632       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);
1633       total_counts++;
1634     }
1635   }
1636   /* assembling */
1637   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1638   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1639   /*
1640   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
1641   */
1642   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1643   if (pcbddc->use_change_of_basis) {
1644     PetscBool qr_needed = PETSC_FALSE;
1645     /* change of basis acts on local interfaces -> dimension is n_B x n_B */
1646     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1647     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1648     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1649     /* work arrays */
1650     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1651     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
1652     /* nonzeros per row */
1653     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1654       if (change_basis[i]) {
1655         qr_needed = PETSC_TRUE;
1656         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1657         for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1658       }
1659     }
1660     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1661     ierr = PetscFree(nnz);CHKERRQ(ierr);
1662     /* Set initial identity in the matrix */
1663     for (i=0;i<pcis->n_B;i++) {
1664       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1665     }
1666 
1667     /* Now we loop on the constraints which need a change of basis */
1668     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
1669     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1) */
1670     /* Change of basis matrix T computed via QR decomposition of constraints */
1671     if (qr_needed) {
1672       /* dual and primal dofs on a single cc */
1673       PetscInt     dual_dofs,primal_dofs;
1674       /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
1675       PetscInt     primal_counter;
1676       /* working stuff for GEQRF */
1677       PetscScalar  *qr_basis,*qr_tau,*qr_work,lqr_work_t;
1678       PetscBLASInt lqr_work;
1679       /* working stuff for UNGQR */
1680       PetscScalar  *gqr_work,lgqr_work_t;
1681       PetscBLASInt lgqr_work;
1682       /* working stuff for TRTRS */
1683       PetscScalar  *trs_rhs;
1684       PetscBLASInt Blas_NRHS;
1685       /* pointers for values insertion into change of basis matrix */
1686       PetscInt     *start_rows,*start_cols;
1687       PetscScalar  *start_vals;
1688       /* working stuff for values insertion */
1689       PetscBool    *is_primal;
1690 
1691       /* space to store Q */
1692       ierr = PetscMalloc((max_size_of_constraint)*(max_size_of_constraint)*sizeof(PetscScalar),&qr_basis);CHKERRQ(ierr);
1693       /* first we issue queries for optimal work */
1694       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1695       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1696       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1697       lqr_work = -1;
1698       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
1699       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
1700       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
1701       ierr = PetscMalloc((PetscInt)PetscRealPart(lqr_work_t)*sizeof(*qr_work),&qr_work);CHKERRQ(ierr);
1702       lgqr_work = -1;
1703       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1704       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
1705       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
1706       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1707       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
1708       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
1709       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
1710       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
1711       ierr = PetscMalloc((PetscInt)PetscRealPart(lgqr_work_t)*sizeof(*gqr_work),&gqr_work);CHKERRQ(ierr);
1712       /* array to store scaling factors for reflectors */
1713       ierr = PetscMalloc(max_constraints*sizeof(*qr_tau),&qr_tau);CHKERRQ(ierr);
1714       /* array to store rhs and solution of triangular solver */
1715       ierr = PetscMalloc(max_constraints*max_constraints*sizeof(*trs_rhs),&trs_rhs);CHKERRQ(ierr);
1716       /* array to store whether a node is primal or not */
1717       ierr = PetscMalloc(pcis->n_B*sizeof(*is_primal),&is_primal);CHKERRQ(ierr);
1718       ierr = PetscMemzero(is_primal,pcis->n_B*sizeof(*is_primal));CHKERRQ(ierr);
1719       for (i=0;i<total_primal_vertices;i++) is_primal[local_to_B[aux_primal_numbering[i]]] = PETSC_TRUE;
1720 
1721       /* allocating workspace for check */
1722       if (pcbddc->dbg_flag) {
1723         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1724         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
1725         ierr = PetscMalloc(max_size_of_constraint*(max_constraints+max_size_of_constraint)*sizeof(*work),&work);CHKERRQ(ierr);
1726       }
1727 
1728       /* loop on constraints and see whether or not they need a change of basis */
1729       /* -> using implicit ordering contained in temp_indices data */
1730       total_counts = pcbddc->n_vertices;
1731       primal_counter = total_counts;
1732       while (total_counts<pcbddc->local_primal_size) {
1733         primal_dofs = 1;
1734         if (change_basis[total_counts]) {
1735           /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
1736           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]]) {
1737             primal_dofs++;
1738           }
1739           /* get constraint info */
1740           size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
1741           dual_dofs = size_of_constraint-primal_dofs;
1742 
1743           /* copy quadrature constraints for change of basis check */
1744           if (pcbddc->dbg_flag) {
1745             ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %d to %d need a change of basis (size %d)\n",total_counts,total_counts+primal_dofs,size_of_constraint);CHKERRQ(ierr);
1746             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1747           }
1748 
1749           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
1750           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1751 
1752           /* compute QR decomposition of constraints */
1753           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1754           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1755           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1756           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1757           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
1758           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
1759           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1760 
1761           /* explictly compute R^-T */
1762           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
1763           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
1764           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1765           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
1766           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1767           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
1768           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1769           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
1770           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
1771           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1772 
1773           /* explcitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
1774           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1775           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1776           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
1777           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1778           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1779           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
1780           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
1781           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1782 
1783           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
1784              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
1785              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
1786           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1787           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1788           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
1789           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1790           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
1791           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1792           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1793           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));
1794           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1795           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1796 
1797           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
1798           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
1799           /* insert cols for primal dofs */
1800           for (j=0;j<primal_dofs;j++) {
1801             start_vals = &qr_basis[j*size_of_constraint];
1802             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
1803             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
1804           }
1805           /* insert cols for dual dofs */
1806           for (j=0,k=0;j<dual_dofs;k++) {
1807             if (!is_primal[temp_indices_to_constraint_B[temp_indices[total_counts]+k]]) {
1808               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
1809               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
1810               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
1811               j++;
1812             }
1813           }
1814 
1815           /* check change of basis */
1816           if (pcbddc->dbg_flag) {
1817             PetscInt   ii,jj;
1818             PetscBool valid_qr=PETSC_TRUE;
1819             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
1820             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1821             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
1822             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1823             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
1824             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
1825             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1826             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));
1827             ierr = PetscFPTrapPop();CHKERRQ(ierr);
1828             for (jj=0;jj<size_of_constraint;jj++) {
1829               for (ii=0;ii<primal_dofs;ii++) {
1830                 if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
1831                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
1832               }
1833             }
1834             if (!valid_qr) {
1835               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
1836               for (jj=0;jj<size_of_constraint;jj++) {
1837                 for (ii=0;ii<primal_dofs;ii++) {
1838                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
1839                     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]));
1840                   }
1841                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
1842                     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]));
1843                   }
1844                 }
1845               }
1846             } else {
1847               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
1848             }
1849           }
1850           /* increment primal counter */
1851           primal_counter += primal_dofs;
1852         } else {
1853           if (pcbddc->dbg_flag) {
1854             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);
1855           }
1856         }
1857         /* increment constraint counter total_counts */
1858         total_counts += primal_dofs;
1859       }
1860       if (pcbddc->dbg_flag) {
1861         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1862         ierr = PetscFree(work);CHKERRQ(ierr);
1863       }
1864       /* free workspace */
1865       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
1866       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
1867       ierr = PetscFree(qr_work);CHKERRQ(ierr);
1868       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
1869       ierr = PetscFree(is_primal);CHKERRQ(ierr);
1870       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
1871     }
1872     /* assembling */
1873     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1874     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1875     /*
1876     ierr = MatView(pcbddc->ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
1877     */
1878   }
1879   /* free workspace */
1880   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
1881   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
1882   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
1883   ierr = PetscFree(change_basis);CHKERRQ(ierr);
1884   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
1885   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
1886   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
1887   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
1888   PetscFunctionReturn(0);
1889 }
1890 
1891 #undef __FUNCT__
1892 #define __FUNCT__ "PCBDDCAnalyzeInterface"
1893 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
1894 {
1895   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
1896   PC_IS       *pcis = (PC_IS*)pc->data;
1897   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
1898   PetscInt    bs,ierr,i,vertex_size;
1899   PetscViewer viewer=pcbddc->dbg_viewer;
1900 
1901   PetscFunctionBegin;
1902   /* Init local Graph struct */
1903   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
1904 
1905   /* Check validity of the csr graph passed in by the user */
1906   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
1907     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
1908   }
1909   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
1910   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
1911     Mat mat_adj;
1912     const PetscInt *xadj,*adjncy;
1913     PetscBool flg_row=PETSC_TRUE;
1914 
1915     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
1916     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1917     if (!flg_row) {
1918       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
1919     }
1920     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
1921     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1922     if (!flg_row) {
1923       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
1924     }
1925     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
1926   }
1927 
1928   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
1929   vertex_size = 1;
1930   if (!pcbddc->n_ISForDofs) {
1931     IS *custom_ISForDofs;
1932 
1933     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
1934     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
1935     for (i=0;i<bs;i++) {
1936       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1937     }
1938     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1939     /* remove my references to IS objects */
1940     for (i=0;i<bs;i++) {
1941       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1942     }
1943     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1944   } else { /* mat block size as vertex size (used for elasticity) */
1945     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1946   }
1947 
1948   /* Setup of Graph */
1949   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1950 
1951   /* Graph's connected components analysis */
1952   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1953 
1954   /* print some info to stdout */
1955   if (pcbddc->dbg_flag) {
1956     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1957   }
1958   PetscFunctionReturn(0);
1959 }
1960 
1961 #undef __FUNCT__
1962 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1963 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1964 {
1965   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1966   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1967   PetscErrorCode ierr;
1968 
1969   PetscFunctionBegin;
1970   n = 0;
1971   vertices = 0;
1972   if (pcbddc->ConstraintMatrix) {
1973     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1974     for (i=0;i<local_primal_size;i++) {
1975       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1976       if (size_of_constraint == 1) n++;
1977       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1978     }
1979     if (vertices_idx) {
1980       ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1981       n = 0;
1982       for (i=0;i<local_primal_size;i++) {
1983         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1984         if (size_of_constraint == 1) {
1985           vertices[n++]=row_cmat_indices[0];
1986         }
1987         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1988       }
1989     }
1990   }
1991   *n_vertices = n;
1992   if (vertices_idx) *vertices_idx = vertices;
1993   PetscFunctionReturn(0);
1994 }
1995 
1996 #undef __FUNCT__
1997 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
1998 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
1999 {
2000   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2001   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
2002   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
2003   PetscBool      *touched;
2004   PetscErrorCode ierr;
2005 
2006   PetscFunctionBegin;
2007   n = 0;
2008   constraints_index = 0;
2009   if (pcbddc->ConstraintMatrix) {
2010     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
2011     max_size_of_constraint = 0;
2012     for (i=0;i<local_primal_size;i++) {
2013       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2014       if (size_of_constraint > 1) {
2015         n++;
2016       }
2017       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
2018       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2019     }
2020     if (constraints_idx) {
2021       ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
2022       ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
2023       ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
2024       ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
2025       n = 0;
2026       for (i=0;i<local_primal_size;i++) {
2027         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2028         if (size_of_constraint > 1) {
2029           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
2030           /* find first untouched local node */
2031           j = 0;
2032           while(touched[row_cmat_indices[j]]) j++;
2033           min_index = row_cmat_global_indices[j];
2034           min_loc = j;
2035           /* search the minimum among nodes not yet touched on the connected component
2036              since there can be more than one constraint on a single cc */
2037           for (j=1;j<size_of_constraint;j++) {
2038             if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
2039               min_index = row_cmat_global_indices[j];
2040               min_loc = j;
2041             }
2042           }
2043           touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
2044           constraints_index[n++] = row_cmat_indices[min_loc];
2045         }
2046         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2047       }
2048       ierr = PetscFree(touched);CHKERRQ(ierr);
2049       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
2050     }
2051   }
2052   *n_constraints = n;
2053   if (constraints_idx) *constraints_idx = constraints_index;
2054   PetscFunctionReturn(0);
2055 }
2056 
2057 /* the next two functions has been adapted from pcis.c */
2058 #undef __FUNCT__
2059 #define __FUNCT__ "PCBDDCApplySchur"
2060 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2061 {
2062   PetscErrorCode ierr;
2063   PC_IS          *pcis = (PC_IS*)(pc->data);
2064 
2065   PetscFunctionBegin;
2066   if (!vec2_B) { vec2_B = v; }
2067   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2068   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
2069   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2070   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
2071   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2072   PetscFunctionReturn(0);
2073 }
2074 
2075 #undef __FUNCT__
2076 #define __FUNCT__ "PCBDDCApplySchurTranspose"
2077 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2078 {
2079   PetscErrorCode ierr;
2080   PC_IS          *pcis = (PC_IS*)(pc->data);
2081 
2082   PetscFunctionBegin;
2083   if (!vec2_B) { vec2_B = v; }
2084   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2085   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
2086   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2087   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
2088   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2089   PetscFunctionReturn(0);
2090 }
2091 
2092 #undef __FUNCT__
2093 #define __FUNCT__ "PCBDDCSubsetNumbering"
2094 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[])
2095 {
2096   Vec            local_vec,global_vec;
2097   IS             seqis,paris;
2098   VecScatter     scatter_ctx;
2099   PetscScalar    *array;
2100   PetscInt       *temp_global_dofs;
2101   PetscScalar    globalsum;
2102   PetscInt       i,j,s;
2103   PetscInt       nlocals,first_index,old_index,max_local;
2104   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
2105   PetscMPIInt    *dof_sizes,*dof_displs;
2106   PetscBool      first_found;
2107   PetscErrorCode ierr;
2108 
2109   PetscFunctionBegin;
2110   /* mpi buffers */
2111   MPI_Comm_size(comm,&size_prec_comm);
2112   MPI_Comm_rank(comm,&rank_prec_comm);
2113   j = ( !rank_prec_comm ? size_prec_comm : 0);
2114   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
2115   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
2116   /* get maximum size of subset */
2117   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
2118   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
2119   max_local = 0;
2120   if (n_local_dofs) {
2121     max_local = temp_global_dofs[0];
2122     for (i=1;i<n_local_dofs;i++) {
2123       if (max_local < temp_global_dofs[i] ) {
2124         max_local = temp_global_dofs[i];
2125       }
2126     }
2127   }
2128   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
2129   max_global++;
2130   max_local = 0;
2131   if (n_local_dofs) {
2132     max_local = local_dofs[0];
2133     for (i=1;i<n_local_dofs;i++) {
2134       if (max_local < local_dofs[i] ) {
2135         max_local = local_dofs[i];
2136       }
2137     }
2138   }
2139   max_local++;
2140   /* allocate workspace */
2141   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
2142   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
2143   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
2144   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
2145   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
2146   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
2147   /* create scatter */
2148   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
2149   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
2150   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
2151   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
2152   ierr = ISDestroy(&paris);CHKERRQ(ierr);
2153   /* init array */
2154   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
2155   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2156   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2157   if (local_dofs_mult) {
2158     for (i=0;i<n_local_dofs;i++) {
2159       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
2160     }
2161   } else {
2162     for (i=0;i<n_local_dofs;i++) {
2163       array[local_dofs[i]]=1.0;
2164     }
2165   }
2166   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2167   /* scatter into global vec and get total number of global dofs */
2168   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2169   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2170   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
2171   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
2172   /* Fill global_vec with cumulative function for global numbering */
2173   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
2174   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
2175   nlocals = 0;
2176   first_index = -1;
2177   first_found = PETSC_FALSE;
2178   for (i=0;i<s;i++) {
2179     if (!first_found && PetscRealPart(array[i]) > 0.0) {
2180       first_found = PETSC_TRUE;
2181       first_index = i;
2182     }
2183     nlocals += (PetscInt)PetscRealPart(array[i]);
2184   }
2185   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2186   if (!rank_prec_comm) {
2187     dof_displs[0]=0;
2188     for (i=1;i<size_prec_comm;i++) {
2189       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
2190     }
2191   }
2192   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2193   if (first_found) {
2194     array[first_index] += (PetscScalar)nlocals;
2195     old_index = first_index;
2196     for (i=first_index+1;i<s;i++) {
2197       if (PetscRealPart(array[i]) > 0.0) {
2198         array[i] += array[old_index];
2199         old_index = i;
2200       }
2201     }
2202   }
2203   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
2204   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2205   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2206   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2207   /* get global ordering of local dofs */
2208   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2209   if (local_dofs_mult) {
2210     for (i=0;i<n_local_dofs;i++) {
2211       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
2212     }
2213   } else {
2214     for (i=0;i<n_local_dofs;i++) {
2215       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
2216     }
2217   }
2218   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2219   /* free workspace */
2220   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
2221   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
2222   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
2223   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
2224   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
2225   /* return pointer to global ordering of local dofs */
2226   *global_numbering_subset = temp_global_dofs;
2227   PetscFunctionReturn(0);
2228 }
2229 
2230 #undef __FUNCT__
2231 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
2232 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
2233 {
2234   PetscInt       i,j;
2235   PetscScalar    *alphas;
2236   PetscErrorCode ierr;
2237 
2238   PetscFunctionBegin;
2239   /* this implements stabilized Gram-Schmidt */
2240   ierr = PetscMalloc(n*sizeof(PetscScalar),&alphas);CHKERRQ(ierr);
2241   for (i=0;i<n;i++) {
2242     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
2243     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
2244     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
2245   }
2246   ierr = PetscFree(alphas);CHKERRQ(ierr);
2247   PetscFunctionReturn(0);
2248 }
2249 
2250 
2251