xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision ac78edfc57d8f19d48ae2e55e4bd407c89988fef)
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->temp_solution);CHKERRQ(ierr);
49   ierr = VecDestroy(&pcbddc->original_rhs);CHKERRQ(ierr);
50   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
51   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
52   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
53   ierr = MatDestroy(&pcbddc->coarse_mat);CHKERRQ(ierr);
54   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
55   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
56   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
57   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
58   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
59   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
60   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
61   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
62   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
63   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
64   ierr = VecDestroy(&pcbddc->vec4_D);CHKERRQ(ierr);
65   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
66   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
67   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
68   ierr = PetscFree(pcbddc->local_primal_indices);CHKERRQ(ierr);
69   ierr = PetscFree(pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
70   ierr = PetscFree(pcbddc->replicated_local_primal_values);CHKERRQ(ierr);
71   ierr = PetscFree(pcbddc->local_primal_displacements);CHKERRQ(ierr);
72   ierr = PetscFree(pcbddc->local_primal_sizes);CHKERRQ(ierr);
73   PetscFunctionReturn(0);
74 }
75 
76 #undef __FUNCT__
77 #define __FUNCT__ "PCBDDCSetUseExactDirichlet"
78 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool use)
79 {
80   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
81 
82   PetscFunctionBegin;
83   pcbddc->use_exact_dirichlet=use;
84   PetscFunctionReturn(0);
85 }
86 
87 #undef __FUNCT__
88 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
89 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, IS is_I_local, IS is_R_local)
90 {
91   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
92   PC_IS          *pcis = (PC_IS*)pc->data;
93   PC             pc_temp;
94   Mat            A_RR;
95   Vec            vec1,vec2,vec3;
96   MatStructure   matstruct;
97   PetscScalar    m_one = -1.0;
98   PetscReal      value;
99   PetscInt       n_D,n_R,use_exact,use_exact_reduced;
100   PetscErrorCode ierr;
101 
102   PetscFunctionBegin;
103   /* Creating PC contexts for local Dirichlet and Neumann problems */
104   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
105 
106   /* DIRICHLET PROBLEM */
107   /* Matrix for Dirichlet problem is pcis->A_II */
108   ierr = ISGetSize(is_I_local,&n_D);CHKERRQ(ierr);
109   if (!pcbddc->ksp_D) { /* create object if not yet build */
110     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
111     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
112     /* default */
113     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
114     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
115     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
116     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
117     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
118   }
119   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,matstruct);CHKERRQ(ierr);
120   /* Allow user's customization */
121   ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
122   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
123   if (!n_D) {
124     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
125     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
126   }
127   /* Set Up KSP for Dirichlet problem of BDDC */
128   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
129   /* set ksp_D into pcis data */
130   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
131   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
132   pcis->ksp_D = pcbddc->ksp_D;
133 
134   /* NEUMANN PROBLEM */
135   /* Matrix for Neumann problem is A_RR -> we need to create it */
136   ierr = ISGetSize(is_R_local,&n_R);CHKERRQ(ierr);
137   ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
138   if (!pcbddc->ksp_R) { /* create object if not yet build */
139     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
140     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
141     /* default */
142     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
143     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
144     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
145     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
146     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
147   }
148   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,matstruct);CHKERRQ(ierr);
149   /* Allow user's customization */
150   ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
151   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
152   if (!n_R) {
153     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
154     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
155   }
156   /* Set Up KSP for Neumann problem of BDDC */
157   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
158 
159   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
160 
161   /* Dirichlet */
162   ierr = MatGetVecs(pcis->A_II,&vec1,&vec2);CHKERRQ(ierr);
163   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
164   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
165   ierr = MatMult(pcis->A_II,vec1,vec2);CHKERRQ(ierr);
166   ierr = KSPSolve(pcbddc->ksp_D,vec2,vec3);CHKERRQ(ierr);
167   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
168   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
169   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
170   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
171   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
172   /* need to be adapted? */
173   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
174   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
175   ierr = PCBDDCSetUseExactDirichlet(pc,(PetscBool)use_exact_reduced);CHKERRQ(ierr);
176   /* print info */
177   if (pcbddc->dbg_flag) {
178     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
179     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
180     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
181     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
182     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
183   }
184   if (n_D && pcbddc->NullSpace && !use_exact_reduced && !pcbddc->inexact_prec_type) {
185     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_I_local);CHKERRQ(ierr);
186   }
187 
188   /* Neumann */
189   ierr = MatGetVecs(A_RR,&vec1,&vec2);CHKERRQ(ierr);
190   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
191   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
192   ierr = MatMult(A_RR,vec1,vec2);CHKERRQ(ierr);
193   ierr = KSPSolve(pcbddc->ksp_R,vec2,vec3);CHKERRQ(ierr);
194   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
195   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
196   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
197   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
198   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
199   /* need to be adapted? */
200   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
201   if (PetscAbsReal(value) > 1.e-4) use_exact = 0;
202   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
203   /* print info */
204   if (pcbddc->dbg_flag) {
205     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
206     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
207   }
208   if (n_R && pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
209     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_R_local);CHKERRQ(ierr);
210   }
211 
212   /* free Neumann problem's matrix */
213   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
214   PetscFunctionReturn(0);
215 }
216 
217 #undef __FUNCT__
218 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
219 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
220 {
221   PetscErrorCode ierr;
222   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
223 
224   PetscFunctionBegin;
225   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
226   if (pcbddc->local_auxmat1) {
227     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
228     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
229   }
230   PetscFunctionReturn(0);
231 }
232 
233 #undef __FUNCT__
234 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
235 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
236 {
237   PetscErrorCode ierr;
238   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
239   PC_IS*            pcis = (PC_IS*)  (pc->data);
240   const PetscScalar zero = 0.0;
241 
242   PetscFunctionBegin;
243   /* Application of PHI^T (or PSI^T)  */
244   if (pcbddc->coarse_psi_B) {
245     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
246     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
247   } else {
248     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
249     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
250   }
251   /* Scatter data of coarse_rhs */
252   if (pcbddc->coarse_rhs) { ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr); }
253   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
254 
255   /* Local solution on R nodes */
256   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
257   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
258   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
259   if (pcbddc->inexact_prec_type) {
260     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
261     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
262   }
263   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
264   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
265   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
266   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
267   if (pcbddc->inexact_prec_type) {
268     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
269     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
270   }
271 
272   /* Coarse solution */
273   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
274   if (pcbddc->coarse_rhs) { /* TODO remove null space when doing multilevel */
275     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
276   }
277   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
278   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
279 
280   /* Sum contributions from two levels */
281   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
282   if (pcbddc->inexact_prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
283   PetscFunctionReturn(0);
284 }
285 
286 #undef __FUNCT__
287 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
288 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
289 {
290   PetscErrorCode ierr;
291   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
292 
293   PetscFunctionBegin;
294   switch (pcbddc->coarse_communications_type) {
295     case SCATTERS_BDDC:
296       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
297       break;
298     case GATHERS_BDDC:
299       break;
300   }
301   PetscFunctionReturn(0);
302 }
303 
304 #undef __FUNCT__
305 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
306 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
307 {
308   PetscErrorCode ierr;
309   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
310   PetscScalar*   array_to;
311   PetscScalar*   array_from;
312   MPI_Comm       comm;
313   PetscInt       i;
314 
315   PetscFunctionBegin;
316   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
317   switch (pcbddc->coarse_communications_type) {
318     case SCATTERS_BDDC:
319       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
320       break;
321     case GATHERS_BDDC:
322       if (vec_from) {
323         ierr = VecGetArray(vec_from,&array_from);CHKERRQ(ierr);
324       }
325       if (vec_to) {
326         ierr = VecGetArray(vec_to,&array_to);CHKERRQ(ierr);
327       }
328       switch(pcbddc->coarse_problem_type){
329         case SEQUENTIAL_BDDC:
330           if (smode == SCATTER_FORWARD) {
331             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);
332             if (vec_to) {
333               if (imode == ADD_VALUES) {
334                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
335                   array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
336                 }
337               } else {
338                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
339                   array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
340                 }
341               }
342             }
343           } else {
344             if (vec_from) {
345               if (imode == ADD_VALUES) {
346                 MPI_Comm vec_from_comm;
347                 ierr = PetscObjectGetComm((PetscObject)(vec_from),&vec_from_comm);CHKERRQ(ierr);
348                 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);
349               }
350               for (i=0;i<pcbddc->replicated_primal_size;i++) {
351                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
352               }
353             }
354             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);
355           }
356           break;
357         case REPLICATED_BDDC:
358           if (smode == SCATTER_FORWARD) {
359             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);
360             if (imode == ADD_VALUES) {
361               for (i=0;i<pcbddc->replicated_primal_size;i++) {
362                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
363               }
364             } else {
365               for (i=0;i<pcbddc->replicated_primal_size;i++) {
366                 array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
367               }
368             }
369           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
370             if (imode == ADD_VALUES) {
371               for (i=0;i<pcbddc->local_primal_size;i++) {
372                 array_to[i]+=array_from[pcbddc->local_primal_indices[i]];
373               }
374             } else {
375               for (i=0;i<pcbddc->local_primal_size;i++) {
376                 array_to[i]=array_from[pcbddc->local_primal_indices[i]];
377               }
378             }
379           }
380           break;
381         case MULTILEVEL_BDDC:
382           break;
383         case PARALLEL_BDDC:
384           break;
385       }
386       if (vec_from) {
387         ierr = VecRestoreArray(vec_from,&array_from);CHKERRQ(ierr);
388       }
389       if (vec_to) {
390         ierr = VecRestoreArray(vec_to,&array_to);CHKERRQ(ierr);
391       }
392       break;
393   }
394   PetscFunctionReturn(0);
395 }
396 
397 #undef __FUNCT__
398 #define __FUNCT__ "PCBDDCConstraintsSetUp"
399 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
400 {
401   PetscErrorCode ierr;
402   PC_IS*         pcis = (PC_IS*)(pc->data);
403   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
404   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
405   PetscInt       *nnz,*is_indices;
406   PetscScalar    *temp_quadrature_constraint;
407   PetscInt       *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B,*local_to_B;
408   PetscInt       local_primal_size,i,j,k,total_counts,max_size_of_constraint;
409   PetscInt       n_vertices,size_of_constraint;
410   PetscReal      real_value;
411   PetscBool      nnsp_has_cnst=PETSC_FALSE,use_nnsp_true=pcbddc->use_nnsp_true;
412   PetscInt       nnsp_size=0,nnsp_addone=0,temp_constraints,temp_start_ptr,n_ISForFaces,n_ISForEdges;
413   IS             *used_IS,ISForVertices,*ISForFaces,*ISForEdges;
414   MatType        impMatType=MATSEQAIJ;
415   PetscBLASInt   Bs,Bt,lwork,lierr;
416   PetscReal      tol=1.0e-8;
417   MatNullSpace   nearnullsp;
418   const Vec      *nearnullvecs;
419   Vec            *localnearnullsp;
420   PetscScalar    *work,*temp_basis,*array_vector,*correlation_mat;
421   PetscReal      *rwork,*singular_vals;
422   PetscBLASInt   Bone=1,*ipiv;
423   Vec            temp_vec;
424   Mat            temp_mat;
425   KSP            temp_ksp;
426   PC             temp_pc;
427   PetscInt       s,start_constraint,dual_dofs;
428   PetscBool      compute_submatrix,useksp=PETSC_FALSE;
429   PetscInt       *aux_primal_permutation,*aux_primal_numbering;
430   PetscBool      boolforchange,*change_basis;
431 /* some ugly conditional declarations */
432 #if defined(PETSC_MISSING_LAPACK_GESVD)
433   PetscScalar    one=1.0,zero=0.0;
434   PetscInt       ii;
435   PetscScalar    *singular_vectors;
436   PetscBLASInt   *iwork,*ifail;
437   PetscReal      dummy_real,abs_tol;
438   PetscBLASInt   eigs_found;
439 #endif
440   PetscBLASInt   dummy_int;
441   PetscScalar    dummy_scalar;
442   PetscBool      used_vertex,get_faces,get_edges,get_vertices;
443 
444   PetscFunctionBegin;
445   /* Get index sets for faces, edges and vertices from graph */
446   get_faces = PETSC_TRUE;
447   get_edges = PETSC_TRUE;
448   get_vertices = PETSC_TRUE;
449   if (pcbddc->vertices_flag) {
450     get_faces = PETSC_FALSE;
451     get_edges = PETSC_FALSE;
452   }
453   if (pcbddc->constraints_flag) {
454     get_vertices = PETSC_FALSE;
455   }
456   if (pcbddc->faces_flag) {
457     get_edges = PETSC_FALSE;
458   }
459   if (pcbddc->edges_flag) {
460     get_faces = PETSC_FALSE;
461   }
462   /* default */
463   if (!get_faces && !get_edges && !get_vertices) {
464     get_vertices = PETSC_TRUE;
465   }
466   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
467   if (pcbddc->dbg_flag) {
468     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
469     i = 0;
470     if (ISForVertices) {
471       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
472     }
473     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
474     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
475     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
476     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
477   }
478   /* check if near null space is attached to global mat */
479   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
480   if (nearnullsp) {
481     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
482   } else { /* if near null space is not provided it uses constants */
483     nnsp_has_cnst = PETSC_TRUE;
484     use_nnsp_true = PETSC_TRUE;
485   }
486   if (nnsp_has_cnst) {
487     nnsp_addone = 1;
488   }
489   /*
490        Evaluate maximum storage size needed by the procedure
491        - temp_indices will contain start index of each constraint stored as follows
492        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
493        - 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
494        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
495                                                                                                                                                          */
496   total_counts = n_ISForFaces+n_ISForEdges;
497   total_counts *= (nnsp_addone+nnsp_size);
498   n_vertices = 0;
499   if (ISForVertices) {
500     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
501   }
502   total_counts += n_vertices;
503   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
504   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
505   total_counts = 0;
506   max_size_of_constraint = 0;
507   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
508     if (i<n_ISForEdges) {
509       used_IS = &ISForEdges[i];
510     } else {
511       used_IS = &ISForFaces[i-n_ISForEdges];
512     }
513     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
514     total_counts += j;
515     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
516   }
517   total_counts *= (nnsp_addone+nnsp_size);
518   total_counts += n_vertices;
519   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
520   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
521   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
522   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
523   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
524   for (i=0;i<pcis->n;i++) {
525     local_to_B[i]=-1;
526   }
527   for (i=0;i<pcis->n_B;i++) {
528     local_to_B[is_indices[i]]=i;
529   }
530   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
531 
532   /* First we issue queries to allocate optimal workspace for LAPACKgesvd or LAPACKsyev/LAPACKheev */
533   rwork = 0;
534   work = 0;
535   singular_vals = 0;
536   temp_basis = 0;
537   correlation_mat = 0;
538   if (!pcbddc->use_nnsp_true) {
539     PetscScalar temp_work;
540 #if defined(PETSC_MISSING_LAPACK_GESVD)
541     /* POD */
542     PetscInt max_n;
543     max_n = nnsp_addone+nnsp_size;
544     /* using some techniques borrowed from Proper Orthogonal Decomposition */
545     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
546     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&singular_vectors);CHKERRQ(ierr);
547     ierr = PetscMalloc(max_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
548     ierr = PetscMalloc(max_size_of_constraint*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
549 #if defined(PETSC_USE_COMPLEX)
550     ierr = PetscMalloc(3*max_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
551 #endif
552     ierr = PetscMalloc(5*max_n*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
553     ierr = PetscMalloc(max_n*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
554     /* now we evaluate the optimal workspace using query with lwork=-1 */
555     ierr = PetscBLASIntCast(max_n,&Bt);CHKERRQ(ierr);
556     lwork=-1;
557     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
558 #if !defined(PETSC_USE_COMPLEX)
559     abs_tol=1.e-8;
560 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,&lierr); */
561     PetscStackCallBLAS("LAPACKsyevx",LAPACKsyevx_("V","A","U",&Bt,correlation_mat,&Bt,&dummy_real,&dummy_real,&dummy_int,&dummy_int,&abs_tol,&eigs_found,singular_vals,singular_vectors,&Bt,&temp_work,&lwork,iwork,ifail,&lierr));
562 #else
563 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,rwork,&lierr); */
564 /*  LAPACK call is missing here! TODO */
565     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
566 #endif
567     if ( lierr ) {
568       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEVX Lapack routine %d",(int)lierr);
569     }
570     ierr = PetscFPTrapPop();CHKERRQ(ierr);
571 #else /* on missing GESVD */
572     /* SVD */
573     PetscInt max_n,min_n;
574     max_n = max_size_of_constraint;
575     min_n = nnsp_addone+nnsp_size;
576     if (max_size_of_constraint < ( nnsp_addone+nnsp_size ) ) {
577       min_n = max_size_of_constraint;
578       max_n = nnsp_addone+nnsp_size;
579     }
580     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
581 #if defined(PETSC_USE_COMPLEX)
582     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
583 #endif
584     /* now we evaluate the optimal workspace using query with lwork=-1 */
585     lwork=-1;
586     ierr = PetscBLASIntCast(max_n,&Bs);CHKERRQ(ierr);
587     ierr = PetscBLASIntCast(min_n,&Bt);CHKERRQ(ierr);
588     dummy_int = Bs;
589     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
590 #if !defined(PETSC_USE_COMPLEX)
591     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,&lierr));
592 #else
593     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[0],&Bs,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,rwork,&lierr));
594 #endif
595     if ( lierr ) {
596       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SVD Lapack routine %d",(int)lierr);
597     }
598     ierr = PetscFPTrapPop();CHKERRQ(ierr);
599 #endif
600     /* Allocate optimal workspace */
601     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
602     total_counts = (PetscInt)lwork;
603     ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&work);CHKERRQ(ierr);
604   }
605   /* get local part of global near null space vectors */
606   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
607   for (k=0;k<nnsp_size;k++) {
608     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
609     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
610     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
611   }
612   /* Now we can loop on constraining sets */
613   total_counts = 0;
614   temp_indices[0] = 0;
615   /* vertices */
616   if (ISForVertices) {
617     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
618     if (nnsp_has_cnst) { /* consider all vertices */
619       for (i=0;i<n_vertices;i++) {
620         temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
621         temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
622         temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
623         temp_indices[total_counts+1]=temp_indices[total_counts]+1;
624         change_basis[total_counts]=PETSC_FALSE;
625         total_counts++;
626       }
627     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
628       for (i=0;i<n_vertices;i++) {
629         used_vertex=PETSC_FALSE;
630         k=0;
631         while (!used_vertex && k<nnsp_size) {
632           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
633           if (PetscAbsScalar(array_vector[is_indices[i]])>0.0) {
634             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
635             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
636             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
637             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
638             change_basis[total_counts]=PETSC_FALSE;
639             total_counts++;
640             used_vertex=PETSC_TRUE;
641           }
642           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
643           k++;
644         }
645       }
646     }
647     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
648     n_vertices = total_counts;
649   }
650   /* edges and faces */
651   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
652     if (i<n_ISForEdges) {
653       used_IS = &ISForEdges[i];
654       boolforchange = pcbddc->use_change_of_basis;
655     } else {
656       used_IS = &ISForFaces[i-n_ISForEdges];
657       boolforchange = pcbddc->use_change_on_faces;
658     }
659     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
660     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
661     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
662     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
663     /* HACK: change of basis should not performed on local periodic nodes */
664     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) {
665       boolforchange = PETSC_FALSE;
666     }
667     if (nnsp_has_cnst) {
668       PetscScalar quad_value;
669       temp_constraints++;
670       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
671       for (j=0;j<size_of_constraint;j++) {
672         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
673         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
674         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
675       }
676       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
677       change_basis[total_counts]=boolforchange;
678       total_counts++;
679     }
680     for (k=0;k<nnsp_size;k++) {
681       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
682       for (j=0;j<size_of_constraint;j++) {
683         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
684         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
685         temp_quadrature_constraint[temp_indices[total_counts]+j]=array_vector[is_indices[j]];
686       }
687       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
688       real_value = 1.0;
689       if (use_nnsp_true) { /* check if array is null on the connected component in case use_nnsp_true has been requested */
690         ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
691         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone));
692       }
693       if (real_value > 0.0) { /* keep indices and values */
694         temp_constraints++;
695         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
696         change_basis[total_counts]=boolforchange;
697         total_counts++;
698       }
699     }
700     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
701     /* perform SVD on the constraint if use_nnsp_true has not be requested by the user */
702     if (!use_nnsp_true) {
703       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
704       ierr = PetscBLASIntCast(temp_constraints,&Bt);CHKERRQ(ierr);
705 
706 #if defined(PETSC_MISSING_LAPACK_GESVD)
707       ierr = PetscMemzero(correlation_mat,Bt*Bt*sizeof(PetscScalar));CHKERRQ(ierr);
708       /* Store upper triangular part of correlation matrix */
709       for (j=0;j<temp_constraints;j++) {
710         for (k=0;k<j+1;k++) {
711           PetscStackCallBLAS("BLASdot",correlation_mat[j*temp_constraints+k]=BLASdot_(&Bs,&temp_quadrature_constraint[temp_indices[temp_start_ptr+j]],&Bone,&temp_quadrature_constraint[temp_indices[temp_start_ptr+k]],&Bone));
712 
713         }
714       }
715       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
716 #if !defined(PETSC_USE_COMPLEX)
717 /*      LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,&lierr); */
718       PetscStackCallBLAS("LAPACKsyevx",LAPACKsyevx_("V","A","U",&Bt,correlation_mat,&Bt,&dummy_real,&dummy_real,&dummy_int,&dummy_int,&abs_tol,&eigs_found,singular_vals,singular_vectors,&Bt,work,&lwork,iwork,ifail,&lierr));
719 #else
720 /*  LAPACK call is missing here! TODO */
721       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
722 #endif
723       if (lierr) {
724         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEVX Lapack routine %d",(int)lierr);
725       }
726       ierr = PetscFPTrapPop();CHKERRQ(ierr);
727       /* retain eigenvalues greater than tol: note that lapack SYEV gives eigs in ascending order */
728       j=0;
729       while (j < Bt && singular_vals[j] < tol) j++;
730       total_counts=total_counts-j;
731       if (j<temp_constraints) {
732         for (k=j;k<Bt;k++) {
733           singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
734         }
735         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
736         PetscStackCallBLAS("BLASgemm_",BLASgemm_("N","N",&Bs,&Bt,&Bt,&one,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,correlation_mat,&Bt,&zero,temp_basis,&Bs));
737         ierr = PetscFPTrapPop();CHKERRQ(ierr);
738         /* copy POD basis into used quadrature memory */
739         for (k=0;k<Bt-j;k++) {
740           for (ii=0;ii<size_of_constraint;ii++) {
741             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[Bt-1-k]*temp_basis[(Bt-1-k)*size_of_constraint+ii];
742           }
743         }
744       }
745 
746 #else  /* on missing GESVD */
747       PetscInt min_n = temp_constraints;
748       if (min_n > size_of_constraint) min_n = size_of_constraint;
749       dummy_int = Bs;
750       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
751 #if !defined(PETSC_USE_COMPLEX)
752       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,&lierr));
753 #else
754       PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Bs,&Bt,&temp_quadrature_constraint[temp_indices[temp_start_ptr]],&Bs,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,rwork,&lierr));
755 #endif
756       if (lierr) {
757         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD Lapack routine %d",(int)lierr);
758       }
759       ierr = PetscFPTrapPop();CHKERRQ(ierr);
760       /* retain eigenvalues greater than tol: note that lapack SVD gives eigs in descending order */
761       j = 0;
762       while (j < min_n && singular_vals[min_n-j-1] < tol) j++;
763       total_counts = total_counts-(PetscInt)Bt+(min_n-j);
764 #endif
765     }
766   }
767   /* free index sets of faces, edges and vertices */
768   for (i=0;i<n_ISForFaces;i++) {
769     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
770   }
771   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
772   for (i=0;i<n_ISForEdges;i++) {
773     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
774   }
775   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
776   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
777 
778   /* set quantities in pcbddc data structure */
779   /* n_vertices defines the number of point primal dofs */
780   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
781   local_primal_size = total_counts;
782   pcbddc->n_vertices = n_vertices;
783   pcbddc->n_constraints = total_counts-n_vertices;
784   pcbddc->local_primal_size = local_primal_size;
785 
786   /* Create constraint matrix */
787   /* The constraint matrix is used to compute the l2g map of primal dofs */
788   /* so we need to set it up properly either with or without change of basis */
789   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
790   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
791   ierr = MatSetSizes(pcbddc->ConstraintMatrix,local_primal_size,pcis->n,local_primal_size,pcis->n);CHKERRQ(ierr);
792   /* compute a local numbering of constraints : vertices first then constraints */
793   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
794   ierr = VecGetArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
795   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
796   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_permutation);CHKERRQ(ierr);
797   total_counts=0;
798   /* find vertices: subdomain corners plus dofs with basis changed */
799   for (i=0;i<local_primal_size;i++) {
800     size_of_constraint=temp_indices[i+1]-temp_indices[i];
801     if (change_basis[i] || size_of_constraint == 1) {
802       k=0;
803       while(k < size_of_constraint && array_vector[temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1]] != 0.0) {
804         k=k+1;
805       }
806       j=temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1];
807       array_vector[j] = 1.0;
808       aux_primal_numbering[total_counts]=j;
809       aux_primal_permutation[total_counts]=total_counts;
810       total_counts++;
811     }
812   }
813   ierr = VecRestoreArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
814   /* permute indices in order to have a sorted set of vertices */
815   ierr = PetscSortIntWithPermutation(total_counts,aux_primal_numbering,aux_primal_permutation);
816   /* nonzero structure */
817   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
818   for (i=0;i<total_counts;i++) {
819     nnz[i]=1;
820   }
821   j=total_counts;
822   for (i=n_vertices;i<local_primal_size;i++) {
823     if (!change_basis[i]) {
824       nnz[j]=temp_indices[i+1]-temp_indices[i];
825       j++;
826     }
827   }
828   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
829   ierr = PetscFree(nnz);CHKERRQ(ierr);
830   /* set values in constraint matrix */
831   for (i=0;i<total_counts;i++) {
832     j = aux_primal_permutation[i];
833     k = aux_primal_numbering[j];
834     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,k,1.0,INSERT_VALUES);CHKERRQ(ierr);
835   }
836   for (i=n_vertices;i<local_primal_size;i++) {
837     if (!change_basis[i]) {
838       size_of_constraint=temp_indices[i+1]-temp_indices[i];
839       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);
840       total_counts++;
841     }
842   }
843   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
844   ierr = PetscFree(aux_primal_permutation);CHKERRQ(ierr);
845   /* assembling */
846   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
847   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
848 
849   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
850   if (pcbddc->use_change_of_basis) {
851     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
852     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
853     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
854     /* work arrays */
855     /* we need to reuse these arrays, so we free them */
856     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
857     ierr = PetscFree(work);CHKERRQ(ierr);
858     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
859     ierr = PetscMalloc((nnsp_addone+nnsp_size)*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
860     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscScalar),&work);CHKERRQ(ierr);
861     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscBLASInt),&ipiv);CHKERRQ(ierr);
862     for (i=0;i<pcis->n_B;i++) {
863       nnz[i]=1;
864     }
865     /* Overestimated nonzeros per row */
866     k=1;
867     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
868       if (change_basis[i]) {
869         size_of_constraint = temp_indices[i+1]-temp_indices[i];
870         if (k < size_of_constraint) {
871           k = size_of_constraint;
872         }
873         for (j=0;j<size_of_constraint;j++) {
874           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
875         }
876       }
877     }
878     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
879     ierr = PetscFree(nnz);CHKERRQ(ierr);
880     /* Temporary array to store indices */
881     ierr = PetscMalloc(k*sizeof(PetscInt),&is_indices);CHKERRQ(ierr);
882     /* Set initial identity in the matrix */
883     for (i=0;i<pcis->n_B;i++) {
884       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
885     }
886     /* Now we loop on the constraints which need a change of basis */
887     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
888     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (6.2.1) */
889     temp_constraints = 0;
890     if (pcbddc->n_vertices < local_primal_size) {
891       temp_start_ptr = temp_indices_to_constraint_B[temp_indices[pcbddc->n_vertices]];
892     }
893     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
894       if (change_basis[i]) {
895         compute_submatrix = PETSC_FALSE;
896         useksp = PETSC_FALSE;
897         if (temp_start_ptr == temp_indices_to_constraint_B[temp_indices[i]]) {
898           temp_constraints++;
899           if (i == local_primal_size -1 ||  temp_start_ptr != temp_indices_to_constraint_B[temp_indices[i+1]]) {
900             compute_submatrix = PETSC_TRUE;
901           }
902         }
903         if (compute_submatrix) {
904           if (temp_constraints > 1 || pcbddc->use_nnsp_true) {
905             useksp = PETSC_TRUE;
906           }
907           size_of_constraint = temp_indices[i+1]-temp_indices[i];
908           if (useksp) { /* experimental TODO: reuse KSP and MAT instead of creating them each time */
909             ierr = MatCreate(PETSC_COMM_SELF,&temp_mat);CHKERRQ(ierr);
910             ierr = MatSetType(temp_mat,impMatType);CHKERRQ(ierr);
911             ierr = MatSetSizes(temp_mat,size_of_constraint,size_of_constraint,size_of_constraint,size_of_constraint);CHKERRQ(ierr);
912             ierr = MatSeqAIJSetPreallocation(temp_mat,size_of_constraint,NULL);CHKERRQ(ierr);
913           }
914           /* First _size_of_constraint-temp_constraints_ columns */
915           dual_dofs = size_of_constraint-temp_constraints;
916           start_constraint = i+1-temp_constraints;
917           for (s=0;s<dual_dofs;s++) {
918             is_indices[0] = s;
919             for (j=0;j<temp_constraints;j++) {
920               for (k=0;k<temp_constraints;k++) {
921                 temp_basis[j*temp_constraints+k]=temp_quadrature_constraint[temp_indices[start_constraint+k]+s+j+1];
922               }
923               work[j]=-temp_quadrature_constraint[temp_indices[start_constraint+j]+s];
924               is_indices[j+1]=s+j+1;
925             }
926             Bt = temp_constraints;
927             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
928             PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&Bt,&Bone,temp_basis,&Bt,ipiv,work,&Bt,&lierr));
929             if ( lierr ) {
930               SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESV Lapack routine %d",(int)lierr);
931             }
932             ierr = PetscFPTrapPop();CHKERRQ(ierr);
933             j = temp_indices_to_constraint_B[temp_indices[start_constraint]+s];
934             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,temp_constraints,&temp_indices_to_constraint_B[temp_indices[start_constraint]+s+1],1,&j,work,INSERT_VALUES);CHKERRQ(ierr);
935             if (useksp) {
936               /* temp mat with transposed rows and columns */
937               ierr = MatSetValues(temp_mat,1,&s,temp_constraints,&is_indices[1],work,INSERT_VALUES);CHKERRQ(ierr);
938               ierr = MatSetValue(temp_mat,is_indices[0],is_indices[0],1.0,INSERT_VALUES);CHKERRQ(ierr);
939             }
940           }
941           if (useksp) {
942             /* last rows of temp_mat */
943             for (j=0;j<size_of_constraint;j++) {
944               is_indices[j] = j;
945             }
946             for (s=0;s<temp_constraints;s++) {
947               k = s + dual_dofs;
948               ierr = MatSetValues(temp_mat,1,&k,size_of_constraint,is_indices,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
949             }
950             ierr = MatAssemblyBegin(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
951             ierr = MatAssemblyEnd(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
952             ierr = MatGetVecs(temp_mat,&temp_vec,NULL);CHKERRQ(ierr);
953             ierr = KSPCreate(PETSC_COMM_SELF,&temp_ksp);CHKERRQ(ierr);
954             ierr = KSPSetOperators(temp_ksp,temp_mat,temp_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
955             ierr = KSPSetType(temp_ksp,KSPPREONLY);CHKERRQ(ierr);
956             ierr = KSPGetPC(temp_ksp,&temp_pc);CHKERRQ(ierr);
957             ierr = PCSetType(temp_pc,PCLU);CHKERRQ(ierr);
958             ierr = KSPSetUp(temp_ksp);CHKERRQ(ierr);
959             for (s=0;s<temp_constraints;s++) {
960               ierr = VecSet(temp_vec,0.0);CHKERRQ(ierr);
961               ierr = VecSetValue(temp_vec,s+dual_dofs,1.0,INSERT_VALUES);CHKERRQ(ierr);
962               ierr = VecAssemblyBegin(temp_vec);CHKERRQ(ierr);
963               ierr = VecAssemblyEnd(temp_vec);CHKERRQ(ierr);
964               ierr = KSPSolve(temp_ksp,temp_vec,temp_vec);CHKERRQ(ierr);
965               ierr = VecGetArray(temp_vec,&array_vector);CHKERRQ(ierr);
966               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
967               /* last columns of change of basis matrix associated to new primal dofs */
968               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,&temp_indices_to_constraint_B[temp_indices[start_constraint+s]],1,&j,array_vector,INSERT_VALUES);CHKERRQ(ierr);
969               ierr = VecRestoreArray(temp_vec,&array_vector);CHKERRQ(ierr);
970             }
971             ierr = MatDestroy(&temp_mat);CHKERRQ(ierr);
972             ierr = KSPDestroy(&temp_ksp);CHKERRQ(ierr);
973             ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
974           } else {
975             /* last columns of change of basis matrix associated to new primal dofs */
976             for (s=0;s<temp_constraints;s++) {
977               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
978               ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,size_of_constraint,&temp_indices_to_constraint_B[temp_indices[start_constraint+s]],1,&j,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
979             }
980           }
981           /* prepare for the next cycle */
982           temp_constraints = 0;
983           if (i != local_primal_size -1 ) {
984             temp_start_ptr = temp_indices_to_constraint_B[temp_indices[i+1]];
985           }
986         }
987       }
988     }
989     /* assembling */
990     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
991     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
992     ierr = PetscFree(ipiv);CHKERRQ(ierr);
993     ierr = PetscFree(is_indices);CHKERRQ(ierr);
994   }
995   /* free workspace no longer needed */
996   ierr = PetscFree(rwork);CHKERRQ(ierr);
997   ierr = PetscFree(work);CHKERRQ(ierr);
998   ierr = PetscFree(temp_basis);CHKERRQ(ierr);
999   ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1000   ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1001   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
1002   ierr = PetscFree(change_basis);CHKERRQ(ierr);
1003   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
1004   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
1005   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
1006   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
1007 #if defined(PETSC_MISSING_LAPACK_GESVD)
1008   ierr = PetscFree(iwork);CHKERRQ(ierr);
1009   ierr = PetscFree(ifail);CHKERRQ(ierr);
1010   ierr = PetscFree(singular_vectors);CHKERRQ(ierr);
1011 #endif
1012   for (k=0;k<nnsp_size;k++) {
1013     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1014   }
1015   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1016   PetscFunctionReturn(0);
1017 }
1018 
1019 #undef __FUNCT__
1020 #define __FUNCT__ "PCBDDCAnalyzeInterface"
1021 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
1022 {
1023   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
1024   PC_IS       *pcis = (PC_IS*)pc->data;
1025   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
1026   PetscInt    bs,ierr,i,vertex_size;
1027   PetscViewer viewer=pcbddc->dbg_viewer;
1028 
1029   PetscFunctionBegin;
1030   /* Init local Graph struct */
1031   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
1032 
1033   /* Check validity of the csr graph passed in by the user */
1034   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
1035     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
1036   }
1037   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
1038   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
1039     Mat mat_adj;
1040     const PetscInt *xadj,*adjncy;
1041     PetscBool flg_row=PETSC_TRUE;
1042 
1043     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
1044     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1045     if (!flg_row) {
1046       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
1047     }
1048     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
1049     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1050     if (!flg_row) {
1051       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
1052     }
1053     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
1054   }
1055 
1056   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
1057   vertex_size = 1;
1058   if (!pcbddc->n_ISForDofs) {
1059     IS *custom_ISForDofs;
1060 
1061     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
1062     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
1063     for (i=0;i<bs;i++) {
1064       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1065     }
1066     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1067     /* remove my references to IS objects */
1068     for (i=0;i<bs;i++) {
1069       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1070     }
1071     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1072   } else { /* mat block size as vertex size (used for elasticity) */
1073     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1074   }
1075 
1076   /* Setup of Graph */
1077   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1078 
1079   /* Graph's connected components analysis */
1080   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1081 
1082   /* print some info to stdout */
1083   if (pcbddc->dbg_flag) {
1084     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1085   }
1086   PetscFunctionReturn(0);
1087 }
1088 
1089 #undef __FUNCT__
1090 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1091 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1092 {
1093   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1094   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1095   PetscErrorCode ierr;
1096 
1097   PetscFunctionBegin;
1098   n = 0;
1099   vertices = 0;
1100   if (pcbddc->ConstraintMatrix) {
1101     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1102     for (i=0;i<local_primal_size;i++) {
1103       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1104       if (size_of_constraint == 1) n++;
1105       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1106     }
1107     ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1108     n = 0;
1109     for (i=0;i<local_primal_size;i++) {
1110       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1111       if (size_of_constraint == 1) {
1112         vertices[n++]=row_cmat_indices[0];
1113       }
1114       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1115     }
1116   }
1117   *n_vertices = n;
1118   *vertices_idx = vertices;
1119   PetscFunctionReturn(0);
1120 }
1121 
1122 #undef __FUNCT__
1123 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
1124 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
1125 {
1126   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1127   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
1128   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
1129   PetscBool      *touched;
1130   PetscErrorCode ierr;
1131 
1132   PetscFunctionBegin;
1133   n = 0;
1134   constraints_index = 0;
1135   if (pcbddc->ConstraintMatrix) {
1136     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
1137     max_size_of_constraint = 0;
1138     for (i=0;i<local_primal_size;i++) {
1139       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1140       if (size_of_constraint > 1) {
1141         n++;
1142       }
1143       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
1144       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1145     }
1146     ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
1147     ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
1148     ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1149     ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
1150     n = 0;
1151     for (i=0;i<local_primal_size;i++) {
1152       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1153       if (size_of_constraint > 1) {
1154         ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
1155         min_index = row_cmat_global_indices[0];
1156         min_loc = 0;
1157         for (j=1;j<size_of_constraint;j++) {
1158           /* there can be more than one constraint on a single connected component */
1159           if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
1160             min_index = row_cmat_global_indices[j];
1161             min_loc = j;
1162           }
1163         }
1164         touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
1165         constraints_index[n++] = row_cmat_indices[min_loc];
1166       }
1167       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1168     }
1169   }
1170   ierr = PetscFree(touched);CHKERRQ(ierr);
1171   ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
1172   *n_constraints = n;
1173   *constraints_idx = constraints_index;
1174   PetscFunctionReturn(0);
1175 }
1176 
1177 /* the next two functions has been adapted from pcis.c */
1178 #undef __FUNCT__
1179 #define __FUNCT__ "PCBDDCApplySchur"
1180 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1181 {
1182   PetscErrorCode ierr;
1183   PC_IS          *pcis = (PC_IS*)(pc->data);
1184 
1185   PetscFunctionBegin;
1186   if (!vec2_B) { vec2_B = v; }
1187   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1188   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
1189   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1190   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
1191   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1192   PetscFunctionReturn(0);
1193 }
1194 
1195 #undef __FUNCT__
1196 #define __FUNCT__ "PCBDDCApplySchurTranspose"
1197 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1198 {
1199   PetscErrorCode ierr;
1200   PC_IS          *pcis = (PC_IS*)(pc->data);
1201 
1202   PetscFunctionBegin;
1203   if (!vec2_B) { vec2_B = v; }
1204   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1205   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
1206   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1207   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
1208   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1209   PetscFunctionReturn(0);
1210 }
1211 
1212 #undef __FUNCT__
1213 #define __FUNCT__ "PCBDDCSubsetNumbering"
1214 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[])
1215 {
1216   Vec            local_vec,global_vec;
1217   IS             seqis,paris;
1218   VecScatter     scatter_ctx;
1219   PetscScalar    *array;
1220   PetscInt       *temp_global_dofs;
1221   PetscScalar    globalsum;
1222   PetscInt       i,j,s;
1223   PetscInt       nlocals,first_index,old_index,max_local;
1224   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
1225   PetscMPIInt    *dof_sizes,*dof_displs;
1226   PetscBool      first_found;
1227   PetscErrorCode ierr;
1228 
1229   PetscFunctionBegin;
1230   /* mpi buffers */
1231   MPI_Comm_size(comm,&size_prec_comm);
1232   MPI_Comm_rank(comm,&rank_prec_comm);
1233   j = ( !rank_prec_comm ? size_prec_comm : 0);
1234   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1235   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1236   /* get maximum size of subset */
1237   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
1238   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
1239   max_local = 0;
1240   if (n_local_dofs) {
1241     max_local = temp_global_dofs[0];
1242     for (i=1;i<n_local_dofs;i++) {
1243       if (max_local < temp_global_dofs[i] ) {
1244         max_local = temp_global_dofs[i];
1245       }
1246     }
1247   }
1248   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
1249   max_global++;
1250   max_local = 0;
1251   if (n_local_dofs) {
1252     max_local = local_dofs[0];
1253     for (i=1;i<n_local_dofs;i++) {
1254       if (max_local < local_dofs[i] ) {
1255         max_local = local_dofs[i];
1256       }
1257     }
1258   }
1259   max_local++;
1260   /* allocate workspace */
1261   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
1262   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
1263   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
1264   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
1265   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
1266   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
1267   /* create scatter */
1268   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
1269   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
1270   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
1271   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
1272   ierr = ISDestroy(&paris);CHKERRQ(ierr);
1273   /* init array */
1274   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1275   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1276   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1277   if (local_dofs_mult) {
1278     for (i=0;i<n_local_dofs;i++) {
1279       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
1280     }
1281   } else {
1282     for (i=0;i<n_local_dofs;i++) {
1283       array[local_dofs[i]]=1.0;
1284     }
1285   }
1286   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1287   /* scatter into global vec and get total number of global dofs */
1288   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1289   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1290   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
1291   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
1292   /* Fill global_vec with cumulative function for global numbering */
1293   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
1294   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
1295   nlocals = 0;
1296   first_index = -1;
1297   first_found = PETSC_FALSE;
1298   for (i=0;i<s;i++) {
1299     if (!first_found && PetscRealPart(array[i]) > 0.0) {
1300       first_found = PETSC_TRUE;
1301       first_index = i;
1302     }
1303     nlocals += (PetscInt)PetscRealPart(array[i]);
1304   }
1305   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1306   if (!rank_prec_comm) {
1307     dof_displs[0]=0;
1308     for (i=1;i<size_prec_comm;i++) {
1309       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1310     }
1311   }
1312   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1313   if (first_found) {
1314     array[first_index] += (PetscScalar)nlocals;
1315     old_index = first_index;
1316     for (i=first_index+1;i<s;i++) {
1317       if (PetscRealPart(array[i]) > 0.0) {
1318         array[i] += array[old_index];
1319         old_index = i;
1320       }
1321     }
1322   }
1323   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
1324   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1325   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1326   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1327   /* get global ordering of local dofs */
1328   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1329   if (local_dofs_mult) {
1330     for (i=0;i<n_local_dofs;i++) {
1331       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
1332     }
1333   } else {
1334     for (i=0;i<n_local_dofs;i++) {
1335       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
1336     }
1337   }
1338   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1339   /* free workspace */
1340   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1341   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1342   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1343   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1344   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1345   /* return pointer to global ordering of local dofs */
1346   *global_numbering_subset = temp_global_dofs;
1347   PetscFunctionReturn(0);
1348 }
1349