xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 88ebb7492cd0215be3d18dc7a81e485fff46f8ca)
1 #include "bddc.h"
2 #include "bddcprivate.h"
3 #include <petscblaslapack.h>
4 
5 #undef __FUNCT__
6 #define __FUNCT__ "PCBDDCResetCustomization"
7 PetscErrorCode PCBDDCResetCustomization(PC pc)
8 {
9   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
10   PetscInt       i;
11   PetscErrorCode ierr;
12 
13   PetscFunctionBegin;
14   ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
15   ierr = ISDestroy(&pcbddc->user_primal_vertices);CHKERRQ(ierr);
16   ierr = MatNullSpaceDestroy(&pcbddc->NullSpace);CHKERRQ(ierr);
17   ierr = ISDestroy(&pcbddc->NeumannBoundaries);CHKERRQ(ierr);
18   ierr = ISDestroy(&pcbddc->DirichletBoundaries);CHKERRQ(ierr);
19   for (i=0;i<pcbddc->n_ISForDofs;i++) {
20     ierr = ISDestroy(&pcbddc->ISForDofs[i]);CHKERRQ(ierr);
21   }
22   ierr = PetscFree(pcbddc->ISForDofs);CHKERRQ(ierr);
23   PetscFunctionReturn(0);
24 }
25 
26 #undef __FUNCT__
27 #define __FUNCT__ "PCBDDCResetTopography"
28 PetscErrorCode PCBDDCResetTopography(PC pc)
29 {
30   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
31   PetscErrorCode ierr;
32 
33   PetscFunctionBegin;
34   ierr = MatDestroy(&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
35   ierr = MatDestroy(&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
36   ierr = PCBDDCGraphReset(pcbddc->mat_graph);CHKERRQ(ierr);
37   PetscFunctionReturn(0);
38 }
39 
40 #undef __FUNCT__
41 #define __FUNCT__ "PCBDDCResetSolvers"
42 PetscErrorCode PCBDDCResetSolvers(PC pc)
43 {
44   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
45   PetscErrorCode ierr;
46 
47   PetscFunctionBegin;
48   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
49   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
50   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
51   ierr = MatDestroy(&pcbddc->coarse_mat);CHKERRQ(ierr);
52   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
53   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
54   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
55   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
56   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
57   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
58   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
59   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
60   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
61   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
62   ierr = VecDestroy(&pcbddc->vec4_D);CHKERRQ(ierr);
63   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
64   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
65   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
66   ierr = PetscFree(pcbddc->local_primal_indices);CHKERRQ(ierr);
67   ierr = PetscFree(pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
68   ierr = PetscFree(pcbddc->replicated_local_primal_values);CHKERRQ(ierr);
69   ierr = PetscFree(pcbddc->local_primal_displacements);CHKERRQ(ierr);
70   ierr = PetscFree(pcbddc->local_primal_sizes);CHKERRQ(ierr);
71   PetscFunctionReturn(0);
72 }
73 
74 #undef __FUNCT__
75 #define __FUNCT__ "PCBDDCCreateWorkVectors"
76 PetscErrorCode PCBDDCCreateWorkVectors(PC pc)
77 {
78   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
79   PC_IS          *pcis = (PC_IS*)pc->data;
80   VecType        impVecType;
81   PetscInt       n_vertices,n_constraints,local_primal_size,n_R;
82   PetscErrorCode ierr;
83 
84   PetscFunctionBegin;
85   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,NULL);CHKERRQ(ierr);
86   ierr = PCBDDCGetPrimalConstraintsLocalIdx(pc,&n_constraints,NULL);CHKERRQ(ierr);
87   local_primal_size = n_constraints+n_vertices;
88   n_R = pcis->n-n_vertices;
89   /* local work vectors */
90   ierr = VecGetType(pcis->vec1_N,&impVecType);CHKERRQ(ierr);
91   ierr = VecDuplicate(pcis->vec1_D,&pcbddc->vec4_D);CHKERRQ(ierr);
92   ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);CHKERRQ(ierr);
93   ierr = VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);CHKERRQ(ierr);
94   ierr = VecSetType(pcbddc->vec1_R,impVecType);CHKERRQ(ierr);
95   ierr = VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);CHKERRQ(ierr);
96   ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);CHKERRQ(ierr);
97   ierr = VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,local_primal_size);CHKERRQ(ierr);
98   ierr = VecSetType(pcbddc->vec1_P,impVecType);CHKERRQ(ierr);
99   if (n_constraints) {
100     ierr = VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);CHKERRQ(ierr);
101     ierr = VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);CHKERRQ(ierr);
102     ierr = VecSetType(pcbddc->vec1_C,impVecType);CHKERRQ(ierr);
103   }
104   PetscFunctionReturn(0);
105 }
106 
107 #undef __FUNCT__
108 #define __FUNCT__ "PCBDDCSetUpCorrectionAndBasis"
109 PetscErrorCode PCBDDCSetUpCorrectionAndBasis(PC pc, IS is_R_local)
110 {
111   PC_IS        *pcis = (PC_IS*)pc->data;
112   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
113   PetscErrorCode ierr;
114   Mat          A_RV,A_VR,A_VV;
115   Mat          M1;
116   Mat          C_CR;
117   Mat          AUXMAT;
118   Vec          vec1_C;
119   Vec          vec2_C;
120   Vec          vec1_V;
121   Vec          vec2_V;
122   IS           is_C_local,is_V_local,is_aux1;
123   ISLocalToGlobalMapping BtoNmap;
124   PetscInt     *nnz;
125   PetscInt     *idx_V_B;
126   PetscInt     *auxindices;
127   PetscInt     index;
128   PetscScalar* array2;
129   MatFactorInfo matinfo;
130   PetscBool    setsym=PETSC_FALSE,issym=PETSC_FALSE;
131   /* old variables */
132   VecType           impVecType;
133   MatType           impMatType;
134   PetscInt          n_R=0;
135   PetscInt          n_D=0;
136   PetscInt          n_B=0;
137   PetscScalar       zero=0.0;
138   PetscScalar       one=1.0;
139   PetscScalar       m_one=-1.0;
140   PetscScalar*      array;
141   PetscScalar       *coarse_submat_vals;
142   PetscInt          *idx_R_local;
143   PetscReal         *coarsefunctions_errors,*constraints_errors;
144   /* auxiliary indices */
145   PetscInt          i,j;
146   /* for verbose output of bddc */
147   PetscViewer       viewer=pcbddc->dbg_viewer;
148   PetscInt          dbg_flag=pcbddc->dbg_flag;
149   /* for counting coarse dofs */
150   PetscInt          n_vertices,n_constraints;
151   PetscInt          size_of_constraint;
152   PetscInt          *row_cmat_indices;
153   PetscScalar       *row_cmat_values;
154   PetscInt          *vertices;
155 
156   PetscFunctionBegin;
157   /* get number of vertices */
158   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,NULL);CHKERRQ(ierr);
159   n_constraints = pcbddc->local_primal_size-n_vertices;
160   /* Set Non-overlapping dimensions */
161   n_B = pcis->n_B; n_D = pcis->n - n_B;
162   n_R = pcis->n-n_vertices;
163 
164   /* Set types for local objects needed by BDDC precondtioner */
165   impMatType = MATSEQDENSE;
166   impVecType = VECSEQ;
167 
168   /* Allocating some extra storage just to be safe */
169   ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
170   ierr = PetscMalloc (pcis->n*sizeof(PetscInt),&auxindices);CHKERRQ(ierr);
171   for (i=0;i<pcis->n;i++) auxindices[i]=i;
172 
173   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,&vertices);CHKERRQ(ierr);
174   /* vertices in boundary numbering */
175   ierr = PetscMalloc(n_vertices*sizeof(PetscInt),&idx_V_B);CHKERRQ(ierr);
176   ierr = ISLocalToGlobalMappingCreateIS(pcis->is_B_local,&BtoNmap);CHKERRQ(ierr);
177   ierr = ISGlobalToLocalMappingApply(BtoNmap,IS_GTOLM_DROP,n_vertices,vertices,&i,idx_V_B);CHKERRQ(ierr);
178   ierr = ISLocalToGlobalMappingDestroy(&BtoNmap);CHKERRQ(ierr);
179   if (i != n_vertices) {
180     SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %d != %d\n",n_vertices,i);
181   }
182 
183   /* some work vectors on vertices and/or constraints */
184   if (n_vertices) {
185     ierr = VecCreate(PETSC_COMM_SELF,&vec1_V);CHKERRQ(ierr);
186     ierr = VecSetSizes(vec1_V,n_vertices,n_vertices);CHKERRQ(ierr);
187     ierr = VecSetType(vec1_V,impVecType);CHKERRQ(ierr);
188     ierr = VecDuplicate(vec1_V,&vec2_V);CHKERRQ(ierr);
189   }
190   if (n_constraints) {
191     ierr = VecDuplicate(pcbddc->vec1_C,&vec1_C);CHKERRQ(ierr);
192     ierr = VecDuplicate(pcbddc->vec1_C,&vec2_C);CHKERRQ(ierr);
193   }
194   /* Precompute stuffs needed for preprocessing and application of BDDC*/
195   if (n_constraints) {
196     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->local_auxmat2);CHKERRQ(ierr);
197     ierr = MatSetSizes(pcbddc->local_auxmat2,n_R,n_constraints,n_R,n_constraints);CHKERRQ(ierr);
198     ierr = MatSetType(pcbddc->local_auxmat2,impMatType);CHKERRQ(ierr);
199     ierr = MatSeqDenseSetPreallocation(pcbddc->local_auxmat2,NULL);CHKERRQ(ierr);
200 
201     /* Create Constraint matrix on R nodes: C_{CR}  */
202     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_C_local);CHKERRQ(ierr);
203     ierr = MatGetSubMatrix(pcbddc->ConstraintMatrix,is_C_local,is_R_local,MAT_INITIAL_MATRIX,&C_CR);CHKERRQ(ierr);
204     ierr = ISDestroy(&is_C_local);CHKERRQ(ierr);
205 
206     /* Assemble local_auxmat2 = - A_{RR}^{-1} C^T_{CR} needed by BDDC application */
207     for (i=0;i<n_constraints;i++) {
208       ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
209       /* Get row of constraint matrix in R numbering */
210       ierr = VecGetArray(pcbddc->vec1_R,&array);CHKERRQ(ierr);
211       ierr = MatGetRow(C_CR,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
212       for (j=0;j<size_of_constraint;j++) array[row_cmat_indices[j]] = -row_cmat_values[j];
213       ierr = MatRestoreRow(C_CR,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
214       ierr = VecRestoreArray(pcbddc->vec1_R,&array);CHKERRQ(ierr);
215 
216       /* Solve for row of constraint matrix in R numbering */
217       ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
218 
219       /* Set values */
220       ierr = VecGetArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
221       ierr = MatSetValues(pcbddc->local_auxmat2,n_R,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
222       ierr = VecRestoreArray(pcbddc->vec2_R,&array);CHKERRQ(ierr);
223     }
224     ierr = MatAssemblyBegin(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
225     ierr = MatAssemblyEnd(pcbddc->local_auxmat2,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
226 
227     /* Assemble AUXMAT = ( LUFactor )( -C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} */
228     ierr = MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AUXMAT);CHKERRQ(ierr);
229     ierr = MatFactorInfoInitialize(&matinfo);CHKERRQ(ierr);
230     ierr = ISCreateStride(PETSC_COMM_SELF,n_constraints,0,1,&is_aux1);CHKERRQ(ierr);
231     ierr = MatLUFactor(AUXMAT,is_aux1,is_aux1,&matinfo);CHKERRQ(ierr);
232     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
233 
234     /* Assemble explicitly M1 = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1} needed in preproc  */
235     ierr = MatCreate(PETSC_COMM_SELF,&M1);CHKERRQ(ierr);
236     ierr = MatSetSizes(M1,n_constraints,n_constraints,n_constraints,n_constraints);CHKERRQ(ierr);
237     ierr = MatSetType(M1,impMatType);CHKERRQ(ierr);
238     ierr = MatSeqDenseSetPreallocation(M1,NULL);CHKERRQ(ierr);
239     for (i=0;i<n_constraints;i++) {
240       ierr = VecSet(vec1_C,zero);CHKERRQ(ierr);
241       ierr = VecSetValue(vec1_C,i,one,INSERT_VALUES);CHKERRQ(ierr);
242       ierr = VecAssemblyBegin(vec1_C);CHKERRQ(ierr);
243       ierr = VecAssemblyEnd(vec1_C);CHKERRQ(ierr);
244       ierr = MatSolve(AUXMAT,vec1_C,vec2_C);CHKERRQ(ierr);
245       ierr = VecScale(vec2_C,m_one);CHKERRQ(ierr);
246       ierr = VecGetArray(vec2_C,&array);CHKERRQ(ierr);
247       ierr = MatSetValues(M1,n_constraints,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
248       ierr = VecRestoreArray(vec2_C,&array);CHKERRQ(ierr);
249     }
250     ierr = MatAssemblyBegin(M1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
251     ierr = MatAssemblyEnd(M1,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
252     ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
253     /* Assemble local_auxmat1 = M1*C_{CR} needed by BDDC application in KSP and in preproc */
254     ierr = MatMatMult(M1,C_CR,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);CHKERRQ(ierr);
255 
256   }
257 
258   /* Get submatrices from subdomain matrix */
259   if (n_vertices) {
260     ierr = ISCreateGeneral(PETSC_COMM_SELF,n_vertices,vertices,PETSC_COPY_VALUES,&is_V_local);CHKERRQ(ierr);
261     ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_V_local,MAT_INITIAL_MATRIX,&A_RV);CHKERRQ(ierr);
262     ierr = MatGetSubMatrix(pcbddc->local_mat,is_V_local,is_R_local,MAT_INITIAL_MATRIX,&A_VR);CHKERRQ(ierr);
263     ierr = MatGetSubMatrix(pcbddc->local_mat,is_V_local,is_V_local,MAT_INITIAL_MATRIX,&A_VV);CHKERRQ(ierr);
264     ierr = ISDestroy(&is_V_local);CHKERRQ(ierr);
265   }
266 
267   /* Matrix of coarse basis functions (local) */
268   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_B);CHKERRQ(ierr);
269   ierr = MatSetSizes(pcbddc->coarse_phi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
270   ierr = MatSetType(pcbddc->coarse_phi_B,impMatType);CHKERRQ(ierr);
271   ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_phi_B,NULL);CHKERRQ(ierr);
272   if (pcbddc->inexact_prec_type || dbg_flag ) {
273     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_phi_D);CHKERRQ(ierr);
274     ierr = MatSetSizes(pcbddc->coarse_phi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
275     ierr = MatSetType(pcbddc->coarse_phi_D,impMatType);CHKERRQ(ierr);
276     ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_phi_D,NULL);CHKERRQ(ierr);
277   }
278 
279   if (dbg_flag) {
280     ierr = ISGetIndices(is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
281     ierr = PetscMalloc(2*pcbddc->local_primal_size*sizeof(*coarsefunctions_errors),&coarsefunctions_errors);CHKERRQ(ierr);
282     ierr = PetscMalloc(2*pcbddc->local_primal_size*sizeof(*constraints_errors),&constraints_errors);CHKERRQ(ierr);
283   }
284   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
285   ierr = PetscMalloc ((pcbddc->local_primal_size)*(pcbddc->local_primal_size)*sizeof(PetscScalar),&coarse_submat_vals);CHKERRQ(ierr);
286 
287   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
288   for (i=0;i<n_vertices;i++){
289     ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
290     ierr = VecSetValue(vec1_V,i,one,INSERT_VALUES);CHKERRQ(ierr);
291     ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
292     ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
293     /* solution of saddle point problem */
294     ierr = MatMult(A_RV,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
295     ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
296     ierr = VecScale(pcbddc->vec1_R,m_one);CHKERRQ(ierr);
297     if (n_constraints) {
298       ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec1_R,vec1_C);CHKERRQ(ierr);
299       ierr = MatMultAdd(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
300       ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
301     }
302     ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr);
303     ierr = MatMultAdd(A_VV,vec1_V,vec2_V,vec2_V);CHKERRQ(ierr);
304 
305     /* Set values in coarse basis function and subdomain part of coarse_mat */
306     /* coarse basis functions */
307     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
308     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
309     ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
310     ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
311     ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
312     ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
313     ierr = MatSetValue(pcbddc->coarse_phi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
314     if ( pcbddc->inexact_prec_type || dbg_flag  ) {
315       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
316       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
317       ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
318       ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
319       ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
320     }
321     /* subdomain contribution to coarse matrix */
322     ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
323     for (j=0; j<n_vertices; j++) coarse_submat_vals[i*pcbddc->local_primal_size+j] = array[j];   /* WARNING -> column major ordering */
324     ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
325     if (n_constraints) {
326       ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
327       for (j=0; j<n_constraints; j++) coarse_submat_vals[i*pcbddc->local_primal_size+j+n_vertices] = array[j];   /* WARNING -> column major ordering */
328       ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
329     }
330 
331     if ( dbg_flag ) {
332       /* assemble subdomain vector on nodes */
333       ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
334       ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
335       ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
336       for (j=0;j<n_R;j++) array[idx_R_local[j]] = array2[j];
337       array[ vertices[i] ] = one;
338       ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
339       ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
340       /* assemble subdomain vector of lagrange multipliers (i.e. primal nodes) */
341       ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
342       ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
343       ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
344       for (j=0;j<n_vertices;j++) array2[j]=array[j];
345       ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
346       if (n_constraints) {
347         ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
348         for (j=0;j<n_constraints;j++) array2[j+n_vertices]=array[j];
349         ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
350       }
351       ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
352       ierr = VecScale(pcbddc->vec1_P,m_one);CHKERRQ(ierr);
353       /* check saddle point solution */
354       ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
355       ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
356       ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i]);CHKERRQ(ierr);
357       ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
358       ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
359       array[i]=array[i]+m_one;  /* shift by the identity matrix */
360       ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
361       ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i]);CHKERRQ(ierr);
362     }
363   }
364 
365   for (i=0;i<n_constraints;i++){
366     ierr = VecSet(vec2_C,zero);CHKERRQ(ierr);
367     ierr = VecSetValue(vec2_C,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
368     ierr = VecAssemblyBegin(vec2_C);CHKERRQ(ierr);
369     ierr = VecAssemblyEnd(vec2_C);CHKERRQ(ierr);
370     /* solution of saddle point problem */
371     ierr = MatMult(M1,vec2_C,vec1_C);CHKERRQ(ierr);
372     ierr = MatMult(pcbddc->local_auxmat2,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
373     ierr = VecScale(vec1_C,m_one);CHKERRQ(ierr);
374     if (n_vertices) { ierr = MatMult(A_VR,pcbddc->vec1_R,vec2_V);CHKERRQ(ierr); }
375     /* Set values in coarse basis function and subdomain part of coarse_mat */
376     /* coarse basis functions */
377     index=i+n_vertices;
378     ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
379     ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
380     ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
381     ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
382     ierr = MatSetValues(pcbddc->coarse_phi_B,n_B,auxindices,1,&index,array,INSERT_VALUES);CHKERRQ(ierr);
383     ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
384     if ( pcbddc->inexact_prec_type || dbg_flag ) {
385       ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
386       ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
387       ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
388       ierr = MatSetValues(pcbddc->coarse_phi_D,n_D,auxindices,1,&index,array,INSERT_VALUES);CHKERRQ(ierr);
389       ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
390     }
391     /* subdomain contribution to coarse matrix */
392     if (n_vertices) {
393       ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
394       for (j=0; j<n_vertices; j++) coarse_submat_vals[index*pcbddc->local_primal_size+j]=array[j]; /* WARNING -> column major ordering */
395       ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
396     }
397     ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
398     for (j=0; j<n_constraints; j++) coarse_submat_vals[index*pcbddc->local_primal_size+j+n_vertices]=array[j]; /* WARNING -> column major ordering */
399     ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
400 
401     if ( dbg_flag ) {
402       /* assemble subdomain vector on nodes */
403       ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
404       ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
405       ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
406       for (j=0;j<n_R;j++) array[idx_R_local[j]] = array2[j];
407       ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
408       ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
409       /* assemble subdomain vector of lagrange multipliers */
410       ierr = VecSet(pcbddc->vec1_P,zero);CHKERRQ(ierr);
411       ierr = VecGetArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
412       if ( n_vertices) {
413         ierr = VecGetArray(vec2_V,&array);CHKERRQ(ierr);
414         for (j=0;j<n_vertices;j++) array2[j]=-array[j];
415         ierr = VecRestoreArray(vec2_V,&array);CHKERRQ(ierr);
416       }
417       ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
418       for (j=0;j<n_constraints;j++) {array2[j+n_vertices]=-array[j];}
419       ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
420       ierr = VecRestoreArray(pcbddc->vec1_P,&array2);CHKERRQ(ierr);
421       /* check saddle point solution */
422       ierr = MatMult(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
423       ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
424       ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[index]);CHKERRQ(ierr);
425       ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
426       ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
427       array[index]=array[index]+m_one; /* shift by the identity matrix */
428       ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
429       ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[index]);CHKERRQ(ierr);
430     }
431   }
432   ierr = MatAssemblyBegin(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
433   ierr = MatAssemblyEnd(pcbddc->coarse_phi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
434   if ( pcbddc->inexact_prec_type || dbg_flag ) {
435     ierr = MatAssemblyBegin(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
436     ierr = MatAssemblyEnd(pcbddc->coarse_phi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
437   }
438   /* compute other basis functions for non-symmetric problems */
439   ierr = MatIsSymmetricKnown(pc->pmat,&setsym,&issym);CHKERRQ(ierr);
440   if ( !setsym || (setsym && !issym) ) {
441     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_psi_B);CHKERRQ(ierr);
442     ierr = MatSetSizes(pcbddc->coarse_psi_B,n_B,pcbddc->local_primal_size,n_B,pcbddc->local_primal_size);CHKERRQ(ierr);
443     ierr = MatSetType(pcbddc->coarse_psi_B,impMatType);CHKERRQ(ierr);
444     ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_psi_B,NULL);CHKERRQ(ierr);
445     if (pcbddc->inexact_prec_type || dbg_flag ) {
446       ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->coarse_psi_D);CHKERRQ(ierr);
447       ierr = MatSetSizes(pcbddc->coarse_psi_D,n_D,pcbddc->local_primal_size,n_D,pcbddc->local_primal_size);CHKERRQ(ierr);
448       ierr = MatSetType(pcbddc->coarse_psi_D,impMatType);CHKERRQ(ierr);
449       ierr = MatSeqDenseSetPreallocation(pcbddc->coarse_psi_D,NULL);CHKERRQ(ierr);
450     }
451     for (i=0;i<pcbddc->local_primal_size;i++) {
452       if (n_constraints) {
453         ierr = VecSet(vec1_C,zero);CHKERRQ(ierr);
454         ierr = VecGetArray(vec1_C,&array);CHKERRQ(ierr);
455         for (j=0;j<n_constraints;j++) {
456           array[j]=coarse_submat_vals[(j+n_vertices)*pcbddc->local_primal_size+i];
457         }
458         ierr = VecRestoreArray(vec1_C,&array);CHKERRQ(ierr);
459       }
460       if (i<n_vertices) {
461         ierr = VecSet(vec1_V,zero);CHKERRQ(ierr);
462         ierr = VecSetValue(vec1_V,i,m_one,INSERT_VALUES);CHKERRQ(ierr);
463         ierr = VecAssemblyBegin(vec1_V);CHKERRQ(ierr);
464         ierr = VecAssemblyEnd(vec1_V);CHKERRQ(ierr);
465         ierr = MatMultTranspose(A_VR,vec1_V,pcbddc->vec1_R);CHKERRQ(ierr);
466         if (n_constraints) {
467           ierr = MatMultTransposeAdd(C_CR,vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
468         }
469       } else {
470         ierr = MatMultTranspose(C_CR,vec1_C,pcbddc->vec1_R);CHKERRQ(ierr);
471       }
472       ierr = KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);CHKERRQ(ierr);
473       ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
474       ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
475       ierr = VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
476       ierr = VecGetArray(pcis->vec1_B,&array);CHKERRQ(ierr);
477       ierr = MatSetValues(pcbddc->coarse_psi_B,n_B,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
478       ierr = VecRestoreArray(pcis->vec1_B,&array);CHKERRQ(ierr);
479       if (i<n_vertices) {
480         ierr = MatSetValue(pcbddc->coarse_psi_B,idx_V_B[i],i,one,INSERT_VALUES);CHKERRQ(ierr);
481       }
482       if ( pcbddc->inexact_prec_type || dbg_flag  ) {
483         ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
484         ierr = VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
485         ierr = VecGetArray(pcis->vec1_D,&array);CHKERRQ(ierr);
486         ierr = MatSetValues(pcbddc->coarse_psi_D,n_D,auxindices,1,&i,array,INSERT_VALUES);CHKERRQ(ierr);
487         ierr = VecRestoreArray(pcis->vec1_D,&array);CHKERRQ(ierr);
488       }
489 
490       if ( dbg_flag ) {
491         /* assemble subdomain vector on nodes */
492         ierr = VecSet(pcis->vec1_N,zero);CHKERRQ(ierr);
493         ierr = VecGetArray(pcis->vec1_N,&array);CHKERRQ(ierr);
494         ierr = VecGetArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
495         for (j=0;j<n_R;j++) array[idx_R_local[j]] = array2[j];
496         if (i<n_vertices) array[vertices[i]] = one;
497         ierr = VecRestoreArray(pcbddc->vec1_R,&array2);CHKERRQ(ierr);
498         ierr = VecRestoreArray(pcis->vec1_N,&array);CHKERRQ(ierr);
499         /* assemble subdomain vector of lagrange multipliers */
500         ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
501         for (j=0;j<pcbddc->local_primal_size;j++) {
502           array[j]=-coarse_submat_vals[j*pcbddc->local_primal_size+i];
503         }
504         ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
505         /* check saddle point solution */
506         ierr = MatMultTranspose(pcbddc->local_mat,pcis->vec1_N,pcis->vec2_N);CHKERRQ(ierr);
507         ierr = MatMultTransposeAdd(pcbddc->ConstraintMatrix,pcbddc->vec1_P,pcis->vec2_N,pcis->vec2_N);CHKERRQ(ierr);
508         ierr = VecNorm(pcis->vec2_N,NORM_INFINITY,&coarsefunctions_errors[i+pcbddc->local_primal_size]);CHKERRQ(ierr);
509         ierr = MatMult(pcbddc->ConstraintMatrix,pcis->vec1_N,pcbddc->vec1_P);CHKERRQ(ierr);
510         ierr = VecGetArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
511         array[i]=array[i]+m_one; /* shift by the identity matrix */
512         ierr = VecRestoreArray(pcbddc->vec1_P,&array);CHKERRQ(ierr);
513         ierr = VecNorm(pcbddc->vec1_P,NORM_INFINITY,&constraints_errors[i+pcbddc->local_primal_size]);CHKERRQ(ierr);
514       }
515     }
516     ierr = MatAssemblyBegin(pcbddc->coarse_psi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
517     ierr = MatAssemblyEnd(pcbddc->coarse_psi_B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
518     if ( pcbddc->inexact_prec_type || dbg_flag ) {
519       ierr = MatAssemblyBegin(pcbddc->coarse_psi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
520       ierr = MatAssemblyEnd(pcbddc->coarse_psi_D,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
521     }
522   }
523   ierr = PetscFree(idx_V_B);CHKERRQ(ierr);
524   /* Checking coarse_sub_mat and coarse basis functios */
525   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
526   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
527   if (dbg_flag) {
528     Mat         coarse_sub_mat;
529     Mat         TM1,TM2,TM3,TM4;
530     Mat         coarse_phi_D,coarse_phi_B;
531     Mat         coarse_psi_D,coarse_psi_B;
532     Mat         A_II,A_BB,A_IB,A_BI;
533     MatType     checkmattype=MATSEQAIJ;
534     PetscReal   real_value;
535 
536     ierr = MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);CHKERRQ(ierr);
537     ierr = MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);CHKERRQ(ierr);
538     ierr = MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);CHKERRQ(ierr);
539     ierr = MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);CHKERRQ(ierr);
540     ierr = MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);CHKERRQ(ierr);
541     ierr = MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);CHKERRQ(ierr);
542     if (pcbddc->coarse_psi_B) {
543       ierr = MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);CHKERRQ(ierr);
544       ierr = MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);CHKERRQ(ierr);
545     }
546     ierr = MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);CHKERRQ(ierr);
547 
548     ierr = PetscViewerASCIIPrintf(viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
549     ierr = PetscViewerASCIIPrintf(viewer,"Check coarse sub mat and local basis functions\n");CHKERRQ(ierr);
550     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
551     if (pcbddc->coarse_psi_B) {
552       ierr = MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
553       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
554       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
555       ierr = MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
556       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
557       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
558       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
559       ierr = MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
560       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
561       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
562       ierr = MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
563       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
564     } else {
565       ierr = MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);CHKERRQ(ierr);
566       ierr = MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);CHKERRQ(ierr);
567       ierr = MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
568       ierr = MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);CHKERRQ(ierr);
569       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
570       ierr = MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);CHKERRQ(ierr);
571       ierr = MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);CHKERRQ(ierr);
572       ierr = MatDestroy(&AUXMAT);CHKERRQ(ierr);
573     }
574     ierr = MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
575     ierr = MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
576     ierr = MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
577     ierr = MatConvert(TM1,MATSEQDENSE,MAT_REUSE_MATRIX,&TM1);CHKERRQ(ierr);
578     ierr = MatAXPY(TM1,m_one,coarse_sub_mat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
579     ierr = MatNorm(TM1,NORM_INFINITY,&real_value);CHKERRQ(ierr);
580     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"----------------------------------\n");CHKERRQ(ierr);
581     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Subdomain %04d \n",PetscGlobalRank);CHKERRQ(ierr);
582     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"matrix error = % 1.14e\n",real_value);CHKERRQ(ierr);
583     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"coarse functions (phi) errors\n");CHKERRQ(ierr);
584     for (i=0;i<pcbddc->local_primal_size;i++) {
585       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local %02d-th function error = % 1.14e\n",i,coarsefunctions_errors[i]);CHKERRQ(ierr);
586     }
587     ierr = PetscViewerASCIISynchronizedPrintf(viewer,"constraints (phi) errors\n");CHKERRQ(ierr);
588     for (i=0;i<pcbddc->local_primal_size;i++) {
589       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local %02d-th function error = % 1.14e\n",i,constraints_errors[i]);CHKERRQ(ierr);
590     }
591     if (pcbddc->coarse_psi_B) {
592       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"coarse functions (psi) errors\n");CHKERRQ(ierr);
593       for (i=pcbddc->local_primal_size;i<2*pcbddc->local_primal_size;i++) {
594         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local %02d-th function error = % 1.14e\n",i-pcbddc->local_primal_size,coarsefunctions_errors[i]);CHKERRQ(ierr);
595       }
596       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"constraints (psi) errors\n");CHKERRQ(ierr);
597       for (i=pcbddc->local_primal_size;i<2*pcbddc->local_primal_size;i++) {
598         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"local %02d-th function error = % 1.14e\n",i-pcbddc->local_primal_size,constraints_errors[i]);CHKERRQ(ierr);
599       }
600     }
601     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
602     ierr = MatDestroy(&A_II);CHKERRQ(ierr);
603     ierr = MatDestroy(&A_BB);CHKERRQ(ierr);
604     ierr = MatDestroy(&A_IB);CHKERRQ(ierr);
605     ierr = MatDestroy(&A_BI);CHKERRQ(ierr);
606     ierr = MatDestroy(&TM1);CHKERRQ(ierr);
607     ierr = MatDestroy(&TM2);CHKERRQ(ierr);
608     ierr = MatDestroy(&TM3);CHKERRQ(ierr);
609     ierr = MatDestroy(&TM4);CHKERRQ(ierr);
610     ierr = MatDestroy(&coarse_phi_D);CHKERRQ(ierr);
611     ierr = MatDestroy(&coarse_phi_B);CHKERRQ(ierr);
612     if (pcbddc->coarse_psi_B) {
613       ierr = MatDestroy(&coarse_psi_D);CHKERRQ(ierr);
614       ierr = MatDestroy(&coarse_psi_B);CHKERRQ(ierr);
615     }
616     ierr = MatDestroy(&coarse_sub_mat);CHKERRQ(ierr);
617     ierr = ISRestoreIndices(is_R_local,(const PetscInt**)&idx_R_local);CHKERRQ(ierr);
618     ierr = PetscFree(coarsefunctions_errors);CHKERRQ(ierr);
619     ierr = PetscFree(constraints_errors);CHKERRQ(ierr);
620   }
621   /* free memory */
622   if (n_vertices) {
623     ierr = PetscFree(vertices);CHKERRQ(ierr);
624     ierr = VecDestroy(&vec1_V);CHKERRQ(ierr);
625     ierr = VecDestroy(&vec2_V);CHKERRQ(ierr);
626     ierr = MatDestroy(&A_RV);CHKERRQ(ierr);
627     ierr = MatDestroy(&A_VR);CHKERRQ(ierr);
628     ierr = MatDestroy(&A_VV);CHKERRQ(ierr);
629   }
630   if (n_constraints) {
631     ierr = VecDestroy(&vec1_C);CHKERRQ(ierr);
632     ierr = VecDestroy(&vec2_C);CHKERRQ(ierr);
633     ierr = MatDestroy(&M1);CHKERRQ(ierr);
634     ierr = MatDestroy(&C_CR);CHKERRQ(ierr);
635   }
636   ierr = PetscFree(auxindices);CHKERRQ(ierr);
637   ierr = PetscFree(nnz);CHKERRQ(ierr);
638   /* create coarse matrix and data structures for message passing associated actual choice of coarse problem type */
639   ierr = PCBDDCSetUpCoarseEnvironment(pc,coarse_submat_vals);CHKERRQ(ierr);
640   ierr = PetscFree(coarse_submat_vals);CHKERRQ(ierr);
641   PetscFunctionReturn(0);
642 }
643 
644 #undef __FUNCT__
645 #define __FUNCT__ "PCBDDCSetUpLocalMatrices"
646 PetscErrorCode PCBDDCSetUpLocalMatrices(PC pc)
647 {
648   PC_IS*            pcis = (PC_IS*)(pc->data);
649   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
650   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
651   /* manage repeated solves */
652   MatReuse          reuse;
653   MatStructure      matstruct;
654   PetscErrorCode    ierr;
655 
656   PetscFunctionBegin;
657   /* get mat flags */
658   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
659   reuse = MAT_INITIAL_MATRIX;
660   if (pc->setupcalled) {
661     /* when matstruct is SAME_PRECONDITIONER, we shouldn't be here */
662     if (matstruct == SAME_PRECONDITIONER) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
663     if (matstruct == SAME_NONZERO_PATTERN) {
664       reuse = MAT_REUSE_MATRIX;
665     } else {
666       reuse = MAT_INITIAL_MATRIX;
667     }
668   }
669   if (reuse == MAT_INITIAL_MATRIX) {
670     ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
671     ierr = MatDestroy(&pcis->A_IB);CHKERRQ(ierr);
672     ierr = MatDestroy(&pcis->A_BI);CHKERRQ(ierr);
673     ierr = MatDestroy(&pcis->A_BB);CHKERRQ(ierr);
674     ierr = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
675   }
676 
677   /* transform local matrices if needed */
678   if (pcbddc->use_change_of_basis) {
679     Mat         change_mat_all;
680     PetscScalar *row_cmat_values;
681     PetscInt    *row_cmat_indices;
682     PetscInt    *nnz,*is_indices,*temp_indices;
683     PetscInt    i,j,k,n_D,n_B;
684 
685     /* Get Non-overlapping dimensions */
686     n_B = pcis->n_B;
687     n_D = pcis->n-n_B;
688 
689     /* compute nonzero structure of change of basis on all local nodes */
690     ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
691     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
692     for (i=0;i<n_D;i++) nnz[is_indices[i]] = 1;
693     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
694     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
695     k=1;
696     for (i=0;i<n_B;i++) {
697       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
698       nnz[is_indices[i]]=j;
699       if (k < j) k = j;
700       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,NULL,NULL);CHKERRQ(ierr);
701     }
702     ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
703     /* assemble change of basis matrix on the whole set of local dofs */
704     ierr = PetscMalloc(k*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
705     ierr = MatCreate(PETSC_COMM_SELF,&change_mat_all);CHKERRQ(ierr);
706     ierr = MatSetSizes(change_mat_all,pcis->n,pcis->n,pcis->n,pcis->n);CHKERRQ(ierr);
707     ierr = MatSetType(change_mat_all,MATSEQAIJ);CHKERRQ(ierr);
708     ierr = MatSeqAIJSetPreallocation(change_mat_all,0,nnz);CHKERRQ(ierr);
709     ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
710     for (i=0;i<n_D;i++) {
711       ierr = MatSetValue(change_mat_all,is_indices[i],is_indices[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
712     }
713     ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
714     ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
715     for (i=0;i<n_B;i++) {
716       ierr = MatGetRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
717       for (k=0; k<j; k++) temp_indices[k]=is_indices[row_cmat_indices[k]];
718       ierr = MatSetValues(change_mat_all,1,&is_indices[i],j,temp_indices,row_cmat_values,INSERT_VALUES);CHKERRQ(ierr);
719       ierr = MatRestoreRow(pcbddc->ChangeOfBasisMatrix,i,&j,(const PetscInt**)&row_cmat_indices,(const PetscScalar**)&row_cmat_values);CHKERRQ(ierr);
720     }
721     ierr = MatAssemblyBegin(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
722     ierr = MatAssemblyEnd(change_mat_all,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
723     /* TODO: HOW TO WORK WITH BAIJ? PtAP not provided */
724     ierr = MatGetBlockSize(matis->A,&i);CHKERRQ(ierr);
725     if (i==1) {
726       ierr = MatPtAP(matis->A,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
727     } else {
728       Mat work_mat;
729       ierr = MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);CHKERRQ(ierr);
730       ierr = MatPtAP(work_mat,change_mat_all,reuse,2.0,&pcbddc->local_mat);CHKERRQ(ierr);
731       ierr = MatDestroy(&work_mat);CHKERRQ(ierr);
732     }
733     ierr = MatDestroy(&change_mat_all);CHKERRQ(ierr);
734     ierr = PetscFree(nnz);CHKERRQ(ierr);
735     ierr = PetscFree(temp_indices);CHKERRQ(ierr);
736   } else {
737     /* without change of basis, the local matrix is unchanged */
738     if (!pcbddc->local_mat) {
739       ierr = PetscObjectReference((PetscObject)matis->A);CHKERRQ(ierr);
740       pcbddc->local_mat = matis->A;
741     }
742   }
743 
744   /* get submatrices */
745   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_I_local,reuse,&pcis->A_II);CHKERRQ(ierr);
746   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_I_local,pcis->is_B_local,reuse,&pcis->A_IB);CHKERRQ(ierr);
747   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_I_local,reuse,&pcis->A_BI);CHKERRQ(ierr);
748   ierr = MatGetSubMatrix(pcbddc->local_mat,pcis->is_B_local,pcis->is_B_local,reuse,&pcis->A_BB);CHKERRQ(ierr);
749   PetscFunctionReturn(0);
750 }
751 
752 #undef __FUNCT__
753 #define __FUNCT__ "PCBDDCSetUpLocalScatters"
754 PetscErrorCode PCBDDCSetUpLocalScatters(PC pc,IS* is_R_local_n)
755 {
756   PC_IS*         pcis = (PC_IS*)(pc->data);
757   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
758   IS             is_R_local,is_aux1,is_aux2;
759   PetscInt       *vertices,*aux_array1,*aux_array2,*is_indices,*idx_R_local;
760   PetscInt       n_vertices,n_constraints,i,j,n_R,n_D,n_B;
761   PetscBool      *array_bool;
762   PetscErrorCode ierr;
763 
764   PetscFunctionBegin;
765   /* Set Non-overlapping dimensions */
766   n_B = pcis->n_B; n_D = pcis->n - n_B;
767   /* get vertex indices from constraint matrix */
768   ierr = PCBDDCGetPrimalVerticesLocalIdx(pc,&n_vertices,&vertices);CHKERRQ(ierr);
769   /* Set number of constraints */
770   n_constraints = pcbddc->local_primal_size-n_vertices;
771   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */
772   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&array_bool);CHKERRQ(ierr);
773   for (i=0;i<pcis->n;i++) array_bool[i] = PETSC_TRUE;
774   for (i=0;i<n_vertices;i++) array_bool[vertices[i]] = PETSC_FALSE;
775   ierr = PetscMalloc((pcis->n-n_vertices)*sizeof(PetscInt),&idx_R_local);CHKERRQ(ierr);
776   for (i=0, n_R=0; i<pcis->n; i++) {
777     if (array_bool[i]) {
778       idx_R_local[n_R] = i;
779       n_R++;
780     }
781   }
782   ierr = PetscFree(vertices);CHKERRQ(ierr);
783   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_R,idx_R_local,PETSC_OWN_POINTER,&is_R_local);CHKERRQ(ierr);
784 
785   /* print some info if requested */
786   if (pcbddc->dbg_flag) {
787     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
788     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
789     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);CHKERRQ(ierr);
790     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);CHKERRQ(ierr);
791     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);
792     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"pcbddc->n_vertices = %d, pcbddc->n_constraints = %d\n",pcbddc->n_vertices,pcbddc->n_constraints);CHKERRQ(ierr);
793     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
794   }
795 
796   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
797   ierr = PetscMalloc((pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
798   ierr = PetscMalloc((pcis->n_B-n_vertices)*sizeof(PetscInt),&aux_array2);CHKERRQ(ierr);
799   ierr = ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
800   for (i=0; i<n_D; i++) array_bool[is_indices[i]] = PETSC_FALSE;
801   ierr = ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
802   for (i=0, j=0; i<n_R; i++) {
803     if (array_bool[idx_R_local[i]]) {
804       aux_array1[j] = i;
805       j++;
806     }
807   }
808   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
809   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
810   for (i=0, j=0; i<n_B; i++) {
811     if (array_bool[is_indices[i]]) {
812       aux_array2[j] = i; j++;
813     }
814   }
815   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
816   ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);CHKERRQ(ierr);
817   ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);CHKERRQ(ierr);
818   ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
819   ierr = ISDestroy(&is_aux2);CHKERRQ(ierr);
820 
821   if (pcbddc->inexact_prec_type || pcbddc->dbg_flag ) {
822     ierr = PetscMalloc(n_D*sizeof(PetscInt),&aux_array1);CHKERRQ(ierr);
823     for (i=0, j=0; i<n_R; i++) {
824       if (!array_bool[idx_R_local[i]]) {
825         aux_array1[j] = i;
826         j++;
827       }
828     }
829     ierr = ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);CHKERRQ(ierr);
830     ierr = VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);CHKERRQ(ierr);
831     ierr = ISDestroy(&is_aux1);CHKERRQ(ierr);
832   }
833   ierr = PetscFree(array_bool);CHKERRQ(ierr);
834   *is_R_local_n = is_R_local;
835   PetscFunctionReturn(0);
836 }
837 
838 #undef __FUNCT__
839 #define __FUNCT__ "PCBDDCSetUseExactDirichlet"
840 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool use)
841 {
842   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
843 
844   PetscFunctionBegin;
845   pcbddc->use_exact_dirichlet=use;
846   PetscFunctionReturn(0);
847 }
848 
849 #undef __FUNCT__
850 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
851 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, IS is_I_local, IS is_R_local)
852 {
853   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
854   PC_IS          *pcis = (PC_IS*)pc->data;
855   PC             pc_temp;
856   Mat            A_RR;
857   Vec            vec1,vec2,vec3;
858   MatStructure   matstruct;
859   PetscScalar    m_one = -1.0;
860   PetscReal      value;
861   PetscInt       n_D,n_R,use_exact,use_exact_reduced;
862   PetscErrorCode ierr;
863 
864   PetscFunctionBegin;
865   /* Creating PC contexts for local Dirichlet and Neumann problems */
866   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
867 
868   /* DIRICHLET PROBLEM */
869   /* Matrix for Dirichlet problem is pcis->A_II */
870   ierr = ISGetSize(is_I_local,&n_D);CHKERRQ(ierr);
871   if (!pcbddc->ksp_D) { /* create object if not yet build */
872     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
873     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
874     /* default */
875     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
876     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
877     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
878     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
879     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
880   }
881   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,matstruct);CHKERRQ(ierr);
882   /* Allow user's customization */
883   ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
884   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
885   if (!n_D) {
886     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
887     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
888   }
889   /* Set Up KSP for Dirichlet problem of BDDC */
890   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
891   /* set ksp_D into pcis data */
892   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
893   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
894   pcis->ksp_D = pcbddc->ksp_D;
895 
896   /* NEUMANN PROBLEM */
897   /* Matrix for Neumann problem is A_RR -> we need to create it */
898   ierr = ISGetSize(is_R_local,&n_R);CHKERRQ(ierr);
899   ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
900   if (!pcbddc->ksp_R) { /* create object if not yet build */
901     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
902     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
903     /* default */
904     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
905     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
906     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
907     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
908     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
909   }
910   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,matstruct);CHKERRQ(ierr);
911   /* Allow user's customization */
912   ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
913   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
914   if (!n_R) {
915     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
916     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
917   }
918   /* Set Up KSP for Neumann problem of BDDC */
919   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
920 
921   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
922 
923   /* Dirichlet */
924   ierr = MatGetVecs(pcis->A_II,&vec1,&vec2);CHKERRQ(ierr);
925   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
926   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
927   ierr = MatMult(pcis->A_II,vec1,vec2);CHKERRQ(ierr);
928   ierr = KSPSolve(pcbddc->ksp_D,vec2,vec3);CHKERRQ(ierr);
929   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
930   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
931   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
932   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
933   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
934   /* need to be adapted? */
935   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
936   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
937   ierr = PCBDDCSetUseExactDirichlet(pc,(PetscBool)use_exact_reduced);CHKERRQ(ierr);
938   /* print info */
939   if (pcbddc->dbg_flag) {
940     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
941     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
942     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
943     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
944     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
945   }
946   if (n_D && pcbddc->NullSpace && !use_exact_reduced && !pcbddc->inexact_prec_type) {
947     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_I_local);CHKERRQ(ierr);
948   }
949 
950   /* Neumann */
951   ierr = MatGetVecs(A_RR,&vec1,&vec2);CHKERRQ(ierr);
952   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
953   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
954   ierr = MatMult(A_RR,vec1,vec2);CHKERRQ(ierr);
955   ierr = KSPSolve(pcbddc->ksp_R,vec2,vec3);CHKERRQ(ierr);
956   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
957   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
958   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
959   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
960   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
961   /* need to be adapted? */
962   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
963   if (PetscAbsReal(value) > 1.e-4) use_exact = 0;
964   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
965   /* print info */
966   if (pcbddc->dbg_flag) {
967     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
968     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
969   }
970   if (n_R && pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
971     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_R_local);CHKERRQ(ierr);
972   }
973 
974   /* free Neumann problem's matrix */
975   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
976   PetscFunctionReturn(0);
977 }
978 
979 #undef __FUNCT__
980 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
981 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
982 {
983   PetscErrorCode ierr;
984   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
985 
986   PetscFunctionBegin;
987   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
988   if (pcbddc->local_auxmat1) {
989     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
990     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
991   }
992   PetscFunctionReturn(0);
993 }
994 
995 #undef __FUNCT__
996 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
997 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
998 {
999   PetscErrorCode ierr;
1000   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
1001   PC_IS*            pcis = (PC_IS*)  (pc->data);
1002   const PetscScalar zero = 0.0;
1003 
1004   PetscFunctionBegin;
1005   /* Application of PHI^T (or PSI^T)  */
1006   if (pcbddc->coarse_psi_B) {
1007     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1008     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1009   } else {
1010     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
1011     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
1012   }
1013   /* Scatter data of coarse_rhs */
1014   if (pcbddc->coarse_rhs) { ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr); }
1015   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1016 
1017   /* Local solution on R nodes */
1018   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
1019   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1020   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1021   if (pcbddc->inexact_prec_type) {
1022     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1023     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1024   }
1025   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
1026   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
1027   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1028   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1029   if (pcbddc->inexact_prec_type) {
1030     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1031     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1032   }
1033 
1034   /* Coarse solution */
1035   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1036   if (pcbddc->coarse_rhs) { /* TODO remove null space when doing multilevel */
1037     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
1038   }
1039   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1040   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1041 
1042   /* Sum contributions from two levels */
1043   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
1044   if (pcbddc->inexact_prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
1045   PetscFunctionReturn(0);
1046 }
1047 
1048 #undef __FUNCT__
1049 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
1050 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
1051 {
1052   PetscErrorCode ierr;
1053   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1054 
1055   PetscFunctionBegin;
1056   switch (pcbddc->coarse_communications_type) {
1057     case SCATTERS_BDDC:
1058       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
1059       break;
1060     case GATHERS_BDDC:
1061       break;
1062   }
1063   PetscFunctionReturn(0);
1064 }
1065 
1066 #undef __FUNCT__
1067 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
1068 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
1069 {
1070   PetscErrorCode ierr;
1071   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
1072   PetscScalar*   array_to;
1073   PetscScalar*   array_from;
1074   MPI_Comm       comm;
1075   PetscInt       i;
1076 
1077   PetscFunctionBegin;
1078   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
1079   switch (pcbddc->coarse_communications_type) {
1080     case SCATTERS_BDDC:
1081       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
1082       break;
1083     case GATHERS_BDDC:
1084       if (vec_from) {
1085         ierr = VecGetArray(vec_from,&array_from);CHKERRQ(ierr);
1086       }
1087       if (vec_to) {
1088         ierr = VecGetArray(vec_to,&array_to);CHKERRQ(ierr);
1089       }
1090       switch(pcbddc->coarse_problem_type){
1091         case SEQUENTIAL_BDDC:
1092           if (smode == SCATTER_FORWARD) {
1093             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);
1094             if (vec_to) {
1095               if (imode == ADD_VALUES) {
1096                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
1097                   array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
1098                 }
1099               } else {
1100                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
1101                   array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
1102                 }
1103               }
1104             }
1105           } else {
1106             if (vec_from) {
1107               if (imode == ADD_VALUES) {
1108                 MPI_Comm vec_from_comm;
1109                 ierr = PetscObjectGetComm((PetscObject)(vec_from),&vec_from_comm);CHKERRQ(ierr);
1110                 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);
1111               }
1112               for (i=0;i<pcbddc->replicated_primal_size;i++) {
1113                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
1114               }
1115             }
1116             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);
1117           }
1118           break;
1119         case REPLICATED_BDDC:
1120           if (smode == SCATTER_FORWARD) {
1121             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);
1122             if (imode == ADD_VALUES) {
1123               for (i=0;i<pcbddc->replicated_primal_size;i++) {
1124                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
1125               }
1126             } else {
1127               for (i=0;i<pcbddc->replicated_primal_size;i++) {
1128                 array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
1129               }
1130             }
1131           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
1132             if (imode == ADD_VALUES) {
1133               for (i=0;i<pcbddc->local_primal_size;i++) {
1134                 array_to[i]+=array_from[pcbddc->local_primal_indices[i]];
1135               }
1136             } else {
1137               for (i=0;i<pcbddc->local_primal_size;i++) {
1138                 array_to[i]=array_from[pcbddc->local_primal_indices[i]];
1139               }
1140             }
1141           }
1142           break;
1143         case MULTILEVEL_BDDC:
1144           break;
1145         case PARALLEL_BDDC:
1146           break;
1147       }
1148       if (vec_from) {
1149         ierr = VecRestoreArray(vec_from,&array_from);CHKERRQ(ierr);
1150       }
1151       if (vec_to) {
1152         ierr = VecRestoreArray(vec_to,&array_to);CHKERRQ(ierr);
1153       }
1154       break;
1155   }
1156   PetscFunctionReturn(0);
1157 }
1158 
1159 /* uncomment for testing purposes */
1160 /* #define PETSC_MISSING_LAPACK_GESVD 1 */
1161 #undef __FUNCT__
1162 #define __FUNCT__ "PCBDDCConstraintsSetUp"
1163 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
1164 {
1165   PetscErrorCode    ierr;
1166   PC_IS*            pcis = (PC_IS*)(pc->data);
1167   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
1168   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
1169   /* constraint and (optionally) change of basis matrix implemented as SeqAIJ */
1170   MatType           impMatType=MATSEQAIJ;
1171   /* one and zero */
1172   PetscScalar       one=1.0,zero=0.0;
1173   /* space to store constraints and their local indices */
1174   PetscScalar       *temp_quadrature_constraint;
1175   PetscInt          *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B;
1176   /* iterators */
1177   PetscInt          i,j,k,total_counts,temp_start_ptr;
1178   /* stuff to store connected components stored in pcbddc->mat_graph */
1179   IS                ISForVertices,*ISForFaces,*ISForEdges,*used_IS;
1180   PetscInt          n_ISForFaces,n_ISForEdges;
1181   PetscBool         get_faces,get_edges,get_vertices;
1182   /* near null space stuff */
1183   MatNullSpace      nearnullsp;
1184   const Vec         *nearnullvecs;
1185   Vec               *localnearnullsp;
1186   PetscBool         nnsp_has_cnst;
1187   PetscInt          nnsp_size;
1188   PetscScalar       *array;
1189   /* BLAS integers */
1190   PetscBLASInt      lwork,lierr;
1191   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
1192   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
1193   /* LAPACK working arrays for SVD or POD */
1194   PetscBool         skip_lapack;
1195   PetscScalar       *work;
1196   PetscReal         *singular_vals;
1197 #if defined(PETSC_USE_COMPLEX)
1198   PetscReal         *rwork;
1199 #endif
1200 #if defined(PETSC_MISSING_LAPACK_GESVD)
1201   PetscBLASInt      Blas_one_2=1;
1202   PetscScalar       *temp_basis,*correlation_mat;
1203 #else
1204   PetscBLASInt      dummy_int_1=1,dummy_int_2=1;
1205   PetscScalar       dummy_scalar_1=0.0,dummy_scalar_2=0.0;
1206 #endif
1207   /* change of basis */
1208   PetscInt          *aux_primal_numbering,*aux_primal_minloc,*global_indices;
1209   PetscBool         boolforchange,*change_basis,*touched;
1210   /* auxiliary stuff */
1211   PetscInt          *nnz,*is_indices,*local_to_B;
1212   /* some quantities */
1213   PetscInt          n_vertices,total_primal_vertices;
1214   PetscInt          size_of_constraint,max_size_of_constraint,max_constraints,temp_constraints;
1215 
1216 
1217   PetscFunctionBegin;
1218   /* Get index sets for faces, edges and vertices from graph */
1219   get_faces = PETSC_TRUE;
1220   get_edges = PETSC_TRUE;
1221   get_vertices = PETSC_TRUE;
1222   if (pcbddc->vertices_flag) {
1223     get_faces = PETSC_FALSE;
1224     get_edges = PETSC_FALSE;
1225   }
1226   if (pcbddc->constraints_flag) {
1227     get_vertices = PETSC_FALSE;
1228   }
1229   if (pcbddc->faces_flag) {
1230     get_edges = PETSC_FALSE;
1231   }
1232   if (pcbddc->edges_flag) {
1233     get_faces = PETSC_FALSE;
1234   }
1235   /* default */
1236   if (!get_faces && !get_edges && !get_vertices) {
1237     get_vertices = PETSC_TRUE;
1238   }
1239   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
1240   /* print some info */
1241   if (pcbddc->dbg_flag) {
1242     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1243     i = 0;
1244     if (ISForVertices) {
1245       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
1246     }
1247     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
1248     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
1249     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
1250     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1251   }
1252   /* check if near null space is attached to global mat */
1253   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
1254   if (nearnullsp) {
1255     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
1256   } else { /* if near null space is not provided BDDC uses constants by default */
1257     nnsp_size = 0;
1258     nnsp_has_cnst = PETSC_TRUE;
1259   }
1260   /* get max number of constraints on a single cc */
1261   max_constraints = nnsp_size;
1262   if (nnsp_has_cnst) max_constraints++;
1263 
1264   /*
1265        Evaluate maximum storage size needed by the procedure
1266        - temp_indices will contain start index of each constraint stored as follows
1267        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
1268        - 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
1269        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
1270                                                                                                                                                          */
1271   total_counts = n_ISForFaces+n_ISForEdges;
1272   total_counts *= max_constraints;
1273   n_vertices = 0;
1274   if (ISForVertices) {
1275     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
1276   }
1277   total_counts += n_vertices;
1278   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
1279   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
1280   total_counts = 0;
1281   max_size_of_constraint = 0;
1282   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1283     if (i<n_ISForEdges) {
1284       used_IS = &ISForEdges[i];
1285     } else {
1286       used_IS = &ISForFaces[i-n_ISForEdges];
1287     }
1288     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
1289     total_counts += j;
1290     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
1291   }
1292   total_counts *= max_constraints;
1293   total_counts += n_vertices;
1294   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
1295   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
1296   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
1297   /* local to boundary numbering */
1298   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
1299   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1300   for (i=0;i<pcis->n;i++) local_to_B[i]=-1;
1301   for (i=0;i<pcis->n_B;i++) local_to_B[is_indices[i]]=i;
1302   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1303   /* get local part of global near null space vectors */
1304   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
1305   for (k=0;k<nnsp_size;k++) {
1306     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
1307     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1308     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1309   }
1310 
1311   /* whether or not to skip lapack calls */
1312   skip_lapack = PETSC_TRUE;
1313   if (n_ISForFaces+n_ISForEdges) skip_lapack = PETSC_FALSE;
1314 
1315   /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
1316   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1317     PetscScalar temp_work;
1318 #if defined(PETSC_MISSING_LAPACK_GESVD)
1319     /* Proper Orthogonal Decomposition (POD) using the snapshot method */
1320     ierr = PetscMalloc(max_constraints*max_constraints*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
1321     ierr = PetscMalloc(max_constraints*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
1322     ierr = PetscMalloc(max_size_of_constraint*max_constraints*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
1323 #if defined(PETSC_USE_COMPLEX)
1324     ierr = PetscMalloc(3*max_constraints*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
1325 #endif
1326     /* now we evaluate the optimal workspace using query with lwork=-1 */
1327     ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1328     ierr = PetscBLASIntCast(max_constraints,&Blas_LDA);CHKERRQ(ierr);
1329     lwork = -1;
1330     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1331 #if !defined(PETSC_USE_COMPLEX)
1332     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
1333 #else
1334     PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
1335 #endif
1336     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1337     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
1338 #else /* on missing GESVD */
1339     /* SVD */
1340     PetscInt max_n,min_n;
1341     max_n = max_size_of_constraint;
1342     min_n = max_constraints;
1343     if (max_size_of_constraint < max_constraints) {
1344       min_n = max_size_of_constraint;
1345       max_n = max_constraints;
1346     }
1347     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
1348 #if defined(PETSC_USE_COMPLEX)
1349     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
1350 #endif
1351     /* now we evaluate the optimal workspace using query with lwork=-1 */
1352     lwork = -1;
1353     ierr = PetscBLASIntCast(max_n,&Blas_M);CHKERRQ(ierr);
1354     ierr = PetscBLASIntCast(min_n,&Blas_N);CHKERRQ(ierr);
1355     ierr = PetscBLASIntCast(max_n,&Blas_LDA);CHKERRQ(ierr);
1356     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1357 #if !defined(PETSC_USE_COMPLEX)
1358     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));
1359 #else
1360     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));
1361 #endif
1362     ierr = PetscFPTrapPop();CHKERRQ(ierr);
1363     if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
1364 #endif /* on missing GESVD */
1365     /* Allocate optimal workspace */
1366     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
1367     ierr = PetscMalloc((PetscInt)lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);
1368   }
1369   /* Now we can loop on constraining sets */
1370   total_counts = 0;
1371   temp_indices[0] = 0;
1372   /* vertices */
1373   if (ISForVertices) {
1374     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1375     if (nnsp_has_cnst) { /* consider all vertices */
1376       for (i=0;i<n_vertices;i++) {
1377         temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
1378         temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
1379         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1380         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1381         change_basis[total_counts]=PETSC_FALSE;
1382         total_counts++;
1383       }
1384     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
1385       PetscBool used_vertex;
1386       for (i=0;i<n_vertices;i++) {
1387         used_vertex = PETSC_FALSE;
1388         k = 0;
1389         while (!used_vertex && k<nnsp_size) {
1390           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1391           if (PetscAbsScalar(array[is_indices[i]])>0.0) {
1392             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
1393             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
1394             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
1395             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
1396             change_basis[total_counts]=PETSC_FALSE;
1397             total_counts++;
1398             used_vertex = PETSC_TRUE;
1399           }
1400           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1401           k++;
1402         }
1403       }
1404     }
1405     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1406     n_vertices = total_counts;
1407   }
1408 
1409   /* edges and faces */
1410   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
1411     if (i<n_ISForEdges) {
1412       used_IS = &ISForEdges[i];
1413       boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
1414     } else {
1415       used_IS = &ISForFaces[i-n_ISForEdges];
1416       boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
1417     }
1418     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
1419     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
1420     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
1421     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1422     /* change of basis should not be performed on local periodic nodes */
1423     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
1424     if (nnsp_has_cnst) {
1425       PetscScalar quad_value;
1426       temp_constraints++;
1427       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
1428       for (j=0;j<size_of_constraint;j++) {
1429         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
1430         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
1431         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
1432       }
1433       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1434       change_basis[total_counts]=boolforchange;
1435       total_counts++;
1436     }
1437     for (k=0;k<nnsp_size;k++) {
1438       PetscReal real_value;
1439       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1440       for (j=0;j<size_of_constraint;j++) {
1441         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
1442         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
1443         temp_quadrature_constraint[temp_indices[total_counts]+j]=array[is_indices[j]];
1444       }
1445       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);CHKERRQ(ierr);
1446       /* check if array is null on the connected component */
1447       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1448       PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,&temp_quadrature_constraint[temp_indices[total_counts]],&Blas_one));
1449       if (real_value > 0.0) { /* keep indices and values */
1450         temp_constraints++;
1451         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
1452         change_basis[total_counts]=boolforchange;
1453         total_counts++;
1454       }
1455     }
1456     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
1457     /* perform SVD on the constraints if use_nnsp_true has not be requested by the user */
1458     if (!pcbddc->use_nnsp_true) {
1459       PetscReal tol = 1.0e-8; /* tolerance for retaining eigenmodes */
1460 
1461 #if defined(PETSC_MISSING_LAPACK_GESVD)
1462       /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
1463          POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
1464          -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
1465             the constraints basis will differ (by a complex factor with absolute value equal to 1)
1466             from that computed using LAPACKgesvd
1467          -> This is due to a different computation of eigenvectors in LAPACKheev
1468          -> The quality of the POD-computed basis will be the same */
1469       ierr = PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));CHKERRQ(ierr);
1470       /* Store upper triangular part of correlation matrix */
1471       ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1472       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1473       for (j=0;j<temp_constraints;j++) {
1474         for (k=0;k<j+1;k++) {
1475           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));
1476         }
1477       }
1478       /* compute eigenvalues and eigenvectors of correlation matrix */
1479       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1480       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDA);CHKERRQ(ierr);
1481 #if !defined(PETSC_USE_COMPLEX)
1482       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
1483 #else
1484       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
1485 #endif
1486       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1487       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
1488       /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
1489       j=0;
1490       while (j < temp_constraints && singular_vals[j] < tol) j++;
1491       total_counts=total_counts-j;
1492       /* scale and copy POD basis into used quadrature memory */
1493       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1494       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1495       ierr = PetscBLASIntCast(temp_constraints,&Blas_K);CHKERRQ(ierr);
1496       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1497       ierr = PetscBLASIntCast(temp_constraints,&Blas_LDB);CHKERRQ(ierr);
1498       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1499       if (j<temp_constraints) {
1500         PetscInt ii;
1501         for (k=j;k<temp_constraints;k++) singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
1502         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1503         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));
1504         ierr = PetscFPTrapPop();CHKERRQ(ierr);
1505         for (k=0;k<temp_constraints-j;k++) {
1506           for (ii=0;ii<size_of_constraint;ii++) {
1507             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];
1508           }
1509         }
1510       }
1511 #else  /* on missing GESVD */
1512       ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1513       ierr = PetscBLASIntCast(temp_constraints,&Blas_N);CHKERRQ(ierr);
1514       ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1515       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1516 #if !defined(PETSC_USE_COMPLEX)
1517       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));
1518 #else
1519       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));
1520 #endif
1521       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
1522       ierr = PetscFPTrapPop();CHKERRQ(ierr);
1523       /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
1524       k = temp_constraints;
1525       if (k > size_of_constraint) k = size_of_constraint;
1526       j = 0;
1527       while (j < k && singular_vals[k-j-1] < tol) j++;
1528       total_counts = total_counts-temp_constraints+k-j;
1529 #endif /* on missing GESVD */
1530     }
1531   }
1532   /* free index sets of faces, edges and vertices */
1533   for (i=0;i<n_ISForFaces;i++) {
1534     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
1535   }
1536   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
1537   for (i=0;i<n_ISForEdges;i++) {
1538     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
1539   }
1540   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
1541   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
1542 
1543   /* free workspace */
1544   if (!pcbddc->use_nnsp_true && !skip_lapack) {
1545     ierr = PetscFree(work);CHKERRQ(ierr);
1546 #if defined(PETSC_USE_COMPLEX)
1547     ierr = PetscFree(rwork);CHKERRQ(ierr);
1548 #endif
1549     ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1550 #if defined(PETSC_MISSING_LAPACK_GESVD)
1551     ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1552     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1553 #endif
1554   }
1555   for (k=0;k<nnsp_size;k++) {
1556     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1557   }
1558   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1559 
1560   /* set quantities in pcbddc data structure */
1561   /* n_vertices defines the number of subdomain corners in the primal space */
1562   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
1563   pcbddc->local_primal_size = total_counts;
1564   pcbddc->n_vertices = n_vertices;
1565   pcbddc->n_constraints = pcbddc->local_primal_size-pcbddc->n_vertices;
1566 
1567   /* Create constraint matrix */
1568   /* The constraint matrix is used to compute the l2g map of primal dofs */
1569   /* so we need to set it up properly either with or without change of basis */
1570   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
1571   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
1572   ierr = MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);CHKERRQ(ierr);
1573   /* array to compute a local numbering of constraints : vertices first then constraints */
1574   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
1575   /* array to select the proper local node (of minimum index with respect to global ordering) when changing the basis */
1576   /* 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 */
1577   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&aux_primal_minloc);CHKERRQ(ierr);
1578   /* auxiliary stuff for basis change */
1579   ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&global_indices);CHKERRQ(ierr);
1580   ierr = PetscMalloc(pcis->n_B*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1581   ierr = PetscMemzero(touched,pcis->n_B*sizeof(PetscBool));CHKERRQ(ierr);
1582 
1583   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
1584   total_primal_vertices=0;
1585   for (i=0;i<pcbddc->local_primal_size;i++) {
1586     size_of_constraint=temp_indices[i+1]-temp_indices[i];
1587     if (size_of_constraint == 1) {
1588       touched[temp_indices_to_constraint_B[temp_indices[i]]]=PETSC_TRUE;
1589       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]];
1590       aux_primal_minloc[total_primal_vertices]=0;
1591       total_primal_vertices++;
1592     } else if (change_basis[i]) { /* Same procedure used in PCBDDCGetPrimalConstraintsLocalIdx */
1593       PetscInt min_loc,min_index;
1594       ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,&temp_indices_to_constraint[temp_indices[i]],global_indices);CHKERRQ(ierr);
1595       /* find first untouched local node */
1596       k = 0;
1597       while (touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) k++;
1598       min_index = global_indices[k];
1599       min_loc = k;
1600       /* search the minimum among global nodes already untouched on the cc */
1601       for (k=1;k<size_of_constraint;k++) {
1602         /* there can be more than one constraint on a single connected component */
1603         if (min_index > global_indices[k] && !touched[temp_indices_to_constraint_B[temp_indices[i]+k]]) {
1604           min_index = global_indices[k];
1605           min_loc = k;
1606         }
1607       }
1608       touched[temp_indices_to_constraint_B[temp_indices[i]+min_loc]] = PETSC_TRUE;
1609       aux_primal_numbering[total_primal_vertices]=temp_indices_to_constraint[temp_indices[i]+min_loc];
1610       aux_primal_minloc[total_primal_vertices]=min_loc;
1611       total_primal_vertices++;
1612     }
1613   }
1614   /* free workspace */
1615   ierr = PetscFree(global_indices);CHKERRQ(ierr);
1616   ierr = PetscFree(touched);CHKERRQ(ierr);
1617   /* permute indices in order to have a sorted set of vertices */
1618   ierr = PetscSortInt(total_primal_vertices,aux_primal_numbering);
1619 
1620   /* nonzero structure of constraint matrix */
1621   ierr = PetscMalloc(pcbddc->local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1622   for (i=0;i<total_primal_vertices;i++) nnz[i]=1;
1623   j=total_primal_vertices;
1624   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1625     if (!change_basis[i]) {
1626       nnz[j]=temp_indices[i+1]-temp_indices[i];
1627       j++;
1628     }
1629   }
1630   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
1631   ierr = PetscFree(nnz);CHKERRQ(ierr);
1632   /* set values in constraint matrix */
1633   for (i=0;i<total_primal_vertices;i++) {
1634     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,aux_primal_numbering[i],1.0,INSERT_VALUES);CHKERRQ(ierr);
1635   }
1636   total_counts = total_primal_vertices;
1637   for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1638     if (!change_basis[i]) {
1639       size_of_constraint=temp_indices[i+1]-temp_indices[i];
1640       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);
1641       total_counts++;
1642     }
1643   }
1644   /* assembling */
1645   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1646   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1647   /*
1648   ierr = MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);CHKERRQ(ierr);
1649   */
1650   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
1651   if (pcbddc->use_change_of_basis) {
1652     PetscBool qr_needed = PETSC_FALSE;
1653     /* change of basis acts on local interfaces -> dimension is n_B x n_B */
1654     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
1655     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
1656     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
1657     /* work arrays */
1658     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
1659     for (i=0;i<pcis->n_B;i++) nnz[i]=1;
1660     /* nonzeros per row */
1661     for (i=pcbddc->n_vertices;i<pcbddc->local_primal_size;i++) {
1662       if (change_basis[i]) {
1663         qr_needed = PETSC_TRUE;
1664         size_of_constraint = temp_indices[i+1]-temp_indices[i];
1665         for (j=0;j<size_of_constraint;j++) nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
1666       }
1667     }
1668     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
1669     ierr = PetscFree(nnz);CHKERRQ(ierr);
1670     /* Set initial identity in the matrix */
1671     for (i=0;i<pcis->n_B;i++) {
1672       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
1673     }
1674 
1675     /* Now we loop on the constraints which need a change of basis */
1676     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
1677     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1) */
1678     /* Change of basis matrix T computed via QR decomposition of constraints */
1679     if (qr_needed) {
1680       /* dual and primal dofs on a single cc */
1681       PetscInt     dual_dofs,primal_dofs;
1682       /* iterator on aux_primal_minloc (ordered as read from nearnullspace: vertices, edges and then constraints) */
1683       PetscInt     primal_counter;
1684       /* working stuff for GEQRF */
1685       PetscScalar  *qr_basis,*qr_tau,*qr_work,lqr_work_t;
1686       PetscBLASInt lqr_work;
1687       /* working stuff for UNGQR */
1688       PetscScalar  *gqr_work,lgqr_work_t;
1689       PetscBLASInt lgqr_work;
1690       /* working stuff for TRTRS */
1691       PetscScalar  *trs_rhs;
1692       PetscBLASInt Blas_NRHS;
1693       /* pointers for values insertion into change of basis matrix */
1694       PetscInt     *start_rows,*start_cols;
1695       PetscScalar  *start_vals;
1696       /* working stuff for values insertion */
1697       PetscBool    *is_primal;
1698 
1699       /* space to store Q */
1700       ierr = PetscMalloc((max_size_of_constraint)*(max_size_of_constraint)*sizeof(PetscScalar),&qr_basis);CHKERRQ(ierr);
1701       /* first we issue queries for optimal work */
1702       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1703       ierr = PetscBLASIntCast(max_constraints,&Blas_N);CHKERRQ(ierr);
1704       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1705       lqr_work = -1;
1706       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
1707       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
1708       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);CHKERRQ(ierr);
1709       ierr = PetscMalloc((PetscInt)PetscRealPart(lqr_work_t)*sizeof(*qr_work),&qr_work);CHKERRQ(ierr);
1710       lgqr_work = -1;
1711       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_M);CHKERRQ(ierr);
1712       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_N);CHKERRQ(ierr);
1713       ierr = PetscBLASIntCast(max_constraints,&Blas_K);CHKERRQ(ierr);
1714       ierr = PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1715       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
1716       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
1717       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
1718       ierr = PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);CHKERRQ(ierr);
1719       ierr = PetscMalloc((PetscInt)PetscRealPart(lgqr_work_t)*sizeof(*gqr_work),&gqr_work);CHKERRQ(ierr);
1720       /* array to store scaling factors for reflectors */
1721       ierr = PetscMalloc(max_constraints*sizeof(*qr_tau),&qr_tau);CHKERRQ(ierr);
1722       /* array to store rhs and solution of triangular solver */
1723       ierr = PetscMalloc(max_constraints*max_constraints*sizeof(*trs_rhs),&trs_rhs);CHKERRQ(ierr);
1724       /* array to store whether a node is primal or not */
1725       ierr = PetscMalloc(pcis->n_B*sizeof(*is_primal),&is_primal);CHKERRQ(ierr);
1726       ierr = PetscMemzero(is_primal,pcis->n_B*sizeof(*is_primal));CHKERRQ(ierr);
1727       for (i=0;i<total_primal_vertices;i++) is_primal[local_to_B[aux_primal_numbering[i]]] = PETSC_TRUE;
1728 
1729       /* allocating workspace for check */
1730       if (pcbddc->dbg_flag) {
1731         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
1732         ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);CHKERRQ(ierr);
1733         ierr = PetscMalloc(max_size_of_constraint*(max_constraints+max_size_of_constraint)*sizeof(*work),&work);CHKERRQ(ierr);
1734       }
1735 
1736       /* loop on constraints and see whether or not they need a change of basis */
1737       /* -> using implicit ordering contained in temp_indices data */
1738       total_counts = pcbddc->n_vertices;
1739       primal_counter = total_counts;
1740       while (total_counts<pcbddc->local_primal_size) {
1741         primal_dofs = 1;
1742         if (change_basis[total_counts]) {
1743           /* get all constraints with same support: if more then one constraint is present on the cc then surely indices are stored contiguosly */
1744           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]]) {
1745             primal_dofs++;
1746           }
1747           /* get constraint info */
1748           size_of_constraint = temp_indices[total_counts+1]-temp_indices[total_counts];
1749           dual_dofs = size_of_constraint-primal_dofs;
1750 
1751           /* copy quadrature constraints for change of basis check */
1752           if (pcbddc->dbg_flag) {
1753             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);
1754             ierr = PetscMemcpy(work,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1755           }
1756 
1757           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
1758           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1759 
1760           /* compute QR decomposition of constraints */
1761           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1762           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1763           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1764           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1765           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
1766           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
1767           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1768 
1769           /* explictly compute R^-T */
1770           ierr = PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));CHKERRQ(ierr);
1771           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
1772           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1773           ierr = PetscBLASIntCast(primal_dofs,&Blas_NRHS);CHKERRQ(ierr);
1774           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1775           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
1776           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1777           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
1778           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
1779           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1780 
1781           /* explcitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
1782           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1783           ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1784           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
1785           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1786           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1787           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
1788           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
1789           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1790 
1791           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
1792              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
1793              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
1794           ierr = PetscBLASIntCast(size_of_constraint,&Blas_M);CHKERRQ(ierr);
1795           ierr = PetscBLASIntCast(primal_dofs,&Blas_N);CHKERRQ(ierr);
1796           ierr = PetscBLASIntCast(primal_dofs,&Blas_K);CHKERRQ(ierr);
1797           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1798           ierr = PetscBLASIntCast(primal_dofs,&Blas_LDB);CHKERRQ(ierr);
1799           ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDC);CHKERRQ(ierr);
1800           ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1801           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));
1802           ierr = PetscFPTrapPop();CHKERRQ(ierr);
1803           ierr = PetscMemcpy(qr_basis,&temp_quadrature_constraint[temp_indices[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));CHKERRQ(ierr);
1804 
1805           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
1806           start_rows = &temp_indices_to_constraint_B[temp_indices[total_counts]];
1807           /* insert cols for primal dofs */
1808           for (j=0;j<primal_dofs;j++) {
1809             start_vals = &qr_basis[j*size_of_constraint];
1810             start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+aux_primal_minloc[primal_counter+j]];
1811             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
1812           }
1813           /* insert cols for dual dofs */
1814           for (j=0,k=0;j<dual_dofs;k++) {
1815             if (!is_primal[temp_indices_to_constraint_B[temp_indices[total_counts]+k]]) {
1816               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
1817               start_cols = &temp_indices_to_constraint_B[temp_indices[total_counts]+k];
1818               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);CHKERRQ(ierr);
1819               j++;
1820             }
1821           }
1822 
1823           /* check change of basis */
1824           if (pcbddc->dbg_flag) {
1825             PetscInt   ii,jj;
1826             PetscBool valid_qr=PETSC_TRUE;
1827             ierr = PetscBLASIntCast(primal_dofs,&Blas_M);CHKERRQ(ierr);
1828             ierr = PetscBLASIntCast(size_of_constraint,&Blas_N);CHKERRQ(ierr);
1829             ierr = PetscBLASIntCast(size_of_constraint,&Blas_K);CHKERRQ(ierr);
1830             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDA);CHKERRQ(ierr);
1831             ierr = PetscBLASIntCast(size_of_constraint,&Blas_LDB);CHKERRQ(ierr);
1832             ierr = PetscBLASIntCast(primal_dofs,&Blas_LDC);CHKERRQ(ierr);
1833             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
1834             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));
1835             ierr = PetscFPTrapPop();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) valid_qr = PETSC_FALSE;
1839                 if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
1840               }
1841             }
1842             if (!valid_qr) {
1843               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
1844               for (jj=0;jj<size_of_constraint;jj++) {
1845                 for (ii=0;ii<primal_dofs;ii++) {
1846                   if (ii != jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
1847                     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]));
1848                   }
1849                   if (ii == jj && PetscAbsScalar(work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
1850                     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]));
1851                   }
1852                 }
1853               }
1854             } else {
1855               ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n",PetscGlobalRank);CHKERRQ(ierr);
1856             }
1857           }
1858           /* increment primal counter */
1859           primal_counter += primal_dofs;
1860         } else {
1861           if (pcbddc->dbg_flag) {
1862             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);
1863           }
1864         }
1865         /* increment constraint counter total_counts */
1866         total_counts += primal_dofs;
1867       }
1868       if (pcbddc->dbg_flag) {
1869         ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
1870         ierr = PetscFree(work);CHKERRQ(ierr);
1871       }
1872       /* free workspace */
1873       ierr = PetscFree(trs_rhs);CHKERRQ(ierr);
1874       ierr = PetscFree(qr_tau);CHKERRQ(ierr);
1875       ierr = PetscFree(qr_work);CHKERRQ(ierr);
1876       ierr = PetscFree(gqr_work);CHKERRQ(ierr);
1877       ierr = PetscFree(is_primal);CHKERRQ(ierr);
1878       ierr = PetscFree(qr_basis);CHKERRQ(ierr);
1879     }
1880     /* assembling */
1881     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1882     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1883     /*
1884     ierr = MatView(pcbddc->ChangeOfBasisMatrix,(PetscViewer)0);CHKERRQ(ierr);
1885     */
1886   }
1887   /* free workspace */
1888   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
1889   ierr = PetscFree(aux_primal_minloc);CHKERRQ(ierr);
1890   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
1891   ierr = PetscFree(change_basis);CHKERRQ(ierr);
1892   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
1893   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
1894   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
1895   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
1896   PetscFunctionReturn(0);
1897 }
1898 
1899 #undef __FUNCT__
1900 #define __FUNCT__ "PCBDDCAnalyzeInterface"
1901 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
1902 {
1903   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
1904   PC_IS       *pcis = (PC_IS*)pc->data;
1905   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
1906   PetscInt    bs,ierr,i,vertex_size;
1907   PetscViewer viewer=pcbddc->dbg_viewer;
1908 
1909   PetscFunctionBegin;
1910   /* Init local Graph struct */
1911   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
1912 
1913   /* Check validity of the csr graph passed in by the user */
1914   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
1915     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
1916   }
1917   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
1918   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
1919     Mat mat_adj;
1920     const PetscInt *xadj,*adjncy;
1921     PetscBool flg_row=PETSC_TRUE;
1922 
1923     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
1924     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1925     if (!flg_row) {
1926       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
1927     }
1928     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
1929     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1930     if (!flg_row) {
1931       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
1932     }
1933     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
1934   }
1935 
1936   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
1937   vertex_size = 1;
1938   if (!pcbddc->n_ISForDofs) {
1939     IS *custom_ISForDofs;
1940 
1941     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
1942     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
1943     for (i=0;i<bs;i++) {
1944       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1945     }
1946     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1947     /* remove my references to IS objects */
1948     for (i=0;i<bs;i++) {
1949       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1950     }
1951     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1952   } else { /* mat block size as vertex size (used for elasticity) */
1953     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1954   }
1955 
1956   /* Setup of Graph */
1957   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1958 
1959   /* Graph's connected components analysis */
1960   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1961 
1962   /* print some info to stdout */
1963   if (pcbddc->dbg_flag) {
1964     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1965   }
1966   PetscFunctionReturn(0);
1967 }
1968 
1969 #undef __FUNCT__
1970 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1971 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1972 {
1973   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1974   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1975   PetscErrorCode ierr;
1976 
1977   PetscFunctionBegin;
1978   n = 0;
1979   vertices = 0;
1980   if (pcbddc->ConstraintMatrix) {
1981     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1982     for (i=0;i<local_primal_size;i++) {
1983       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1984       if (size_of_constraint == 1) n++;
1985       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1986     }
1987     if (vertices_idx) {
1988       ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1989       n = 0;
1990       for (i=0;i<local_primal_size;i++) {
1991         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1992         if (size_of_constraint == 1) {
1993           vertices[n++]=row_cmat_indices[0];
1994         }
1995         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1996       }
1997     }
1998   }
1999   *n_vertices = n;
2000   if (vertices_idx) *vertices_idx = vertices;
2001   PetscFunctionReturn(0);
2002 }
2003 
2004 #undef __FUNCT__
2005 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
2006 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
2007 {
2008   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
2009   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
2010   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
2011   PetscBool      *touched;
2012   PetscErrorCode ierr;
2013 
2014   PetscFunctionBegin;
2015   n = 0;
2016   constraints_index = 0;
2017   if (pcbddc->ConstraintMatrix) {
2018     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
2019     max_size_of_constraint = 0;
2020     for (i=0;i<local_primal_size;i++) {
2021       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2022       if (size_of_constraint > 1) {
2023         n++;
2024       }
2025       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
2026       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
2027     }
2028     if (constraints_idx) {
2029       ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
2030       ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
2031       ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
2032       ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
2033       n = 0;
2034       for (i=0;i<local_primal_size;i++) {
2035         ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2036         if (size_of_constraint > 1) {
2037           ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
2038           /* find first untouched local node */
2039           j = 0;
2040           while(touched[row_cmat_indices[j]]) j++;
2041           min_index = row_cmat_global_indices[j];
2042           min_loc = j;
2043           /* search the minimum among nodes not yet touched on the connected component
2044              since there can be more than one constraint on a single cc */
2045           for (j=1;j<size_of_constraint;j++) {
2046             if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
2047               min_index = row_cmat_global_indices[j];
2048               min_loc = j;
2049             }
2050           }
2051           touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
2052           constraints_index[n++] = row_cmat_indices[min_loc];
2053         }
2054         ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
2055       }
2056       ierr = PetscFree(touched);CHKERRQ(ierr);
2057       ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
2058     }
2059   }
2060   *n_constraints = n;
2061   if (constraints_idx) *constraints_idx = constraints_index;
2062   PetscFunctionReturn(0);
2063 }
2064 
2065 /* the next two functions has been adapted from pcis.c */
2066 #undef __FUNCT__
2067 #define __FUNCT__ "PCBDDCApplySchur"
2068 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2069 {
2070   PetscErrorCode ierr;
2071   PC_IS          *pcis = (PC_IS*)(pc->data);
2072 
2073   PetscFunctionBegin;
2074   if (!vec2_B) { vec2_B = v; }
2075   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2076   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
2077   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2078   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
2079   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2080   PetscFunctionReturn(0);
2081 }
2082 
2083 #undef __FUNCT__
2084 #define __FUNCT__ "PCBDDCApplySchurTranspose"
2085 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
2086 {
2087   PetscErrorCode ierr;
2088   PC_IS          *pcis = (PC_IS*)(pc->data);
2089 
2090   PetscFunctionBegin;
2091   if (!vec2_B) { vec2_B = v; }
2092   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
2093   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
2094   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
2095   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
2096   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
2097   PetscFunctionReturn(0);
2098 }
2099 
2100 #undef __FUNCT__
2101 #define __FUNCT__ "PCBDDCSubsetNumbering"
2102 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[])
2103 {
2104   Vec            local_vec,global_vec;
2105   IS             seqis,paris;
2106   VecScatter     scatter_ctx;
2107   PetscScalar    *array;
2108   PetscInt       *temp_global_dofs;
2109   PetscScalar    globalsum;
2110   PetscInt       i,j,s;
2111   PetscInt       nlocals,first_index,old_index,max_local;
2112   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
2113   PetscMPIInt    *dof_sizes,*dof_displs;
2114   PetscBool      first_found;
2115   PetscErrorCode ierr;
2116 
2117   PetscFunctionBegin;
2118   /* mpi buffers */
2119   MPI_Comm_size(comm,&size_prec_comm);
2120   MPI_Comm_rank(comm,&rank_prec_comm);
2121   j = ( !rank_prec_comm ? size_prec_comm : 0);
2122   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
2123   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
2124   /* get maximum size of subset */
2125   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
2126   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
2127   max_local = 0;
2128   if (n_local_dofs) {
2129     max_local = temp_global_dofs[0];
2130     for (i=1;i<n_local_dofs;i++) {
2131       if (max_local < temp_global_dofs[i] ) {
2132         max_local = temp_global_dofs[i];
2133       }
2134     }
2135   }
2136   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
2137   max_global++;
2138   max_local = 0;
2139   if (n_local_dofs) {
2140     max_local = local_dofs[0];
2141     for (i=1;i<n_local_dofs;i++) {
2142       if (max_local < local_dofs[i] ) {
2143         max_local = local_dofs[i];
2144       }
2145     }
2146   }
2147   max_local++;
2148   /* allocate workspace */
2149   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
2150   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
2151   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
2152   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
2153   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
2154   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
2155   /* create scatter */
2156   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
2157   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
2158   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
2159   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
2160   ierr = ISDestroy(&paris);CHKERRQ(ierr);
2161   /* init array */
2162   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
2163   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2164   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2165   if (local_dofs_mult) {
2166     for (i=0;i<n_local_dofs;i++) {
2167       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
2168     }
2169   } else {
2170     for (i=0;i<n_local_dofs;i++) {
2171       array[local_dofs[i]]=1.0;
2172     }
2173   }
2174   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2175   /* scatter into global vec and get total number of global dofs */
2176   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2177   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2178   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
2179   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
2180   /* Fill global_vec with cumulative function for global numbering */
2181   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
2182   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
2183   nlocals = 0;
2184   first_index = -1;
2185   first_found = PETSC_FALSE;
2186   for (i=0;i<s;i++) {
2187     if (!first_found && PetscRealPart(array[i]) > 0.0) {
2188       first_found = PETSC_TRUE;
2189       first_index = i;
2190     }
2191     nlocals += (PetscInt)PetscRealPart(array[i]);
2192   }
2193   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2194   if (!rank_prec_comm) {
2195     dof_displs[0]=0;
2196     for (i=1;i<size_prec_comm;i++) {
2197       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
2198     }
2199   }
2200   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
2201   if (first_found) {
2202     array[first_index] += (PetscScalar)nlocals;
2203     old_index = first_index;
2204     for (i=first_index+1;i<s;i++) {
2205       if (PetscRealPart(array[i]) > 0.0) {
2206         array[i] += array[old_index];
2207         old_index = i;
2208       }
2209     }
2210   }
2211   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
2212   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
2213   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2214   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
2215   /* get global ordering of local dofs */
2216   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
2217   if (local_dofs_mult) {
2218     for (i=0;i<n_local_dofs;i++) {
2219       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
2220     }
2221   } else {
2222     for (i=0;i<n_local_dofs;i++) {
2223       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
2224     }
2225   }
2226   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
2227   /* free workspace */
2228   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
2229   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
2230   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
2231   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
2232   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
2233   /* return pointer to global ordering of local dofs */
2234   *global_numbering_subset = temp_global_dofs;
2235   PetscFunctionReturn(0);
2236 }
2237 
2238 #undef __FUNCT__
2239 #define __FUNCT__ "PCBDDCOrthonormalizeVecs"
2240 PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
2241 {
2242   PetscInt       i,j;
2243   PetscScalar    *alphas;
2244   PetscErrorCode ierr;
2245 
2246   PetscFunctionBegin;
2247   /* this implements stabilized Gram-Schmidt */
2248   ierr = PetscMalloc(n*sizeof(PetscScalar),&alphas);CHKERRQ(ierr);
2249   for (i=0;i<n;i++) {
2250     ierr = VecNormalize(vecs[i],NULL);CHKERRQ(ierr);
2251     if (i<n) { ierr = VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]);CHKERRQ(ierr); }
2252     for (j=i+1;j<n;j++) { ierr = VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]);CHKERRQ(ierr); }
2253   }
2254   ierr = PetscFree(alphas);CHKERRQ(ierr);
2255   PetscFunctionReturn(0);
2256 }
2257 
2258 
2259