xref: /petsc/src/ksp/pc/impls/bddc/bddcprivate.c (revision 304d26fa6202911715a8243a0b051d78abeaec05)
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 = MatDestroy(&pcbddc->local_mat);CHKERRQ(ierr);
51   ierr = VecDestroy(&pcbddc->coarse_vec);CHKERRQ(ierr);
52   ierr = VecDestroy(&pcbddc->coarse_rhs);CHKERRQ(ierr);
53   ierr = KSPDestroy(&pcbddc->coarse_ksp);CHKERRQ(ierr);
54   ierr = MatDestroy(&pcbddc->coarse_mat);CHKERRQ(ierr);
55   ierr = MatDestroy(&pcbddc->coarse_phi_B);CHKERRQ(ierr);
56   ierr = MatDestroy(&pcbddc->coarse_phi_D);CHKERRQ(ierr);
57   ierr = MatDestroy(&pcbddc->coarse_psi_B);CHKERRQ(ierr);
58   ierr = MatDestroy(&pcbddc->coarse_psi_D);CHKERRQ(ierr);
59   ierr = VecDestroy(&pcbddc->vec1_P);CHKERRQ(ierr);
60   ierr = VecDestroy(&pcbddc->vec1_C);CHKERRQ(ierr);
61   ierr = MatDestroy(&pcbddc->local_auxmat1);CHKERRQ(ierr);
62   ierr = MatDestroy(&pcbddc->local_auxmat2);CHKERRQ(ierr);
63   ierr = VecDestroy(&pcbddc->vec1_R);CHKERRQ(ierr);
64   ierr = VecDestroy(&pcbddc->vec2_R);CHKERRQ(ierr);
65   ierr = VecDestroy(&pcbddc->vec4_D);CHKERRQ(ierr);
66   ierr = VecScatterDestroy(&pcbddc->R_to_B);CHKERRQ(ierr);
67   ierr = VecScatterDestroy(&pcbddc->R_to_D);CHKERRQ(ierr);
68   ierr = VecScatterDestroy(&pcbddc->coarse_loc_to_glob);CHKERRQ(ierr);
69   ierr = PetscFree(pcbddc->local_primal_indices);CHKERRQ(ierr);
70   ierr = PetscFree(pcbddc->replicated_local_primal_indices);CHKERRQ(ierr);
71   ierr = PetscFree(pcbddc->replicated_local_primal_values);CHKERRQ(ierr);
72   ierr = PetscFree(pcbddc->local_primal_displacements);CHKERRQ(ierr);
73   ierr = PetscFree(pcbddc->local_primal_sizes);CHKERRQ(ierr);
74   PetscFunctionReturn(0);
75 }
76 
77 #undef __FUNCT__
78 #define __FUNCT__ "PCBDDCSetUseExactDirichlet"
79 PetscErrorCode PCBDDCSetUseExactDirichlet(PC pc,PetscBool use)
80 {
81   PC_BDDC  *pcbddc = (PC_BDDC*)pc->data;
82 
83   PetscFunctionBegin;
84   pcbddc->use_exact_dirichlet=use;
85   PetscFunctionReturn(0);
86 }
87 
88 #undef __FUNCT__
89 #define __FUNCT__ "PCBDDCSetUpLocalSolvers"
90 PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, IS is_I_local, IS is_R_local)
91 {
92   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
93   PC_IS          *pcis = (PC_IS*)pc->data;
94   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
95   PC             pc_temp;
96   Mat            A_RR;
97   Vec            vec1,vec2,vec3;
98   MatStructure   matstruct;
99   PetscScalar    m_one = -1.0;
100   PetscReal      value;
101   PetscInt       n_D,n_R,use_exact,use_exact_reduced;
102   PetscErrorCode ierr;
103 
104   PetscFunctionBegin;
105   /* Creating PC contexts for local Dirichlet and Neumann problems */
106   ierr = PCGetOperators(pc,NULL,NULL,&matstruct);CHKERRQ(ierr);
107 
108   /* when matstruct is SAME_PRECONDITIONER, we shouldn't be here */
109 
110   /* DIRICHLET PROBLEM */
111   /* Matrix for Dirichlet problem is A_II */
112   /* HACK: A_II can be changed between nonlinear iterations */
113   if (pc->setupcalled) { /* we dont need to rebuild dirichlet problem the first time we build BDDC */
114     if (matstruct == SAME_PRECONDITIONER) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen");
115     if (matstruct == SAME_NONZERO_PATTERN) {
116       ierr = MatGetSubMatrix(matis->A,is_I_local,is_I_local,MAT_REUSE_MATRIX,&pcis->A_II);CHKERRQ(ierr);
117     } else {
118       ierr = MatDestroy(&pcis->A_II);CHKERRQ(ierr);
119       ierr = MatGetSubMatrix(matis->A,is_I_local,is_I_local,MAT_INITIAL_MATRIX,&pcis->A_II);CHKERRQ(ierr);
120     }
121   }
122   ierr = ISGetSize(is_I_local,&n_D);CHKERRQ(ierr);
123   if (!pcbddc->ksp_D) { /* create object if not yet build */
124     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);CHKERRQ(ierr);
125     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);CHKERRQ(ierr);
126     /* default */
127     ierr = KSPSetType(pcbddc->ksp_D,KSPPREONLY);CHKERRQ(ierr);
128     ierr = KSPSetOptionsPrefix(pcbddc->ksp_D,"dirichlet_");CHKERRQ(ierr);
129     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
130     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
131     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
132   }
133   ierr = KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II,matstruct);CHKERRQ(ierr);
134   /* Allow user's customization */
135   ierr = KSPSetFromOptions(pcbddc->ksp_D);CHKERRQ(ierr);
136   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
137   if (!n_D) {
138     ierr = KSPGetPC(pcbddc->ksp_D,&pc_temp);CHKERRQ(ierr);
139     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
140   }
141   /* Set Up KSP for Dirichlet problem of BDDC */
142   ierr = KSPSetUp(pcbddc->ksp_D);CHKERRQ(ierr);
143   /* set ksp_D into pcis data */
144   ierr = KSPDestroy(&pcis->ksp_D);CHKERRQ(ierr);
145   ierr = PetscObjectReference((PetscObject)pcbddc->ksp_D);CHKERRQ(ierr);
146   pcis->ksp_D = pcbddc->ksp_D;
147 
148   /* NEUMANN PROBLEM */
149   /* Matrix for Neumann problem is A_RR -> we need to create it */
150   ierr = ISGetSize(is_R_local,&n_R);CHKERRQ(ierr);
151   ierr = MatGetSubMatrix(pcbddc->local_mat,is_R_local,is_R_local,MAT_INITIAL_MATRIX,&A_RR);CHKERRQ(ierr);
152   if (!pcbddc->ksp_R) { /* create object if not yet build */
153     ierr = KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);CHKERRQ(ierr);
154     ierr = PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);CHKERRQ(ierr);
155     /* default */
156     ierr = KSPSetType(pcbddc->ksp_R,KSPPREONLY);CHKERRQ(ierr);
157     ierr = KSPSetOptionsPrefix(pcbddc->ksp_R,"neumann_");CHKERRQ(ierr);
158     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
159     ierr = PCSetType(pc_temp,PCLU);CHKERRQ(ierr);
160     ierr = PCFactorSetReuseFill(pc_temp,PETSC_TRUE);CHKERRQ(ierr);
161   }
162   ierr = KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR,matstruct);CHKERRQ(ierr);
163   /* Allow user's customization */
164   ierr = KSPSetFromOptions(pcbddc->ksp_R);CHKERRQ(ierr);
165   /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
166   if (!n_R) {
167     ierr = KSPGetPC(pcbddc->ksp_R,&pc_temp);CHKERRQ(ierr);
168     ierr = PCSetType(pc_temp,PCNONE);CHKERRQ(ierr);
169   }
170   /* Set Up KSP for Neumann problem of BDDC */
171   ierr = KSPSetUp(pcbddc->ksp_R);CHKERRQ(ierr);
172 
173   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
174 
175   /* Dirichlet */
176   ierr = MatGetVecs(pcis->A_II,&vec1,&vec2);CHKERRQ(ierr);
177   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
178   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
179   ierr = MatMult(pcis->A_II,vec1,vec2);CHKERRQ(ierr);
180   ierr = KSPSolve(pcbddc->ksp_D,vec2,vec3);CHKERRQ(ierr);
181   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
182   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
183   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
184   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
185   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
186   /* need to be adapted? */
187   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
188   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
189   ierr = PCBDDCSetUseExactDirichlet(pc,(PetscBool)use_exact_reduced);CHKERRQ(ierr);
190   /* print info */
191   if (pcbddc->dbg_flag) {
192     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
193     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");CHKERRQ(ierr);
194     ierr = PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Checking solution of Dirichlet and Neumann problems\n");CHKERRQ(ierr);
195     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
196     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
197   }
198   if (n_D && pcbddc->NullSpace && !use_exact_reduced && !pcbddc->inexact_prec_type) {
199     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_I_local);CHKERRQ(ierr);
200   }
201 
202   /* Neumann */
203   ierr = MatGetVecs(A_RR,&vec1,&vec2);CHKERRQ(ierr);
204   ierr = VecDuplicate(vec1,&vec3);CHKERRQ(ierr);
205   ierr = VecSetRandom(vec1,NULL);CHKERRQ(ierr);
206   ierr = MatMult(A_RR,vec1,vec2);CHKERRQ(ierr);
207   ierr = KSPSolve(pcbddc->ksp_R,vec2,vec3);CHKERRQ(ierr);
208   ierr = VecAXPY(vec3,m_one,vec1);CHKERRQ(ierr);
209   ierr = VecNorm(vec3,NORM_INFINITY,&value);CHKERRQ(ierr);
210   ierr = VecDestroy(&vec1);CHKERRQ(ierr);
211   ierr = VecDestroy(&vec2);CHKERRQ(ierr);
212   ierr = VecDestroy(&vec3);CHKERRQ(ierr);
213   /* need to be adapted? */
214   use_exact = (PetscAbsReal(value) > 1.e-4 ? 0 : 1);
215   if (PetscAbsReal(value) > 1.e-4) use_exact = 0;
216   ierr = MPI_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_INT,MPI_LAND,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
217   /* print info */
218   if (pcbddc->dbg_flag) {
219     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for  Neumann  solve = % 1.14e \n",PetscGlobalRank,value);CHKERRQ(ierr);
220     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
221   }
222   if (n_R && pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
223     ierr = PCBDDCNullSpaceAssembleCorrection(pc,is_R_local);CHKERRQ(ierr);
224   }
225 
226   /* free Neumann problem's matrix */
227   ierr = MatDestroy(&A_RR);CHKERRQ(ierr);
228   PetscFunctionReturn(0);
229 }
230 
231 #undef __FUNCT__
232 #define __FUNCT__ "PCBDDCSolveSaddlePoint"
233 static PetscErrorCode  PCBDDCSolveSaddlePoint(PC pc)
234 {
235   PetscErrorCode ierr;
236   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
237 
238   PetscFunctionBegin;
239   ierr = KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);CHKERRQ(ierr);
240   if (pcbddc->local_auxmat1) {
241     ierr = MatMult(pcbddc->local_auxmat1,pcbddc->vec2_R,pcbddc->vec1_C);CHKERRQ(ierr);
242     ierr = MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec2_R,pcbddc->vec2_R);CHKERRQ(ierr);
243   }
244   PetscFunctionReturn(0);
245 }
246 
247 #undef __FUNCT__
248 #define __FUNCT__ "PCBDDCApplyInterfacePreconditioner"
249 PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc)
250 {
251   PetscErrorCode ierr;
252   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
253   PC_IS*            pcis = (PC_IS*)  (pc->data);
254   const PetscScalar zero = 0.0;
255 
256   PetscFunctionBegin;
257   /* Application of PHI^T (or PSI^T)  */
258   if (pcbddc->coarse_psi_B) {
259     ierr = MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
260     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
261   } else {
262     ierr = MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);CHKERRQ(ierr);
263     if (pcbddc->inexact_prec_type) { ierr = MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);CHKERRQ(ierr); }
264   }
265   /* Scatter data of coarse_rhs */
266   if (pcbddc->coarse_rhs) { ierr = VecSet(pcbddc->coarse_rhs,zero);CHKERRQ(ierr); }
267   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
268 
269   /* Local solution on R nodes */
270   ierr = VecSet(pcbddc->vec1_R,zero);CHKERRQ(ierr);
271   ierr = VecScatterBegin(pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
272   ierr = VecScatterEnd  (pcbddc->R_to_B,pcis->vec1_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
273   if (pcbddc->inexact_prec_type) {
274     ierr = VecScatterBegin(pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
275     ierr = VecScatterEnd  (pcbddc->R_to_D,pcis->vec1_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
276   }
277   ierr = PCBDDCSolveSaddlePoint(pc);CHKERRQ(ierr);
278   ierr = VecSet(pcis->vec1_B,zero);CHKERRQ(ierr);
279   ierr = VecScatterBegin(pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
280   ierr = VecScatterEnd  (pcbddc->R_to_B,pcbddc->vec2_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
281   if (pcbddc->inexact_prec_type) {
282     ierr = VecScatterBegin(pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
283     ierr = VecScatterEnd  (pcbddc->R_to_D,pcbddc->vec2_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
284   }
285 
286   /* Coarse solution */
287   ierr = PCBDDCScatterCoarseDataEnd(pc,pcbddc->vec1_P,pcbddc->coarse_rhs,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
288   if (pcbddc->coarse_rhs) { /* TODO remove null space when doing multilevel */
289     ierr = KSPSolve(pcbddc->coarse_ksp,pcbddc->coarse_rhs,pcbddc->coarse_vec);CHKERRQ(ierr);
290   }
291   ierr = PCBDDCScatterCoarseDataBegin(pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
292   ierr = PCBDDCScatterCoarseDataEnd  (pc,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
293 
294   /* Sum contributions from two levels */
295   ierr = MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);CHKERRQ(ierr);
296   if (pcbddc->inexact_prec_type) { ierr = MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);CHKERRQ(ierr); }
297   PetscFunctionReturn(0);
298 }
299 
300 #undef __FUNCT__
301 #define __FUNCT__ "PCBDDCScatterCoarseDataBegin"
302 PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
303 {
304   PetscErrorCode ierr;
305   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
306 
307   PetscFunctionBegin;
308   switch (pcbddc->coarse_communications_type) {
309     case SCATTERS_BDDC:
310       ierr = VecScatterBegin(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
311       break;
312     case GATHERS_BDDC:
313       break;
314   }
315   PetscFunctionReturn(0);
316 }
317 
318 #undef __FUNCT__
319 #define __FUNCT__ "PCBDDCScatterCoarseDataEnd"
320 PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc,Vec vec_from, Vec vec_to, InsertMode imode, ScatterMode smode)
321 {
322   PetscErrorCode ierr;
323   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
324   PetscScalar*   array_to;
325   PetscScalar*   array_from;
326   MPI_Comm       comm;
327   PetscInt       i;
328 
329   PetscFunctionBegin;
330   ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
331   switch (pcbddc->coarse_communications_type) {
332     case SCATTERS_BDDC:
333       ierr = VecScatterEnd(pcbddc->coarse_loc_to_glob,vec_from,vec_to,imode,smode);CHKERRQ(ierr);
334       break;
335     case GATHERS_BDDC:
336       if (vec_from) {
337         ierr = VecGetArray(vec_from,&array_from);CHKERRQ(ierr);
338       }
339       if (vec_to) {
340         ierr = VecGetArray(vec_to,&array_to);CHKERRQ(ierr);
341       }
342       switch(pcbddc->coarse_problem_type){
343         case SEQUENTIAL_BDDC:
344           if (smode == SCATTER_FORWARD) {
345             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);
346             if (vec_to) {
347               if (imode == ADD_VALUES) {
348                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
349                   array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
350                 }
351               } else {
352                 for (i=0;i<pcbddc->replicated_primal_size;i++) {
353                   array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
354                 }
355               }
356             }
357           } else {
358             if (vec_from) {
359               if (imode == ADD_VALUES) {
360                 MPI_Comm vec_from_comm;
361                 ierr = PetscObjectGetComm((PetscObject)(vec_from),&vec_from_comm);CHKERRQ(ierr);
362                 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);
363               }
364               for (i=0;i<pcbddc->replicated_primal_size;i++) {
365                 pcbddc->replicated_local_primal_values[i]=array_from[pcbddc->replicated_local_primal_indices[i]];
366               }
367             }
368             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);
369           }
370           break;
371         case REPLICATED_BDDC:
372           if (smode == SCATTER_FORWARD) {
373             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);
374             if (imode == ADD_VALUES) {
375               for (i=0;i<pcbddc->replicated_primal_size;i++) {
376                 array_to[pcbddc->replicated_local_primal_indices[i]]+=pcbddc->replicated_local_primal_values[i];
377               }
378             } else {
379               for (i=0;i<pcbddc->replicated_primal_size;i++) {
380                 array_to[pcbddc->replicated_local_primal_indices[i]]=pcbddc->replicated_local_primal_values[i];
381               }
382             }
383           } else { /* no communications needed for SCATTER_REVERSE since needed data is already present */
384             if (imode == ADD_VALUES) {
385               for (i=0;i<pcbddc->local_primal_size;i++) {
386                 array_to[i]+=array_from[pcbddc->local_primal_indices[i]];
387               }
388             } else {
389               for (i=0;i<pcbddc->local_primal_size;i++) {
390                 array_to[i]=array_from[pcbddc->local_primal_indices[i]];
391               }
392             }
393           }
394           break;
395         case MULTILEVEL_BDDC:
396           break;
397         case PARALLEL_BDDC:
398           break;
399       }
400       if (vec_from) {
401         ierr = VecRestoreArray(vec_from,&array_from);CHKERRQ(ierr);
402       }
403       if (vec_to) {
404         ierr = VecRestoreArray(vec_to,&array_to);CHKERRQ(ierr);
405       }
406       break;
407   }
408   PetscFunctionReturn(0);
409 }
410 
411 #undef __FUNCT__
412 #define __FUNCT__ "PCBDDCConstraintsSetUp"
413 PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
414 {
415   PetscErrorCode ierr;
416   PC_IS*         pcis = (PC_IS*)(pc->data);
417   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
418   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
419   PetscInt       *nnz,*is_indices;
420   PetscScalar    *temp_quadrature_constraint;
421   PetscInt       *temp_indices,*temp_indices_to_constraint,*temp_indices_to_constraint_B,*local_to_B;
422   PetscInt       local_primal_size,i,j,k,total_counts,max_size_of_constraint;
423   PetscInt       n_vertices,size_of_constraint;
424   PetscReal      real_value;
425   PetscBool      nnsp_has_cnst=PETSC_FALSE,use_nnsp_true=pcbddc->use_nnsp_true;
426   PetscInt       nnsp_size=0,nnsp_addone=0,temp_constraints,temp_start_ptr,n_ISForFaces,n_ISForEdges;
427   IS             *used_IS,ISForVertices,*ISForFaces,*ISForEdges;
428   MatType        impMatType=MATSEQAIJ;
429   PetscBLASInt   Bs,Bt,lwork,lierr;
430   PetscReal      tol=1.0e-8;
431   MatNullSpace   nearnullsp;
432   const Vec      *nearnullvecs;
433   Vec            *localnearnullsp;
434   PetscScalar    *work,*temp_basis,*array_vector,*correlation_mat;
435   PetscReal      *rwork,*singular_vals;
436   PetscBLASInt   Bone=1,*ipiv;
437   Vec            temp_vec;
438   Mat            temp_mat;
439   KSP            temp_ksp;
440   PC             temp_pc;
441   PetscInt       s,start_constraint,dual_dofs;
442   PetscBool      compute_submatrix,useksp=PETSC_FALSE;
443   PetscInt       *aux_primal_permutation,*aux_primal_numbering;
444   PetscBool      boolforchange,*change_basis;
445 /* some ugly conditional declarations */
446 #if defined(PETSC_MISSING_LAPACK_GESVD)
447   PetscScalar    one=1.0,zero=0.0;
448   PetscInt       ii;
449   PetscScalar    *singular_vectors;
450   PetscBLASInt   *iwork,*ifail;
451   PetscReal      dummy_real,abs_tol;
452   PetscBLASInt   eigs_found;
453 #endif
454   PetscBLASInt   dummy_int;
455   PetscScalar    dummy_scalar;
456   PetscBool      used_vertex,get_faces,get_edges,get_vertices;
457 
458   PetscFunctionBegin;
459   /* Get index sets for faces, edges and vertices from graph */
460   get_faces = PETSC_TRUE;
461   get_edges = PETSC_TRUE;
462   get_vertices = PETSC_TRUE;
463   if (pcbddc->vertices_flag) {
464     get_faces = PETSC_FALSE;
465     get_edges = PETSC_FALSE;
466   }
467   if (pcbddc->constraints_flag) {
468     get_vertices = PETSC_FALSE;
469   }
470   if (pcbddc->faces_flag) {
471     get_edges = PETSC_FALSE;
472   }
473   if (pcbddc->edges_flag) {
474     get_faces = PETSC_FALSE;
475   }
476   /* default */
477   if (!get_faces && !get_edges && !get_vertices) {
478     get_vertices = PETSC_TRUE;
479   }
480   ierr = PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,get_faces,get_edges,get_vertices,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
481   if (pcbddc->dbg_flag) {
482     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");CHKERRQ(ierr);
483     i = 0;
484     if (ISForVertices) {
485       ierr = ISGetSize(ISForVertices,&i);CHKERRQ(ierr);
486     }
487     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices\n",PetscGlobalRank,i);CHKERRQ(ierr);
488     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges\n",PetscGlobalRank,n_ISForEdges);CHKERRQ(ierr);
489     ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces\n",PetscGlobalRank,n_ISForFaces);CHKERRQ(ierr);
490     ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
491   }
492   /* check if near null space is attached to global mat */
493   ierr = MatGetNearNullSpace(pc->pmat,&nearnullsp);CHKERRQ(ierr);
494   if (nearnullsp) {
495     ierr = MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);CHKERRQ(ierr);
496   } else { /* if near null space is not provided it uses constants */
497     nnsp_has_cnst = PETSC_TRUE;
498     use_nnsp_true = PETSC_TRUE;
499   }
500   if (nnsp_has_cnst) {
501     nnsp_addone = 1;
502   }
503   /*
504        Evaluate maximum storage size needed by the procedure
505        - temp_indices will contain start index of each constraint stored as follows
506        - temp_indices_to_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the indices (in local numbering) on which the constraint acts
507        - 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
508        - temp_quadrature_constraint  [temp_indices[i],...,temp[indices[i+1]-1] will contain the scalars representing the constraint itself
509                                                                                                                                                          */
510   total_counts = n_ISForFaces+n_ISForEdges;
511   total_counts *= (nnsp_addone+nnsp_size);
512   n_vertices = 0;
513   if (ISForVertices) {
514     ierr = ISGetSize(ISForVertices,&n_vertices);CHKERRQ(ierr);
515   }
516   total_counts += n_vertices;
517   ierr = PetscMalloc((total_counts+1)*sizeof(PetscInt),&temp_indices);CHKERRQ(ierr);
518   ierr = PetscMalloc((total_counts+1)*sizeof(PetscBool),&change_basis);CHKERRQ(ierr);
519   total_counts = 0;
520   max_size_of_constraint = 0;
521   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
522     if (i<n_ISForEdges) {
523       used_IS = &ISForEdges[i];
524     } else {
525       used_IS = &ISForFaces[i-n_ISForEdges];
526     }
527     ierr = ISGetSize(*used_IS,&j);CHKERRQ(ierr);
528     total_counts += j;
529     max_size_of_constraint = PetscMax(j,max_size_of_constraint);
530   }
531   total_counts *= (nnsp_addone+nnsp_size);
532   total_counts += n_vertices;
533   ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&temp_quadrature_constraint);CHKERRQ(ierr);
534   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint);CHKERRQ(ierr);
535   ierr = PetscMalloc(total_counts*sizeof(PetscInt),&temp_indices_to_constraint_B);CHKERRQ(ierr);
536   ierr = PetscMalloc(pcis->n*sizeof(PetscInt),&local_to_B);CHKERRQ(ierr);
537   ierr = ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
538   for (i=0;i<pcis->n;i++) {
539     local_to_B[i]=-1;
540   }
541   for (i=0;i<pcis->n_B;i++) {
542     local_to_B[is_indices[i]]=i;
543   }
544   ierr = ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);CHKERRQ(ierr);
545 
546   /* First we issue queries to allocate optimal workspace for LAPACKgesvd or LAPACKsyev/LAPACKheev */
547   rwork = 0;
548   work = 0;
549   singular_vals = 0;
550   temp_basis = 0;
551   correlation_mat = 0;
552   if (!pcbddc->use_nnsp_true) {
553     PetscScalar temp_work;
554 #if defined(PETSC_MISSING_LAPACK_GESVD)
555     /* POD */
556     PetscInt max_n;
557     max_n = nnsp_addone+nnsp_size;
558     /* using some techniques borrowed from Proper Orthogonal Decomposition */
559     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&correlation_mat);CHKERRQ(ierr);
560     ierr = PetscMalloc(max_n*max_n*sizeof(PetscScalar),&singular_vectors);CHKERRQ(ierr);
561     ierr = PetscMalloc(max_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
562     ierr = PetscMalloc(max_size_of_constraint*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
563 #if defined(PETSC_USE_COMPLEX)
564     ierr = PetscMalloc(3*max_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
565 #endif
566     ierr = PetscMalloc(5*max_n*sizeof(PetscBLASInt),&iwork);CHKERRQ(ierr);
567     ierr = PetscMalloc(max_n*sizeof(PetscBLASInt),&ifail);CHKERRQ(ierr);
568     /* now we evaluate the optimal workspace using query with lwork=-1 */
569     ierr = PetscBLASIntCast(max_n,&Bt);CHKERRQ(ierr);
570     lwork=-1;
571     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
572 #if !defined(PETSC_USE_COMPLEX)
573     abs_tol=1.e-8;
574 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,&lierr); */
575     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));
576 #else
577 /*    LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,&temp_work,&lwork,rwork,&lierr); */
578 /*  LAPACK call is missing here! TODO */
579     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
580 #endif
581     if ( lierr ) {
582       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEVX Lapack routine %d",(int)lierr);
583     }
584     ierr = PetscFPTrapPop();CHKERRQ(ierr);
585 #else /* on missing GESVD */
586     /* SVD */
587     PetscInt max_n,min_n;
588     max_n = max_size_of_constraint;
589     min_n = nnsp_addone+nnsp_size;
590     if (max_size_of_constraint < ( nnsp_addone+nnsp_size ) ) {
591       min_n = max_size_of_constraint;
592       max_n = nnsp_addone+nnsp_size;
593     }
594     ierr = PetscMalloc(min_n*sizeof(PetscReal),&singular_vals);CHKERRQ(ierr);
595 #if defined(PETSC_USE_COMPLEX)
596     ierr = PetscMalloc(5*min_n*sizeof(PetscReal),&rwork);CHKERRQ(ierr);
597 #endif
598     /* now we evaluate the optimal workspace using query with lwork=-1 */
599     lwork=-1;
600     ierr = PetscBLASIntCast(max_n,&Bs);CHKERRQ(ierr);
601     ierr = PetscBLASIntCast(min_n,&Bt);CHKERRQ(ierr);
602     dummy_int = Bs;
603     ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
604 #if !defined(PETSC_USE_COMPLEX)
605     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));
606 #else
607     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));
608 #endif
609     if ( lierr ) {
610       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SVD Lapack routine %d",(int)lierr);
611     }
612     ierr = PetscFPTrapPop();CHKERRQ(ierr);
613 #endif
614     /* Allocate optimal workspace */
615     ierr = PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);CHKERRQ(ierr);
616     total_counts = (PetscInt)lwork;
617     ierr = PetscMalloc(total_counts*sizeof(PetscScalar),&work);CHKERRQ(ierr);
618   }
619   /* get local part of global near null space vectors */
620   ierr = PetscMalloc(nnsp_size*sizeof(Vec),&localnearnullsp);CHKERRQ(ierr);
621   for (k=0;k<nnsp_size;k++) {
622     ierr = VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);CHKERRQ(ierr);
623     ierr = VecScatterBegin(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
624     ierr = VecScatterEnd(matis->ctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
625   }
626   /* Now we can loop on constraining sets */
627   total_counts = 0;
628   temp_indices[0] = 0;
629   /* vertices */
630   if (ISForVertices) {
631     ierr = ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
632     if (nnsp_has_cnst) { /* consider all vertices */
633       for (i=0;i<n_vertices;i++) {
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       }
641     } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
642       for (i=0;i<n_vertices;i++) {
643         used_vertex=PETSC_FALSE;
644         k=0;
645         while (!used_vertex && k<nnsp_size) {
646           ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
647           if (PetscAbsScalar(array_vector[is_indices[i]])>0.0) {
648             temp_indices_to_constraint[temp_indices[total_counts]]=is_indices[i];
649             temp_indices_to_constraint_B[temp_indices[total_counts]]=local_to_B[is_indices[i]];
650             temp_quadrature_constraint[temp_indices[total_counts]]=1.0;
651             temp_indices[total_counts+1]=temp_indices[total_counts]+1;
652             change_basis[total_counts]=PETSC_FALSE;
653             total_counts++;
654             used_vertex=PETSC_TRUE;
655           }
656           ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
657           k++;
658         }
659       }
660     }
661     ierr = ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);CHKERRQ(ierr);
662     n_vertices = total_counts;
663   }
664   /* edges and faces */
665   for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
666     if (i<n_ISForEdges) {
667       used_IS = &ISForEdges[i];
668       boolforchange = pcbddc->use_change_of_basis;
669     } else {
670       used_IS = &ISForFaces[i-n_ISForEdges];
671       boolforchange = pcbddc->use_change_on_faces;
672     }
673     temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */
674     temp_start_ptr = total_counts; /* need to know the starting index of constraints stored */
675     ierr = ISGetSize(*used_IS,&size_of_constraint);CHKERRQ(ierr);
676     ierr = ISGetIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
677     /* HACK: change of basis should not performed on local periodic nodes */
678     if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) {
679       boolforchange = PETSC_FALSE;
680     }
681     if (nnsp_has_cnst) {
682       PetscScalar quad_value;
683       temp_constraints++;
684       quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
685       for (j=0;j<size_of_constraint;j++) {
686         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
687         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
688         temp_quadrature_constraint[temp_indices[total_counts]+j]=quad_value;
689       }
690       temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
691       change_basis[total_counts]=boolforchange;
692       total_counts++;
693     }
694     for (k=0;k<nnsp_size;k++) {
695       ierr = VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
696       for (j=0;j<size_of_constraint;j++) {
697         temp_indices_to_constraint[temp_indices[total_counts]+j]=is_indices[j];
698         temp_indices_to_constraint_B[temp_indices[total_counts]+j]=local_to_B[is_indices[j]];
699         temp_quadrature_constraint[temp_indices[total_counts]+j]=array_vector[is_indices[j]];
700       }
701       ierr = VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array_vector);CHKERRQ(ierr);
702       real_value = 1.0;
703       if (use_nnsp_true) { /* check if array is null on the connected component in case use_nnsp_true has been requested */
704         ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
705         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Bs,&temp_quadrature_constraint[temp_indices[total_counts]],&Bone));
706       }
707       if (real_value > 0.0) { /* keep indices and values */
708         temp_constraints++;
709         temp_indices[total_counts+1]=temp_indices[total_counts]+size_of_constraint;  /* store new starting point */
710         change_basis[total_counts]=boolforchange;
711         total_counts++;
712       }
713     }
714     ierr = ISRestoreIndices(*used_IS,(const PetscInt**)&is_indices);CHKERRQ(ierr);
715     /* perform SVD on the constraint if use_nnsp_true has not be requested by the user */
716     if (!use_nnsp_true) {
717       ierr = PetscBLASIntCast(size_of_constraint,&Bs);CHKERRQ(ierr);
718       ierr = PetscBLASIntCast(temp_constraints,&Bt);CHKERRQ(ierr);
719 
720 #if defined(PETSC_MISSING_LAPACK_GESVD)
721       ierr = PetscMemzero(correlation_mat,Bt*Bt*sizeof(PetscScalar));CHKERRQ(ierr);
722       /* Store upper triangular part of correlation matrix */
723       for (j=0;j<temp_constraints;j++) {
724         for (k=0;k<j+1;k++) {
725           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));
726 
727         }
728       }
729       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
730 #if !defined(PETSC_USE_COMPLEX)
731 /*      LAPACKsyev_("V","U",&Bt,correlation_mat,&Bt,singular_vals,work,&lwork,&lierr); */
732       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));
733 #else
734 /*  LAPACK call is missing here! TODO */
735       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not yet implemented for complexes when PETSC_MISSING_GESVD = 1");
736 #endif
737       if (lierr) {
738         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEVX Lapack routine %d",(int)lierr);
739       }
740       ierr = PetscFPTrapPop();CHKERRQ(ierr);
741       /* retain eigenvalues greater than tol: note that lapack SYEV gives eigs in ascending order */
742       j=0;
743       while (j < Bt && singular_vals[j] < tol) j++;
744       total_counts=total_counts-j;
745       if (j<temp_constraints) {
746         for (k=j;k<Bt;k++) {
747           singular_vals[k]=1.0/PetscSqrtReal(singular_vals[k]);
748         }
749         ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
750         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));
751         ierr = PetscFPTrapPop();CHKERRQ(ierr);
752         /* copy POD basis into used quadrature memory */
753         for (k=0;k<Bt-j;k++) {
754           for (ii=0;ii<size_of_constraint;ii++) {
755             temp_quadrature_constraint[temp_indices[temp_start_ptr+k]+ii]=singular_vals[Bt-1-k]*temp_basis[(Bt-1-k)*size_of_constraint+ii];
756           }
757         }
758       }
759 
760 #else  /* on missing GESVD */
761       PetscInt min_n = temp_constraints;
762       if (min_n > size_of_constraint) min_n = size_of_constraint;
763       dummy_int = Bs;
764       ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
765 #if !defined(PETSC_USE_COMPLEX)
766       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));
767 #else
768       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));
769 #endif
770       if (lierr) {
771         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD Lapack routine %d",(int)lierr);
772       }
773       ierr = PetscFPTrapPop();CHKERRQ(ierr);
774       /* retain eigenvalues greater than tol: note that lapack SVD gives eigs in descending order */
775       j = 0;
776       while (j < min_n && singular_vals[min_n-j-1] < tol) j++;
777       total_counts = total_counts-(PetscInt)Bt+(min_n-j);
778 #endif
779     }
780   }
781   /* free index sets of faces, edges and vertices */
782   for (i=0;i<n_ISForFaces;i++) {
783     ierr = ISDestroy(&ISForFaces[i]);CHKERRQ(ierr);
784   }
785   ierr = PetscFree(ISForFaces);CHKERRQ(ierr);
786   for (i=0;i<n_ISForEdges;i++) {
787     ierr = ISDestroy(&ISForEdges[i]);CHKERRQ(ierr);
788   }
789   ierr = PetscFree(ISForEdges);CHKERRQ(ierr);
790   ierr = ISDestroy(&ISForVertices);CHKERRQ(ierr);
791 
792   /* set quantities in pcbddc data structure */
793   /* n_vertices defines the number of point primal dofs */
794   /* n_constraints defines the number of averages (they can be point primal dofs if change of basis is requested) */
795   local_primal_size = total_counts;
796   pcbddc->n_vertices = n_vertices;
797   pcbddc->n_constraints = total_counts-n_vertices;
798   pcbddc->local_primal_size = local_primal_size;
799 
800   /* Create constraint matrix */
801   /* The constraint matrix is used to compute the l2g map of primal dofs */
802   /* so we need to set it up properly either with or without change of basis */
803   ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);CHKERRQ(ierr);
804   ierr = MatSetType(pcbddc->ConstraintMatrix,impMatType);CHKERRQ(ierr);
805   ierr = MatSetSizes(pcbddc->ConstraintMatrix,local_primal_size,pcis->n,local_primal_size,pcis->n);CHKERRQ(ierr);
806   /* compute a local numbering of constraints : vertices first then constraints */
807   ierr = VecSet(pcis->vec1_N,0.0);CHKERRQ(ierr);
808   ierr = VecGetArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
809   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_numbering);CHKERRQ(ierr);
810   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&aux_primal_permutation);CHKERRQ(ierr);
811   total_counts=0;
812   /* find vertices: subdomain corners plus dofs with basis changed */
813   for (i=0;i<local_primal_size;i++) {
814     size_of_constraint=temp_indices[i+1]-temp_indices[i];
815     if (change_basis[i] || size_of_constraint == 1) {
816       k=0;
817       while(k < size_of_constraint && array_vector[temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1]] != 0.0) {
818         k=k+1;
819       }
820       j=temp_indices_to_constraint[temp_indices[i]+size_of_constraint-k-1];
821       array_vector[j] = 1.0;
822       aux_primal_numbering[total_counts]=j;
823       aux_primal_permutation[total_counts]=total_counts;
824       total_counts++;
825     }
826   }
827   ierr = VecRestoreArray(pcis->vec1_N,&array_vector);CHKERRQ(ierr);
828   /* permute indices in order to have a sorted set of vertices */
829   ierr = PetscSortIntWithPermutation(total_counts,aux_primal_numbering,aux_primal_permutation);
830   /* nonzero structure */
831   ierr = PetscMalloc(local_primal_size*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
832   for (i=0;i<total_counts;i++) {
833     nnz[i]=1;
834   }
835   j=total_counts;
836   for (i=n_vertices;i<local_primal_size;i++) {
837     if (!change_basis[i]) {
838       nnz[j]=temp_indices[i+1]-temp_indices[i];
839       j++;
840     }
841   }
842   ierr = MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);CHKERRQ(ierr);
843   ierr = PetscFree(nnz);CHKERRQ(ierr);
844   /* set values in constraint matrix */
845   for (i=0;i<total_counts;i++) {
846     j = aux_primal_permutation[i];
847     k = aux_primal_numbering[j];
848     ierr = MatSetValue(pcbddc->ConstraintMatrix,i,k,1.0,INSERT_VALUES);CHKERRQ(ierr);
849   }
850   for (i=n_vertices;i<local_primal_size;i++) {
851     if (!change_basis[i]) {
852       size_of_constraint=temp_indices[i+1]-temp_indices[i];
853       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);
854       total_counts++;
855     }
856   }
857   ierr = PetscFree(aux_primal_numbering);CHKERRQ(ierr);
858   ierr = PetscFree(aux_primal_permutation);CHKERRQ(ierr);
859   /* assembling */
860   ierr = MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
861   ierr = MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
862 
863   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
864   if (pcbddc->use_change_of_basis) {
865     ierr = MatCreate(PETSC_COMM_SELF,&pcbddc->ChangeOfBasisMatrix);CHKERRQ(ierr);
866     ierr = MatSetType(pcbddc->ChangeOfBasisMatrix,impMatType);CHKERRQ(ierr);
867     ierr = MatSetSizes(pcbddc->ChangeOfBasisMatrix,pcis->n_B,pcis->n_B,pcis->n_B,pcis->n_B);CHKERRQ(ierr);
868     /* work arrays */
869     /* we need to reuse these arrays, so we free them */
870     ierr = PetscFree(temp_basis);CHKERRQ(ierr);
871     ierr = PetscFree(work);CHKERRQ(ierr);
872     ierr = PetscMalloc(pcis->n_B*sizeof(PetscInt),&nnz);CHKERRQ(ierr);
873     ierr = PetscMalloc((nnsp_addone+nnsp_size)*(nnsp_addone+nnsp_size)*sizeof(PetscScalar),&temp_basis);CHKERRQ(ierr);
874     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscScalar),&work);CHKERRQ(ierr);
875     ierr = PetscMalloc((nnsp_addone+nnsp_size)*sizeof(PetscBLASInt),&ipiv);CHKERRQ(ierr);
876     for (i=0;i<pcis->n_B;i++) {
877       nnz[i]=1;
878     }
879     /* Overestimated nonzeros per row */
880     k=1;
881     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
882       if (change_basis[i]) {
883         size_of_constraint = temp_indices[i+1]-temp_indices[i];
884         if (k < size_of_constraint) {
885           k = size_of_constraint;
886         }
887         for (j=0;j<size_of_constraint;j++) {
888           nnz[temp_indices_to_constraint_B[temp_indices[i]+j]] = size_of_constraint;
889         }
890       }
891     }
892     ierr = MatSeqAIJSetPreallocation(pcbddc->ChangeOfBasisMatrix,0,nnz);CHKERRQ(ierr);
893     ierr = PetscFree(nnz);CHKERRQ(ierr);
894     /* Temporary array to store indices */
895     ierr = PetscMalloc(k*sizeof(PetscInt),&is_indices);CHKERRQ(ierr);
896     /* Set initial identity in the matrix */
897     for (i=0;i<pcis->n_B;i++) {
898       ierr = MatSetValue(pcbddc->ChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);CHKERRQ(ierr);
899     }
900     /* Now we loop on the constraints which need a change of basis */
901     /* Change of basis matrix is evaluated as the FIRST APPROACH in */
902     /* Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (6.2.1) */
903     temp_constraints = 0;
904     if (pcbddc->n_vertices < local_primal_size) {
905       temp_start_ptr = temp_indices_to_constraint_B[temp_indices[pcbddc->n_vertices]];
906     }
907     for (i=pcbddc->n_vertices;i<local_primal_size;i++) {
908       if (change_basis[i]) {
909         compute_submatrix = PETSC_FALSE;
910         useksp = PETSC_FALSE;
911         if (temp_start_ptr == temp_indices_to_constraint_B[temp_indices[i]]) {
912           temp_constraints++;
913           if (i == local_primal_size -1 ||  temp_start_ptr != temp_indices_to_constraint_B[temp_indices[i+1]]) {
914             compute_submatrix = PETSC_TRUE;
915           }
916         }
917         if (compute_submatrix) {
918           if (temp_constraints > 1 || pcbddc->use_nnsp_true) {
919             useksp = PETSC_TRUE;
920           }
921           size_of_constraint = temp_indices[i+1]-temp_indices[i];
922           if (useksp) { /* experimental TODO: reuse KSP and MAT instead of creating them each time */
923             ierr = MatCreate(PETSC_COMM_SELF,&temp_mat);CHKERRQ(ierr);
924             ierr = MatSetType(temp_mat,impMatType);CHKERRQ(ierr);
925             ierr = MatSetSizes(temp_mat,size_of_constraint,size_of_constraint,size_of_constraint,size_of_constraint);CHKERRQ(ierr);
926             ierr = MatSeqAIJSetPreallocation(temp_mat,size_of_constraint,NULL);CHKERRQ(ierr);
927           }
928           /* First _size_of_constraint-temp_constraints_ columns */
929           dual_dofs = size_of_constraint-temp_constraints;
930           start_constraint = i+1-temp_constraints;
931           for (s=0;s<dual_dofs;s++) {
932             is_indices[0] = s;
933             for (j=0;j<temp_constraints;j++) {
934               for (k=0;k<temp_constraints;k++) {
935                 temp_basis[j*temp_constraints+k]=temp_quadrature_constraint[temp_indices[start_constraint+k]+s+j+1];
936               }
937               work[j]=-temp_quadrature_constraint[temp_indices[start_constraint+j]+s];
938               is_indices[j+1]=s+j+1;
939             }
940             Bt = temp_constraints;
941             ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
942             PetscStackCallBLAS("LAPACKgesv",LAPACKgesv_(&Bt,&Bone,temp_basis,&Bt,ipiv,work,&Bt,&lierr));
943             if ( lierr ) {
944               SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESV Lapack routine %d",(int)lierr);
945             }
946             ierr = PetscFPTrapPop();CHKERRQ(ierr);
947             j = temp_indices_to_constraint_B[temp_indices[start_constraint]+s];
948             ierr = MatSetValues(pcbddc->ChangeOfBasisMatrix,temp_constraints,&temp_indices_to_constraint_B[temp_indices[start_constraint]+s+1],1,&j,work,INSERT_VALUES);CHKERRQ(ierr);
949             if (useksp) {
950               /* temp mat with transposed rows and columns */
951               ierr = MatSetValues(temp_mat,1,&s,temp_constraints,&is_indices[1],work,INSERT_VALUES);CHKERRQ(ierr);
952               ierr = MatSetValue(temp_mat,is_indices[0],is_indices[0],1.0,INSERT_VALUES);CHKERRQ(ierr);
953             }
954           }
955           if (useksp) {
956             /* last rows of temp_mat */
957             for (j=0;j<size_of_constraint;j++) {
958               is_indices[j] = j;
959             }
960             for (s=0;s<temp_constraints;s++) {
961               k = s + dual_dofs;
962               ierr = MatSetValues(temp_mat,1,&k,size_of_constraint,is_indices,&temp_quadrature_constraint[temp_indices[start_constraint+s]],INSERT_VALUES);CHKERRQ(ierr);
963             }
964             ierr = MatAssemblyBegin(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
965             ierr = MatAssemblyEnd(temp_mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
966             ierr = MatGetVecs(temp_mat,&temp_vec,NULL);CHKERRQ(ierr);
967             ierr = KSPCreate(PETSC_COMM_SELF,&temp_ksp);CHKERRQ(ierr);
968             ierr = KSPSetOperators(temp_ksp,temp_mat,temp_mat,SAME_PRECONDITIONER);CHKERRQ(ierr);
969             ierr = KSPSetType(temp_ksp,KSPPREONLY);CHKERRQ(ierr);
970             ierr = KSPGetPC(temp_ksp,&temp_pc);CHKERRQ(ierr);
971             ierr = PCSetType(temp_pc,PCLU);CHKERRQ(ierr);
972             ierr = KSPSetUp(temp_ksp);CHKERRQ(ierr);
973             for (s=0;s<temp_constraints;s++) {
974               ierr = VecSet(temp_vec,0.0);CHKERRQ(ierr);
975               ierr = VecSetValue(temp_vec,s+dual_dofs,1.0,INSERT_VALUES);CHKERRQ(ierr);
976               ierr = VecAssemblyBegin(temp_vec);CHKERRQ(ierr);
977               ierr = VecAssemblyEnd(temp_vec);CHKERRQ(ierr);
978               ierr = KSPSolve(temp_ksp,temp_vec,temp_vec);CHKERRQ(ierr);
979               ierr = VecGetArray(temp_vec,&array_vector);CHKERRQ(ierr);
980               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
981               /* last columns of change of basis matrix associated to new primal dofs */
982               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);
983               ierr = VecRestoreArray(temp_vec,&array_vector);CHKERRQ(ierr);
984             }
985             ierr = MatDestroy(&temp_mat);CHKERRQ(ierr);
986             ierr = KSPDestroy(&temp_ksp);CHKERRQ(ierr);
987             ierr = VecDestroy(&temp_vec);CHKERRQ(ierr);
988           } else {
989             /* last columns of change of basis matrix associated to new primal dofs */
990             for (s=0;s<temp_constraints;s++) {
991               j = temp_indices_to_constraint_B[temp_indices[start_constraint+s]+size_of_constraint-s-1];
992               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);
993             }
994           }
995           /* prepare for the next cycle */
996           temp_constraints = 0;
997           if (i != local_primal_size -1 ) {
998             temp_start_ptr = temp_indices_to_constraint_B[temp_indices[i+1]];
999           }
1000         }
1001       }
1002     }
1003     /* assembling */
1004     ierr = MatAssemblyBegin(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1005     ierr = MatAssemblyEnd(pcbddc->ChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1006     ierr = PetscFree(ipiv);CHKERRQ(ierr);
1007     ierr = PetscFree(is_indices);CHKERRQ(ierr);
1008   }
1009   /* free workspace no longer needed */
1010   ierr = PetscFree(rwork);CHKERRQ(ierr);
1011   ierr = PetscFree(work);CHKERRQ(ierr);
1012   ierr = PetscFree(temp_basis);CHKERRQ(ierr);
1013   ierr = PetscFree(singular_vals);CHKERRQ(ierr);
1014   ierr = PetscFree(correlation_mat);CHKERRQ(ierr);
1015   ierr = PetscFree(temp_indices);CHKERRQ(ierr);
1016   ierr = PetscFree(change_basis);CHKERRQ(ierr);
1017   ierr = PetscFree(temp_indices_to_constraint);CHKERRQ(ierr);
1018   ierr = PetscFree(temp_indices_to_constraint_B);CHKERRQ(ierr);
1019   ierr = PetscFree(local_to_B);CHKERRQ(ierr);
1020   ierr = PetscFree(temp_quadrature_constraint);CHKERRQ(ierr);
1021 #if defined(PETSC_MISSING_LAPACK_GESVD)
1022   ierr = PetscFree(iwork);CHKERRQ(ierr);
1023   ierr = PetscFree(ifail);CHKERRQ(ierr);
1024   ierr = PetscFree(singular_vectors);CHKERRQ(ierr);
1025 #endif
1026   for (k=0;k<nnsp_size;k++) {
1027     ierr = VecDestroy(&localnearnullsp[k]);CHKERRQ(ierr);
1028   }
1029   ierr = PetscFree(localnearnullsp);CHKERRQ(ierr);
1030   PetscFunctionReturn(0);
1031 }
1032 
1033 #undef __FUNCT__
1034 #define __FUNCT__ "PCBDDCAnalyzeInterface"
1035 PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
1036 {
1037   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
1038   PC_IS       *pcis = (PC_IS*)pc->data;
1039   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
1040   PetscInt    bs,ierr,i,vertex_size;
1041   PetscViewer viewer=pcbddc->dbg_viewer;
1042 
1043   PetscFunctionBegin;
1044   /* Init local Graph struct */
1045   ierr = PCBDDCGraphInit(pcbddc->mat_graph,matis->mapping);CHKERRQ(ierr);
1046 
1047   /* Check validity of the csr graph passed in by the user */
1048   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
1049     ierr = PCBDDCGraphResetCSR(pcbddc->mat_graph);CHKERRQ(ierr);
1050   }
1051   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
1052   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
1053     Mat mat_adj;
1054     const PetscInt *xadj,*adjncy;
1055     PetscBool flg_row=PETSC_TRUE;
1056 
1057     ierr = MatConvert(matis->A,MATMPIADJ,MAT_INITIAL_MATRIX,&mat_adj);CHKERRQ(ierr);
1058     ierr = MatGetRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1059     if (!flg_row) {
1060       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatGetRowIJ called in %s\n",__FUNCT__);
1061     }
1062     ierr = PCBDDCSetLocalAdjacencyGraph(pc,i,xadj,adjncy,PETSC_COPY_VALUES);CHKERRQ(ierr);
1063     ierr = MatRestoreRowIJ(mat_adj,0,PETSC_TRUE,PETSC_FALSE,&i,&xadj,&adjncy,&flg_row);CHKERRQ(ierr);
1064     if (!flg_row) {
1065       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in MatRestoreRowIJ called in %s\n",__FUNCT__);
1066     }
1067     ierr = MatDestroy(&mat_adj);CHKERRQ(ierr);
1068   }
1069 
1070   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting */
1071   vertex_size = 1;
1072   if (!pcbddc->n_ISForDofs) {
1073     IS *custom_ISForDofs;
1074 
1075     ierr = MatGetBlockSize(matis->A,&bs);CHKERRQ(ierr);
1076     ierr = PetscMalloc(bs*sizeof(IS),&custom_ISForDofs);CHKERRQ(ierr);
1077     for (i=0;i<bs;i++) {
1078       ierr = ISCreateStride(PETSC_COMM_SELF,pcis->n/bs,i,bs,&custom_ISForDofs[i]);CHKERRQ(ierr);
1079     }
1080     ierr = PCBDDCSetDofsSplitting(pc,bs,custom_ISForDofs);CHKERRQ(ierr);
1081     /* remove my references to IS objects */
1082     for (i=0;i<bs;i++) {
1083       ierr = ISDestroy(&custom_ISForDofs[i]);CHKERRQ(ierr);
1084     }
1085     ierr = PetscFree(custom_ISForDofs);CHKERRQ(ierr);
1086   } else { /* mat block size as vertex size (used for elasticity) */
1087     ierr = MatGetBlockSize(matis->A,&vertex_size);CHKERRQ(ierr);
1088   }
1089 
1090   /* Setup of Graph */
1091   ierr = PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundaries,pcbddc->DirichletBoundaries,pcbddc->n_ISForDofs,pcbddc->ISForDofs,pcbddc->user_primal_vertices);
1092 
1093   /* Graph's connected components analysis */
1094   ierr = PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);CHKERRQ(ierr);
1095 
1096   /* print some info to stdout */
1097   if (pcbddc->dbg_flag) {
1098     ierr = PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
1099   }
1100   PetscFunctionReturn(0);
1101 }
1102 
1103 #undef __FUNCT__
1104 #define __FUNCT__ "PCBDDCGetPrimalVerticesLocalIdx"
1105 PetscErrorCode  PCBDDCGetPrimalVerticesLocalIdx(PC pc, PetscInt *n_vertices, PetscInt *vertices_idx[])
1106 {
1107   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1108   PetscInt       *vertices,*row_cmat_indices,n,i,size_of_constraint,local_primal_size;
1109   PetscErrorCode ierr;
1110 
1111   PetscFunctionBegin;
1112   n = 0;
1113   vertices = 0;
1114   if (pcbddc->ConstraintMatrix) {
1115     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&i);CHKERRQ(ierr);
1116     for (i=0;i<local_primal_size;i++) {
1117       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1118       if (size_of_constraint == 1) n++;
1119       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1120     }
1121     ierr = PetscMalloc(n*sizeof(PetscInt),&vertices);CHKERRQ(ierr);
1122     n = 0;
1123     for (i=0;i<local_primal_size;i++) {
1124       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1125       if (size_of_constraint == 1) {
1126         vertices[n++]=row_cmat_indices[0];
1127       }
1128       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1129     }
1130   }
1131   *n_vertices = n;
1132   *vertices_idx = vertices;
1133   PetscFunctionReturn(0);
1134 }
1135 
1136 #undef __FUNCT__
1137 #define __FUNCT__ "PCBDDCGetPrimalConstraintsLocalIdx"
1138 PetscErrorCode  PCBDDCGetPrimalConstraintsLocalIdx(PC pc, PetscInt *n_constraints, PetscInt *constraints_idx[])
1139 {
1140   PC_BDDC        *pcbddc = (PC_BDDC*)(pc->data);
1141   PetscInt       *constraints_index,*row_cmat_indices,*row_cmat_global_indices;
1142   PetscInt       n,i,j,size_of_constraint,local_primal_size,local_size,max_size_of_constraint,min_index,min_loc;
1143   PetscBool      *touched;
1144   PetscErrorCode ierr;
1145 
1146   PetscFunctionBegin;
1147   n = 0;
1148   constraints_index = 0;
1149   if (pcbddc->ConstraintMatrix) {
1150     ierr = MatGetSize(pcbddc->ConstraintMatrix,&local_primal_size,&local_size);CHKERRQ(ierr);
1151     max_size_of_constraint = 0;
1152     for (i=0;i<local_primal_size;i++) {
1153       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1154       if (size_of_constraint > 1) {
1155         n++;
1156       }
1157       max_size_of_constraint = PetscMax(size_of_constraint,max_size_of_constraint);
1158       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,NULL,NULL);CHKERRQ(ierr);
1159     }
1160     ierr = PetscMalloc(n*sizeof(PetscInt),&constraints_index);CHKERRQ(ierr);
1161     ierr = PetscMalloc(max_size_of_constraint*sizeof(PetscInt),&row_cmat_global_indices);CHKERRQ(ierr);
1162     ierr = PetscMalloc(local_size*sizeof(PetscBool),&touched);CHKERRQ(ierr);
1163     ierr = PetscMemzero(touched,local_size*sizeof(PetscBool));CHKERRQ(ierr);
1164     n = 0;
1165     for (i=0;i<local_primal_size;i++) {
1166       ierr = MatGetRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1167       if (size_of_constraint > 1) {
1168         ierr = ISLocalToGlobalMappingApply(pcbddc->mat_graph->l2gmap,size_of_constraint,row_cmat_indices,row_cmat_global_indices);CHKERRQ(ierr);
1169         min_index = row_cmat_global_indices[0];
1170         min_loc = 0;
1171         for (j=1;j<size_of_constraint;j++) {
1172           /* there can be more than one constraint on a single connected component */
1173           if (min_index > row_cmat_global_indices[j] && !touched[row_cmat_indices[j]]) {
1174             min_index = row_cmat_global_indices[j];
1175             min_loc = j;
1176           }
1177         }
1178         touched[row_cmat_indices[min_loc]] = PETSC_TRUE;
1179         constraints_index[n++] = row_cmat_indices[min_loc];
1180       }
1181       ierr = MatRestoreRow(pcbddc->ConstraintMatrix,i,&size_of_constraint,(const PetscInt**)&row_cmat_indices,NULL);CHKERRQ(ierr);
1182     }
1183   }
1184   ierr = PetscFree(touched);CHKERRQ(ierr);
1185   ierr = PetscFree(row_cmat_global_indices);CHKERRQ(ierr);
1186   *n_constraints = n;
1187   *constraints_idx = constraints_index;
1188   PetscFunctionReturn(0);
1189 }
1190 
1191 /* the next two functions has been adapted from pcis.c */
1192 #undef __FUNCT__
1193 #define __FUNCT__ "PCBDDCApplySchur"
1194 PetscErrorCode  PCBDDCApplySchur(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1195 {
1196   PetscErrorCode ierr;
1197   PC_IS          *pcis = (PC_IS*)(pc->data);
1198 
1199   PetscFunctionBegin;
1200   if (!vec2_B) { vec2_B = v; }
1201   ierr = MatMult(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1202   ierr = MatMult(pcis->A_IB,v,vec1_D);CHKERRQ(ierr);
1203   ierr = KSPSolve(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1204   ierr = MatMult(pcis->A_BI,vec2_D,vec2_B);CHKERRQ(ierr);
1205   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1206   PetscFunctionReturn(0);
1207 }
1208 
1209 #undef __FUNCT__
1210 #define __FUNCT__ "PCBDDCApplySchurTranspose"
1211 PetscErrorCode  PCBDDCApplySchurTranspose(PC pc, Vec v, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
1212 {
1213   PetscErrorCode ierr;
1214   PC_IS          *pcis = (PC_IS*)(pc->data);
1215 
1216   PetscFunctionBegin;
1217   if (!vec2_B) { vec2_B = v; }
1218   ierr = MatMultTranspose(pcis->A_BB,v,vec1_B);CHKERRQ(ierr);
1219   ierr = MatMultTranspose(pcis->A_BI,v,vec1_D);CHKERRQ(ierr);
1220   ierr = KSPSolveTranspose(pcis->ksp_D,vec1_D,vec2_D);CHKERRQ(ierr);
1221   ierr = MatMultTranspose(pcis->A_IB,vec2_D,vec2_B);CHKERRQ(ierr);
1222   ierr = VecAXPY(vec1_B,-1.0,vec2_B);CHKERRQ(ierr);
1223   PetscFunctionReturn(0);
1224 }
1225 
1226 #undef __FUNCT__
1227 #define __FUNCT__ "PCBDDCSubsetNumbering"
1228 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[])
1229 {
1230   Vec            local_vec,global_vec;
1231   IS             seqis,paris;
1232   VecScatter     scatter_ctx;
1233   PetscScalar    *array;
1234   PetscInt       *temp_global_dofs;
1235   PetscScalar    globalsum;
1236   PetscInt       i,j,s;
1237   PetscInt       nlocals,first_index,old_index,max_local;
1238   PetscMPIInt    rank_prec_comm,size_prec_comm,max_global;
1239   PetscMPIInt    *dof_sizes,*dof_displs;
1240   PetscBool      first_found;
1241   PetscErrorCode ierr;
1242 
1243   PetscFunctionBegin;
1244   /* mpi buffers */
1245   MPI_Comm_size(comm,&size_prec_comm);
1246   MPI_Comm_rank(comm,&rank_prec_comm);
1247   j = ( !rank_prec_comm ? size_prec_comm : 0);
1248   ierr = PetscMalloc(j*sizeof(*dof_sizes),&dof_sizes);CHKERRQ(ierr);
1249   ierr = PetscMalloc(j*sizeof(*dof_displs),&dof_displs);CHKERRQ(ierr);
1250   /* get maximum size of subset */
1251   ierr = PetscMalloc(n_local_dofs*sizeof(PetscInt),&temp_global_dofs);CHKERRQ(ierr);
1252   ierr = ISLocalToGlobalMappingApply(l2gmap,n_local_dofs,local_dofs,temp_global_dofs);CHKERRQ(ierr);
1253   max_local = 0;
1254   if (n_local_dofs) {
1255     max_local = temp_global_dofs[0];
1256     for (i=1;i<n_local_dofs;i++) {
1257       if (max_local < temp_global_dofs[i] ) {
1258         max_local = temp_global_dofs[i];
1259       }
1260     }
1261   }
1262   ierr = MPI_Allreduce(&max_local,&max_global,1,MPIU_INT,MPI_MAX,comm);
1263   max_global++;
1264   max_local = 0;
1265   if (n_local_dofs) {
1266     max_local = local_dofs[0];
1267     for (i=1;i<n_local_dofs;i++) {
1268       if (max_local < local_dofs[i] ) {
1269         max_local = local_dofs[i];
1270       }
1271     }
1272   }
1273   max_local++;
1274   /* allocate workspace */
1275   ierr = VecCreate(PETSC_COMM_SELF,&local_vec);CHKERRQ(ierr);
1276   ierr = VecSetSizes(local_vec,PETSC_DECIDE,max_local);CHKERRQ(ierr);
1277   ierr = VecSetType(local_vec,VECSEQ);CHKERRQ(ierr);
1278   ierr = VecCreate(comm,&global_vec);CHKERRQ(ierr);
1279   ierr = VecSetSizes(global_vec,PETSC_DECIDE,max_global);CHKERRQ(ierr);
1280   ierr = VecSetType(global_vec,VECMPI);CHKERRQ(ierr);
1281   /* create scatter */
1282   ierr = ISCreateGeneral(PETSC_COMM_SELF,n_local_dofs,local_dofs,PETSC_COPY_VALUES,&seqis);CHKERRQ(ierr);
1283   ierr = ISCreateGeneral(comm,n_local_dofs,temp_global_dofs,PETSC_COPY_VALUES,&paris);CHKERRQ(ierr);
1284   ierr = VecScatterCreate(local_vec,seqis,global_vec,paris,&scatter_ctx);CHKERRQ(ierr);
1285   ierr = ISDestroy(&seqis);CHKERRQ(ierr);
1286   ierr = ISDestroy(&paris);CHKERRQ(ierr);
1287   /* init array */
1288   ierr = VecSet(global_vec,0.0);CHKERRQ(ierr);
1289   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1290   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1291   if (local_dofs_mult) {
1292     for (i=0;i<n_local_dofs;i++) {
1293       array[local_dofs[i]]=(PetscScalar)local_dofs_mult[i];
1294     }
1295   } else {
1296     for (i=0;i<n_local_dofs;i++) {
1297       array[local_dofs[i]]=1.0;
1298     }
1299   }
1300   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1301   /* scatter into global vec and get total number of global dofs */
1302   ierr = VecScatterBegin(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1303   ierr = VecScatterEnd(scatter_ctx,local_vec,global_vec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1304   ierr = VecSum(global_vec,&globalsum);CHKERRQ(ierr);
1305   *n_global_subset = (PetscInt)PetscRealPart(globalsum);
1306   /* Fill global_vec with cumulative function for global numbering */
1307   ierr = VecGetArray(global_vec,&array);CHKERRQ(ierr);
1308   ierr = VecGetLocalSize(global_vec,&s);CHKERRQ(ierr);
1309   nlocals = 0;
1310   first_index = -1;
1311   first_found = PETSC_FALSE;
1312   for (i=0;i<s;i++) {
1313     if (!first_found && PetscRealPart(array[i]) > 0.0) {
1314       first_found = PETSC_TRUE;
1315       first_index = i;
1316     }
1317     nlocals += (PetscInt)PetscRealPart(array[i]);
1318   }
1319   ierr = MPI_Gather(&nlocals,1,MPIU_INT,dof_sizes,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1320   if (!rank_prec_comm) {
1321     dof_displs[0]=0;
1322     for (i=1;i<size_prec_comm;i++) {
1323       dof_displs[i] = dof_displs[i-1]+dof_sizes[i-1];
1324     }
1325   }
1326   ierr = MPI_Scatter(dof_displs,1,MPIU_INT,&nlocals,1,MPIU_INT,0,comm);CHKERRQ(ierr);
1327   if (first_found) {
1328     array[first_index] += (PetscScalar)nlocals;
1329     old_index = first_index;
1330     for (i=first_index+1;i<s;i++) {
1331       if (PetscRealPart(array[i]) > 0.0) {
1332         array[i] += array[old_index];
1333         old_index = i;
1334       }
1335     }
1336   }
1337   ierr = VecRestoreArray(global_vec,&array);CHKERRQ(ierr);
1338   ierr = VecSet(local_vec,0.0);CHKERRQ(ierr);
1339   ierr = VecScatterBegin(scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1340   ierr = VecScatterEnd  (scatter_ctx,global_vec,local_vec,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1341   /* get global ordering of local dofs */
1342   ierr = VecGetArray(local_vec,&array);CHKERRQ(ierr);
1343   if (local_dofs_mult) {
1344     for (i=0;i<n_local_dofs;i++) {
1345       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-local_dofs_mult[i];
1346     }
1347   } else {
1348     for (i=0;i<n_local_dofs;i++) {
1349       temp_global_dofs[i] = (PetscInt)PetscRealPart(array[local_dofs[i]])-1;
1350     }
1351   }
1352   ierr = VecRestoreArray(local_vec,&array);CHKERRQ(ierr);
1353   /* free workspace */
1354   ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
1355   ierr = VecDestroy(&local_vec);CHKERRQ(ierr);
1356   ierr = VecDestroy(&global_vec);CHKERRQ(ierr);
1357   ierr = PetscFree(dof_sizes);CHKERRQ(ierr);
1358   ierr = PetscFree(dof_displs);CHKERRQ(ierr);
1359   /* return pointer to global ordering of local dofs */
1360   *global_numbering_subset = temp_global_dofs;
1361   PetscFunctionReturn(0);
1362 }
1363