Actual source code: bddcprivate.c

  1: #include <../src/mat/impls/aij/seq/aij.h>
  2: #include <../src/ksp/pc/impls/bddc/bddc.h>
  3: #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
  4: #include <../src/mat/impls/dense/seq/dense.h>
  5: #include <petscdmplex.h>
  6: #include <petscblaslapack.h>
  7: #include <petsc/private/sfimpl.h>
  8: #include <petsc/private/dmpleximpl.h>
  9: #include <petscdmda.h>

 11: static PetscErrorCode MatMPIAIJRestrict(Mat,MPI_Comm,Mat*);

 13: /* if range is true,  it returns B s.t. span{B} = range(A)
 14:    if range is false, it returns B s.t. range(B) _|_ range(A) */
 15: PetscErrorCode MatDenseOrthogonalRangeOrComplement(Mat A, PetscBool range, PetscInt lw, PetscScalar *work, PetscReal *rwork, Mat *B)
 16: {
 17:   PetscScalar    *uwork,*data,*U, ds = 0.;
 18:   PetscReal      *sing;
 19:   PetscBLASInt   bM,bN,lwork,lierr,di = 1;
 20:   PetscInt       ulw,i,nr,nc,n;
 22: #if defined(PETSC_USE_COMPLEX)
 23:   PetscReal      *rwork2;
 24: #endif

 27:   MatGetSize(A,&nr,&nc);
 28:   if (!nr || !nc) return(0);

 30:   /* workspace */
 31:   if (!work) {
 32:     ulw  = PetscMax(PetscMax(1,5*PetscMin(nr,nc)),3*PetscMin(nr,nc)+PetscMax(nr,nc));
 33:     PetscMalloc1(ulw,&uwork);
 34:   } else {
 35:     ulw   = lw;
 36:     uwork = work;
 37:   }
 38:   n = PetscMin(nr,nc);
 39:   if (!rwork) {
 40:     PetscMalloc1(n,&sing);
 41:   } else {
 42:     sing = rwork;
 43:   }

 45:   /* SVD */
 46:   PetscMalloc1(nr*nr,&U);
 47:   PetscBLASIntCast(nr,&bM);
 48:   PetscBLASIntCast(nc,&bN);
 49:   PetscBLASIntCast(ulw,&lwork);
 50:   MatDenseGetArray(A,&data);
 51:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
 52: #if !defined(PETSC_USE_COMPLEX)
 53:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","N",&bM,&bN,data,&bM,sing,U,&bM,&ds,&di,uwork,&lwork,&lierr));
 54: #else
 55:   PetscMalloc1(5*n,&rwork2);
 56:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","N",&bM,&bN,data,&bM,sing,U,&bM,&ds,&di,uwork,&lwork,rwork2,&lierr));
 57:   PetscFree(rwork2);
 58: #endif
 59:   PetscFPTrapPop();
 60:   if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
 61:   MatDenseRestoreArray(A,&data);
 62:   for (i=0;i<n;i++) if (sing[i] < PETSC_SMALL) break;
 63:   if (!rwork) {
 64:     PetscFree(sing);
 65:   }
 66:   if (!work) {
 67:     PetscFree(uwork);
 68:   }
 69:   /* create B */
 70:   if (!range) {
 71:     MatCreateSeqDense(PETSC_COMM_SELF,nr,nr-i,NULL,B);
 72:     MatDenseGetArray(*B,&data);
 73:     PetscArraycpy(data,U+nr*i,(nr-i)*nr);
 74:   } else {
 75:     MatCreateSeqDense(PETSC_COMM_SELF,nr,i,NULL,B);
 76:     MatDenseGetArray(*B,&data);
 77:     PetscArraycpy(data,U,i*nr);
 78:   }
 79:   MatDenseRestoreArray(*B,&data);
 80:   PetscFree(U);
 81:   return(0);
 82: }

 84: /* TODO REMOVE */
 85: #if defined(PRINT_GDET)
 86: static int inc = 0;
 87: static int lev = 0;
 88: #endif

 90: PetscErrorCode PCBDDCComputeNedelecChangeEdge(Mat lG, IS edge, IS extrow, IS extcol, IS corners, Mat* Gins, Mat* GKins, PetscScalar cvals[2], PetscScalar *work, PetscReal *rwork)
 91: {
 93:   Mat            GE,GEd;
 94:   PetscInt       rsize,csize,esize;
 95:   PetscScalar    *ptr;

 98:   ISGetSize(edge,&esize);
 99:   if (!esize) return(0);
100:   ISGetSize(extrow,&rsize);
101:   ISGetSize(extcol,&csize);

103:   /* gradients */
104:   ptr  = work + 5*esize;
105:   MatCreateSubMatrix(lG,extrow,extcol,MAT_INITIAL_MATRIX,&GE);
106:   MatCreateSeqDense(PETSC_COMM_SELF,rsize,csize,ptr,Gins);
107:   MatConvert(GE,MATSEQDENSE,MAT_REUSE_MATRIX,Gins);
108:   MatDestroy(&GE);

110:   /* constants */
111:   ptr += rsize*csize;
112:   MatCreateSeqDense(PETSC_COMM_SELF,esize,csize,ptr,&GEd);
113:   MatCreateSubMatrix(lG,edge,extcol,MAT_INITIAL_MATRIX,&GE);
114:   MatConvert(GE,MATSEQDENSE,MAT_REUSE_MATRIX,&GEd);
115:   MatDestroy(&GE);
116:   MatDenseOrthogonalRangeOrComplement(GEd,PETSC_FALSE,5*esize,work,rwork,GKins);
117:   MatDestroy(&GEd);

119:   if (corners) {
120:     Mat               GEc;
121:     const PetscScalar *vals;
122:     PetscScalar       v;

124:     MatCreateSubMatrix(lG,edge,corners,MAT_INITIAL_MATRIX,&GEc);
125:     MatTransposeMatMult(GEc,*GKins,MAT_INITIAL_MATRIX,1.0,&GEd);
126:     MatDenseGetArrayRead(GEd,&vals);
127:     /* v    = PetscAbsScalar(vals[0]) */;
128:     v    = 1.;
129:     cvals[0] = vals[0]/v;
130:     cvals[1] = vals[1]/v;
131:     MatDenseRestoreArrayRead(GEd,&vals);
132:     MatScale(*GKins,1./v);
133: #if defined(PRINT_GDET)
134:     {
135:       PetscViewer viewer;
136:       char filename[256];
137:       sprintf(filename,"Gdet_l%d_r%d_cc%d.m",lev,PetscGlobalRank,inc++);
138:       PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);
139:       PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
140:       PetscObjectSetName((PetscObject)GEc,"GEc");
141:       MatView(GEc,viewer);
142:       PetscObjectSetName((PetscObject)(*GKins),"GK");
143:       MatView(*GKins,viewer);
144:       PetscObjectSetName((PetscObject)GEd,"Gproj");
145:       MatView(GEd,viewer);
146:       PetscViewerDestroy(&viewer);
147:     }
148: #endif
149:     MatDestroy(&GEd);
150:     MatDestroy(&GEc);
151:   }

153:   return(0);
154: }

156: PetscErrorCode PCBDDCNedelecSupport(PC pc)
157: {
158:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
159:   Mat_IS                 *matis = (Mat_IS*)pc->pmat->data;
160:   Mat                    G,T,conn,lG,lGt,lGis,lGall,lGe,lGinit;
161:   Vec                    tvec;
162:   PetscSF                sfv;
163:   ISLocalToGlobalMapping el2g,vl2g,fl2g,al2g;
164:   MPI_Comm               comm;
165:   IS                     lned,primals,allprimals,nedfieldlocal;
166:   IS                     *eedges,*extrows,*extcols,*alleedges;
167:   PetscBT                btv,bte,btvc,btb,btbd,btvcand,btvi,btee,bter;
168:   PetscScalar            *vals,*work;
169:   PetscReal              *rwork;
170:   const PetscInt         *idxs,*ii,*jj,*iit,*jjt;
171:   PetscInt               ne,nv,Lv,order,n,field;
172:   PetscInt               n_neigh,*neigh,*n_shared,**shared;
173:   PetscInt               i,j,extmem,cum,maxsize,nee;
174:   PetscInt               *extrow,*extrowcum,*marks,*vmarks,*gidxs;
175:   PetscInt               *sfvleaves,*sfvroots;
176:   PetscInt               *corners,*cedges;
177:   PetscInt               *ecount,**eneighs,*vcount,**vneighs;
178:   PetscInt               *emarks;
179:   PetscBool              print,eerr,done,lrc[2],conforming,global,singular,setprimal;
180:   PetscErrorCode         ierr;

183:   /* If the discrete gradient is defined for a subset of dofs and global is true,
184:      it assumes G is given in global ordering for all the dofs.
185:      Otherwise, the ordering is global for the Nedelec field */
186:   order      = pcbddc->nedorder;
187:   conforming = pcbddc->conforming;
188:   field      = pcbddc->nedfield;
189:   global     = pcbddc->nedglobal;
190:   setprimal  = PETSC_FALSE;
191:   print      = PETSC_FALSE;
192:   singular   = PETSC_FALSE;

194:   /* Command line customization */
195:   PetscOptionsBegin(PetscObjectComm((PetscObject)pc),((PetscObject)pc)->prefix,"BDDC Nedelec options","PC");
196:   PetscOptionsBool("-pc_bddc_nedelec_field_primal","All edge dofs set as primals: Toselli's algorithm C",NULL,setprimal,&setprimal,NULL);
197:   PetscOptionsBool("-pc_bddc_nedelec_singular","Infer nullspace from discrete gradient",NULL,singular,&singular,NULL);
198:   PetscOptionsInt("-pc_bddc_nedelec_order","Test variable order code (to be removed)",NULL,order,&order,NULL);
199:   /* print debug info TODO: to be removed */
200:   PetscOptionsBool("-pc_bddc_nedelec_print","Print debug info",NULL,print,&print,NULL);
201:   PetscOptionsEnd();

203:   /* Return if there are no edges in the decomposition and the problem is not singular */
204:   MatGetLocalToGlobalMapping(pc->pmat,&al2g,NULL);
205:   ISLocalToGlobalMappingGetSize(al2g,&n);
206:   PetscObjectGetComm((PetscObject)pc,&comm);
207:   if (!singular) {
208:     VecGetArrayRead(matis->counter,(const PetscScalar**)&vals);
209:     lrc[0] = PETSC_FALSE;
210:     for (i=0;i<n;i++) {
211:       if (PetscRealPart(vals[i]) > 2.) {
212:         lrc[0] = PETSC_TRUE;
213:         break;
214:       }
215:     }
216:     VecRestoreArrayRead(matis->counter,(const PetscScalar**)&vals);
217:     MPIU_Allreduce(&lrc[0],&lrc[1],1,MPIU_BOOL,MPI_LOR,comm);
218:     if (!lrc[1]) return(0);
219:   }

221:   /* Get Nedelec field */
222:   if (pcbddc->n_ISForDofsLocal && field >= pcbddc->n_ISForDofsLocal) SETERRQ2(comm,PETSC_ERR_USER,"Invalid field for Nedelec %D: number of fields is %D",field,pcbddc->n_ISForDofsLocal);
223:   if (pcbddc->n_ISForDofsLocal && field >= 0) {
224:     PetscObjectReference((PetscObject)pcbddc->ISForDofsLocal[field]);
225:     nedfieldlocal = pcbddc->ISForDofsLocal[field];
226:     ISGetLocalSize(nedfieldlocal,&ne);
227:   } else if (!pcbddc->n_ISForDofsLocal && field != PETSC_DECIDE) {
228:     ne            = n;
229:     nedfieldlocal = NULL;
230:     global        = PETSC_TRUE;
231:   } else if (field == PETSC_DECIDE) {
232:     PetscInt rst,ren,*idx;

234:     PetscArrayzero(matis->sf_leafdata,n);
235:     PetscArrayzero(matis->sf_rootdata,pc->pmat->rmap->n);
236:     MatGetOwnershipRange(pcbddc->discretegradient,&rst,&ren);
237:     for (i=rst;i<ren;i++) {
238:       PetscInt nc;

240:       MatGetRow(pcbddc->discretegradient,i,&nc,NULL,NULL);
241:       if (nc > 1) matis->sf_rootdata[i-rst] = 1;
242:       MatRestoreRow(pcbddc->discretegradient,i,&nc,NULL,NULL);
243:     }
244:     PetscSFBcastBegin(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
245:     PetscSFBcastEnd(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
246:     PetscMalloc1(n,&idx);
247:     for (i=0,ne=0;i<n;i++) if (matis->sf_leafdata[i]) idx[ne++] = i;
248:     ISCreateGeneral(comm,ne,idx,PETSC_OWN_POINTER,&nedfieldlocal);
249:   } else {
250:     SETERRQ(comm,PETSC_ERR_USER,"When multiple fields are present, the Nedelec field has to be specified");
251:   }

253:   /* Sanity checks */
254:   if (!order && !conforming) SETERRQ(comm,PETSC_ERR_SUP,"Variable order and non-conforming spaces are not supported at the same time");
255:   if (pcbddc->user_ChangeOfBasisMatrix) SETERRQ(comm,PETSC_ERR_SUP,"Cannot generate Nedelec support with user defined change of basis");
256:   if (order && ne%order) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_USER,"The number of local edge dofs %D it's not a multiple of the order %D",ne,order);

258:   /* Just set primal dofs and return */
259:   if (setprimal) {
260:     IS       enedfieldlocal;
261:     PetscInt *eidxs;

263:     PetscMalloc1(ne,&eidxs);
264:     VecGetArrayRead(matis->counter,(const PetscScalar**)&vals);
265:     if (nedfieldlocal) {
266:       ISGetIndices(nedfieldlocal,&idxs);
267:       for (i=0,cum=0;i<ne;i++) {
268:         if (PetscRealPart(vals[idxs[i]]) > 2.) {
269:           eidxs[cum++] = idxs[i];
270:         }
271:       }
272:       ISRestoreIndices(nedfieldlocal,&idxs);
273:     } else {
274:       for (i=0,cum=0;i<ne;i++) {
275:         if (PetscRealPart(vals[i]) > 2.) {
276:           eidxs[cum++] = i;
277:         }
278:       }
279:     }
280:     VecRestoreArrayRead(matis->counter,(const PetscScalar**)&vals);
281:     ISCreateGeneral(comm,cum,eidxs,PETSC_COPY_VALUES,&enedfieldlocal);
282:     PCBDDCSetPrimalVerticesLocalIS(pc,enedfieldlocal);
283:     PetscFree(eidxs);
284:     ISDestroy(&nedfieldlocal);
285:     ISDestroy(&enedfieldlocal);
286:     return(0);
287:   }

289:   /* Compute some l2g maps */
290:   if (nedfieldlocal) {
291:     IS is;

293:     /* need to map from the local Nedelec field to local numbering */
294:     ISLocalToGlobalMappingCreateIS(nedfieldlocal,&fl2g);
295:     /* need to map from the local Nedelec field to global numbering for the whole dofs*/
296:     ISLocalToGlobalMappingApplyIS(al2g,nedfieldlocal,&is);
297:     ISLocalToGlobalMappingCreateIS(is,&al2g);
298:     /* need to map from the local Nedelec field to global numbering (for Nedelec only) */
299:     if (global) {
300:       PetscObjectReference((PetscObject)al2g);
301:       el2g = al2g;
302:     } else {
303:       IS gis;

305:       ISRenumber(is,NULL,NULL,&gis);
306:       ISLocalToGlobalMappingCreateIS(gis,&el2g);
307:       ISDestroy(&gis);
308:     }
309:     ISDestroy(&is);
310:   } else {
311:     /* restore default */
312:     pcbddc->nedfield = -1;
313:     /* one ref for the destruction of al2g, one for el2g */
314:     PetscObjectReference((PetscObject)al2g);
315:     PetscObjectReference((PetscObject)al2g);
316:     el2g = al2g;
317:     fl2g = NULL;
318:   }

320:   /* Start communication to drop connections for interior edges (for cc analysis only) */
321:   PetscArrayzero(matis->sf_leafdata,n);
322:   PetscArrayzero(matis->sf_rootdata,pc->pmat->rmap->n);
323:   if (nedfieldlocal) {
324:     ISGetIndices(nedfieldlocal,&idxs);
325:     for (i=0;i<ne;i++) matis->sf_leafdata[idxs[i]] = 1;
326:     ISRestoreIndices(nedfieldlocal,&idxs);
327:   } else {
328:     for (i=0;i<ne;i++) matis->sf_leafdata[i] = 1;
329:   }
330:   PetscSFReduceBegin(matis->sf,MPIU_INT,matis->sf_leafdata,matis->sf_rootdata,MPI_SUM);
331:   PetscSFReduceEnd(matis->sf,MPIU_INT,matis->sf_leafdata,matis->sf_rootdata,MPI_SUM);

333:   if (!singular) { /* drop connections with interior edges to avoid unneeded communications and memory movements */
334:     MatDuplicate(pcbddc->discretegradient,MAT_COPY_VALUES,&G);
335:     MatSetOption(G,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);
336:     if (global) {
337:       PetscInt rst;

339:       MatGetOwnershipRange(G,&rst,NULL);
340:       for (i=0,cum=0;i<pc->pmat->rmap->n;i++) {
341:         if (matis->sf_rootdata[i] < 2) {
342:           matis->sf_rootdata[cum++] = i + rst;
343:         }
344:       }
345:       MatSetOption(G,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE);
346:       MatZeroRows(G,cum,matis->sf_rootdata,0.,NULL,NULL);
347:     } else {
348:       PetscInt *tbz;

350:       PetscMalloc1(ne,&tbz);
351:       PetscSFBcastBegin(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
352:       PetscSFBcastEnd(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
353:       ISGetIndices(nedfieldlocal,&idxs);
354:       for (i=0,cum=0;i<ne;i++)
355:         if (matis->sf_leafdata[idxs[i]] == 1)
356:           tbz[cum++] = i;
357:       ISRestoreIndices(nedfieldlocal,&idxs);
358:       ISLocalToGlobalMappingApply(el2g,cum,tbz,tbz);
359:       MatZeroRows(G,cum,tbz,0.,NULL,NULL);
360:       PetscFree(tbz);
361:     }
362:   } else { /* we need the entire G to infer the nullspace */
363:     PetscObjectReference((PetscObject)pcbddc->discretegradient);
364:     G    = pcbddc->discretegradient;
365:   }

367:   /* Extract subdomain relevant rows of G */
368:   ISLocalToGlobalMappingGetIndices(el2g,&idxs);
369:   ISCreateGeneral(comm,ne,idxs,PETSC_USE_POINTER,&lned);
370:   MatCreateSubMatrix(G,lned,NULL,MAT_INITIAL_MATRIX,&lGall);
371:   ISLocalToGlobalMappingRestoreIndices(el2g,&idxs);
372:   ISDestroy(&lned);
373:   MatConvert(lGall,MATIS,MAT_INITIAL_MATRIX,&lGis);
374:   MatDestroy(&lGall);
375:   MatISGetLocalMat(lGis,&lG);

377:   /* SF for nodal dofs communications */
378:   MatGetLocalSize(G,NULL,&Lv);
379:   MatGetLocalToGlobalMapping(lGis,NULL,&vl2g);
380:   PetscObjectReference((PetscObject)vl2g);
381:   ISLocalToGlobalMappingGetSize(vl2g,&nv);
382:   PetscSFCreate(comm,&sfv);
383:   ISLocalToGlobalMappingGetIndices(vl2g,&idxs);
384:   PetscSFSetGraphLayout(sfv,lGis->cmap,nv,NULL,PETSC_OWN_POINTER,idxs);
385:   ISLocalToGlobalMappingRestoreIndices(vl2g,&idxs);
386:   i    = singular ? 2 : 1;
387:   PetscMalloc2(i*nv,&sfvleaves,i*Lv,&sfvroots);

389:   /* Destroy temporary G created in MATIS format and modified G */
390:   PetscObjectReference((PetscObject)lG);
391:   MatDestroy(&lGis);
392:   MatDestroy(&G);

394:   if (print) {
395:     PetscObjectSetName((PetscObject)lG,"initial_lG");
396:     MatView(lG,NULL);
397:   }

399:   /* Save lG for values insertion in change of basis */
400:   MatDuplicate(lG,MAT_COPY_VALUES,&lGinit);

402:   /* Analyze the edge-nodes connections (duplicate lG) */
403:   MatDuplicate(lG,MAT_COPY_VALUES,&lGe);
404:   MatSetOption(lGe,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);
405:   PetscBTCreate(nv,&btv);
406:   PetscBTCreate(ne,&bte);
407:   PetscBTCreate(ne,&btb);
408:   PetscBTCreate(ne,&btbd);
409:   PetscBTCreate(nv,&btvcand);
410:   /* need to import the boundary specification to ensure the
411:      proper detection of coarse edges' endpoints */
412:   if (pcbddc->DirichletBoundariesLocal) {
413:     IS is;

415:     if (fl2g) {
416:       ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_MASK,pcbddc->DirichletBoundariesLocal,&is);
417:     } else {
418:       is = pcbddc->DirichletBoundariesLocal;
419:     }
420:     ISGetLocalSize(is,&cum);
421:     ISGetIndices(is,&idxs);
422:     for (i=0;i<cum;i++) {
423:       if (idxs[i] >= 0) {
424:         PetscBTSet(btb,idxs[i]);
425:         PetscBTSet(btbd,idxs[i]);
426:       }
427:     }
428:     ISRestoreIndices(is,&idxs);
429:     if (fl2g) {
430:       ISDestroy(&is);
431:     }
432:   }
433:   if (pcbddc->NeumannBoundariesLocal) {
434:     IS is;

436:     if (fl2g) {
437:       ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_MASK,pcbddc->NeumannBoundariesLocal,&is);
438:     } else {
439:       is = pcbddc->NeumannBoundariesLocal;
440:     }
441:     ISGetLocalSize(is,&cum);
442:     ISGetIndices(is,&idxs);
443:     for (i=0;i<cum;i++) {
444:       if (idxs[i] >= 0) {
445:         PetscBTSet(btb,idxs[i]);
446:       }
447:     }
448:     ISRestoreIndices(is,&idxs);
449:     if (fl2g) {
450:       ISDestroy(&is);
451:     }
452:   }

454:   /* Count neighs per dof */
455:   ISLocalToGlobalMappingGetNodeInfo(el2g,NULL,&ecount,&eneighs);
456:   ISLocalToGlobalMappingGetNodeInfo(vl2g,NULL,&vcount,&vneighs);

458:   /* need to remove coarse faces' dofs and coarse edges' dirichlet dofs
459:      for proper detection of coarse edges' endpoints */
460:   PetscBTCreate(ne,&btee);
461:   for (i=0;i<ne;i++) {
462:     if ((ecount[i] > 2 && !PetscBTLookup(btbd,i)) || (ecount[i] == 2 && PetscBTLookup(btb,i))) {
463:       PetscBTSet(btee,i);
464:     }
465:   }
466:   PetscMalloc1(ne,&marks);
467:   if (!conforming) {
468:     MatTranspose(lGe,MAT_INITIAL_MATRIX,&lGt);
469:     MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
470:   }
471:   MatGetRowIJ(lGe,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
472:   MatSeqAIJGetArray(lGe,&vals);
473:   cum  = 0;
474:   for (i=0;i<ne;i++) {
475:     /* eliminate rows corresponding to edge dofs belonging to coarse faces */
476:     if (!PetscBTLookup(btee,i)) {
477:       marks[cum++] = i;
478:       continue;
479:     }
480:     /* set badly connected edge dofs as primal */
481:     if (!conforming) {
482:       if (ii[i+1]-ii[i] != order + 1) { /* every row of G on the coarse edge should list order+1 nodal dofs */
483:         marks[cum++] = i;
484:         PetscBTSet(bte,i);
485:         for (j=ii[i];j<ii[i+1];j++) {
486:           PetscBTSet(btv,jj[j]);
487:         }
488:       } else {
489:         /* every edge dofs should be connected trough a certain number of nodal dofs
490:            to other edge dofs belonging to coarse edges
491:            - at most 2 endpoints
492:            - order-1 interior nodal dofs
493:            - no undefined nodal dofs (nconn < order)
494:         */
495:         PetscInt ends = 0,ints = 0, undef = 0;
496:         for (j=ii[i];j<ii[i+1];j++) {
497:           PetscInt v = jj[j],k;
498:           PetscInt nconn = iit[v+1]-iit[v];
499:           for (k=iit[v];k<iit[v+1];k++) if (!PetscBTLookup(btee,jjt[k])) nconn--;
500:           if (nconn > order) ends++;
501:           else if (nconn == order) ints++;
502:           else undef++;
503:         }
504:         if (undef || ends > 2 || ints != order -1) {
505:           marks[cum++] = i;
506:           PetscBTSet(bte,i);
507:           for (j=ii[i];j<ii[i+1];j++) {
508:             PetscBTSet(btv,jj[j]);
509:           }
510:         }
511:       }
512:     }
513:     /* We assume the order on the element edge is ii[i+1]-ii[i]-1 */
514:     if (!order && ii[i+1] != ii[i]) {
515:       PetscScalar val = 1./(ii[i+1]-ii[i]-1);
516:       for (j=ii[i];j<ii[i+1];j++) vals[j] = val;
517:     }
518:   }
519:   PetscBTDestroy(&btee);
520:   MatSeqAIJRestoreArray(lGe,&vals);
521:   MatRestoreRowIJ(lGe,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
522:   if (!conforming) {
523:     MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
524:     MatDestroy(&lGt);
525:   }
526:   MatZeroRows(lGe,cum,marks,0.,NULL,NULL);

528:   /* identify splitpoints and corner candidates */
529:   MatTranspose(lGe,MAT_INITIAL_MATRIX,&lGt);
530:   if (print) {
531:     PetscObjectSetName((PetscObject)lGe,"edgerestr_lG");
532:     MatView(lGe,NULL);
533:     PetscObjectSetName((PetscObject)lGt,"edgerestr_lGt");
534:     MatView(lGt,NULL);
535:   }
536:   MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
537:   MatSeqAIJGetArray(lGt,&vals);
538:   for (i=0;i<nv;i++) {
539:     PetscInt  ord = order, test = ii[i+1]-ii[i], vc = vcount[i];
540:     PetscBool sneighs = PETSC_TRUE, bdir = PETSC_FALSE;
541:     if (!order) { /* variable order */
542:       PetscReal vorder = 0.;

544:       for (j=ii[i];j<ii[i+1];j++) vorder += PetscRealPart(vals[j]);
545:       test = PetscFloorReal(vorder+10.*PETSC_SQRT_MACHINE_EPSILON);
546:       if (vorder-test > PETSC_SQRT_MACHINE_EPSILON) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected value for vorder: %g (%D)",vorder,test);
547:       ord  = 1;
548:     }
549:     if (PetscUnlikelyDebug(test%ord)) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected number of edge dofs %D connected with nodal dof %D with order %D",test,i,ord);
550:     for (j=ii[i];j<ii[i+1] && sneighs;j++) {
551:       if (PetscBTLookup(btbd,jj[j])) {
552:         bdir = PETSC_TRUE;
553:         break;
554:       }
555:       if (vc != ecount[jj[j]]) {
556:         sneighs = PETSC_FALSE;
557:       } else {
558:         PetscInt k,*vn = vneighs[i], *en = eneighs[jj[j]];
559:         for (k=0;k<vc;k++) {
560:           if (vn[k] != en[k]) {
561:             sneighs = PETSC_FALSE;
562:             break;
563:           }
564:         }
565:       }
566:     }
567:     if (!sneighs || test >= 3*ord || bdir) { /* splitpoints */
568:       if (print) PetscPrintf(PETSC_COMM_SELF,"SPLITPOINT %D (%D %D %D)\n",i,!sneighs,test >= 3*ord,bdir);
569:       PetscBTSet(btv,i);
570:     } else if (test == ord) {
571:       if (order == 1 || (!order && ii[i+1]-ii[i] == 1)) {
572:         if (print) PetscPrintf(PETSC_COMM_SELF,"ENDPOINT %D\n",i);
573:         PetscBTSet(btv,i);
574:       } else {
575:         if (print) PetscPrintf(PETSC_COMM_SELF,"CORNER CANDIDATE %D\n",i);
576:         PetscBTSet(btvcand,i);
577:       }
578:     }
579:   }
580:   ISLocalToGlobalMappingRestoreNodeInfo(el2g,NULL,&ecount,&eneighs);
581:   ISLocalToGlobalMappingRestoreNodeInfo(vl2g,NULL,&vcount,&vneighs);
582:   PetscBTDestroy(&btbd);

584:   /* a candidate is valid if it is connected to another candidate via a non-primal edge dof */
585:   if (order != 1) {
586:     if (print) PetscPrintf(PETSC_COMM_SELF,"INSPECTING CANDIDATES\n");
587:     MatGetRowIJ(lGe,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
588:     for (i=0;i<nv;i++) {
589:       if (PetscBTLookup(btvcand,i)) {
590:         PetscBool found = PETSC_FALSE;
591:         for (j=ii[i];j<ii[i+1] && !found;j++) {
592:           PetscInt k,e = jj[j];
593:           if (PetscBTLookup(bte,e)) continue;
594:           for (k=iit[e];k<iit[e+1];k++) {
595:             PetscInt v = jjt[k];
596:             if (v != i && PetscBTLookup(btvcand,v)) {
597:               found = PETSC_TRUE;
598:               break;
599:             }
600:           }
601:         }
602:         if (!found) {
603:           if (print) PetscPrintf(PETSC_COMM_SELF,"  CANDIDATE %D CLEARED\n",i);
604:           PetscBTClear(btvcand,i);
605:         } else {
606:           if (print) PetscPrintf(PETSC_COMM_SELF,"  CANDIDATE %D ACCEPTED\n",i);
607:         }
608:       }
609:     }
610:     MatRestoreRowIJ(lGe,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
611:   }
612:   MatSeqAIJRestoreArray(lGt,&vals);
613:   MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
614:   MatDestroy(&lGe);

616:   /* Get the local G^T explicitly */
617:   MatDestroy(&lGt);
618:   MatTranspose(lG,MAT_INITIAL_MATRIX,&lGt);
619:   MatSetOption(lGt,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);

621:   /* Mark interior nodal dofs */
622:   ISLocalToGlobalMappingGetInfo(vl2g,&n_neigh,&neigh,&n_shared,&shared);
623:   PetscBTCreate(nv,&btvi);
624:   for (i=1;i<n_neigh;i++) {
625:     for (j=0;j<n_shared[i];j++) {
626:       PetscBTSet(btvi,shared[i][j]);
627:     }
628:   }
629:   ISLocalToGlobalMappingRestoreInfo(vl2g,&n_neigh,&neigh,&n_shared,&shared);

631:   /* communicate corners and splitpoints */
632:   PetscMalloc1(nv,&vmarks);
633:   PetscArrayzero(sfvleaves,nv);
634:   PetscArrayzero(sfvroots,Lv);
635:   for (i=0;i<nv;i++) if (PetscUnlikely(PetscBTLookup(btv,i))) sfvleaves[i] = 1;

637:   if (print) {
638:     IS tbz;

640:     cum = 0;
641:     for (i=0;i<nv;i++)
642:       if (sfvleaves[i])
643:         vmarks[cum++] = i;

645:     ISCreateGeneral(PETSC_COMM_SELF,cum,vmarks,PETSC_COPY_VALUES,&tbz);
646:     PetscObjectSetName((PetscObject)tbz,"corners_to_be_zeroed_local");
647:     ISView(tbz,NULL);
648:     ISDestroy(&tbz);
649:   }

651:   PetscSFReduceBegin(sfv,MPIU_INT,sfvleaves,sfvroots,MPI_SUM);
652:   PetscSFReduceEnd(sfv,MPIU_INT,sfvleaves,sfvroots,MPI_SUM);
653:   PetscSFBcastBegin(sfv,MPIU_INT,sfvroots,sfvleaves,MPI_REPLACE);
654:   PetscSFBcastEnd(sfv,MPIU_INT,sfvroots,sfvleaves,MPI_REPLACE);

656:   /* Zero rows of lGt corresponding to identified corners
657:      and interior nodal dofs */
658:   cum = 0;
659:   for (i=0;i<nv;i++) {
660:     if (sfvleaves[i]) {
661:       vmarks[cum++] = i;
662:       PetscBTSet(btv,i);
663:     }
664:     if (!PetscBTLookup(btvi,i)) vmarks[cum++] = i;
665:   }
666:   PetscBTDestroy(&btvi);
667:   if (print) {
668:     IS tbz;

670:     ISCreateGeneral(PETSC_COMM_SELF,cum,vmarks,PETSC_COPY_VALUES,&tbz);
671:     PetscObjectSetName((PetscObject)tbz,"corners_to_be_zeroed_with_interior");
672:     ISView(tbz,NULL);
673:     ISDestroy(&tbz);
674:   }
675:   MatZeroRows(lGt,cum,vmarks,0.,NULL,NULL);
676:   PetscFree(vmarks);
677:   PetscSFDestroy(&sfv);
678:   PetscFree2(sfvleaves,sfvroots);

680:   /* Recompute G */
681:   MatDestroy(&lG);
682:   MatTranspose(lGt,MAT_INITIAL_MATRIX,&lG);
683:   if (print) {
684:     PetscObjectSetName((PetscObject)lG,"used_lG");
685:     MatView(lG,NULL);
686:     PetscObjectSetName((PetscObject)lGt,"used_lGt");
687:     MatView(lGt,NULL);
688:   }

690:   /* Get primal dofs (if any) */
691:   cum = 0;
692:   for (i=0;i<ne;i++) {
693:     if (PetscUnlikely(PetscBTLookup(bte,i))) marks[cum++] = i;
694:   }
695:   if (fl2g) {
696:     ISLocalToGlobalMappingApply(fl2g,cum,marks,marks);
697:   }
698:   ISCreateGeneral(comm,cum,marks,PETSC_COPY_VALUES,&primals);
699:   if (print) {
700:     PetscObjectSetName((PetscObject)primals,"prescribed_primal_dofs");
701:     ISView(primals,NULL);
702:   }
703:   PetscBTDestroy(&bte);
704:   /* TODO: what if the user passed in some of them ?  */
705:   PCBDDCSetPrimalVerticesLocalIS(pc,primals);
706:   ISDestroy(&primals);

708:   /* Compute edge connectivity */
709:   PetscObjectSetOptionsPrefix((PetscObject)lG,"econn_");

711:   /* Symbolic conn = lG*lGt */
712:   MatProductCreate(lG,lGt,NULL,&conn);
713:   MatProductSetType(conn,MATPRODUCT_AB);
714:   MatProductSetAlgorithm(conn,"default");
715:   MatProductSetFill(conn,PETSC_DEFAULT);
716:   PetscObjectSetOptionsPrefix((PetscObject)conn,"econn_");
717:   MatProductSetFromOptions(conn);
718:   MatProductSymbolic(conn);

720:   MatGetRowIJ(conn,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
721:   if (fl2g) {
722:     PetscBT   btf;
723:     PetscInt  *iia,*jja,*iiu,*jju;
724:     PetscBool rest = PETSC_FALSE,free = PETSC_FALSE;

726:     /* create CSR for all local dofs */
727:     PetscMalloc1(n+1,&iia);
728:     if (pcbddc->mat_graph->nvtxs_csr) { /* the user has passed in a CSR graph */
729:       if (pcbddc->mat_graph->nvtxs_csr != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_USER,"Invalid size of CSR graph %D. Should be %D",pcbddc->mat_graph->nvtxs_csr,n);
730:       iiu = pcbddc->mat_graph->xadj;
731:       jju = pcbddc->mat_graph->adjncy;
732:     } else if (pcbddc->use_local_adj) {
733:       rest = PETSC_TRUE;
734:       MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&i,(const PetscInt**)&iiu,(const PetscInt**)&jju,&done);
735:     } else {
736:       free   = PETSC_TRUE;
737:       PetscMalloc2(n+1,&iiu,n,&jju);
738:       iiu[0] = 0;
739:       for (i=0;i<n;i++) {
740:         iiu[i+1] = i+1;
741:         jju[i]   = -1;
742:       }
743:     }

745:     /* import sizes of CSR */
746:     iia[0] = 0;
747:     for (i=0;i<n;i++) iia[i+1] = iiu[i+1]-iiu[i];

749:     /* overwrite entries corresponding to the Nedelec field */
750:     PetscBTCreate(n,&btf);
751:     ISGetIndices(nedfieldlocal,&idxs);
752:     for (i=0;i<ne;i++) {
753:       PetscBTSet(btf,idxs[i]);
754:       iia[idxs[i]+1] = ii[i+1]-ii[i];
755:     }

757:     /* iia in CSR */
758:     for (i=0;i<n;i++) iia[i+1] += iia[i];

760:     /* jja in CSR */
761:     PetscMalloc1(iia[n],&jja);
762:     for (i=0;i<n;i++)
763:       if (!PetscBTLookup(btf,i))
764:         for (j=0;j<iiu[i+1]-iiu[i];j++)
765:           jja[iia[i]+j] = jju[iiu[i]+j];

767:     /* map edge dofs connectivity */
768:     if (jj) {
769:       ISLocalToGlobalMappingApply(fl2g,ii[ne],jj,(PetscInt *)jj);
770:       for (i=0;i<ne;i++) {
771:         PetscInt e = idxs[i];
772:         for (j=0;j<ii[i+1]-ii[i];j++) jja[iia[e]+j] = jj[ii[i]+j];
773:       }
774:     }
775:     ISRestoreIndices(nedfieldlocal,&idxs);
776:     PCBDDCSetLocalAdjacencyGraph(pc,n,iia,jja,PETSC_OWN_POINTER);
777:     if (rest) {
778:       MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&i,(const PetscInt**)&iiu,(const PetscInt**)&jju,&done);
779:     }
780:     if (free) {
781:       PetscFree2(iiu,jju);
782:     }
783:     PetscBTDestroy(&btf);
784:   } else {
785:     PCBDDCSetLocalAdjacencyGraph(pc,n,ii,jj,PETSC_USE_POINTER);
786:   }

788:   /* Analyze interface for edge dofs */
789:   PCBDDCAnalyzeInterface(pc);
790:   pcbddc->mat_graph->twodim = PETSC_FALSE;

792:   /* Get coarse edges in the edge space */
793:   PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,&nee,&alleedges,&allprimals);
794:   MatRestoreRowIJ(conn,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);

796:   if (fl2g) {
797:     ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_DROP,allprimals,&primals);
798:     PetscMalloc1(nee,&eedges);
799:     for (i=0;i<nee;i++) {
800:       ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_DROP,alleedges[i],&eedges[i]);
801:     }
802:   } else {
803:     eedges  = alleedges;
804:     primals = allprimals;
805:   }

807:   /* Mark fine edge dofs with their coarse edge id */
808:   PetscArrayzero(marks,ne);
809:   ISGetLocalSize(primals,&cum);
810:   ISGetIndices(primals,&idxs);
811:   for (i=0;i<cum;i++) marks[idxs[i]] = nee+1;
812:   ISRestoreIndices(primals,&idxs);
813:   if (print) {
814:     PetscObjectSetName((PetscObject)primals,"obtained_primal_dofs");
815:     ISView(primals,NULL);
816:   }

818:   maxsize = 0;
819:   for (i=0;i<nee;i++) {
820:     PetscInt size,mark = i+1;

822:     ISGetLocalSize(eedges[i],&size);
823:     ISGetIndices(eedges[i],&idxs);
824:     for (j=0;j<size;j++) marks[idxs[j]] = mark;
825:     ISRestoreIndices(eedges[i],&idxs);
826:     maxsize = PetscMax(maxsize,size);
827:   }

829:   /* Find coarse edge endpoints */
830:   MatGetRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
831:   MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
832:   for (i=0;i<nee;i++) {
833:     PetscInt mark = i+1,size;

835:     ISGetLocalSize(eedges[i],&size);
836:     if (!size && nedfieldlocal) continue;
837:     if (!size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected zero sized edge %D",i);
838:     ISGetIndices(eedges[i],&idxs);
839:     if (print) {
840:       PetscPrintf(PETSC_COMM_SELF,"ENDPOINTS ANALYSIS EDGE %D\n",i);
841:       ISView(eedges[i],NULL);
842:     }
843:     for (j=0;j<size;j++) {
844:       PetscInt k, ee = idxs[j];
845:       if (print) PetscPrintf(PETSC_COMM_SELF,"  idx %D\n",ee);
846:       for (k=ii[ee];k<ii[ee+1];k++) {
847:         if (print) PetscPrintf(PETSC_COMM_SELF,"    inspect %D\n",jj[k]);
848:         if (PetscBTLookup(btv,jj[k])) {
849:           if (print) PetscPrintf(PETSC_COMM_SELF,"      corner found (already set) %D\n",jj[k]);
850:         } else if (PetscBTLookup(btvcand,jj[k])) { /* is it ok? */
851:           PetscInt  k2;
852:           PetscBool corner = PETSC_FALSE;
853:           for (k2 = iit[jj[k]];k2 < iit[jj[k]+1];k2++) {
854:             if (print) PetscPrintf(PETSC_COMM_SELF,"        INSPECTING %D: mark %D (ref mark %D), boundary %D\n",jjt[k2],marks[jjt[k2]],mark,!!PetscBTLookup(btb,jjt[k2]));
855:             /* it's a corner if either is connected with an edge dof belonging to a different cc or
856:                if the edge dof lie on the natural part of the boundary */
857:             if ((marks[jjt[k2]] && marks[jjt[k2]] != mark) || (!marks[jjt[k2]] && PetscBTLookup(btb,jjt[k2]))) {
858:               corner = PETSC_TRUE;
859:               break;
860:             }
861:           }
862:           if (corner) { /* found the nodal dof corresponding to the endpoint of the edge */
863:             if (print) PetscPrintf(PETSC_COMM_SELF,"        corner found %D\n",jj[k]);
864:             PetscBTSet(btv,jj[k]);
865:           } else {
866:             if (print) PetscPrintf(PETSC_COMM_SELF,"        no corners found\n");
867:           }
868:         }
869:       }
870:     }
871:     ISRestoreIndices(eedges[i],&idxs);
872:   }
873:   MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
874:   MatRestoreRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
875:   PetscBTDestroy(&btb);

877:   /* Reset marked primal dofs */
878:   ISGetLocalSize(primals,&cum);
879:   ISGetIndices(primals,&idxs);
880:   for (i=0;i<cum;i++) marks[idxs[i]] = 0;
881:   ISRestoreIndices(primals,&idxs);

883:   /* Now use the initial lG */
884:   MatDestroy(&lG);
885:   MatDestroy(&lGt);
886:   lG   = lGinit;
887:   MatTranspose(lG,MAT_INITIAL_MATRIX,&lGt);

889:   /* Compute extended cols indices */
890:   PetscBTCreate(nv,&btvc);
891:   PetscBTCreate(nee,&bter);
892:   MatGetRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
893:   MatSeqAIJGetMaxRowNonzeros(lG,&i);
894:   i   *= maxsize;
895:   PetscCalloc1(nee,&extcols);
896:   PetscMalloc2(i,&extrow,i,&gidxs);
897:   eerr = PETSC_FALSE;
898:   for (i=0;i<nee;i++) {
899:     PetscInt size,found = 0;

901:     cum  = 0;
902:     ISGetLocalSize(eedges[i],&size);
903:     if (!size && nedfieldlocal) continue;
904:     if (!size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected zero sized edge %D",i);
905:     ISGetIndices(eedges[i],&idxs);
906:     PetscBTMemzero(nv,btvc);
907:     for (j=0;j<size;j++) {
908:       PetscInt k,ee = idxs[j];
909:       for (k=ii[ee];k<ii[ee+1];k++) {
910:         PetscInt vv = jj[k];
911:         if (!PetscBTLookup(btv,vv)) extrow[cum++] = vv;
912:         else if (!PetscBTLookupSet(btvc,vv)) found++;
913:       }
914:     }
915:     ISRestoreIndices(eedges[i],&idxs);
916:     PetscSortRemoveDupsInt(&cum,extrow);
917:     ISLocalToGlobalMappingApply(vl2g,cum,extrow,gidxs);
918:     PetscSortIntWithArray(cum,gidxs,extrow);
919:     ISCreateGeneral(PETSC_COMM_SELF,cum,extrow,PETSC_COPY_VALUES,&extcols[i]);
920:     /* it may happen that endpoints are not defined at this point
921:        if it is the case, mark this edge for a second pass */
922:     if (cum != size -1 || found != 2) {
923:       PetscBTSet(bter,i);
924:       if (print) {
925:         PetscObjectSetName((PetscObject)eedges[i],"error_edge");
926:         ISView(eedges[i],NULL);
927:         PetscObjectSetName((PetscObject)extcols[i],"error_extcol");
928:         ISView(extcols[i],NULL);
929:       }
930:       eerr = PETSC_TRUE;
931:     }
932:   }
933:   /* if (eerr) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected SIZE OF EDGE > EXTCOL FIRST PASS"); */
934:   MPIU_Allreduce(&eerr,&done,1,MPIU_BOOL,MPI_LOR,comm);
935:   if (done) {
936:     PetscInt *newprimals;

938:     PetscMalloc1(ne,&newprimals);
939:     ISGetLocalSize(primals,&cum);
940:     ISGetIndices(primals,&idxs);
941:     PetscArraycpy(newprimals,idxs,cum);
942:     ISRestoreIndices(primals,&idxs);
943:     MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
944:     if (print) PetscPrintf(PETSC_COMM_SELF,"DOING SECOND PASS (eerr %D)\n",eerr);
945:     for (i=0;i<nee;i++) {
946:       PetscBool has_candidates = PETSC_FALSE;
947:       if (PetscBTLookup(bter,i)) {
948:         PetscInt size,mark = i+1;

950:         ISGetLocalSize(eedges[i],&size);
951:         ISGetIndices(eedges[i],&idxs);
952:         /* for (j=0;j<size;j++) newprimals[cum++] = idxs[j]; */
953:         for (j=0;j<size;j++) {
954:           PetscInt k,ee = idxs[j];
955:           if (print) PetscPrintf(PETSC_COMM_SELF,"Inspecting edge dof %D [%D %D)\n",ee,ii[ee],ii[ee+1]);
956:           for (k=ii[ee];k<ii[ee+1];k++) {
957:             /* set all candidates located on the edge as corners */
958:             if (PetscBTLookup(btvcand,jj[k])) {
959:               PetscInt k2,vv = jj[k];
960:               has_candidates = PETSC_TRUE;
961:               if (print) PetscPrintf(PETSC_COMM_SELF,"  Candidate set to vertex %D\n",vv);
962:               PetscBTSet(btv,vv);
963:               /* set all edge dofs connected to candidate as primals */
964:               for (k2=iit[vv];k2<iit[vv+1];k2++) {
965:                 if (marks[jjt[k2]] == mark) {
966:                   PetscInt k3,ee2 = jjt[k2];
967:                   if (print) PetscPrintf(PETSC_COMM_SELF,"    Connected edge dof set to primal %D\n",ee2);
968:                   newprimals[cum++] = ee2;
969:                   /* finally set the new corners */
970:                   for (k3=ii[ee2];k3<ii[ee2+1];k3++) {
971:                     if (print) PetscPrintf(PETSC_COMM_SELF,"      Connected nodal dof set to vertex %D\n",jj[k3]);
972:                     PetscBTSet(btv,jj[k3]);
973:                   }
974:                 }
975:               }
976:             } else {
977:               if (print) PetscPrintf(PETSC_COMM_SELF,"  Not a candidate vertex %D\n",jj[k]);
978:             }
979:           }
980:         }
981:         if (!has_candidates) { /* circular edge */
982:           PetscInt k, ee = idxs[0],*tmarks;

984:           PetscCalloc1(ne,&tmarks);
985:           if (print) PetscPrintf(PETSC_COMM_SELF,"  Circular edge %D\n",i);
986:           for (k=ii[ee];k<ii[ee+1];k++) {
987:             PetscInt k2;
988:             if (print) PetscPrintf(PETSC_COMM_SELF,"    Set to corner %D\n",jj[k]);
989:             PetscBTSet(btv,jj[k]);
990:             for (k2=iit[jj[k]];k2<iit[jj[k]+1];k2++) tmarks[jjt[k2]]++;
991:           }
992:           for (j=0;j<size;j++) {
993:             if (tmarks[idxs[j]] > 1) {
994:               if (print) PetscPrintf(PETSC_COMM_SELF,"  Edge dof set to primal %D\n",idxs[j]);
995:               newprimals[cum++] = idxs[j];
996:             }
997:           }
998:           PetscFree(tmarks);
999:         }
1000:         ISRestoreIndices(eedges[i],&idxs);
1001:       }
1002:       ISDestroy(&extcols[i]);
1003:     }
1004:     PetscFree(extcols);
1005:     MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
1006:     PetscSortRemoveDupsInt(&cum,newprimals);
1007:     if (fl2g) {
1008:       ISLocalToGlobalMappingApply(fl2g,cum,newprimals,newprimals);
1009:       ISDestroy(&primals);
1010:       for (i=0;i<nee;i++) {
1011:         ISDestroy(&eedges[i]);
1012:       }
1013:       PetscFree(eedges);
1014:     }
1015:     PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,&nee,&alleedges,&allprimals);
1016:     ISCreateGeneral(comm,cum,newprimals,PETSC_COPY_VALUES,&primals);
1017:     PetscFree(newprimals);
1018:     PCBDDCSetPrimalVerticesLocalIS(pc,primals);
1019:     ISDestroy(&primals);
1020:     PCBDDCAnalyzeInterface(pc);
1021:     pcbddc->mat_graph->twodim = PETSC_FALSE;
1022:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,&nee,&alleedges,&allprimals);
1023:     if (fl2g) {
1024:       ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_DROP,allprimals,&primals);
1025:       PetscMalloc1(nee,&eedges);
1026:       for (i=0;i<nee;i++) {
1027:         ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_DROP,alleedges[i],&eedges[i]);
1028:       }
1029:     } else {
1030:       eedges  = alleedges;
1031:       primals = allprimals;
1032:     }
1033:     PetscCalloc1(nee,&extcols);

1035:     /* Mark again */
1036:     PetscArrayzero(marks,ne);
1037:     for (i=0;i<nee;i++) {
1038:       PetscInt size,mark = i+1;

1040:       ISGetLocalSize(eedges[i],&size);
1041:       ISGetIndices(eedges[i],&idxs);
1042:       for (j=0;j<size;j++) marks[idxs[j]] = mark;
1043:       ISRestoreIndices(eedges[i],&idxs);
1044:     }
1045:     if (print) {
1046:       PetscObjectSetName((PetscObject)primals,"obtained_primal_dofs_secondpass");
1047:       ISView(primals,NULL);
1048:     }

1050:     /* Recompute extended cols */
1051:     eerr = PETSC_FALSE;
1052:     for (i=0;i<nee;i++) {
1053:       PetscInt size;

1055:       cum  = 0;
1056:       ISGetLocalSize(eedges[i],&size);
1057:       if (!size && nedfieldlocal) continue;
1058:       if (!size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected zero sized edge %D",i);
1059:       ISGetIndices(eedges[i],&idxs);
1060:       for (j=0;j<size;j++) {
1061:         PetscInt k,ee = idxs[j];
1062:         for (k=ii[ee];k<ii[ee+1];k++) if (!PetscBTLookup(btv,jj[k])) extrow[cum++] = jj[k];
1063:       }
1064:       ISRestoreIndices(eedges[i],&idxs);
1065:       PetscSortRemoveDupsInt(&cum,extrow);
1066:       ISLocalToGlobalMappingApply(vl2g,cum,extrow,gidxs);
1067:       PetscSortIntWithArray(cum,gidxs,extrow);
1068:       ISCreateGeneral(PETSC_COMM_SELF,cum,extrow,PETSC_COPY_VALUES,&extcols[i]);
1069:       if (cum != size -1) {
1070:         if (print) {
1071:           PetscObjectSetName((PetscObject)eedges[i],"error_edge_secondpass");
1072:           ISView(eedges[i],NULL);
1073:           PetscObjectSetName((PetscObject)extcols[i],"error_extcol_secondpass");
1074:           ISView(extcols[i],NULL);
1075:         }
1076:         eerr = PETSC_TRUE;
1077:       }
1078:     }
1079:   }
1080:   MatRestoreRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1081:   PetscFree2(extrow,gidxs);
1082:   PetscBTDestroy(&bter);
1083:   if (print) { PCBDDCGraphASCIIView(pcbddc->mat_graph,5,PETSC_VIEWER_STDOUT_SELF); }
1084:   /* an error should not occur at this point */
1085:   if (eerr) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected SIZE OF EDGE > EXTCOL SECOND PASS");

1087:   /* Check the number of endpoints */
1088:   MatGetRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1089:   PetscMalloc1(2*nee,&corners);
1090:   PetscMalloc1(nee,&cedges);
1091:   for (i=0;i<nee;i++) {
1092:     PetscInt size, found = 0, gc[2];

1094:     /* init with defaults */
1095:     cedges[i] = corners[i*2] = corners[i*2+1] = -1;
1096:     ISGetLocalSize(eedges[i],&size);
1097:     if (!size && nedfieldlocal) continue;
1098:     if (!size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected zero sized edge %D",i);
1099:     ISGetIndices(eedges[i],&idxs);
1100:     PetscBTMemzero(nv,btvc);
1101:     for (j=0;j<size;j++) {
1102:       PetscInt k,ee = idxs[j];
1103:       for (k=ii[ee];k<ii[ee+1];k++) {
1104:         PetscInt vv = jj[k];
1105:         if (PetscBTLookup(btv,vv) && !PetscBTLookupSet(btvc,vv)) {
1106:           if (found == 2) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Found more then two corners for edge %D",i);
1107:           corners[i*2+found++] = vv;
1108:         }
1109:       }
1110:     }
1111:     if (found != 2) {
1112:       PetscInt e;
1113:       if (fl2g) {
1114:         ISLocalToGlobalMappingApply(fl2g,1,idxs,&e);
1115:       } else {
1116:         e = idxs[0];
1117:       }
1118:       SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Found %D corners for edge %D (astart %D, estart %D)",found,i,e,idxs[0]);
1119:     }

1121:     /* get primal dof index on this coarse edge */
1122:     ISLocalToGlobalMappingApply(vl2g,2,corners+2*i,gc);
1123:     if (gc[0] > gc[1]) {
1124:       PetscInt swap  = corners[2*i];
1125:       corners[2*i]   = corners[2*i+1];
1126:       corners[2*i+1] = swap;
1127:     }
1128:     cedges[i] = idxs[size-1];
1129:     ISRestoreIndices(eedges[i],&idxs);
1130:     if (print) PetscPrintf(PETSC_COMM_SELF,"EDGE %D: ce %D, corners (%D,%D)\n",i,cedges[i],corners[2*i],corners[2*i+1]);
1131:   }
1132:   MatRestoreRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1133:   PetscBTDestroy(&btvc);

1135:   if (PetscDefined(USE_DEBUG)) {
1136:     /* Inspects columns of lG (rows of lGt) and make sure the change of basis will
1137:      not interfere with neighbouring coarse edges */
1138:     PetscMalloc1(nee+1,&emarks);
1139:     MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1140:     for (i=0;i<nv;i++) {
1141:       PetscInt emax = 0,eemax = 0;

1143:       if (ii[i+1]==ii[i] || PetscBTLookup(btv,i)) continue;
1144:       PetscArrayzero(emarks,nee+1);
1145:       for (j=ii[i];j<ii[i+1];j++) emarks[marks[jj[j]]]++;
1146:       for (j=1;j<nee+1;j++) {
1147:         if (emax < emarks[j]) {
1148:           emax = emarks[j];
1149:           eemax = j;
1150:         }
1151:       }
1152:       /* not relevant for edges */
1153:       if (!eemax) continue;

1155:       for (j=ii[i];j<ii[i+1];j++) {
1156:         if (marks[jj[j]] && marks[jj[j]] != eemax) {
1157:           SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_SUP,"Found 2 coarse edges (id %D and %D) connected through the %D nodal dof at edge dof %D",marks[jj[j]]-1,eemax,i,jj[j]);
1158:         }
1159:       }
1160:     }
1161:     PetscFree(emarks);
1162:     MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1163:   }

1165:   /* Compute extended rows indices for edge blocks of the change of basis */
1166:   MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1167:   MatSeqAIJGetMaxRowNonzeros(lGt,&extmem);
1168:   extmem *= maxsize;
1169:   PetscMalloc1(extmem*nee,&extrow);
1170:   PetscMalloc1(nee,&extrows);
1171:   PetscCalloc1(nee,&extrowcum);
1172:   for (i=0;i<nv;i++) {
1173:     PetscInt mark = 0,size,start;

1175:     if (ii[i+1]==ii[i] || PetscBTLookup(btv,i)) continue;
1176:     for (j=ii[i];j<ii[i+1];j++)
1177:       if (marks[jj[j]] && !mark)
1178:         mark = marks[jj[j]];

1180:     /* not relevant */
1181:     if (!mark) continue;

1183:     /* import extended row */
1184:     mark--;
1185:     start = mark*extmem+extrowcum[mark];
1186:     size = ii[i+1]-ii[i];
1187:     if (extrowcum[mark] + size > extmem) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not enough memory allocated %D > %D",extrowcum[mark] + size,extmem);
1188:     PetscArraycpy(extrow+start,jj+ii[i],size);
1189:     extrowcum[mark] += size;
1190:   }
1191:   MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1192:   MatDestroy(&lGt);
1193:   PetscFree(marks);

1195:   /* Compress extrows */
1196:   cum  = 0;
1197:   for (i=0;i<nee;i++) {
1198:     PetscInt size = extrowcum[i],*start = extrow + i*extmem;
1199:     PetscSortRemoveDupsInt(&size,start);
1200:     ISCreateGeneral(PETSC_COMM_SELF,size,start,PETSC_USE_POINTER,&extrows[i]);
1201:     cum  = PetscMax(cum,size);
1202:   }
1203:   PetscFree(extrowcum);
1204:   PetscBTDestroy(&btv);
1205:   PetscBTDestroy(&btvcand);

1207:   /* Workspace for lapack inner calls and VecSetValues */
1208:   PetscMalloc2((5+cum+maxsize)*maxsize,&work,maxsize,&rwork);

1210:   /* Create change of basis matrix (preallocation can be improved) */
1211:   MatCreate(comm,&T);
1212:   MatSetSizes(T,pc->pmat->rmap->n,pc->pmat->rmap->n,
1213:                        pc->pmat->rmap->N,pc->pmat->rmap->N);
1214:   MatSetType(T,MATAIJ);
1215:   MatSeqAIJSetPreallocation(T,10,NULL);
1216:   MatMPIAIJSetPreallocation(T,10,NULL,10,NULL);
1217:   MatSetLocalToGlobalMapping(T,al2g,al2g);
1218:   MatSetOption(T,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
1219:   MatSetOption(T,MAT_ROW_ORIENTED,PETSC_FALSE);
1220:   ISLocalToGlobalMappingDestroy(&al2g);

1222:   /* Defaults to identity */
1223:   MatCreateVecs(pc->pmat,&tvec,NULL);
1224:   VecSet(tvec,1.0);
1225:   MatDiagonalSet(T,tvec,INSERT_VALUES);
1226:   VecDestroy(&tvec);

1228:   /* Create discrete gradient for the coarser level if needed */
1229:   MatDestroy(&pcbddc->nedcG);
1230:   ISDestroy(&pcbddc->nedclocal);
1231:   if (pcbddc->current_level < pcbddc->max_levels) {
1232:     ISLocalToGlobalMapping cel2g,cvl2g;
1233:     IS                     wis,gwis;
1234:     PetscInt               cnv,cne;

1236:     ISCreateGeneral(comm,nee,cedges,PETSC_COPY_VALUES,&wis);
1237:     if (fl2g) {
1238:       ISLocalToGlobalMappingApplyIS(fl2g,wis,&pcbddc->nedclocal);
1239:     } else {
1240:       PetscObjectReference((PetscObject)wis);
1241:       pcbddc->nedclocal = wis;
1242:     }
1243:     ISLocalToGlobalMappingApplyIS(el2g,wis,&gwis);
1244:     ISDestroy(&wis);
1245:     ISRenumber(gwis,NULL,&cne,&wis);
1246:     ISLocalToGlobalMappingCreateIS(wis,&cel2g);
1247:     ISDestroy(&wis);
1248:     ISDestroy(&gwis);

1250:     ISCreateGeneral(comm,2*nee,corners,PETSC_USE_POINTER,&wis);
1251:     ISLocalToGlobalMappingApplyIS(vl2g,wis,&gwis);
1252:     ISDestroy(&wis);
1253:     ISRenumber(gwis,NULL,&cnv,&wis);
1254:     ISLocalToGlobalMappingCreateIS(wis,&cvl2g);
1255:     ISDestroy(&wis);
1256:     ISDestroy(&gwis);

1258:     MatCreate(comm,&pcbddc->nedcG);
1259:     MatSetSizes(pcbddc->nedcG,PETSC_DECIDE,PETSC_DECIDE,cne,cnv);
1260:     MatSetType(pcbddc->nedcG,MATAIJ);
1261:     MatSeqAIJSetPreallocation(pcbddc->nedcG,2,NULL);
1262:     MatMPIAIJSetPreallocation(pcbddc->nedcG,2,NULL,2,NULL);
1263:     MatSetLocalToGlobalMapping(pcbddc->nedcG,cel2g,cvl2g);
1264:     ISLocalToGlobalMappingDestroy(&cel2g);
1265:     ISLocalToGlobalMappingDestroy(&cvl2g);
1266:   }
1267:   ISLocalToGlobalMappingDestroy(&vl2g);

1269: #if defined(PRINT_GDET)
1270:   inc = 0;
1271:   lev = pcbddc->current_level;
1272: #endif

1274:   /* Insert values in the change of basis matrix */
1275:   for (i=0;i<nee;i++) {
1276:     Mat         Gins = NULL, GKins = NULL;
1277:     IS          cornersis = NULL;
1278:     PetscScalar cvals[2];

1280:     if (pcbddc->nedcG) {
1281:       ISCreateGeneral(PETSC_COMM_SELF,2,corners+2*i,PETSC_USE_POINTER,&cornersis);
1282:     }
1283:     PCBDDCComputeNedelecChangeEdge(lG,eedges[i],extrows[i],extcols[i],cornersis,&Gins,&GKins,cvals,work,rwork);
1284:     if (Gins && GKins) {
1285:       const PetscScalar *data;
1286:       const PetscInt    *rows,*cols;
1287:       PetscInt          nrh,nch,nrc,ncc;

1289:       ISGetIndices(eedges[i],&cols);
1290:       /* H1 */
1291:       ISGetIndices(extrows[i],&rows);
1292:       MatGetSize(Gins,&nrh,&nch);
1293:       MatDenseGetArrayRead(Gins,&data);
1294:       MatSetValuesLocal(T,nrh,rows,nch,cols,data,INSERT_VALUES);
1295:       MatDenseRestoreArrayRead(Gins,&data);
1296:       ISRestoreIndices(extrows[i],&rows);
1297:       /* complement */
1298:       MatGetSize(GKins,&nrc,&ncc);
1299:       if (!ncc) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Constant function has not been generated for coarse edge %D",i);
1300:       if (ncc + nch != nrc) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_PLIB,"The sum of the number of columns of GKins %D and Gins %D does not match %D for coarse edge %D",ncc,nch,nrc,i);
1301:       if (ncc != 1 && pcbddc->nedcG) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot generate the coarse discrete gradient for coarse edge %D with ncc %D",i,ncc);
1302:       MatDenseGetArrayRead(GKins,&data);
1303:       MatSetValuesLocal(T,nrc,cols,ncc,cols+nch,data,INSERT_VALUES);
1304:       MatDenseRestoreArrayRead(GKins,&data);

1306:       /* coarse discrete gradient */
1307:       if (pcbddc->nedcG) {
1308:         PetscInt cols[2];

1310:         cols[0] = 2*i;
1311:         cols[1] = 2*i+1;
1312:         MatSetValuesLocal(pcbddc->nedcG,1,&i,2,cols,cvals,INSERT_VALUES);
1313:       }
1314:       ISRestoreIndices(eedges[i],&cols);
1315:     }
1316:     ISDestroy(&extrows[i]);
1317:     ISDestroy(&extcols[i]);
1318:     ISDestroy(&cornersis);
1319:     MatDestroy(&Gins);
1320:     MatDestroy(&GKins);
1321:   }
1322:   ISLocalToGlobalMappingDestroy(&el2g);

1324:   /* Start assembling */
1325:   MatAssemblyBegin(T,MAT_FINAL_ASSEMBLY);
1326:   if (pcbddc->nedcG) {
1327:     MatAssemblyBegin(pcbddc->nedcG,MAT_FINAL_ASSEMBLY);
1328:   }

1330:   /* Free */
1331:   if (fl2g) {
1332:     ISDestroy(&primals);
1333:     for (i=0;i<nee;i++) {
1334:       ISDestroy(&eedges[i]);
1335:     }
1336:     PetscFree(eedges);
1337:   }

1339:   /* hack mat_graph with primal dofs on the coarse edges */
1340:   {
1341:     PCBDDCGraph graph   = pcbddc->mat_graph;
1342:     PetscInt    *oqueue = graph->queue;
1343:     PetscInt    *ocptr  = graph->cptr;
1344:     PetscInt    ncc,*idxs;

1346:     /* find first primal edge */
1347:     if (pcbddc->nedclocal) {
1348:       ISGetIndices(pcbddc->nedclocal,(const PetscInt**)&idxs);
1349:     } else {
1350:       if (fl2g) {
1351:         ISLocalToGlobalMappingApply(fl2g,nee,cedges,cedges);
1352:       }
1353:       idxs = cedges;
1354:     }
1355:     cum = 0;
1356:     while (cum < nee && cedges[cum] < 0) cum++;

1358:     /* adapt connected components */
1359:     PetscMalloc2(graph->nvtxs+1,&graph->cptr,ocptr[graph->ncc],&graph->queue);
1360:     graph->cptr[0] = 0;
1361:     for (i=0,ncc=0;i<graph->ncc;i++) {
1362:       PetscInt lc = ocptr[i+1]-ocptr[i];
1363:       if (cum != nee && oqueue[ocptr[i+1]-1] == cedges[cum]) { /* this cc has a primal dof */
1364:         graph->cptr[ncc+1] = graph->cptr[ncc]+1;
1365:         graph->queue[graph->cptr[ncc]] = cedges[cum];
1366:         ncc++;
1367:         lc--;
1368:         cum++;
1369:         while (cum < nee && cedges[cum] < 0) cum++;
1370:       }
1371:       graph->cptr[ncc+1] = graph->cptr[ncc] + lc;
1372:       for (j=0;j<lc;j++) graph->queue[graph->cptr[ncc]+j] = oqueue[ocptr[i]+j];
1373:       ncc++;
1374:     }
1375:     graph->ncc = ncc;
1376:     if (pcbddc->nedclocal) {
1377:       ISRestoreIndices(pcbddc->nedclocal,(const PetscInt**)&idxs);
1378:     }
1379:     PetscFree2(ocptr,oqueue);
1380:   }
1381:   ISLocalToGlobalMappingDestroy(&fl2g);
1382:   PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,&nee,&alleedges,&allprimals);
1383:   PCBDDCGraphResetCSR(pcbddc->mat_graph);
1384:   MatDestroy(&conn);

1386:   ISDestroy(&nedfieldlocal);
1387:   PetscFree(extrow);
1388:   PetscFree2(work,rwork);
1389:   PetscFree(corners);
1390:   PetscFree(cedges);
1391:   PetscFree(extrows);
1392:   PetscFree(extcols);
1393:   MatDestroy(&lG);

1395:   /* Complete assembling */
1396:   MatAssemblyEnd(T,MAT_FINAL_ASSEMBLY);
1397:   if (pcbddc->nedcG) {
1398:     MatAssemblyEnd(pcbddc->nedcG,MAT_FINAL_ASSEMBLY);
1399: #if 0
1400:     PetscObjectSetName((PetscObject)pcbddc->nedcG,"coarse_G");
1401:     MatView(pcbddc->nedcG,NULL);
1402: #endif
1403:   }

1405:   /* set change of basis */
1406:   PCBDDCSetChangeOfBasisMat(pc,T,singular);
1407:   MatDestroy(&T);

1409:   return(0);
1410: }

1412: /* the near-null space of BDDC carries information on quadrature weights,
1413:    and these can be collinear -> so cheat with MatNullSpaceCreate
1414:    and create a suitable set of basis vectors first */
1415: PetscErrorCode PCBDDCNullSpaceCreate(MPI_Comm comm, PetscBool has_const, PetscInt nvecs, Vec quad_vecs[], MatNullSpace *nnsp)
1416: {
1418:   PetscInt       i;

1421:   for (i=0;i<nvecs;i++) {
1422:     PetscInt first,last;

1424:     VecGetOwnershipRange(quad_vecs[i],&first,&last);
1425:     if (last-first < 2*nvecs && has_const) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented");
1426:     if (i>=first && i < last) {
1427:       PetscScalar *data;
1428:       VecGetArray(quad_vecs[i],&data);
1429:       if (!has_const) {
1430:         data[i-first] = 1.;
1431:       } else {
1432:         data[2*i-first] = 1./PetscSqrtReal(2.);
1433:         data[2*i-first+1] = -1./PetscSqrtReal(2.);
1434:       }
1435:       VecRestoreArray(quad_vecs[i],&data);
1436:     }
1437:     PetscObjectStateIncrease((PetscObject)quad_vecs[i]);
1438:   }
1439:   MatNullSpaceCreate(comm,has_const,nvecs,quad_vecs,nnsp);
1440:   for (i=0;i<nvecs;i++) { /* reset vectors */
1441:     PetscInt first,last;
1442:     VecLockReadPop(quad_vecs[i]);
1443:     VecGetOwnershipRange(quad_vecs[i],&first,&last);
1444:     if (i>=first && i < last) {
1445:       PetscScalar *data;
1446:       VecGetArray(quad_vecs[i],&data);
1447:       if (!has_const) {
1448:         data[i-first] = 0.;
1449:       } else {
1450:         data[2*i-first] = 0.;
1451:         data[2*i-first+1] = 0.;
1452:       }
1453:       VecRestoreArray(quad_vecs[i],&data);
1454:     }
1455:     PetscObjectStateIncrease((PetscObject)quad_vecs[i]);
1456:     VecLockReadPush(quad_vecs[i]);
1457:   }
1458:   return(0);
1459: }

1461: PetscErrorCode PCBDDCComputeNoNetFlux(Mat A, Mat divudotp, PetscBool transpose, IS vl2l, PCBDDCGraph graph, MatNullSpace *nnsp)
1462: {
1463:   Mat                    loc_divudotp;
1464:   Vec                    p,v,vins,quad_vec,*quad_vecs;
1465:   ISLocalToGlobalMapping map;
1466:   PetscScalar            *vals;
1467:   const PetscScalar      *array;
1468:   PetscInt               i,maxneighs = 0,maxsize,*gidxs;
1469:   PetscInt               n_neigh,*neigh,*n_shared,**shared;
1470:   PetscMPIInt            rank;
1471:   PetscErrorCode         ierr;

1474:   ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
1475:   for (i=0;i<n_neigh;i++) maxneighs = PetscMax(graph->count[shared[i][0]]+1,maxneighs);
1476:   MPIU_Allreduce(MPI_IN_PLACE,&maxneighs,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)A));
1477:   if (!maxneighs) {
1478:     ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
1479:     *nnsp = NULL;
1480:     return(0);
1481:   }
1482:   maxsize = 0;
1483:   for (i=0;i<n_neigh;i++) maxsize = PetscMax(n_shared[i],maxsize);
1484:   PetscMalloc2(maxsize,&gidxs,maxsize,&vals);
1485:   /* create vectors to hold quadrature weights */
1486:   MatCreateVecs(A,&quad_vec,NULL);
1487:   if (!transpose) {
1488:     MatGetLocalToGlobalMapping(A,&map,NULL);
1489:   } else {
1490:     MatGetLocalToGlobalMapping(A,NULL,&map);
1491:   }
1492:   VecDuplicateVecs(quad_vec,maxneighs,&quad_vecs);
1493:   VecDestroy(&quad_vec);
1494:   PCBDDCNullSpaceCreate(PetscObjectComm((PetscObject)A),PETSC_FALSE,maxneighs,quad_vecs,nnsp);
1495:   for (i=0;i<maxneighs;i++) {
1496:     VecLockReadPop(quad_vecs[i]);
1497:   }

1499:   /* compute local quad vec */
1500:   MatISGetLocalMat(divudotp,&loc_divudotp);
1501:   if (!transpose) {
1502:     MatCreateVecs(loc_divudotp,&v,&p);
1503:   } else {
1504:     MatCreateVecs(loc_divudotp,&p,&v);
1505:   }
1506:   VecSet(p,1.);
1507:   if (!transpose) {
1508:     MatMultTranspose(loc_divudotp,p,v);
1509:   } else {
1510:     MatMult(loc_divudotp,p,v);
1511:   }
1512:   if (vl2l) {
1513:     Mat        lA;
1514:     VecScatter sc;

1516:     MatISGetLocalMat(A,&lA);
1517:     MatCreateVecs(lA,&vins,NULL);
1518:     VecScatterCreate(v,NULL,vins,vl2l,&sc);
1519:     VecScatterBegin(sc,v,vins,INSERT_VALUES,SCATTER_FORWARD);
1520:     VecScatterEnd(sc,v,vins,INSERT_VALUES,SCATTER_FORWARD);
1521:     VecScatterDestroy(&sc);
1522:   } else {
1523:     vins = v;
1524:   }
1525:   VecGetArrayRead(vins,&array);
1526:   VecDestroy(&p);

1528:   /* insert in global quadrature vecs */
1529:   MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);
1530:   for (i=1;i<n_neigh;i++) {
1531:     const PetscInt    *idxs;
1532:     PetscInt          idx,nn,j;

1534:     idxs = shared[i];
1535:     nn   = n_shared[i];
1536:     for (j=0;j<nn;j++) vals[j] = array[idxs[j]];
1537:     PetscFindInt(rank,graph->count[idxs[0]],graph->neighbours_set[idxs[0]],&idx);
1538:     idx  = -(idx+1);
1539:     if (idx < 0 || idx >= maxneighs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid index %D not in [0,%D)",idx,maxneighs);
1540:     ISLocalToGlobalMappingApply(map,nn,idxs,gidxs);
1541:     VecSetValues(quad_vecs[idx],nn,gidxs,vals,INSERT_VALUES);
1542:   }
1543:   ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
1544:   VecRestoreArrayRead(vins,&array);
1545:   if (vl2l) {
1546:     VecDestroy(&vins);
1547:   }
1548:   VecDestroy(&v);
1549:   PetscFree2(gidxs,vals);

1551:   /* assemble near null space */
1552:   for (i=0;i<maxneighs;i++) {
1553:     VecAssemblyBegin(quad_vecs[i]);
1554:   }
1555:   for (i=0;i<maxneighs;i++) {
1556:     VecAssemblyEnd(quad_vecs[i]);
1557:     VecViewFromOptions(quad_vecs[i],NULL,"-pc_bddc_quad_vecs_view");
1558:     VecLockReadPush(quad_vecs[i]);
1559:   }
1560:   VecDestroyVecs(maxneighs,&quad_vecs);
1561:   return(0);
1562: }

1564: PetscErrorCode PCBDDCAddPrimalVerticesLocalIS(PC pc, IS primalv)
1565: {
1566:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

1570:   if (primalv) {
1571:     if (pcbddc->user_primal_vertices_local) {
1572:       IS list[2], newp;

1574:       list[0] = primalv;
1575:       list[1] = pcbddc->user_primal_vertices_local;
1576:       ISConcatenate(PetscObjectComm((PetscObject)pc),2,list,&newp);
1577:       ISSortRemoveDups(newp);
1578:       ISDestroy(&list[1]);
1579:       pcbddc->user_primal_vertices_local = newp;
1580:     } else {
1581:       PCBDDCSetPrimalVerticesLocalIS(pc,primalv);
1582:     }
1583:   }
1584:   return(0);
1585: }

1587: static PetscErrorCode func_coords_private(PetscInt dim, PetscReal t, const PetscReal X[], PetscInt Nf, PetscScalar *out, void *ctx)
1588: {
1589:   PetscInt f, *comp  = (PetscInt *)ctx;

1592:   for (f=0;f<Nf;f++) out[f] = X[*comp];
1593:   return(0);
1594: }

1596: PetscErrorCode PCBDDCComputeLocalTopologyInfo(PC pc)
1597: {
1599:   Vec            local,global;
1600:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1601:   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
1602:   PetscBool      monolithic = PETSC_FALSE;

1605:   PetscOptionsBegin(PetscObjectComm((PetscObject)pc),((PetscObject)pc)->prefix,"BDDC topology options","PC");
1606:   PetscOptionsBool("-pc_bddc_monolithic","Discard any information on dofs splitting",NULL,monolithic,&monolithic,NULL);
1607:   PetscOptionsEnd();
1608:   /* need to convert from global to local topology information and remove references to information in global ordering */
1609:   MatCreateVecs(pc->pmat,&global,NULL);
1610:   MatCreateVecs(matis->A,&local,NULL);
1611:   VecBindToCPU(global,PETSC_TRUE);
1612:   VecBindToCPU(local,PETSC_TRUE);
1613:   if (monolithic) { /* just get block size to properly compute vertices */
1614:     if (pcbddc->vertex_size == 1) {
1615:       MatGetBlockSize(pc->pmat,&pcbddc->vertex_size);
1616:     }
1617:     goto boundary;
1618:   }

1620:   if (pcbddc->user_provided_isfordofs) {
1621:     if (pcbddc->n_ISForDofs) {
1622:       PetscInt i;

1624:       PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);
1625:       for (i=0;i<pcbddc->n_ISForDofs;i++) {
1626:         PetscInt bs;

1628:         PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);
1629:         ISGetBlockSize(pcbddc->ISForDofs[i],&bs);
1630:         ISSetBlockSize(pcbddc->ISForDofsLocal[i],bs);
1631:         ISDestroy(&pcbddc->ISForDofs[i]);
1632:       }
1633:       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
1634:       pcbddc->n_ISForDofs = 0;
1635:       PetscFree(pcbddc->ISForDofs);
1636:     }
1637:   } else {
1638:     if (!pcbddc->n_ISForDofsLocal) { /* field split not present */
1639:       DM dm;

1641:       MatGetDM(pc->pmat, &dm);
1642:       if (!dm) {
1643:         PCGetDM(pc, &dm);
1644:       }
1645:       if (dm) {
1646:         IS      *fields;
1647:         PetscInt nf,i;

1649:         DMCreateFieldDecomposition(dm,&nf,NULL,&fields,NULL);
1650:         PetscMalloc1(nf,&pcbddc->ISForDofsLocal);
1651:         for (i=0;i<nf;i++) {
1652:           PetscInt bs;

1654:           PCBDDCGlobalToLocal(matis->rctx,global,local,fields[i],&pcbddc->ISForDofsLocal[i]);
1655:           ISGetBlockSize(fields[i],&bs);
1656:           ISSetBlockSize(pcbddc->ISForDofsLocal[i],bs);
1657:           ISDestroy(&fields[i]);
1658:         }
1659:         PetscFree(fields);
1660:         pcbddc->n_ISForDofsLocal = nf;
1661:       } else { /* See if MATIS has fields attached by the conversion from MatNest */
1662:         PetscContainer   c;

1664:         PetscObjectQuery((PetscObject)pc->pmat,"_convert_nest_lfields",(PetscObject*)&c);
1665:         if (c) {
1666:           MatISLocalFields lf;
1667:           PetscContainerGetPointer(c,(void**)&lf);
1668:           PCBDDCSetDofsSplittingLocal(pc,lf->nr,lf->rf);
1669:         } else { /* fallback, create the default fields if bs > 1 */
1670:           PetscInt i, n = matis->A->rmap->n;
1671:           MatGetBlockSize(pc->pmat,&i);
1672:           if (i > 1) {
1673:             pcbddc->n_ISForDofsLocal = i;
1674:             PetscMalloc1(pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal);
1675:             for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1676:               ISCreateStride(PetscObjectComm((PetscObject)pc),n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);
1677:             }
1678:           }
1679:         }
1680:       }
1681:     } else {
1682:       PetscInt i;
1683:       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1684:         PCBDDCConsistencyCheckIS(pc,MPI_LAND,&pcbddc->ISForDofsLocal[i]);
1685:       }
1686:     }
1687:   }

1689: boundary:
1690:   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) {
1691:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);
1692:   } else if (pcbddc->DirichletBoundariesLocal) {
1693:     PCBDDCConsistencyCheckIS(pc,MPI_LAND,&pcbddc->DirichletBoundariesLocal);
1694:   }
1695:   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) {
1696:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);
1697:   } else if (pcbddc->NeumannBoundariesLocal) {
1698:     PCBDDCConsistencyCheckIS(pc,MPI_LOR,&pcbddc->NeumannBoundariesLocal);
1699:   }
1700:   if (!pcbddc->user_primal_vertices_local && pcbddc->user_primal_vertices) {
1701:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->user_primal_vertices,&pcbddc->user_primal_vertices_local);
1702:   }
1703:   VecDestroy(&global);
1704:   VecDestroy(&local);
1705:   /* detect local disconnected subdomains if requested (use matis->A) */
1706:   if (pcbddc->detect_disconnected) {
1707:     IS        primalv = NULL;
1708:     PetscInt  i;
1709:     PetscBool filter = pcbddc->detect_disconnected_filter;

1711:     for (i=0;i<pcbddc->n_local_subs;i++) {
1712:       ISDestroy(&pcbddc->local_subs[i]);
1713:     }
1714:     PetscFree(pcbddc->local_subs);
1715:     PCBDDCDetectDisconnectedComponents(pc,filter,&pcbddc->n_local_subs,&pcbddc->local_subs,&primalv);
1716:     PCBDDCAddPrimalVerticesLocalIS(pc,primalv);
1717:     ISDestroy(&primalv);
1718:   }
1719:   /* early stage corner detection */
1720:   {
1721:     DM dm;

1723:     MatGetDM(pc->pmat,&dm);
1724:     if (!dm) {
1725:       PCGetDM(pc,&dm);
1726:     }
1727:     if (dm) {
1728:       PetscBool isda;

1730:       PetscObjectTypeCompare((PetscObject)dm,DMDA,&isda);
1731:       if (isda) {
1732:         ISLocalToGlobalMapping l2l;
1733:         IS                     corners;
1734:         Mat                    lA;
1735:         PetscBool              gl,lo;

1737:         {
1738:           Vec               cvec;
1739:           const PetscScalar *coords;
1740:           PetscInt          dof,n,cdim;
1741:           PetscBool         memc = PETSC_TRUE;

1743:           DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
1744:           DMGetCoordinates(dm,&cvec);
1745:           VecGetLocalSize(cvec,&n);
1746:           VecGetBlockSize(cvec,&cdim);
1747:           n   /= cdim;
1748:           PetscFree(pcbddc->mat_graph->coords);
1749:           PetscMalloc1(dof*n*cdim,&pcbddc->mat_graph->coords);
1750:           VecGetArrayRead(cvec,&coords);
1751: #if defined(PETSC_USE_COMPLEX)
1752:           memc = PETSC_FALSE;
1753: #endif
1754:           if (dof != 1) memc = PETSC_FALSE;
1755:           if (memc) {
1756:             PetscArraycpy(pcbddc->mat_graph->coords,coords,cdim*n*dof);
1757:           } else { /* BDDC graph does not use any blocked information, we need to replicate the data */
1758:             PetscReal *bcoords = pcbddc->mat_graph->coords;
1759:             PetscInt  i, b, d;

1761:             for (i=0;i<n;i++) {
1762:               for (b=0;b<dof;b++) {
1763:                 for (d=0;d<cdim;d++) {
1764:                   bcoords[i*dof*cdim + b*cdim + d] = PetscRealPart(coords[i*cdim+d]);
1765:                 }
1766:               }
1767:             }
1768:           }
1769:           VecRestoreArrayRead(cvec,&coords);
1770:           pcbddc->mat_graph->cdim  = cdim;
1771:           pcbddc->mat_graph->cnloc = dof*n;
1772:           pcbddc->mat_graph->cloc  = PETSC_FALSE;
1773:         }
1774:         DMDAGetSubdomainCornersIS(dm,&corners);
1775:         MatISGetLocalMat(pc->pmat,&lA);
1776:         MatGetLocalToGlobalMapping(lA,&l2l,NULL);
1777:         MatISRestoreLocalMat(pc->pmat,&lA);
1778:         lo   = (PetscBool)(l2l && corners);
1779:         MPIU_Allreduce(&lo,&gl,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));
1780:         if (gl) { /* From PETSc's DMDA */
1781:           const PetscInt    *idx;
1782:           PetscInt          dof,bs,*idxout,n;

1784:           DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
1785:           ISLocalToGlobalMappingGetBlockSize(l2l,&bs);
1786:           ISGetLocalSize(corners,&n);
1787:           ISGetIndices(corners,&idx);
1788:           if (bs == dof) {
1789:             PetscMalloc1(n,&idxout);
1790:             ISLocalToGlobalMappingApplyBlock(l2l,n,idx,idxout);
1791:           } else { /* the original DMDA local-to-local map have been modified */
1792:             PetscInt i,d;

1794:             PetscMalloc1(dof*n,&idxout);
1795:             for (i=0;i<n;i++) for (d=0;d<dof;d++) idxout[dof*i+d] = dof*idx[i]+d;
1796:             ISLocalToGlobalMappingApply(l2l,dof*n,idxout,idxout);

1798:             bs = 1;
1799:             n *= dof;
1800:           }
1801:           ISRestoreIndices(corners,&idx);
1802:           DMDARestoreSubdomainCornersIS(dm,&corners);
1803:           ISCreateBlock(PetscObjectComm((PetscObject)pc),bs,n,idxout,PETSC_OWN_POINTER,&corners);
1804:           PCBDDCAddPrimalVerticesLocalIS(pc,corners);
1805:           ISDestroy(&corners);
1806:           pcbddc->corner_selected  = PETSC_TRUE;
1807:           pcbddc->corner_selection = PETSC_TRUE;
1808:         }
1809:         if (corners) {
1810:           DMDARestoreSubdomainCornersIS(dm,&corners);
1811:         }
1812:       }
1813:     }
1814:   }
1815:   if (pcbddc->corner_selection && !pcbddc->mat_graph->cdim) {
1816:     DM dm;

1818:     MatGetDM(pc->pmat,&dm);
1819:     if (!dm) {
1820:       PCGetDM(pc,&dm);
1821:     }
1822:     if (dm) { /* this can get very expensive, I need to find a faster alternative */
1823:       Vec            vcoords;
1824:       PetscSection   section;
1825:       PetscReal      *coords;
1826:       PetscInt       d,cdim,nl,nf,**ctxs;
1827:       PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *);

1829:       DMGetCoordinateDim(dm,&cdim);
1830:       DMGetLocalSection(dm,&section);
1831:       PetscSectionGetNumFields(section,&nf);
1832:       DMCreateGlobalVector(dm,&vcoords);
1833:       VecGetLocalSize(vcoords,&nl);
1834:       PetscMalloc1(nl*cdim,&coords);
1835:       PetscMalloc2(nf,&funcs,nf,&ctxs);
1836:       PetscMalloc1(nf,&ctxs[0]);
1837:       for (d=0;d<nf;d++) funcs[d] = func_coords_private;
1838:       for (d=1;d<nf;d++) ctxs[d] = ctxs[d-1] + 1;
1839:       for (d=0;d<cdim;d++) {
1840:         PetscInt          i;
1841:         const PetscScalar *v;

1843:         for (i=0;i<nf;i++) ctxs[i][0] = d;
1844:         DMProjectFunction(dm,0.0,funcs,(void**)ctxs,INSERT_VALUES,vcoords);
1845:         VecGetArrayRead(vcoords,&v);
1846:         for (i=0;i<nl;i++) coords[i*cdim+d] = PetscRealPart(v[i]);
1847:         VecRestoreArrayRead(vcoords,&v);
1848:       }
1849:       VecDestroy(&vcoords);
1850:       PCSetCoordinates(pc,cdim,nl,coords);
1851:       PetscFree(coords);
1852:       PetscFree(ctxs[0]);
1853:       PetscFree2(funcs,ctxs);
1854:     }
1855:   }
1856:   return(0);
1857: }

1859: PetscErrorCode PCBDDCConsistencyCheckIS(PC pc, MPI_Op mop, IS *is)
1860: {
1861:   Mat_IS          *matis = (Mat_IS*)(pc->pmat->data);
1862:   PetscErrorCode  ierr;
1863:   IS              nis;
1864:   const PetscInt  *idxs;
1865:   PetscInt        i,nd,n = matis->A->rmap->n,*nidxs,nnd;

1868:   if (mop != MPI_LAND && mop != MPI_LOR) SETERRQ(PetscObjectComm((PetscObject)(pc)),PETSC_ERR_SUP,"Supported are MPI_LAND and MPI_LOR");
1869:   if (mop == MPI_LAND) {
1870:     /* init rootdata with true */
1871:     for (i=0;i<pc->pmat->rmap->n;i++) matis->sf_rootdata[i] = 1;
1872:   } else {
1873:     PetscArrayzero(matis->sf_rootdata,pc->pmat->rmap->n);
1874:   }
1875:   PetscArrayzero(matis->sf_leafdata,n);
1876:   ISGetLocalSize(*is,&nd);
1877:   ISGetIndices(*is,&idxs);
1878:   for (i=0;i<nd;i++)
1879:     if (-1 < idxs[i] && idxs[i] < n)
1880:       matis->sf_leafdata[idxs[i]] = 1;
1881:   ISRestoreIndices(*is,&idxs);
1882:   PetscSFReduceBegin(matis->sf,MPIU_INT,matis->sf_leafdata,matis->sf_rootdata,mop);
1883:   PetscSFReduceEnd(matis->sf,MPIU_INT,matis->sf_leafdata,matis->sf_rootdata,mop);
1884:   PetscSFBcastBegin(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
1885:   PetscSFBcastEnd(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
1886:   if (mop == MPI_LAND) {
1887:     PetscMalloc1(nd,&nidxs);
1888:   } else {
1889:     PetscMalloc1(n,&nidxs);
1890:   }
1891:   for (i=0,nnd=0;i<n;i++)
1892:     if (matis->sf_leafdata[i])
1893:       nidxs[nnd++] = i;
1894:   ISCreateGeneral(PetscObjectComm((PetscObject)(*is)),nnd,nidxs,PETSC_OWN_POINTER,&nis);
1895:   ISDestroy(is);
1896:   *is  = nis;
1897:   return(0);
1898: }

1900: PetscErrorCode PCBDDCBenignRemoveInterior(PC pc,Vec r,Vec z)
1901: {
1902:   PC_IS             *pcis = (PC_IS*)(pc->data);
1903:   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1904:   PetscErrorCode    ierr;

1907:   if (!pcbddc->benign_have_null) {
1908:     return(0);
1909:   }
1910:   if (pcbddc->ChangeOfBasisMatrix) {
1911:     Vec swap;

1913:     MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);
1914:     swap = pcbddc->work_change;
1915:     pcbddc->work_change = r;
1916:     r = swap;
1917:   }
1918:   VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
1919:   VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
1920:   PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][0],pc,0,0,0);
1921:   KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);
1922:   PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][0],pc,0,0,0);
1923:   KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);
1924:   VecSet(z,0.);
1925:   VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
1926:   VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
1927:   if (pcbddc->ChangeOfBasisMatrix) {
1928:     pcbddc->work_change = r;
1929:     VecCopy(z,pcbddc->work_change);
1930:     MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);
1931:   }
1932:   return(0);
1933: }

1935: PetscErrorCode PCBDDCBenignMatMult_Private_Private(Mat A, Vec x, Vec y, PetscBool transpose)
1936: {
1937:   PCBDDCBenignMatMult_ctx ctx;
1938:   PetscErrorCode          ierr;
1939:   PetscBool               apply_right,apply_left,reset_x;

1942:   MatShellGetContext(A,&ctx);
1943:   if (transpose) {
1944:     apply_right = ctx->apply_left;
1945:     apply_left = ctx->apply_right;
1946:   } else {
1947:     apply_right = ctx->apply_right;
1948:     apply_left = ctx->apply_left;
1949:   }
1950:   reset_x = PETSC_FALSE;
1951:   if (apply_right) {
1952:     const PetscScalar *ax;
1953:     PetscInt          nl,i;

1955:     VecGetLocalSize(x,&nl);
1956:     VecGetArrayRead(x,&ax);
1957:     PetscArraycpy(ctx->work,ax,nl);
1958:     VecRestoreArrayRead(x,&ax);
1959:     for (i=0;i<ctx->benign_n;i++) {
1960:       PetscScalar    sum,val;
1961:       const PetscInt *idxs;
1962:       PetscInt       nz,j;
1963:       ISGetLocalSize(ctx->benign_zerodiag_subs[i],&nz);
1964:       ISGetIndices(ctx->benign_zerodiag_subs[i],&idxs);
1965:       sum = 0.;
1966:       if (ctx->apply_p0) {
1967:         val = ctx->work[idxs[nz-1]];
1968:         for (j=0;j<nz-1;j++) {
1969:           sum += ctx->work[idxs[j]];
1970:           ctx->work[idxs[j]] += val;
1971:         }
1972:       } else {
1973:         for (j=0;j<nz-1;j++) {
1974:           sum += ctx->work[idxs[j]];
1975:         }
1976:       }
1977:       ctx->work[idxs[nz-1]] -= sum;
1978:       ISRestoreIndices(ctx->benign_zerodiag_subs[i],&idxs);
1979:     }
1980:     VecPlaceArray(x,ctx->work);
1981:     reset_x = PETSC_TRUE;
1982:   }
1983:   if (transpose) {
1984:     MatMultTranspose(ctx->A,x,y);
1985:   } else {
1986:     MatMult(ctx->A,x,y);
1987:   }
1988:   if (reset_x) {
1989:     VecResetArray(x);
1990:   }
1991:   if (apply_left) {
1992:     PetscScalar *ay;
1993:     PetscInt    i;

1995:     VecGetArray(y,&ay);
1996:     for (i=0;i<ctx->benign_n;i++) {
1997:       PetscScalar    sum,val;
1998:       const PetscInt *idxs;
1999:       PetscInt       nz,j;
2000:       ISGetLocalSize(ctx->benign_zerodiag_subs[i],&nz);
2001:       ISGetIndices(ctx->benign_zerodiag_subs[i],&idxs);
2002:       val = -ay[idxs[nz-1]];
2003:       if (ctx->apply_p0) {
2004:         sum = 0.;
2005:         for (j=0;j<nz-1;j++) {
2006:           sum += ay[idxs[j]];
2007:           ay[idxs[j]] += val;
2008:         }
2009:         ay[idxs[nz-1]] += sum;
2010:       } else {
2011:         for (j=0;j<nz-1;j++) {
2012:           ay[idxs[j]] += val;
2013:         }
2014:         ay[idxs[nz-1]] = 0.;
2015:       }
2016:       ISRestoreIndices(ctx->benign_zerodiag_subs[i],&idxs);
2017:     }
2018:     VecRestoreArray(y,&ay);
2019:   }
2020:   return(0);
2021: }

2023: PetscErrorCode PCBDDCBenignMatMultTranspose_Private(Mat A, Vec x, Vec y)
2024: {

2028:   PCBDDCBenignMatMult_Private_Private(A,x,y,PETSC_TRUE);
2029:   return(0);
2030: }

2032: PetscErrorCode PCBDDCBenignMatMult_Private(Mat A, Vec x, Vec y)
2033: {

2037:   PCBDDCBenignMatMult_Private_Private(A,x,y,PETSC_FALSE);
2038:   return(0);
2039: }

2041: PetscErrorCode PCBDDCBenignShellMat(PC pc, PetscBool restore)
2042: {
2043:   PC_IS                   *pcis = (PC_IS*)pc->data;
2044:   PC_BDDC                 *pcbddc = (PC_BDDC*)pc->data;
2045:   PCBDDCBenignMatMult_ctx ctx;
2046:   PetscErrorCode          ierr;

2049:   if (!restore) {
2050:     Mat                A_IB,A_BI;
2051:     PetscScalar        *work;
2052:     PCBDDCReuseSolvers reuse = pcbddc->sub_schurs ? pcbddc->sub_schurs->reuse_solver : NULL;

2054:     if (pcbddc->benign_original_mat) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Benign original mat has not been restored");
2055:     if (!pcbddc->benign_change || !pcbddc->benign_n || pcbddc->benign_change_explicit) return(0);
2056:     PetscMalloc1(pcis->n,&work);
2057:     MatCreate(PETSC_COMM_SELF,&A_IB);
2058:     MatSetSizes(A_IB,pcis->n-pcis->n_B,pcis->n_B,PETSC_DECIDE,PETSC_DECIDE);
2059:     MatSetType(A_IB,MATSHELL);
2060:     MatShellSetOperation(A_IB,MATOP_MULT,(void (*)(void))PCBDDCBenignMatMult_Private);
2061:     MatShellSetOperation(A_IB,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCBenignMatMultTranspose_Private);
2062:     PetscNew(&ctx);
2063:     MatShellSetContext(A_IB,ctx);
2064:     ctx->apply_left = PETSC_TRUE;
2065:     ctx->apply_right = PETSC_FALSE;
2066:     ctx->apply_p0 = PETSC_FALSE;
2067:     ctx->benign_n = pcbddc->benign_n;
2068:     if (reuse) {
2069:       ctx->benign_zerodiag_subs = reuse->benign_zerodiag_subs;
2070:       ctx->free = PETSC_FALSE;
2071:     } else { /* TODO: could be optimized for successive solves */
2072:       ISLocalToGlobalMapping N_to_D;
2073:       PetscInt               i;

2075:       ISLocalToGlobalMappingCreateIS(pcis->is_I_local,&N_to_D);
2076:       PetscMalloc1(pcbddc->benign_n,&ctx->benign_zerodiag_subs);
2077:       for (i=0;i<pcbddc->benign_n;i++) {
2078:         ISGlobalToLocalMappingApplyIS(N_to_D,IS_GTOLM_DROP,pcbddc->benign_zerodiag_subs[i],&ctx->benign_zerodiag_subs[i]);
2079:       }
2080:       ISLocalToGlobalMappingDestroy(&N_to_D);
2081:       ctx->free = PETSC_TRUE;
2082:     }
2083:     ctx->A = pcis->A_IB;
2084:     ctx->work = work;
2085:     MatSetUp(A_IB);
2086:     MatAssemblyBegin(A_IB,MAT_FINAL_ASSEMBLY);
2087:     MatAssemblyEnd(A_IB,MAT_FINAL_ASSEMBLY);
2088:     pcis->A_IB = A_IB;

2090:     /* A_BI as A_IB^T */
2091:     MatCreateTranspose(A_IB,&A_BI);
2092:     pcbddc->benign_original_mat = pcis->A_BI;
2093:     pcis->A_BI = A_BI;
2094:   } else {
2095:     if (!pcbddc->benign_original_mat) {
2096:       return(0);
2097:     }
2098:     MatShellGetContext(pcis->A_IB,&ctx);
2099:     MatDestroy(&pcis->A_IB);
2100:     pcis->A_IB = ctx->A;
2101:     ctx->A = NULL;
2102:     MatDestroy(&pcis->A_BI);
2103:     pcis->A_BI = pcbddc->benign_original_mat;
2104:     pcbddc->benign_original_mat = NULL;
2105:     if (ctx->free) {
2106:       PetscInt i;
2107:       for (i=0;i<ctx->benign_n;i++) {
2108:         ISDestroy(&ctx->benign_zerodiag_subs[i]);
2109:       }
2110:       PetscFree(ctx->benign_zerodiag_subs);
2111:     }
2112:     PetscFree(ctx->work);
2113:     PetscFree(ctx);
2114:   }
2115:   return(0);
2116: }

2118: /* used just in bddc debug mode */
2119: PetscErrorCode PCBDDCBenignProject(PC pc, IS is1, IS is2, Mat *B)
2120: {
2121:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2122:   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
2123:   Mat            An;

2127:   MatPtAP(matis->A,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&An);
2128:   MatZeroRowsColumns(An,pcbddc->benign_n,pcbddc->benign_p0_lidx,1.0,NULL,NULL);
2129:   if (is1) {
2130:     MatCreateSubMatrix(An,is1,is2,MAT_INITIAL_MATRIX,B);
2131:     MatDestroy(&An);
2132:   } else {
2133:     *B = An;
2134:   }
2135:   return(0);
2136: }

2138: /* TODO: add reuse flag */
2139: PetscErrorCode MatSeqAIJCompress(Mat A, Mat *B)
2140: {
2141:   Mat            Bt;
2142:   PetscScalar    *a,*bdata;
2143:   const PetscInt *ii,*ij;
2144:   PetscInt       m,n,i,nnz,*bii,*bij;
2145:   PetscBool      flg_row;

2149:   MatGetSize(A,&n,&m);
2150:   MatGetRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&ij,&flg_row);
2151:   MatSeqAIJGetArray(A,&a);
2152:   nnz = n;
2153:   for (i=0;i<ii[n];i++) {
2154:     if (PetscLikely(PetscAbsScalar(a[i]) > PETSC_SMALL)) nnz++;
2155:   }
2156:   PetscMalloc1(n+1,&bii);
2157:   PetscMalloc1(nnz,&bij);
2158:   PetscMalloc1(nnz,&bdata);
2159:   nnz = 0;
2160:   bii[0] = 0;
2161:   for (i=0;i<n;i++) {
2162:     PetscInt j;
2163:     for (j=ii[i];j<ii[i+1];j++) {
2164:       PetscScalar entry = a[j];
2165:       if (PetscLikely(PetscAbsScalar(entry) > PETSC_SMALL) || (n == m && ij[j] == i)) {
2166:         bij[nnz] = ij[j];
2167:         bdata[nnz] = entry;
2168:         nnz++;
2169:       }
2170:     }
2171:     bii[i+1] = nnz;
2172:   }
2173:   MatSeqAIJRestoreArray(A,&a);
2174:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),n,m,bii,bij,bdata,&Bt);
2175:   MatRestoreRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&ij,&flg_row);
2176:   {
2177:     Mat_SeqAIJ *b = (Mat_SeqAIJ*)(Bt->data);
2178:     b->free_a = PETSC_TRUE;
2179:     b->free_ij = PETSC_TRUE;
2180:   }
2181:   if (*B == A) {
2182:     MatDestroy(&A);
2183:   }
2184:   *B = Bt;
2185:   return(0);
2186: }

2188: PetscErrorCode PCBDDCDetectDisconnectedComponents(PC pc, PetscBool filter, PetscInt *ncc, IS* cc[], IS* primalv)
2189: {
2190:   Mat                    B = NULL;
2191:   DM                     dm;
2192:   IS                     is_dummy,*cc_n;
2193:   ISLocalToGlobalMapping l2gmap_dummy;
2194:   PCBDDCGraph            graph;
2195:   PetscInt               *xadj_filtered = NULL,*adjncy_filtered = NULL;
2196:   PetscInt               i,n;
2197:   PetscInt               *xadj,*adjncy;
2198:   PetscBool              isplex = PETSC_FALSE;
2199:   PetscErrorCode         ierr;

2202:   if (ncc) *ncc = 0;
2203:   if (cc) *cc = NULL;
2204:   if (primalv) *primalv = NULL;
2205:   PCBDDCGraphCreate(&graph);
2206:   MatGetDM(pc->pmat,&dm);
2207:   if (!dm) {
2208:     PCGetDM(pc,&dm);
2209:   }
2210:   if (dm) {
2211:     PetscObjectTypeCompare((PetscObject)dm,DMPLEX,&isplex);
2212:   }
2213:   if (filter) isplex = PETSC_FALSE;

2215:   if (isplex) { /* this code has been modified from plexpartition.c */
2216:     PetscInt       p, pStart, pEnd, a, adjSize, idx, size, nroots;
2217:     PetscInt      *adj = NULL;
2218:     IS             cellNumbering;
2219:     const PetscInt *cellNum;
2220:     PetscBool      useCone, useClosure;
2221:     PetscSection   section;
2222:     PetscSegBuffer adjBuffer;
2223:     PetscSF        sfPoint;

2226:     DMPlexGetHeightStratum(dm, 0, &pStart, &pEnd);
2227:     DMGetPointSF(dm, &sfPoint);
2228:     PetscSFGetGraph(sfPoint, &nroots, NULL, NULL, NULL);
2229:     /* Build adjacency graph via a section/segbuffer */
2230:     PetscSectionCreate(PetscObjectComm((PetscObject) dm), &section);
2231:     PetscSectionSetChart(section, pStart, pEnd);
2232:     PetscSegBufferCreate(sizeof(PetscInt),1000,&adjBuffer);
2233:     /* Always use FVM adjacency to create partitioner graph */
2234:     DMGetBasicAdjacency(dm, &useCone, &useClosure);
2235:     DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);
2236:     DMPlexGetCellNumbering(dm, &cellNumbering);
2237:     ISGetIndices(cellNumbering, &cellNum);
2238:     for (n = 0, p = pStart; p < pEnd; p++) {
2239:       /* Skip non-owned cells in parallel (ParMetis expects no overlap) */
2240:       if (nroots > 0) {if (cellNum[p] < 0) continue;}
2241:       adjSize = PETSC_DETERMINE;
2242:       DMPlexGetAdjacency(dm, p, &adjSize, &adj);
2243:       for (a = 0; a < adjSize; ++a) {
2244:         const PetscInt point = adj[a];
2245:         if (pStart <= point && point < pEnd) {
2246:           PetscInt *PETSC_RESTRICT pBuf;
2247:           PetscSectionAddDof(section, p, 1);
2248:           PetscSegBufferGetInts(adjBuffer, 1, &pBuf);
2249:           *pBuf = point;
2250:         }
2251:       }
2252:       n++;
2253:     }
2254:     DMSetBasicAdjacency(dm, useCone, useClosure);
2255:     /* Derive CSR graph from section/segbuffer */
2256:     PetscSectionSetUp(section);
2257:     PetscSectionGetStorageSize(section, &size);
2258:     PetscMalloc1(n+1, &xadj);
2259:     for (idx = 0, p = pStart; p < pEnd; p++) {
2260:       if (nroots > 0) {if (cellNum[p] < 0) continue;}
2261:       PetscSectionGetOffset(section, p, &(xadj[idx++]));
2262:     }
2263:     xadj[n] = size;
2264:     PetscSegBufferExtractAlloc(adjBuffer, &adjncy);
2265:     /* Clean up */
2266:     PetscSegBufferDestroy(&adjBuffer);
2267:     PetscSectionDestroy(&section);
2268:     PetscFree(adj);
2269:     graph->xadj = xadj;
2270:     graph->adjncy = adjncy;
2271:   } else {
2272:     Mat       A;
2273:     PetscBool isseqaij, flg_row;

2275:     MatISGetLocalMat(pc->pmat,&A);
2276:     if (!A->rmap->N || !A->cmap->N) {
2277:       PCBDDCGraphDestroy(&graph);
2278:       return(0);
2279:     }
2280:     PetscObjectBaseTypeCompare((PetscObject)A,MATSEQAIJ,&isseqaij);
2281:     if (!isseqaij && filter) {
2282:       PetscBool isseqdense;

2284:       PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&isseqdense);
2285:       if (!isseqdense) {
2286:         MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&B);
2287:       } else { /* TODO: rectangular case and LDA */
2288:         PetscScalar *array;
2289:         PetscReal   chop=1.e-6;

2291:         MatDuplicate(A,MAT_COPY_VALUES,&B);
2292:         MatDenseGetArray(B,&array);
2293:         MatGetSize(B,&n,NULL);
2294:         for (i=0;i<n;i++) {
2295:           PetscInt j;
2296:           for (j=i+1;j<n;j++) {
2297:             PetscReal thresh = chop*(PetscAbsScalar(array[i*(n+1)])+PetscAbsScalar(array[j*(n+1)]));
2298:             if (PetscAbsScalar(array[i*n+j]) < thresh) array[i*n+j] = 0.;
2299:             if (PetscAbsScalar(array[j*n+i]) < thresh) array[j*n+i] = 0.;
2300:           }
2301:         }
2302:         MatDenseRestoreArray(B,&array);
2303:         MatConvert(B,MATSEQAIJ,MAT_INPLACE_MATRIX,&B);
2304:       }
2305:     } else {
2306:       PetscObjectReference((PetscObject)A);
2307:       B = A;
2308:     }
2309:     MatGetRowIJ(B,0,PETSC_TRUE,PETSC_FALSE,&n,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);

2311:     /* if filter is true, then removes entries lower than PETSC_SMALL in magnitude */
2312:     if (filter) {
2313:       PetscScalar *data;
2314:       PetscInt    j,cum;

2316:       PetscCalloc2(n+1,&xadj_filtered,xadj[n],&adjncy_filtered);
2317:       MatSeqAIJGetArray(B,&data);
2318:       cum = 0;
2319:       for (i=0;i<n;i++) {
2320:         PetscInt t;

2322:         for (j=xadj[i];j<xadj[i+1];j++) {
2323:           if (PetscUnlikely(PetscAbsScalar(data[j]) < PETSC_SMALL)) {
2324:             continue;
2325:           }
2326:           adjncy_filtered[cum+xadj_filtered[i]++] = adjncy[j];
2327:         }
2328:         t = xadj_filtered[i];
2329:         xadj_filtered[i] = cum;
2330:         cum += t;
2331:       }
2332:       MatSeqAIJRestoreArray(B,&data);
2333:       graph->xadj = xadj_filtered;
2334:       graph->adjncy = adjncy_filtered;
2335:     } else {
2336:       graph->xadj = xadj;
2337:       graph->adjncy = adjncy;
2338:     }
2339:   }
2340:   /* compute local connected components using PCBDDCGraph */
2341:   ISCreateStride(PETSC_COMM_SELF,n,0,1,&is_dummy);
2342:   ISLocalToGlobalMappingCreateIS(is_dummy,&l2gmap_dummy);
2343:   ISDestroy(&is_dummy);
2344:   PCBDDCGraphInit(graph,l2gmap_dummy,n,PETSC_MAX_INT);
2345:   ISLocalToGlobalMappingDestroy(&l2gmap_dummy);
2346:   PCBDDCGraphSetUp(graph,1,NULL,NULL,0,NULL,NULL);
2347:   PCBDDCGraphComputeConnectedComponents(graph);

2349:   /* partial clean up */
2350:   PetscFree2(xadj_filtered,adjncy_filtered);
2351:   if (B) {
2352:     PetscBool flg_row;
2353:     MatRestoreRowIJ(B,0,PETSC_TRUE,PETSC_FALSE,&n,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
2354:     MatDestroy(&B);
2355:   }
2356:   if (isplex) {
2357:     PetscFree(xadj);
2358:     PetscFree(adjncy);
2359:   }

2361:   /* get back data */
2362:   if (isplex) {
2363:     if (ncc) *ncc = graph->ncc;
2364:     if (cc || primalv) {
2365:       Mat          A;
2366:       PetscBT      btv,btvt;
2367:       PetscSection subSection;
2368:       PetscInt     *ids,cum,cump,*cids,*pids;

2370:       DMPlexGetSubdomainSection(dm,&subSection);
2371:       MatISGetLocalMat(pc->pmat,&A);
2372:       PetscMalloc3(A->rmap->n,&ids,graph->ncc+1,&cids,A->rmap->n,&pids);
2373:       PetscBTCreate(A->rmap->n,&btv);
2374:       PetscBTCreate(A->rmap->n,&btvt);

2376:       cids[0] = 0;
2377:       for (i = 0, cump = 0, cum = 0; i < graph->ncc; i++) {
2378:         PetscInt j;

2380:         PetscBTMemzero(A->rmap->n,btvt);
2381:         for (j = graph->cptr[i]; j < graph->cptr[i+1]; j++) {
2382:           PetscInt k, size, *closure = NULL, cell = graph->queue[j];

2384:           DMPlexGetTransitiveClosure(dm,cell,PETSC_TRUE,&size,&closure);
2385:           for (k = 0; k < 2*size; k += 2) {
2386:             PetscInt s, pp, p = closure[k], off, dof, cdof;

2388:             PetscSectionGetConstraintDof(subSection,p,&cdof);
2389:             PetscSectionGetOffset(subSection,p,&off);
2390:             PetscSectionGetDof(subSection,p,&dof);
2391:             for (s = 0; s < dof-cdof; s++) {
2392:               if (PetscBTLookupSet(btvt,off+s)) continue;
2393:               if (!PetscBTLookup(btv,off+s)) {
2394:                 ids[cum++] = off+s;
2395:               } else { /* cross-vertex */
2396:                 pids[cump++] = off+s;
2397:               }
2398:             }
2399:             DMPlexGetTreeParent(dm,p,&pp,NULL);
2400:             if (pp != p) {
2401:               PetscSectionGetConstraintDof(subSection,pp,&cdof);
2402:               PetscSectionGetOffset(subSection,pp,&off);
2403:               PetscSectionGetDof(subSection,pp,&dof);
2404:               for (s = 0; s < dof-cdof; s++) {
2405:                 if (PetscBTLookupSet(btvt,off+s)) continue;
2406:                 if (!PetscBTLookup(btv,off+s)) {
2407:                   ids[cum++] = off+s;
2408:                 } else { /* cross-vertex */
2409:                   pids[cump++] = off+s;
2410:                 }
2411:               }
2412:             }
2413:           }
2414:           DMPlexRestoreTransitiveClosure(dm,cell,PETSC_TRUE,&size,&closure);
2415:         }
2416:         cids[i+1] = cum;
2417:         /* mark dofs as already assigned */
2418:         for (j = cids[i]; j < cids[i+1]; j++) {
2419:           PetscBTSet(btv,ids[j]);
2420:         }
2421:       }
2422:       if (cc) {
2423:         PetscMalloc1(graph->ncc,&cc_n);
2424:         for (i = 0; i < graph->ncc; i++) {
2425:           ISCreateGeneral(PETSC_COMM_SELF,cids[i+1]-cids[i],ids+cids[i],PETSC_COPY_VALUES,&cc_n[i]);
2426:         }
2427:         *cc = cc_n;
2428:       }
2429:       if (primalv) {
2430:         ISCreateGeneral(PetscObjectComm((PetscObject)pc),cump,pids,PETSC_COPY_VALUES,primalv);
2431:       }
2432:       PetscFree3(ids,cids,pids);
2433:       PetscBTDestroy(&btv);
2434:       PetscBTDestroy(&btvt);
2435:     }
2436:   } else {
2437:     if (ncc) *ncc = graph->ncc;
2438:     if (cc) {
2439:       PetscMalloc1(graph->ncc,&cc_n);
2440:       for (i=0;i<graph->ncc;i++) {
2441:         ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],graph->queue+graph->cptr[i],PETSC_COPY_VALUES,&cc_n[i]);
2442:       }
2443:       *cc = cc_n;
2444:     }
2445:   }
2446:   /* clean up graph */
2447:   graph->xadj = NULL;
2448:   graph->adjncy = NULL;
2449:   PCBDDCGraphDestroy(&graph);
2450:   return(0);
2451: }

2453: PetscErrorCode PCBDDCBenignCheck(PC pc, IS zerodiag)
2454: {
2455:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
2456:   PC_IS*         pcis = (PC_IS*)(pc->data);
2457:   IS             dirIS = NULL;
2458:   PetscInt       i;

2462:   PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);
2463:   if (zerodiag) {
2464:     Mat            A;
2465:     Vec            vec3_N;
2466:     PetscScalar    *vals;
2467:     const PetscInt *idxs;
2468:     PetscInt       nz,*count;

2470:     /* p0 */
2471:     VecSet(pcis->vec1_N,0.);
2472:     PetscMalloc1(pcis->n,&vals);
2473:     ISGetLocalSize(zerodiag,&nz);
2474:     ISGetIndices(zerodiag,&idxs);
2475:     for (i=0;i<nz;i++) vals[i] = 1.;
2476:     VecSetValues(pcis->vec1_N,nz,idxs,vals,INSERT_VALUES);
2477:     VecAssemblyBegin(pcis->vec1_N);
2478:     VecAssemblyEnd(pcis->vec1_N);
2479:     /* v_I */
2480:     VecSetRandom(pcis->vec2_N,NULL);
2481:     for (i=0;i<nz;i++) vals[i] = 0.;
2482:     VecSetValues(pcis->vec2_N,nz,idxs,vals,INSERT_VALUES);
2483:     ISRestoreIndices(zerodiag,&idxs);
2484:     ISGetIndices(pcis->is_B_local,&idxs);
2485:     for (i=0;i<pcis->n_B;i++) vals[i] = 0.;
2486:     VecSetValues(pcis->vec2_N,pcis->n_B,idxs,vals,INSERT_VALUES);
2487:     ISRestoreIndices(pcis->is_B_local,&idxs);
2488:     if (dirIS) {
2489:       PetscInt n;

2491:       ISGetLocalSize(dirIS,&n);
2492:       ISGetIndices(dirIS,&idxs);
2493:       for (i=0;i<n;i++) vals[i] = 0.;
2494:       VecSetValues(pcis->vec2_N,n,idxs,vals,INSERT_VALUES);
2495:       ISRestoreIndices(dirIS,&idxs);
2496:     }
2497:     VecAssemblyBegin(pcis->vec2_N);
2498:     VecAssemblyEnd(pcis->vec2_N);
2499:     VecDuplicate(pcis->vec1_N,&vec3_N);
2500:     VecSet(vec3_N,0.);
2501:     MatISGetLocalMat(pc->pmat,&A);
2502:     MatMult(A,pcis->vec1_N,vec3_N);
2503:     VecDot(vec3_N,pcis->vec2_N,&vals[0]);
2504:     if (PetscAbsScalar(vals[0]) > 1.e-1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Benign trick can not be applied! b(v_I,p_0) = %1.6e (should be numerically 0.)",PetscAbsScalar(vals[0]));
2505:     PetscFree(vals);
2506:     VecDestroy(&vec3_N);

2508:     /* there should not be any pressure dofs lying on the interface */
2509:     PetscCalloc1(pcis->n,&count);
2510:     ISGetIndices(pcis->is_B_local,&idxs);
2511:     for (i=0;i<pcis->n_B;i++) count[idxs[i]]++;
2512:     ISRestoreIndices(pcis->is_B_local,&idxs);
2513:     ISGetIndices(zerodiag,&idxs);
2514:     for (i=0;i<nz;i++) if (count[idxs[i]]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Benign trick can not be applied! pressure dof %D is an interface dof",idxs[i]);
2515:     ISRestoreIndices(zerodiag,&idxs);
2516:     PetscFree(count);
2517:   }
2518:   ISDestroy(&dirIS);

2520:   /* check PCBDDCBenignGetOrSetP0 */
2521:   VecSetRandom(pcis->vec1_global,NULL);
2522:   for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = -PetscGlobalRank-i;
2523:   PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_FALSE);
2524:   for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = 1;
2525:   PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_TRUE);
2526:   for (i=0;i<pcbddc->benign_n;i++) {
2527:     PetscInt val = PetscRealPart(pcbddc->benign_p0[i]);
2528:     if (val != -PetscGlobalRank-i) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error testing PCBDDCBenignGetOrSetP0! Found %g at %D instead of %g",PetscRealPart(pcbddc->benign_p0[i]),i,-PetscGlobalRank-i);
2529:   }
2530:   return(0);
2531: }

2533: PetscErrorCode PCBDDCBenignDetectSaddlePoint(PC pc, PetscBool reuse, IS *zerodiaglocal)
2534: {
2535:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
2536:   IS             pressures = NULL,zerodiag = NULL,*bzerodiag = NULL,zerodiag_save,*zerodiag_subs;
2537:   PetscInt       nz,n,benign_n,bsp = 1;
2538:   PetscInt       *interior_dofs,n_interior_dofs,nneu;
2539:   PetscBool      sorted,have_null,has_null_pressures,recompute_zerodiag,checkb;

2543:   if (reuse) goto project_b0;
2544:   PetscSFDestroy(&pcbddc->benign_sf);
2545:   MatDestroy(&pcbddc->benign_B0);
2546:   for (n=0;n<pcbddc->benign_n;n++) {
2547:     ISDestroy(&pcbddc->benign_zerodiag_subs[n]);
2548:   }
2549:   PetscFree(pcbddc->benign_zerodiag_subs);
2550:   has_null_pressures = PETSC_TRUE;
2551:   have_null = PETSC_TRUE;
2552:   /* if a local information on dofs is present, gets pressure dofs from command line (uses the last field is not provided)
2553:      Without local information, it uses only the zerodiagonal dofs (ok if the pressure block is all zero and it is a scalar field)
2554:      Checks if all the pressure dofs in each subdomain have a zero diagonal
2555:      If not, a change of basis on pressures is not needed
2556:      since the local Schur complements are already SPD
2557:   */
2558:   if (pcbddc->n_ISForDofsLocal) {
2559:     IS        iP = NULL;
2560:     PetscInt  p,*pp;
2561:     PetscBool flg;

2563:     PetscMalloc1(pcbddc->n_ISForDofsLocal,&pp);
2564:     n    = pcbddc->n_ISForDofsLocal;
2565:     PetscOptionsBegin(PetscObjectComm((PetscObject)pc),((PetscObject)pc)->prefix,"BDDC benign options","PC");
2566:     PetscOptionsIntArray("-pc_bddc_pressure_field","Field id for pressures",NULL,pp,&n,&flg);
2567:     PetscOptionsEnd();
2568:     if (!flg) {
2569:       n = 1;
2570:       pp[0] = pcbddc->n_ISForDofsLocal-1;
2571:     }

2573:     bsp = 0;
2574:     for (p=0;p<n;p++) {
2575:       PetscInt bs;

2577:       if (pp[p] < 0 || pp[p] > pcbddc->n_ISForDofsLocal-1) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_USER,"Invalid field id for pressures %D",pp[p]);
2578:       ISGetBlockSize(pcbddc->ISForDofsLocal[pp[p]],&bs);
2579:       bsp += bs;
2580:     }
2581:     PetscMalloc1(bsp,&bzerodiag);
2582:     bsp  = 0;
2583:     for (p=0;p<n;p++) {
2584:       const PetscInt *idxs;
2585:       PetscInt       b,bs,npl,*bidxs;

2587:       ISGetBlockSize(pcbddc->ISForDofsLocal[pp[p]],&bs);
2588:       ISGetLocalSize(pcbddc->ISForDofsLocal[pp[p]],&npl);
2589:       ISGetIndices(pcbddc->ISForDofsLocal[pp[p]],&idxs);
2590:       PetscMalloc1(npl/bs,&bidxs);
2591:       for (b=0;b<bs;b++) {
2592:         PetscInt i;

2594:         for (i=0;i<npl/bs;i++) bidxs[i] = idxs[bs*i+b];
2595:         ISCreateGeneral(PETSC_COMM_SELF,npl/bs,bidxs,PETSC_COPY_VALUES,&bzerodiag[bsp]);
2596:         bsp++;
2597:       }
2598:       PetscFree(bidxs);
2599:       ISRestoreIndices(pcbddc->ISForDofsLocal[pp[p]],&idxs);
2600:     }
2601:     ISConcatenate(PETSC_COMM_SELF,bsp,bzerodiag,&pressures);

2603:     /* remove zeroed out pressures if we are setting up a BDDC solver for a saddle-point FETI-DP */
2604:     PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP",(PetscObject*)&iP);
2605:     if (iP) {
2606:       IS newpressures;

2608:       ISDifference(pressures,iP,&newpressures);
2609:       ISDestroy(&pressures);
2610:       pressures = newpressures;
2611:     }
2612:     ISSorted(pressures,&sorted);
2613:     if (!sorted) {
2614:       ISSort(pressures);
2615:     }
2616:     PetscFree(pp);
2617:   }

2619:   /* pcis has not been setup yet, so get the local size from the subdomain matrix */
2620:   MatGetLocalSize(pcbddc->local_mat,&n,NULL);
2621:   if (!n) pcbddc->benign_change_explicit = PETSC_TRUE;
2622:   MatFindZeroDiagonals(pcbddc->local_mat,&zerodiag);
2623:   ISSorted(zerodiag,&sorted);
2624:   if (!sorted) {
2625:     ISSort(zerodiag);
2626:   }
2627:   PetscObjectReference((PetscObject)zerodiag);
2628:   zerodiag_save = zerodiag;
2629:   ISGetLocalSize(zerodiag,&nz);
2630:   if (!nz) {
2631:     if (n) have_null = PETSC_FALSE;
2632:     has_null_pressures = PETSC_FALSE;
2633:     ISDestroy(&zerodiag);
2634:   }
2635:   recompute_zerodiag = PETSC_FALSE;

2637:   /* in case disconnected subdomains info is present, split the pressures accordingly (otherwise the benign trick could fail) */
2638:   zerodiag_subs    = NULL;
2639:   benign_n         = 0;
2640:   n_interior_dofs  = 0;
2641:   interior_dofs    = NULL;
2642:   nneu             = 0;
2643:   if (pcbddc->NeumannBoundariesLocal) {
2644:     ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&nneu);
2645:   }
2646:   checkb = (PetscBool)(!pcbddc->NeumannBoundariesLocal || pcbddc->current_level);
2647:   if (checkb) { /* need to compute interior nodes */
2648:     PetscInt n,i,j;
2649:     PetscInt n_neigh,*neigh,*n_shared,**shared;
2650:     PetscInt *iwork;

2652:     ISLocalToGlobalMappingGetSize(pc->pmat->rmap->mapping,&n);
2653:     ISLocalToGlobalMappingGetInfo(pc->pmat->rmap->mapping,&n_neigh,&neigh,&n_shared,&shared);
2654:     PetscCalloc1(n,&iwork);
2655:     PetscMalloc1(n,&interior_dofs);
2656:     for (i=1;i<n_neigh;i++)
2657:       for (j=0;j<n_shared[i];j++)
2658:           iwork[shared[i][j]] += 1;
2659:     for (i=0;i<n;i++)
2660:       if (!iwork[i])
2661:         interior_dofs[n_interior_dofs++] = i;
2662:     PetscFree(iwork);
2663:     ISLocalToGlobalMappingRestoreInfo(pc->pmat->rmap->mapping,&n_neigh,&neigh,&n_shared,&shared);
2664:   }
2665:   if (has_null_pressures) {
2666:     IS             *subs;
2667:     PetscInt       nsubs,i,j,nl;
2668:     const PetscInt *idxs;
2669:     PetscScalar    *array;
2670:     Vec            *work;
2671:     Mat_IS*        matis = (Mat_IS*)(pc->pmat->data);

2673:     subs  = pcbddc->local_subs;
2674:     nsubs = pcbddc->n_local_subs;
2675:     /* these vectors are needed to check if the constant on pressures is in the kernel of the local operator B (i.e. B(v_I,p0) should be zero) */
2676:     if (checkb) {
2677:       VecDuplicateVecs(matis->y,2,&work);
2678:       ISGetLocalSize(zerodiag,&nl);
2679:       ISGetIndices(zerodiag,&idxs);
2680:       /* work[0] = 1_p */
2681:       VecSet(work[0],0.);
2682:       VecGetArray(work[0],&array);
2683:       for (j=0;j<nl;j++) array[idxs[j]] = 1.;
2684:       VecRestoreArray(work[0],&array);
2685:       /* work[0] = 1_v */
2686:       VecSet(work[1],1.);
2687:       VecGetArray(work[1],&array);
2688:       for (j=0;j<nl;j++) array[idxs[j]] = 0.;
2689:       VecRestoreArray(work[1],&array);
2690:       ISRestoreIndices(zerodiag,&idxs);
2691:     }

2693:     if (nsubs > 1 || bsp > 1) {
2694:       IS       *is;
2695:       PetscInt b,totb;

2697:       totb  = bsp;
2698:       is    = bsp > 1 ? bzerodiag : &zerodiag;
2699:       nsubs = PetscMax(nsubs,1);
2700:       PetscCalloc1(nsubs*totb,&zerodiag_subs);
2701:       for (b=0;b<totb;b++) {
2702:         for (i=0;i<nsubs;i++) {
2703:           ISLocalToGlobalMapping l2g;
2704:           IS                     t_zerodiag_subs;
2705:           PetscInt               nl;

2707:           if (subs) {
2708:             ISLocalToGlobalMappingCreateIS(subs[i],&l2g);
2709:           } else {
2710:             IS tis;

2712:             MatGetLocalSize(pcbddc->local_mat,&nl,NULL);
2713:             ISCreateStride(PETSC_COMM_SELF,nl,0,1,&tis);
2714:             ISLocalToGlobalMappingCreateIS(tis,&l2g);
2715:             ISDestroy(&tis);
2716:           }
2717:           ISGlobalToLocalMappingApplyIS(l2g,IS_GTOLM_DROP,is[b],&t_zerodiag_subs);
2718:           ISGetLocalSize(t_zerodiag_subs,&nl);
2719:           if (nl) {
2720:             PetscBool valid = PETSC_TRUE;

2722:             if (checkb) {
2723:               VecSet(matis->x,0);
2724:               ISGetLocalSize(subs[i],&nl);
2725:               ISGetIndices(subs[i],&idxs);
2726:               VecGetArray(matis->x,&array);
2727:               for (j=0;j<nl;j++) array[idxs[j]] = 1.;
2728:               VecRestoreArray(matis->x,&array);
2729:               ISRestoreIndices(subs[i],&idxs);
2730:               VecPointwiseMult(matis->x,work[0],matis->x);
2731:               MatMult(matis->A,matis->x,matis->y);
2732:               VecPointwiseMult(matis->y,work[1],matis->y);
2733:               VecGetArray(matis->y,&array);
2734:               for (j=0;j<n_interior_dofs;j++) {
2735:                 if (PetscAbsScalar(array[interior_dofs[j]]) > PETSC_SMALL) {
2736:                   valid = PETSC_FALSE;
2737:                   break;
2738:                 }
2739:               }
2740:               VecRestoreArray(matis->y,&array);
2741:             }
2742:             if (valid && nneu) {
2743:               const PetscInt *idxs;
2744:               PetscInt       nzb;

2746:               ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);
2747:               ISGlobalToLocalMappingApply(l2g,IS_GTOLM_DROP,nneu,idxs,&nzb,NULL);
2748:               ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);
2749:               if (nzb) valid = PETSC_FALSE;
2750:             }
2751:             if (valid && pressures) {
2752:               IS       t_pressure_subs,tmp;
2753:               PetscInt i1,i2;

2755:               ISGlobalToLocalMappingApplyIS(l2g,IS_GTOLM_DROP,pressures,&t_pressure_subs);
2756:               ISEmbed(t_zerodiag_subs,t_pressure_subs,PETSC_TRUE,&tmp);
2757:               ISGetLocalSize(tmp,&i1);
2758:               ISGetLocalSize(t_zerodiag_subs,&i2);
2759:               if (i2 != i1) valid = PETSC_FALSE;
2760:               ISDestroy(&t_pressure_subs);
2761:               ISDestroy(&tmp);
2762:             }
2763:             if (valid) {
2764:               ISLocalToGlobalMappingApplyIS(l2g,t_zerodiag_subs,&zerodiag_subs[benign_n]);
2765:               benign_n++;
2766:             } else recompute_zerodiag = PETSC_TRUE;
2767:           }
2768:           ISDestroy(&t_zerodiag_subs);
2769:           ISLocalToGlobalMappingDestroy(&l2g);
2770:         }
2771:       }
2772:     } else { /* there's just one subdomain (or zero if they have not been detected */
2773:       PetscBool valid = PETSC_TRUE;

2775:       if (nneu) valid = PETSC_FALSE;
2776:       if (valid && pressures) {
2777:         ISEqual(pressures,zerodiag,&valid);
2778:       }
2779:       if (valid && checkb) {
2780:         MatMult(matis->A,work[0],matis->x);
2781:         VecPointwiseMult(matis->x,work[1],matis->x);
2782:         VecGetArray(matis->x,&array);
2783:         for (j=0;j<n_interior_dofs;j++) {
2784:           if (PetscAbsScalar(array[interior_dofs[j]]) > PETSC_SMALL) {
2785:             valid = PETSC_FALSE;
2786:             break;
2787:           }
2788:         }
2789:         VecRestoreArray(matis->x,&array);
2790:       }
2791:       if (valid) {
2792:         benign_n = 1;
2793:         PetscMalloc1(benign_n,&zerodiag_subs);
2794:         PetscObjectReference((PetscObject)zerodiag);
2795:         zerodiag_subs[0] = zerodiag;
2796:       }
2797:     }
2798:     if (checkb) {
2799:       VecDestroyVecs(2,&work);
2800:     }
2801:   }
2802:   PetscFree(interior_dofs);

2804:   if (!benign_n) {
2805:     PetscInt n;

2807:     ISDestroy(&zerodiag);
2808:     recompute_zerodiag = PETSC_FALSE;
2809:     MatGetLocalSize(pcbddc->local_mat,&n,NULL);
2810:     if (n) have_null = PETSC_FALSE;
2811:   }

2813:   /* final check for null pressures */
2814:   if (zerodiag && pressures) {
2815:     ISEqual(pressures,zerodiag,&have_null);
2816:   }

2818:   if (recompute_zerodiag) {
2819:     ISDestroy(&zerodiag);
2820:     if (benign_n == 1) {
2821:       PetscObjectReference((PetscObject)zerodiag_subs[0]);
2822:       zerodiag = zerodiag_subs[0];
2823:     } else {
2824:       PetscInt i,nzn,*new_idxs;

2826:       nzn = 0;
2827:       for (i=0;i<benign_n;i++) {
2828:         PetscInt ns;
2829:         ISGetLocalSize(zerodiag_subs[i],&ns);
2830:         nzn += ns;
2831:       }
2832:       PetscMalloc1(nzn,&new_idxs);
2833:       nzn = 0;
2834:       for (i=0;i<benign_n;i++) {
2835:         PetscInt ns,*idxs;
2836:         ISGetLocalSize(zerodiag_subs[i],&ns);
2837:         ISGetIndices(zerodiag_subs[i],(const PetscInt**)&idxs);
2838:         PetscArraycpy(new_idxs+nzn,idxs,ns);
2839:         ISRestoreIndices(zerodiag_subs[i],(const PetscInt**)&idxs);
2840:         nzn += ns;
2841:       }
2842:       PetscSortInt(nzn,new_idxs);
2843:       ISCreateGeneral(PETSC_COMM_SELF,nzn,new_idxs,PETSC_OWN_POINTER,&zerodiag);
2844:     }
2845:     have_null = PETSC_FALSE;
2846:   }

2848:   /* determines if the coarse solver will be singular or not */
2849:   MPIU_Allreduce(&have_null,&pcbddc->benign_null,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));

2851:   /* Prepare matrix to compute no-net-flux */
2852:   if (pcbddc->compute_nonetflux && !pcbddc->divudotp) {
2853:     Mat                    A,loc_divudotp;
2854:     ISLocalToGlobalMapping rl2g,cl2g,l2gmap;
2855:     IS                     row,col,isused = NULL;
2856:     PetscInt               M,N,n,st,n_isused;

2858:     if (pressures) {
2859:       isused = pressures;
2860:     } else {
2861:       isused = zerodiag_save;
2862:     }
2863:     MatGetLocalToGlobalMapping(pc->pmat,&l2gmap,NULL);
2864:     MatISGetLocalMat(pc->pmat,&A);
2865:     MatGetLocalSize(A,&n,NULL);
2866:     if (!isused && n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Don't know how to extract div u dot p! Please provide the pressure field");
2867:     n_isused = 0;
2868:     if (isused) {
2869:       ISGetLocalSize(isused,&n_isused);
2870:     }
2871:     MPI_Scan(&n_isused,&st,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
2872:     st = st-n_isused;
2873:     if (n) {
2874:       const PetscInt *gidxs;

2876:       MatCreateSubMatrix(A,isused,NULL,MAT_INITIAL_MATRIX,&loc_divudotp);
2877:       ISLocalToGlobalMappingGetIndices(l2gmap,&gidxs);
2878:       /* TODO: extend ISCreateStride with st = PETSC_DECIDE */
2879:       ISCreateStride(PetscObjectComm((PetscObject)pc),n_isused,st,1,&row);
2880:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),n,gidxs,PETSC_COPY_VALUES,&col);
2881:       ISLocalToGlobalMappingRestoreIndices(l2gmap,&gidxs);
2882:     } else {
2883:       MatCreateSeqAIJ(PETSC_COMM_SELF,0,0,1,NULL,&loc_divudotp);
2884:       ISCreateStride(PetscObjectComm((PetscObject)pc),n_isused,st,1,&row);
2885:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),0,NULL,PETSC_COPY_VALUES,&col);
2886:     }
2887:     MatGetSize(pc->pmat,NULL,&N);
2888:     ISGetSize(row,&M);
2889:     ISLocalToGlobalMappingCreateIS(row,&rl2g);
2890:     ISLocalToGlobalMappingCreateIS(col,&cl2g);
2891:     ISDestroy(&row);
2892:     ISDestroy(&col);
2893:     MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->divudotp);
2894:     MatSetType(pcbddc->divudotp,MATIS);
2895:     MatSetSizes(pcbddc->divudotp,PETSC_DECIDE,PETSC_DECIDE,M,N);
2896:     MatSetLocalToGlobalMapping(pcbddc->divudotp,rl2g,cl2g);
2897:     ISLocalToGlobalMappingDestroy(&rl2g);
2898:     ISLocalToGlobalMappingDestroy(&cl2g);
2899:     MatISSetLocalMat(pcbddc->divudotp,loc_divudotp);
2900:     MatDestroy(&loc_divudotp);
2901:     MatAssemblyBegin(pcbddc->divudotp,MAT_FINAL_ASSEMBLY);
2902:     MatAssemblyEnd(pcbddc->divudotp,MAT_FINAL_ASSEMBLY);
2903:   }
2904:   ISDestroy(&zerodiag_save);
2905:   ISDestroy(&pressures);
2906:   if (bzerodiag) {
2907:     PetscInt i;

2909:     for (i=0;i<bsp;i++) {
2910:       ISDestroy(&bzerodiag[i]);
2911:     }
2912:     PetscFree(bzerodiag);
2913:   }
2914:   pcbddc->benign_n = benign_n;
2915:   pcbddc->benign_zerodiag_subs = zerodiag_subs;

2917:   /* determines if the problem has subdomains with 0 pressure block */
2918:   have_null = (PetscBool)(!!pcbddc->benign_n);
2919:   MPIU_Allreduce(&have_null,&pcbddc->benign_have_null,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));

2921: project_b0:
2922:   MatGetLocalSize(pcbddc->local_mat,&n,NULL);
2923:   /* change of basis and p0 dofs */
2924:   if (pcbddc->benign_n) {
2925:     PetscInt i,s,*nnz;

2927:     /* local change of basis for pressures */
2928:     MatDestroy(&pcbddc->benign_change);
2929:     MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat),&pcbddc->benign_change);
2930:     MatSetType(pcbddc->benign_change,MATAIJ);
2931:     MatSetSizes(pcbddc->benign_change,n,n,PETSC_DECIDE,PETSC_DECIDE);
2932:     PetscMalloc1(n,&nnz);
2933:     for (i=0;i<n;i++) nnz[i] = 1; /* defaults to identity */
2934:     for (i=0;i<pcbddc->benign_n;i++) {
2935:       const PetscInt *idxs;
2936:       PetscInt       nzs,j;

2938:       ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nzs);
2939:       ISGetIndices(pcbddc->benign_zerodiag_subs[i],&idxs);
2940:       for (j=0;j<nzs-1;j++) nnz[idxs[j]] = 2; /* change on pressures */
2941:       nnz[idxs[nzs-1]] = nzs; /* last local pressure dof in subdomain */
2942:       ISRestoreIndices(pcbddc->benign_zerodiag_subs[i],&idxs);
2943:     }
2944:     MatSeqAIJSetPreallocation(pcbddc->benign_change,0,nnz);
2945:     MatSetOption(pcbddc->benign_change,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
2946:     PetscFree(nnz);
2947:     /* set identity by default */
2948:     for (i=0;i<n;i++) {
2949:       MatSetValue(pcbddc->benign_change,i,i,1.,INSERT_VALUES);
2950:     }
2951:     PetscFree3(pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx,pcbddc->benign_p0);
2952:     PetscMalloc3(pcbddc->benign_n,&pcbddc->benign_p0_lidx,pcbddc->benign_n,&pcbddc->benign_p0_gidx,pcbddc->benign_n,&pcbddc->benign_p0);
2953:     /* set change on pressures */
2954:     for (s=0;s<pcbddc->benign_n;s++) {
2955:       PetscScalar    *array;
2956:       const PetscInt *idxs;
2957:       PetscInt       nzs;

2959:       ISGetLocalSize(pcbddc->benign_zerodiag_subs[s],&nzs);
2960:       ISGetIndices(pcbddc->benign_zerodiag_subs[s],&idxs);
2961:       for (i=0;i<nzs-1;i++) {
2962:         PetscScalar vals[2];
2963:         PetscInt    cols[2];

2965:         cols[0] = idxs[i];
2966:         cols[1] = idxs[nzs-1];
2967:         vals[0] = 1.;
2968:         vals[1] = 1.;
2969:         MatSetValues(pcbddc->benign_change,1,cols,2,cols,vals,INSERT_VALUES);
2970:       }
2971:       PetscMalloc1(nzs,&array);
2972:       for (i=0;i<nzs-1;i++) array[i] = -1.;
2973:       array[nzs-1] = 1.;
2974:       MatSetValues(pcbddc->benign_change,1,idxs+nzs-1,nzs,idxs,array,INSERT_VALUES);
2975:       /* store local idxs for p0 */
2976:       pcbddc->benign_p0_lidx[s] = idxs[nzs-1];
2977:       ISRestoreIndices(pcbddc->benign_zerodiag_subs[s],&idxs);
2978:       PetscFree(array);
2979:     }
2980:     MatAssemblyBegin(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);
2981:     MatAssemblyEnd(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);

2983:     /* project if needed */
2984:     if (pcbddc->benign_change_explicit) {
2985:       Mat M;

2987:       MatPtAP(pcbddc->local_mat,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&M);
2988:       MatDestroy(&pcbddc->local_mat);
2989:       MatSeqAIJCompress(M,&pcbddc->local_mat);
2990:       MatDestroy(&M);
2991:     }
2992:     /* store global idxs for p0 */
2993:     ISLocalToGlobalMappingApply(pc->pmat->rmap->mapping,pcbddc->benign_n,pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx);
2994:   }
2995:   *zerodiaglocal = zerodiag;
2996:   return(0);
2997: }

2999: PetscErrorCode PCBDDCBenignGetOrSetP0(PC pc, Vec v, PetscBool get)
3000: {
3001:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
3002:   PetscScalar    *array;

3006:   if (!pcbddc->benign_sf) {
3007:     PetscSFCreate(PetscObjectComm((PetscObject)pc),&pcbddc->benign_sf);
3008:     PetscSFSetGraphLayout(pcbddc->benign_sf,pc->pmat->rmap,pcbddc->benign_n,NULL,PETSC_OWN_POINTER,pcbddc->benign_p0_gidx);
3009:   }
3010:   if (get) {
3011:     VecGetArrayRead(v,(const PetscScalar**)&array);
3012:     PetscSFBcastBegin(pcbddc->benign_sf,MPIU_SCALAR,array,pcbddc->benign_p0,MPI_REPLACE);
3013:     PetscSFBcastEnd(pcbddc->benign_sf,MPIU_SCALAR,array,pcbddc->benign_p0,MPI_REPLACE);
3014:     VecRestoreArrayRead(v,(const PetscScalar**)&array);
3015:   } else {
3016:     VecGetArray(v,&array);
3017:     PetscSFReduceBegin(pcbddc->benign_sf,MPIU_SCALAR,pcbddc->benign_p0,array,MPI_REPLACE);
3018:     PetscSFReduceEnd(pcbddc->benign_sf,MPIU_SCALAR,pcbddc->benign_p0,array,MPI_REPLACE);
3019:     VecRestoreArray(v,&array);
3020:   }
3021:   return(0);
3022: }

3024: PetscErrorCode PCBDDCBenignPopOrPushB0(PC pc, PetscBool pop)
3025: {
3026:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;

3030:   /* TODO: add error checking
3031:     - avoid nested pop (or push) calls.
3032:     - cannot push before pop.
3033:     - cannot call this if pcbddc->local_mat is NULL
3034:   */
3035:   if (!pcbddc->benign_n) {
3036:     return(0);
3037:   }
3038:   if (pop) {
3039:     if (pcbddc->benign_change_explicit) {
3040:       IS       is_p0;
3041:       MatReuse reuse;

3043:       /* extract B_0 */
3044:       reuse = MAT_INITIAL_MATRIX;
3045:       if (pcbddc->benign_B0) {
3046:         reuse = MAT_REUSE_MATRIX;
3047:       }
3048:       ISCreateGeneral(PETSC_COMM_SELF,pcbddc->benign_n,pcbddc->benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);
3049:       MatCreateSubMatrix(pcbddc->local_mat,is_p0,NULL,reuse,&pcbddc->benign_B0);
3050:       /* remove rows and cols from local problem */
3051:       MatSetOption(pcbddc->local_mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
3052:       MatSetOption(pcbddc->local_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
3053:       MatZeroRowsColumnsIS(pcbddc->local_mat,is_p0,1.0,NULL,NULL);
3054:       ISDestroy(&is_p0);
3055:     } else {
3056:       Mat_IS      *matis = (Mat_IS*)pc->pmat->data;
3057:       PetscScalar *vals;
3058:       PetscInt    i,n,*idxs_ins;

3060:       VecGetLocalSize(matis->y,&n);
3061:       PetscMalloc2(n,&idxs_ins,n,&vals);
3062:       if (!pcbddc->benign_B0) {
3063:         PetscInt *nnz;
3064:         MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat),&pcbddc->benign_B0);
3065:         MatSetType(pcbddc->benign_B0,MATAIJ);
3066:         MatSetSizes(pcbddc->benign_B0,pcbddc->benign_n,n,PETSC_DECIDE,PETSC_DECIDE);
3067:         PetscMalloc1(pcbddc->benign_n,&nnz);
3068:         for (i=0;i<pcbddc->benign_n;i++) {
3069:           ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nnz[i]);
3070:           nnz[i] = n - nnz[i];
3071:         }
3072:         MatSeqAIJSetPreallocation(pcbddc->benign_B0,0,nnz);
3073:         MatSetOption(pcbddc->benign_B0,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
3074:         PetscFree(nnz);
3075:       }

3077:       for (i=0;i<pcbddc->benign_n;i++) {
3078:         PetscScalar *array;
3079:         PetscInt    *idxs,j,nz,cum;

3081:         VecSet(matis->x,0.);
3082:         ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nz);
3083:         ISGetIndices(pcbddc->benign_zerodiag_subs[i],(const PetscInt**)&idxs);
3084:         for (j=0;j<nz;j++) vals[j] = 1.;
3085:         VecSetValues(matis->x,nz,idxs,vals,INSERT_VALUES);
3086:         VecAssemblyBegin(matis->x);
3087:         VecAssemblyEnd(matis->x);
3088:         VecSet(matis->y,0.);
3089:         MatMult(matis->A,matis->x,matis->y);
3090:         VecGetArray(matis->y,&array);
3091:         cum = 0;
3092:         for (j=0;j<n;j++) {
3093:           if (PetscUnlikely(PetscAbsScalar(array[j]) > PETSC_SMALL)) {
3094:             vals[cum] = array[j];
3095:             idxs_ins[cum] = j;
3096:             cum++;
3097:           }
3098:         }
3099:         MatSetValues(pcbddc->benign_B0,1,&i,cum,idxs_ins,vals,INSERT_VALUES);
3100:         VecRestoreArray(matis->y,&array);
3101:         ISRestoreIndices(pcbddc->benign_zerodiag_subs[i],(const PetscInt**)&idxs);
3102:       }
3103:       MatAssemblyBegin(pcbddc->benign_B0,MAT_FINAL_ASSEMBLY);
3104:       MatAssemblyEnd(pcbddc->benign_B0,MAT_FINAL_ASSEMBLY);
3105:       PetscFree2(idxs_ins,vals);
3106:     }
3107:   } else { /* push */
3108:     if (pcbddc->benign_change_explicit) {
3109:       PetscInt i;

3111:       for (i=0;i<pcbddc->benign_n;i++) {
3112:         PetscScalar *B0_vals;
3113:         PetscInt    *B0_cols,B0_ncol;

3115:         MatGetRow(pcbddc->benign_B0,i,&B0_ncol,(const PetscInt**)&B0_cols,(const PetscScalar**)&B0_vals);
3116:         MatSetValues(pcbddc->local_mat,1,pcbddc->benign_p0_lidx+i,B0_ncol,B0_cols,B0_vals,INSERT_VALUES);
3117:         MatSetValues(pcbddc->local_mat,B0_ncol,B0_cols,1,pcbddc->benign_p0_lidx+i,B0_vals,INSERT_VALUES);
3118:         MatSetValue(pcbddc->local_mat,pcbddc->benign_p0_lidx[i],pcbddc->benign_p0_lidx[i],0.0,INSERT_VALUES);
3119:         MatRestoreRow(pcbddc->benign_B0,i,&B0_ncol,(const PetscInt**)&B0_cols,(const PetscScalar**)&B0_vals);
3120:       }
3121:       MatAssemblyBegin(pcbddc->local_mat,MAT_FINAL_ASSEMBLY);
3122:       MatAssemblyEnd(pcbddc->local_mat,MAT_FINAL_ASSEMBLY);
3123:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot push B0!");
3124:   }
3125:   return(0);
3126: }

3128: PetscErrorCode PCBDDCAdaptiveSelection(PC pc)
3129: {
3130:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
3131:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
3132:   PetscBLASInt    B_dummyint,B_neigs,B_ierr,B_lwork;
3133:   PetscBLASInt    *B_iwork,*B_ifail;
3134:   PetscScalar     *work,lwork;
3135:   PetscScalar     *St,*S,*eigv;
3136:   PetscScalar     *Sarray,*Starray;
3137:   PetscReal       *eigs,thresh,lthresh,uthresh;
3138:   PetscInt        i,nmax,nmin,nv,cum,mss,cum2,cumarray,maxneigs;
3139:   PetscBool       allocated_S_St;
3140: #if defined(PETSC_USE_COMPLEX)
3141:   PetscReal       *rwork;
3142: #endif
3143:   PetscErrorCode  ierr;

3146:   if (!sub_schurs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Adaptive selection of constraints requires SubSchurs data");
3147:   if (!sub_schurs->schur_explicit) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS and/or MKL_CPARDISO");
3148:   if (sub_schurs->n_subs && (!sub_schurs->is_symmetric)) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_SUP,"Adaptive selection not yet implemented for this matrix pencil (herm %d, symm %d, posdef %d)",sub_schurs->is_hermitian,sub_schurs->is_symmetric,sub_schurs->is_posdef);
3149:   PetscLogEventBegin(PC_BDDC_AdaptiveSetUp[pcbddc->current_level],pc,0,0,0);

3151:   if (pcbddc->dbg_flag) {
3152:     PetscViewerFlush(pcbddc->dbg_viewer);
3153:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
3154:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check adaptive selection of constraints\n");
3155:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
3156:   }

3158:   if (pcbddc->dbg_flag) {
3159:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d cc %D (%d,%d).\n",PetscGlobalRank,sub_schurs->n_subs,sub_schurs->is_hermitian,sub_schurs->is_posdef);
3160:   }

3162:   /* max size of subsets */
3163:   mss = 0;
3164:   for (i=0;i<sub_schurs->n_subs;i++) {
3165:     PetscInt subset_size;

3167:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
3168:     mss = PetscMax(mss,subset_size);
3169:   }

3171:   /* min/max and threshold */
3172:   nmax = pcbddc->adaptive_nmax > 0 ? pcbddc->adaptive_nmax : mss;
3173:   nmin = pcbddc->adaptive_nmin > 0 ? pcbddc->adaptive_nmin : 0;
3174:   nmax = PetscMax(nmin,nmax);
3175:   allocated_S_St = PETSC_FALSE;
3176:   if (nmin || !sub_schurs->is_posdef) { /* XXX */
3177:     allocated_S_St = PETSC_TRUE;
3178:   }

3180:   /* allocate lapack workspace */
3181:   cum = cum2 = 0;
3182:   maxneigs = 0;
3183:   for (i=0;i<sub_schurs->n_subs;i++) {
3184:     PetscInt n,subset_size;

3186:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
3187:     n = PetscMin(subset_size,nmax);
3188:     cum += subset_size;
3189:     cum2 += subset_size*n;
3190:     maxneigs = PetscMax(maxneigs,n);
3191:   }
3192:   lwork = 0;
3193:   if (mss) {
3194:     if (sub_schurs->is_symmetric) {
3195:       PetscScalar  sdummy = 0.;
3196:       PetscBLASInt B_itype = 1;
3197:       PetscBLASInt B_N = mss, idummy = 0;
3198:       PetscReal    rdummy = 0.,zero = 0.0;
3199:       PetscReal    eps = 0.0; /* dlamch? */

3201:       B_lwork = -1;
3202:       /* some implementations may complain about NULL pointers, even if we are querying */
3203:       S = &sdummy;
3204:       St = &sdummy;
3205:       eigs = &rdummy;
3206:       eigv = &sdummy;
3207:       B_iwork = &idummy;
3208:       B_ifail = &idummy;
3209: #if defined(PETSC_USE_COMPLEX)
3210:       rwork = &rdummy;
3211: #endif
3212:       thresh = 1.0;
3213:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
3214: #if defined(PETSC_USE_COMPLEX)
3215:       PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&zero,&thresh,&B_dummyint,&B_dummyint,&eps,&B_neigs,eigs,eigv,&B_N,&lwork,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3216: #else
3217:       PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&zero,&thresh,&B_dummyint,&B_dummyint,&eps,&B_neigs,eigs,eigv,&B_N,&lwork,&B_lwork,B_iwork,B_ifail,&B_ierr));
3218: #endif
3219:       if (B_ierr != 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYGVX Lapack routine %d",(int)B_ierr);
3220:       PetscFPTrapPop();
3221:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented");
3222:   }

3224:   nv = 0;
3225:   if (sub_schurs->is_vertices && pcbddc->use_vertices) { /* complement set of active subsets, each entry is a vertex (boundary made by active subsets, vertices and dirichlet dofs) */
3226:     ISGetLocalSize(sub_schurs->is_vertices,&nv);
3227:   }
3228:   PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);
3229:   if (allocated_S_St) {
3230:     PetscMalloc2(mss*mss,&S,mss*mss,&St);
3231:   }
3232:   PetscMalloc5(mss*mss,&eigv,mss,&eigs,B_lwork,&work,5*mss,&B_iwork,mss,&B_ifail);
3233: #if defined(PETSC_USE_COMPLEX)
3234:   PetscMalloc1(7*mss,&rwork);
3235: #endif
3236:   PetscMalloc5(nv+sub_schurs->n_subs,&pcbddc->adaptive_constraints_n,
3237:                       nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_idxs_ptr,
3238:                       nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_data_ptr,
3239:                       nv+cum,&pcbddc->adaptive_constraints_idxs,
3240:                       nv+cum2,&pcbddc->adaptive_constraints_data);
3241:   PetscArrayzero(pcbddc->adaptive_constraints_n,nv+sub_schurs->n_subs);

3243:   maxneigs = 0;
3244:   cum = cumarray = 0;
3245:   pcbddc->adaptive_constraints_idxs_ptr[0] = 0;
3246:   pcbddc->adaptive_constraints_data_ptr[0] = 0;
3247:   if (sub_schurs->is_vertices && pcbddc->use_vertices) {
3248:     const PetscInt *idxs;

3250:     ISGetIndices(sub_schurs->is_vertices,&idxs);
3251:     for (cum=0;cum<nv;cum++) {
3252:       pcbddc->adaptive_constraints_n[cum] = 1;
3253:       pcbddc->adaptive_constraints_idxs[cum] = idxs[cum];
3254:       pcbddc->adaptive_constraints_data[cum] = 1.0;
3255:       pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum]+1;
3256:       pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum]+1;
3257:     }
3258:     ISRestoreIndices(sub_schurs->is_vertices,&idxs);
3259:   }

3261:   if (mss) { /* multilevel */
3262:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);
3263:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);
3264:   }

3266:   lthresh = pcbddc->adaptive_threshold[0];
3267:   uthresh = pcbddc->adaptive_threshold[1];
3268:   for (i=0;i<sub_schurs->n_subs;i++) {
3269:     const PetscInt *idxs;
3270:     PetscReal      upper,lower;
3271:     PetscInt       j,subset_size,eigs_start = 0;
3272:     PetscBLASInt   B_N;
3273:     PetscBool      same_data = PETSC_FALSE;
3274:     PetscBool      scal = PETSC_FALSE;

3276:     if (pcbddc->use_deluxe_scaling) {
3277:       upper = PETSC_MAX_REAL;
3278:       lower = uthresh;
3279:     } else {
3280:       if (!sub_schurs->is_posdef) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented without deluxe scaling");
3281:       upper = 1./uthresh;
3282:       lower = 0.;
3283:     }
3284:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
3285:     ISGetIndices(sub_schurs->is_subs[i],&idxs);
3286:     PetscBLASIntCast(subset_size,&B_N);
3287:     /* this is experimental: we assume the dofs have been properly grouped to have
3288:        the diagonal blocks Schur complements either positive or negative definite (true for Stokes) */
3289:     if (!sub_schurs->is_posdef) {
3290:       Mat T;

3292:       for (j=0;j<subset_size;j++) {
3293:         if (PetscRealPart(*(Sarray+cumarray+j*(subset_size+1))) < 0.0) {
3294:           MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,Sarray+cumarray,&T);
3295:           MatScale(T,-1.0);
3296:           MatDestroy(&T);
3297:           MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,Starray+cumarray,&T);
3298:           MatScale(T,-1.0);
3299:           MatDestroy(&T);
3300:           if (sub_schurs->change_primal_sub) {
3301:             PetscInt       nz,k;
3302:             const PetscInt *idxs;

3304:             ISGetLocalSize(sub_schurs->change_primal_sub[i],&nz);
3305:             ISGetIndices(sub_schurs->change_primal_sub[i],&idxs);
3306:             for (k=0;k<nz;k++) {
3307:               *( Sarray + cumarray + idxs[k]*(subset_size+1)) *= -1.0;
3308:               *(Starray + cumarray + idxs[k]*(subset_size+1))  = 0.0;
3309:             }
3310:             ISRestoreIndices(sub_schurs->change_primal_sub[i],&idxs);
3311:           }
3312:           scal = PETSC_TRUE;
3313:           break;
3314:         }
3315:       }
3316:     }

3318:     if (allocated_S_St) { /* S and S_t should be copied since we could need them later */
3319:       if (sub_schurs->is_symmetric) {
3320:         PetscInt j,k;
3321:         if (sub_schurs->n_subs == 1) { /* zeroing memory to use PetscArraycmp() later */
3322:           PetscArrayzero(S,subset_size*subset_size);
3323:           PetscArrayzero(St,subset_size*subset_size);
3324:         }
3325:         for (j=0;j<subset_size;j++) {
3326:           for (k=j;k<subset_size;k++) {
3327:             S [j*subset_size+k] = Sarray [cumarray+j*subset_size+k];
3328:             St[j*subset_size+k] = Starray[cumarray+j*subset_size+k];
3329:           }
3330:         }
3331:       } else {
3332:         PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3333:         PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3334:       }
3335:     } else {
3336:       S = Sarray + cumarray;
3337:       St = Starray + cumarray;
3338:     }
3339:     /* see if we can save some work */
3340:     if (sub_schurs->n_subs == 1 && pcbddc->use_deluxe_scaling) {
3341:       PetscArraycmp(S,St,subset_size*subset_size,&same_data);
3342:     }

3344:     if (same_data && !sub_schurs->change) { /* there's no need of constraints here */
3345:       B_neigs = 0;
3346:     } else {
3347:       if (sub_schurs->is_symmetric) {
3348:         PetscBLASInt B_itype = 1;
3349:         PetscBLASInt B_IL, B_IU;
3350:         PetscReal    eps = -1.0; /* dlamch? */
3351:         PetscInt     nmin_s;
3352:         PetscBool    compute_range;

3354:         B_neigs = 0;
3355:         compute_range = (PetscBool)!same_data;
3356:         if (nmin >= subset_size) compute_range = PETSC_FALSE;

3358:         if (pcbddc->dbg_flag) {
3359:           PetscInt nc = 0;

3361:           if (sub_schurs->change_primal_sub) {
3362:             ISGetLocalSize(sub_schurs->change_primal_sub[i],&nc);
3363:           }
3364:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Computing for sub %D/%D size %D count %D fid %D (range %d) (change %D).\n",i,sub_schurs->n_subs,subset_size,pcbddc->mat_graph->count[idxs[0]]+1,pcbddc->mat_graph->which_dof[idxs[0]],compute_range,nc);
3365:         }

3367:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
3368:         if (compute_range) {

3370:           /* ask for eigenvalues larger than thresh */
3371:           if (sub_schurs->is_posdef) {
3372: #if defined(PETSC_USE_COMPLEX)
3373:             PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&lower,&upper,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3374: #else
3375:             PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&lower,&upper,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3376: #endif
3377:             PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3378:           } else { /* no theory so far, but it works nicely */
3379:             PetscInt  recipe = 0,recipe_m = 1;
3380:             PetscReal bb[2];

3382:             PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe",&recipe,NULL);
3383:             switch (recipe) {
3384:             case 0:
3385:               if (scal) { bb[0] = PETSC_MIN_REAL; bb[1] = lthresh; }
3386:               else { bb[0] = uthresh; bb[1] = PETSC_MAX_REAL; }
3387: #if defined(PETSC_USE_COMPLEX)
3388:               PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3389: #else
3390:               PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3391: #endif
3392:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3393:               break;
3394:             case 1:
3395:               bb[0] = PETSC_MIN_REAL; bb[1] = lthresh*lthresh;
3396: #if defined(PETSC_USE_COMPLEX)
3397:               PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3398: #else
3399:               PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3400: #endif
3401:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3402:               if (!scal) {
3403:                 PetscBLASInt B_neigs2 = 0;

3405:                 bb[0] = PetscMax(lthresh*lthresh,uthresh); bb[1] = PETSC_MAX_REAL;
3406:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3407:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3408: #if defined(PETSC_USE_COMPLEX)
3409:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*B_N,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3410: #else
3411:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*B_N,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3412: #endif
3413:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3414:                 B_neigs += B_neigs2;
3415:               }
3416:               break;
3417:             case 2:
3418:               if (scal) {
3419:                 bb[0] = PETSC_MIN_REAL;
3420:                 bb[1] = 0;
3421: #if defined(PETSC_USE_COMPLEX)
3422:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3423: #else
3424:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3425: #endif
3426:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3427:               } else {
3428:                 PetscBLASInt B_neigs2 = 0;
3429:                 PetscBool    import = PETSC_FALSE;

3431:                 lthresh = PetscMax(lthresh,0.0);
3432:                 if (lthresh > 0.0) {
3433:                   bb[0] = PETSC_MIN_REAL;
3434:                   bb[1] = lthresh*lthresh;

3436:                   import = PETSC_TRUE;
3437: #if defined(PETSC_USE_COMPLEX)
3438:                   PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3439: #else
3440:                   PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3441: #endif
3442:                   PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3443:                 }
3444:                 bb[0] = PetscMax(lthresh*lthresh,uthresh);
3445:                 bb[1] = PETSC_MAX_REAL;
3446:                 if (import) {
3447:                   PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3448:                   PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3449:                 }
3450: #if defined(PETSC_USE_COMPLEX)
3451:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*B_N,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3452: #else
3453:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*B_N,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3454: #endif
3455:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3456:                 B_neigs += B_neigs2;
3457:               }
3458:               break;
3459:             case 3:
3460:               if (scal) {
3461:                 PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe3_min_scal",&recipe_m,NULL);
3462:               } else {
3463:                 PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe3_min",&recipe_m,NULL);
3464:               }
3465:               if (!scal) {
3466:                 bb[0] = uthresh;
3467:                 bb[1] = PETSC_MAX_REAL;
3468: #if defined(PETSC_USE_COMPLEX)
3469:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3470: #else
3471:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3472: #endif
3473:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3474:               }
3475:               if (recipe_m > 0 && B_N - B_neigs > 0) {
3476:                 PetscBLASInt B_neigs2 = 0;

3478:                 B_IL = 1;
3479:                 PetscBLASIntCast(PetscMin(recipe_m,B_N - B_neigs),&B_IU);
3480:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3481:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3482: #if defined(PETSC_USE_COMPLEX)
3483:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&lower,&upper,&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*B_N,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3484: #else
3485:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&lower,&upper,&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*B_N,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3486: #endif
3487:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3488:                 B_neigs += B_neigs2;
3489:               }
3490:               break;
3491:             case 4:
3492:               bb[0] = PETSC_MIN_REAL; bb[1] = lthresh;
3493: #if defined(PETSC_USE_COMPLEX)
3494:               PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3495: #else
3496:               PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3497: #endif
3498:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3499:               {
3500:                 PetscBLASInt B_neigs2 = 0;

3502:                 bb[0] = PetscMax(lthresh+PETSC_SMALL,uthresh); bb[1] = PETSC_MAX_REAL;
3503:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3504:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3505: #if defined(PETSC_USE_COMPLEX)
3506:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*B_N,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3507: #else
3508:                 PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*B_N,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3509: #endif
3510:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3511:                 B_neigs += B_neigs2;
3512:               }
3513:               break;
3514:             case 5: /* same as before: first compute all eigenvalues, then filter */
3515: #if defined(PETSC_USE_COMPLEX)
3516:               PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","A","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3517: #else
3518:               PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","A","L",&B_N,St,&B_N,S,&B_N,&bb[0],&bb[1],&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3519: #endif
3520:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3521:               {
3522:                 PetscInt e,k,ne;
3523:                 for (e=0,ne=0;e<B_neigs;e++) {
3524:                   if (eigs[e] < lthresh || eigs[e] > uthresh) {
3525:                     for (k=0;k<B_N;k++) S[ne*B_N+k] = eigv[e*B_N+k];
3526:                     eigs[ne] = eigs[e];
3527:                     ne++;
3528:                   }
3529:                 }
3530:                 PetscArraycpy(eigv,S,B_N*ne);
3531:                 B_neigs = ne;
3532:               }
3533:               break;
3534:             default:
3535:               SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Unknown recipe %D",recipe);
3536:             }
3537:           }
3538:         } else if (!same_data) { /* this is just to see all the eigenvalues */
3539:           B_IU = PetscMax(1,PetscMin(B_N,nmax));
3540:           B_IL = 1;
3541: #if defined(PETSC_USE_COMPLEX)
3542:           PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&lower,&upper,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3543: #else
3544:           PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&lower,&upper,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3545: #endif
3546:           PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3547:         } else { /* same_data is true, so just get the adaptive functional requested by the user */
3548:           PetscInt k;
3549:           if (!sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
3550:           ISGetLocalSize(sub_schurs->change_primal_sub[i],&nmax);
3551:           PetscBLASIntCast(nmax,&B_neigs);
3552:           nmin = nmax;
3553:           PetscArrayzero(eigv,subset_size*nmax);
3554:           for (k=0;k<nmax;k++) {
3555:             eigs[k] = 1./PETSC_SMALL;
3556:             eigv[k*(subset_size+1)] = 1.0;
3557:           }
3558:         }
3559:         PetscFPTrapPop();
3560:         if (B_ierr) {
3561:           if (B_ierr < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
3562:           else if (B_ierr <= B_N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: %d eigenvalues failed to converge",(int)B_ierr);
3563:           else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: leading minor of order %d is not positive definite",(int)B_ierr-B_N-1);
3564:         }

3566:         if (B_neigs > nmax) {
3567:           if (pcbddc->dbg_flag) {
3568:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, more than maximum required %D.\n",B_neigs,nmax);
3569:           }
3570:           if (pcbddc->use_deluxe_scaling) eigs_start = scal ? 0 : B_neigs-nmax;
3571:           B_neigs = nmax;
3572:         }

3574:         nmin_s = PetscMin(nmin,B_N);
3575:         if (B_neigs < nmin_s) {
3576:           PetscBLASInt B_neigs2 = 0;

3578:           if (pcbddc->use_deluxe_scaling) {
3579:             if (scal) {
3580:               B_IU = nmin_s;
3581:               B_IL = B_neigs + 1;
3582:             } else {
3583:               B_IL = B_N - nmin_s + 1;
3584:               B_IU = B_N - B_neigs;
3585:             }
3586:           } else {
3587:             B_IL = B_neigs + 1;
3588:             B_IU = nmin_s;
3589:           }
3590:           if (pcbddc->dbg_flag) {
3591:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, less than minimum required %D. Asking for %d to %d incl (fortran like)\n",B_neigs,nmin,B_IL,B_IU);
3592:           }
3593:           if (sub_schurs->is_symmetric) {
3594:             PetscInt j,k;
3595:             for (j=0;j<subset_size;j++) {
3596:               for (k=j;k<subset_size;k++) {
3597:                 S [j*subset_size+k] = Sarray [cumarray+j*subset_size+k];
3598:                 St[j*subset_size+k] = Starray[cumarray+j*subset_size+k];
3599:               }
3600:             }
3601:           } else {
3602:             PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3603:             PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3604:           }
3605:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
3606: #if defined(PETSC_USE_COMPLEX)
3607:           PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&lower,&upper,&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*subset_size,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
3608: #else
3609:           PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&lower,&upper,&B_IL,&B_IU,&eps,&B_neigs2,eigs+B_neigs,eigv+B_neigs*subset_size,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
3610: #endif
3611:           PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3612:           PetscFPTrapPop();
3613:           B_neigs += B_neigs2;
3614:         }
3615:         if (B_ierr) {
3616:           if (B_ierr < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
3617:           else if (B_ierr <= B_N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: %d eigenvalues failed to converge",(int)B_ierr);
3618:           else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: leading minor of order %d is not positive definite",(int)B_ierr-B_N-1);
3619:         }
3620:         if (pcbddc->dbg_flag) {
3621:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Got %d eigs\n",B_neigs);
3622:           for (j=0;j<B_neigs;j++) {
3623:             if (eigs[j] == 0.0) {
3624:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     Inf\n");
3625:             } else {
3626:               if (pcbddc->use_deluxe_scaling) {
3627:                 PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",eigs[j+eigs_start]);
3628:               } else {
3629:                 PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",1./eigs[j+eigs_start]);
3630:               }
3631:             }
3632:           }
3633:         }
3634:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented");
3635:     }
3636:     /* change the basis back to the original one */
3637:     if (sub_schurs->change) {
3638:       Mat change,phi,phit;

3640:       if (pcbddc->dbg_flag > 2) {
3641:         PetscInt ii;
3642:         for (ii=0;ii<B_neigs;ii++) {
3643:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector (old basis) %d/%d (%d)\n",ii,B_neigs,B_N);
3644:           for (j=0;j<B_N;j++) {
3645: #if defined(PETSC_USE_COMPLEX)
3646:             PetscReal r = PetscRealPart(eigv[(ii+eigs_start)*subset_size+j]);
3647:             PetscReal c = PetscImaginaryPart(eigv[(ii+eigs_start)*subset_size+j]);
3648:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e + %1.4e i\n",r,c);
3649: #else
3650:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",eigv[(ii+eigs_start)*subset_size+j]);
3651: #endif
3652:           }
3653:         }
3654:       }
3655:       KSPGetOperators(sub_schurs->change[i],&change,NULL);
3656:       MatCreateSeqDense(PETSC_COMM_SELF,subset_size,B_neigs,eigv+eigs_start*subset_size,&phit);
3657:       MatMatMult(change,phit,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&phi);
3658:       MatCopy(phi,phit,SAME_NONZERO_PATTERN);
3659:       MatDestroy(&phit);
3660:       MatDestroy(&phi);
3661:     }
3662:     maxneigs = PetscMax(B_neigs,maxneigs);
3663:     pcbddc->adaptive_constraints_n[i+nv] = B_neigs;
3664:     if (B_neigs) {
3665:       PetscArraycpy(pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum],eigv+eigs_start*subset_size,B_neigs*subset_size);

3667:       if (pcbddc->dbg_flag > 1) {
3668:         PetscInt ii;
3669:         for (ii=0;ii<B_neigs;ii++) {
3670:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector %d/%d (%d)\n",ii,B_neigs,B_N);
3671:           for (j=0;j<B_N;j++) {
3672: #if defined(PETSC_USE_COMPLEX)
3673:             PetscReal r = PetscRealPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
3674:             PetscReal c = PetscImaginaryPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
3675:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e + %1.4e i\n",r,c);
3676: #else
3677:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
3678: #endif
3679:           }
3680:         }
3681:       }
3682:       PetscArraycpy(pcbddc->adaptive_constraints_idxs+pcbddc->adaptive_constraints_idxs_ptr[cum],idxs,subset_size);
3683:       pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum] + subset_size;
3684:       pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum] + subset_size*B_neigs;
3685:       cum++;
3686:     }
3687:     ISRestoreIndices(sub_schurs->is_subs[i],&idxs);
3688:     /* shift for next computation */
3689:     cumarray += subset_size*subset_size;
3690:   }
3691:   if (pcbddc->dbg_flag) {
3692:     PetscViewerFlush(pcbddc->dbg_viewer);
3693:   }

3695:   if (mss) {
3696:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);
3697:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);
3698:     /* destroy matrices (junk) */
3699:     MatDestroy(&sub_schurs->sum_S_Ej_inv_all);
3700:     MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);
3701:   }
3702:   if (allocated_S_St) {
3703:     PetscFree2(S,St);
3704:   }
3705:   PetscFree5(eigv,eigs,work,B_iwork,B_ifail);
3706: #if defined(PETSC_USE_COMPLEX)
3707:   PetscFree(rwork);
3708: #endif
3709:   if (pcbddc->dbg_flag) {
3710:     PetscInt maxneigs_r;
3711:     MPIU_Allreduce(&maxneigs,&maxneigs_r,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));
3712:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of constraints per cc %D\n",maxneigs_r);
3713:   }
3714:   PetscLogEventEnd(PC_BDDC_AdaptiveSetUp[pcbddc->current_level],pc,0,0,0);
3715:   return(0);
3716: }

3718: PetscErrorCode PCBDDCSetUpSolvers(PC pc)
3719: {
3720:   PetscScalar    *coarse_submat_vals;

3724:   /* Setup local scatters R_to_B and (optionally) R_to_D */
3725:   /* PCBDDCSetUpLocalWorkVectors should be called first! */
3726:   PCBDDCSetUpLocalScatters(pc);

3728:   /* Setup local neumann solver ksp_R */
3729:   /* PCBDDCSetUpLocalScatters should be called first! */
3730:   PCBDDCSetUpLocalSolvers(pc,PETSC_FALSE,PETSC_TRUE);

3732:   /*
3733:      Setup local correction and local part of coarse basis.
3734:      Gives back the dense local part of the coarse matrix in column major ordering
3735:   */
3736:   PCBDDCSetUpCorrection(pc,&coarse_submat_vals);

3738:   /* Compute total number of coarse nodes and setup coarse solver */
3739:   PCBDDCSetUpCoarseSolver(pc,coarse_submat_vals);

3741:   /* free */
3742:   PetscFree(coarse_submat_vals);
3743:   return(0);
3744: }

3746: PetscErrorCode PCBDDCResetCustomization(PC pc)
3747: {
3748:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

3752:   ISDestroy(&pcbddc->user_primal_vertices);
3753:   ISDestroy(&pcbddc->user_primal_vertices_local);
3754:   ISDestroy(&pcbddc->NeumannBoundaries);
3755:   ISDestroy(&pcbddc->NeumannBoundariesLocal);
3756:   ISDestroy(&pcbddc->DirichletBoundaries);
3757:   MatNullSpaceDestroy(&pcbddc->onearnullspace);
3758:   PetscFree(pcbddc->onearnullvecs_state);
3759:   ISDestroy(&pcbddc->DirichletBoundariesLocal);
3760:   PCBDDCSetDofsSplitting(pc,0,NULL);
3761:   PCBDDCSetDofsSplittingLocal(pc,0,NULL);
3762:   return(0);
3763: }

3765: PetscErrorCode PCBDDCResetTopography(PC pc)
3766: {
3767:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
3768:   PetscInt       i;

3772:   MatDestroy(&pcbddc->nedcG);
3773:   ISDestroy(&pcbddc->nedclocal);
3774:   MatDestroy(&pcbddc->discretegradient);
3775:   MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);
3776:   MatDestroy(&pcbddc->ChangeOfBasisMatrix);
3777:   MatDestroy(&pcbddc->switch_static_change);
3778:   VecDestroy(&pcbddc->work_change);
3779:   MatDestroy(&pcbddc->ConstraintMatrix);
3780:   MatDestroy(&pcbddc->divudotp);
3781:   ISDestroy(&pcbddc->divudotp_vl2l);
3782:   PCBDDCGraphDestroy(&pcbddc->mat_graph);
3783:   for (i=0;i<pcbddc->n_local_subs;i++) {
3784:     ISDestroy(&pcbddc->local_subs[i]);
3785:   }
3786:   pcbddc->n_local_subs = 0;
3787:   PetscFree(pcbddc->local_subs);
3788:   PCBDDCSubSchursDestroy(&pcbddc->sub_schurs);
3789:   pcbddc->graphanalyzed        = PETSC_FALSE;
3790:   pcbddc->recompute_topography = PETSC_TRUE;
3791:   pcbddc->corner_selected      = PETSC_FALSE;
3792:   return(0);
3793: }

3795: PetscErrorCode PCBDDCResetSolvers(PC pc)
3796: {
3797:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

3801:   VecDestroy(&pcbddc->coarse_vec);
3802:   if (pcbddc->coarse_phi_B) {
3803:     PetscScalar *array;
3804:     MatDenseGetArray(pcbddc->coarse_phi_B,&array);
3805:     PetscFree(array);
3806:   }
3807:   MatDestroy(&pcbddc->coarse_phi_B);
3808:   MatDestroy(&pcbddc->coarse_phi_D);
3809:   MatDestroy(&pcbddc->coarse_psi_B);
3810:   MatDestroy(&pcbddc->coarse_psi_D);
3811:   VecDestroy(&pcbddc->vec1_P);
3812:   VecDestroy(&pcbddc->vec1_C);
3813:   MatDestroy(&pcbddc->local_auxmat2);
3814:   MatDestroy(&pcbddc->local_auxmat1);
3815:   VecDestroy(&pcbddc->vec1_R);
3816:   VecDestroy(&pcbddc->vec2_R);
3817:   ISDestroy(&pcbddc->is_R_local);
3818:   VecScatterDestroy(&pcbddc->R_to_B);
3819:   VecScatterDestroy(&pcbddc->R_to_D);
3820:   VecScatterDestroy(&pcbddc->coarse_loc_to_glob);
3821:   KSPReset(pcbddc->ksp_D);
3822:   KSPReset(pcbddc->ksp_R);
3823:   KSPReset(pcbddc->coarse_ksp);
3824:   MatDestroy(&pcbddc->local_mat);
3825:   PetscFree(pcbddc->primal_indices_local_idxs);
3826:   PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);
3827:   PetscFree(pcbddc->global_primal_indices);
3828:   ISDestroy(&pcbddc->coarse_subassembling);
3829:   MatDestroy(&pcbddc->benign_change);
3830:   VecDestroy(&pcbddc->benign_vec);
3831:   PCBDDCBenignShellMat(pc,PETSC_TRUE);
3832:   MatDestroy(&pcbddc->benign_B0);
3833:   PetscSFDestroy(&pcbddc->benign_sf);
3834:   if (pcbddc->benign_zerodiag_subs) {
3835:     PetscInt i;
3836:     for (i=0;i<pcbddc->benign_n;i++) {
3837:       ISDestroy(&pcbddc->benign_zerodiag_subs[i]);
3838:     }
3839:     PetscFree(pcbddc->benign_zerodiag_subs);
3840:   }
3841:   PetscFree3(pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx,pcbddc->benign_p0);
3842:   return(0);
3843: }

3845: PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
3846: {
3847:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
3848:   PC_IS          *pcis = (PC_IS*)pc->data;
3849:   VecType        impVecType;
3850:   PetscInt       n_constraints,n_R,old_size;

3854:   n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - pcbddc->n_vertices;
3855:   n_R = pcis->n - pcbddc->n_vertices;
3856:   VecGetType(pcis->vec1_N,&impVecType);
3857:   /* local work vectors (try to avoid unneeded work)*/
3858:   /* R nodes */
3859:   old_size = -1;
3860:   if (pcbddc->vec1_R) {
3861:     VecGetSize(pcbddc->vec1_R,&old_size);
3862:   }
3863:   if (n_R != old_size) {
3864:     VecDestroy(&pcbddc->vec1_R);
3865:     VecDestroy(&pcbddc->vec2_R);
3866:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);
3867:     VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);
3868:     VecSetType(pcbddc->vec1_R,impVecType);
3869:     VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);
3870:   }
3871:   /* local primal dofs */
3872:   old_size = -1;
3873:   if (pcbddc->vec1_P) {
3874:     VecGetSize(pcbddc->vec1_P,&old_size);
3875:   }
3876:   if (pcbddc->local_primal_size != old_size) {
3877:     VecDestroy(&pcbddc->vec1_P);
3878:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);
3879:     VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,pcbddc->local_primal_size);
3880:     VecSetType(pcbddc->vec1_P,impVecType);
3881:   }
3882:   /* local explicit constraints */
3883:   old_size = -1;
3884:   if (pcbddc->vec1_C) {
3885:     VecGetSize(pcbddc->vec1_C,&old_size);
3886:   }
3887:   if (n_constraints && n_constraints != old_size) {
3888:     VecDestroy(&pcbddc->vec1_C);
3889:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);
3890:     VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);
3891:     VecSetType(pcbddc->vec1_C,impVecType);
3892:   }
3893:   return(0);
3894: }

3896: PetscErrorCode PCBDDCSetUpCorrection(PC pc, PetscScalar **coarse_submat_vals_n)
3897: {
3898:   PetscErrorCode  ierr;
3899:   /* pointers to pcis and pcbddc */
3900:   PC_IS*          pcis = (PC_IS*)pc->data;
3901:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
3902:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
3903:   /* submatrices of local problem */
3904:   Mat             A_RV,A_VR,A_VV,local_auxmat2_R;
3905:   /* submatrices of local coarse problem */
3906:   Mat             S_VV,S_CV,S_VC,S_CC;
3907:   /* working matrices */
3908:   Mat             C_CR;
3909:   /* additional working stuff */
3910:   PC              pc_R;
3911:   Mat             F,Brhs = NULL;
3912:   Vec             dummy_vec;
3913:   PetscBool       isLU,isCHOL,need_benign_correction,sparserhs;
3914:   PetscScalar     *coarse_submat_vals; /* TODO: use a PETSc matrix */
3915:   PetscScalar     *work;
3916:   PetscInt        *idx_V_B;
3917:   PetscInt        lda_rhs,n,n_vertices,n_constraints,*p0_lidx_I;
3918:   PetscInt        i,n_R,n_D,n_B;
3919:   PetscScalar     one=1.0,m_one=-1.0;

3922:   if (!pcbddc->symmetric_primal && pcbddc->benign_n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Non-symmetric primal basis computation with benign trick not yet implemented");
3923:   PetscLogEventBegin(PC_BDDC_CorrectionSetUp[pcbddc->current_level],pc,0,0,0);

3925:   /* Set Non-overlapping dimensions */
3926:   n_vertices = pcbddc->n_vertices;
3927:   n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - n_vertices;
3928:   n_B = pcis->n_B;
3929:   n_D = pcis->n - n_B;
3930:   n_R = pcis->n - n_vertices;

3932:   /* vertices in boundary numbering */
3933:   PetscMalloc1(n_vertices,&idx_V_B);
3934:   ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,n_vertices,pcbddc->local_primal_ref_node,&i,idx_V_B);
3935:   if (i != n_vertices) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for BDDC vertices! %D != %D",n_vertices,i);

3937:   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
3938:   PetscCalloc1(pcbddc->local_primal_size*pcbddc->local_primal_size,&coarse_submat_vals);
3939:   MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_vertices,coarse_submat_vals,&S_VV);
3940:   MatDenseSetLDA(S_VV,pcbddc->local_primal_size);
3941:   MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_vertices,coarse_submat_vals+n_vertices,&S_CV);
3942:   MatDenseSetLDA(S_CV,pcbddc->local_primal_size);
3943:   MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_constraints,coarse_submat_vals+pcbddc->local_primal_size*n_vertices,&S_VC);
3944:   MatDenseSetLDA(S_VC,pcbddc->local_primal_size);
3945:   MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_constraints,coarse_submat_vals+(pcbddc->local_primal_size+1)*n_vertices,&S_CC);
3946:   MatDenseSetLDA(S_CC,pcbddc->local_primal_size);

3948:   /* determine if can use MatSolve routines instead of calling KSPSolve on ksp_R */
3949:   KSPGetPC(pcbddc->ksp_R,&pc_R);
3950:   PCSetUp(pc_R);
3951:   PetscObjectTypeCompare((PetscObject)pc_R,PCLU,&isLU);
3952:   PetscObjectTypeCompare((PetscObject)pc_R,PCCHOLESKY,&isCHOL);
3953:   lda_rhs = n_R;
3954:   need_benign_correction = PETSC_FALSE;
3955:   if (isLU || isCHOL) {
3956:     PCFactorGetMatrix(pc_R,&F);
3957:   } else if (sub_schurs && sub_schurs->reuse_solver) {
3958:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
3959:     MatFactorType      type;

3961:     F = reuse_solver->F;
3962:     MatGetFactorType(F,&type);
3963:     if (type == MAT_FACTOR_CHOLESKY) isCHOL = PETSC_TRUE;
3964:     if (type == MAT_FACTOR_LU) isLU = PETSC_TRUE;
3965:     MatGetSize(F,&lda_rhs,NULL);
3966:     need_benign_correction = (PetscBool)(!!reuse_solver->benign_n);
3967:   } else F = NULL;

3969:   /* determine if we can use a sparse right-hand side */
3970:   sparserhs = PETSC_FALSE;
3971:   if (F) {
3972:     MatSolverType solver;

3974:     MatFactorGetSolverType(F,&solver);
3975:     PetscStrcmp(solver,MATSOLVERMUMPS,&sparserhs);
3976:   }

3978:   /* allocate workspace */
3979:   n = 0;
3980:   if (n_constraints) {
3981:     n += lda_rhs*n_constraints;
3982:   }
3983:   if (n_vertices) {
3984:     n = PetscMax(2*lda_rhs*n_vertices,n);
3985:     n = PetscMax((lda_rhs+n_B)*n_vertices,n);
3986:   }
3987:   if (!pcbddc->symmetric_primal) {
3988:     n = PetscMax(2*lda_rhs*pcbddc->local_primal_size,n);
3989:   }
3990:   PetscMalloc1(n,&work);

3992:   /* create dummy vector to modify rhs and sol of MatMatSolve (work array will never be used) */
3993:   dummy_vec = NULL;
3994:   if (need_benign_correction && lda_rhs != n_R && F) {
3995:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&dummy_vec);
3996:     VecSetSizes(dummy_vec,lda_rhs,PETSC_DECIDE);
3997:     VecSetType(dummy_vec,((PetscObject)pcis->vec1_N)->type_name);
3998:   }

4000:   MatDestroy(&pcbddc->local_auxmat1);
4001:   MatDestroy(&pcbddc->local_auxmat2);

4003:   /* Precompute stuffs needed for preprocessing and application of BDDC*/
4004:   if (n_constraints) {
4005:     Mat         M3,C_B;
4006:     IS          is_aux;
4007:     PetscScalar *array,*array2;

4009:     /* Extract constraints on R nodes: C_{CR}  */
4010:     ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);
4011:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);
4012:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);

4014:     /* Assemble         local_auxmat2_R =        (- A_{RR}^{-1} C^T_{CR}) needed by BDDC setup */
4015:     /* Assemble pcbddc->local_auxmat2   = R_to_B (- A_{RR}^{-1} C^T_{CR}) needed by BDDC application */
4016:     if (!sparserhs) {
4017:       PetscArrayzero(work,lda_rhs*n_constraints);
4018:       for (i=0;i<n_constraints;i++) {
4019:         const PetscScalar *row_cmat_values;
4020:         const PetscInt    *row_cmat_indices;
4021:         PetscInt          size_of_constraint,j;

4023:         MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);
4024:         for (j=0;j<size_of_constraint;j++) {
4025:           work[row_cmat_indices[j]+i*lda_rhs] = -row_cmat_values[j];
4026:         }
4027:         MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);
4028:       }
4029:       MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,work,&Brhs);
4030:     } else {
4031:       Mat tC_CR;

4033:       MatScale(C_CR,-1.0);
4034:       if (lda_rhs != n_R) {
4035:         PetscScalar *aa;
4036:         PetscInt    r,*ii,*jj;
4037:         PetscBool   done;

4039:         MatGetRowIJ(C_CR,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
4040:         if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"GetRowIJ failed");
4041:         MatSeqAIJGetArray(C_CR,&aa);
4042:         MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,n_constraints,lda_rhs,ii,jj,aa,&tC_CR);
4043:         MatRestoreRowIJ(C_CR,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
4044:         if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"RestoreRowIJ failed");
4045:       } else {
4046:         PetscObjectReference((PetscObject)C_CR);
4047:         tC_CR = C_CR;
4048:       }
4049:       MatCreateTranspose(tC_CR,&Brhs);
4050:       MatDestroy(&tC_CR);
4051:     }
4052:     MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,NULL,&local_auxmat2_R);
4053:     if (F) {
4054:       if (need_benign_correction) {
4055:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

4057:         /* rhs is already zero on interior dofs, no need to change the rhs */
4058:         PetscArrayzero(reuse_solver->benign_save_vals,pcbddc->benign_n);
4059:       }
4060:       MatMatSolve(F,Brhs,local_auxmat2_R);
4061:       if (need_benign_correction) {
4062:         PetscScalar        *marr;
4063:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

4065:         MatDenseGetArray(local_auxmat2_R,&marr);
4066:         if (lda_rhs != n_R) {
4067:           for (i=0;i<n_constraints;i++) {
4068:             VecPlaceArray(dummy_vec,marr+i*lda_rhs);
4069:             PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_TRUE,PETSC_TRUE);
4070:             VecResetArray(dummy_vec);
4071:           }
4072:         } else {
4073:           for (i=0;i<n_constraints;i++) {
4074:             VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
4075:             PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_TRUE,PETSC_TRUE);
4076:             VecResetArray(pcbddc->vec1_R);
4077:           }
4078:         }
4079:         MatDenseRestoreArray(local_auxmat2_R,&marr);
4080:       }
4081:     } else {
4082:       PetscScalar *marr;

4084:       MatDenseGetArray(local_auxmat2_R,&marr);
4085:       for (i=0;i<n_constraints;i++) {
4086:         VecPlaceArray(pcbddc->vec1_R,work+i*lda_rhs);
4087:         VecPlaceArray(pcbddc->vec2_R,marr+i*lda_rhs);
4088:         KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
4089:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
4090:         VecResetArray(pcbddc->vec1_R);
4091:         VecResetArray(pcbddc->vec2_R);
4092:       }
4093:       MatDenseRestoreArray(local_auxmat2_R,&marr);
4094:     }
4095:     if (sparserhs) {
4096:       MatScale(C_CR,-1.0);
4097:     }
4098:     MatDestroy(&Brhs);
4099:     if (!pcbddc->switch_static) {
4100:       MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_constraints,NULL,&pcbddc->local_auxmat2);
4101:       MatDenseGetArray(pcbddc->local_auxmat2,&array);
4102:       MatDenseGetArray(local_auxmat2_R,&array2);
4103:       for (i=0;i<n_constraints;i++) {
4104:         VecPlaceArray(pcbddc->vec1_R,array2+i*lda_rhs);
4105:         VecPlaceArray(pcis->vec1_B,array+i*n_B);
4106:         VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4107:         VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4108:         VecResetArray(pcis->vec1_B);
4109:         VecResetArray(pcbddc->vec1_R);
4110:       }
4111:       MatDenseRestoreArray(local_auxmat2_R,&array2);
4112:       MatDenseRestoreArray(pcbddc->local_auxmat2,&array);
4113:       MatMatMult(C_B,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);
4114:     } else {
4115:       if (lda_rhs != n_R) {
4116:         IS dummy;

4118:         ISCreateStride(PETSC_COMM_SELF,n_R,0,1,&dummy);
4119:         MatCreateSubMatrix(local_auxmat2_R,dummy,NULL,MAT_INITIAL_MATRIX,&pcbddc->local_auxmat2);
4120:         ISDestroy(&dummy);
4121:       } else {
4122:         PetscObjectReference((PetscObject)local_auxmat2_R);
4123:         pcbddc->local_auxmat2 = local_auxmat2_R;
4124:       }
4125:       MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);
4126:     }
4127:     ISDestroy(&is_aux);
4128:     /* Assemble explicitly S_CC = ( C_{CR} A_{RR}^{-1} C^T_{CR})^{-1}  */
4129:     MatScale(M3,m_one);
4130:     if (isCHOL) {
4131:       MatCholeskyFactor(M3,NULL,NULL);
4132:     } else {
4133:       MatLUFactor(M3,NULL,NULL,NULL);
4134:     }
4135:     MatSeqDenseInvertFactors_Private(M3);
4136:     /* Assemble local_auxmat1 = S_CC*C_{CB} needed by BDDC application in KSP and in preproc */
4137:     MatMatMult(M3,C_B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);
4138:     MatDestroy(&C_B);
4139:     MatCopy(M3,S_CC,SAME_NONZERO_PATTERN); /* S_CC can have a different LDA, MatMatSolve doesn't support it */
4140:     MatDestroy(&M3);
4141:   }

4143:   /* Get submatrices from subdomain matrix */
4144:   if (n_vertices) {
4145: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4146:     PetscBool oldpin;
4147: #endif
4148:     PetscBool isaij;
4149:     IS        is_aux;

4151:     if (sub_schurs && sub_schurs->reuse_solver) { /* is_R_local is not sorted, ISComplement doesn't like it */
4152:       IS tis;

4154:       ISDuplicate(pcbddc->is_R_local,&tis);
4155:       ISSort(tis);
4156:       ISComplement(tis,0,pcis->n,&is_aux);
4157:       ISDestroy(&tis);
4158:     } else {
4159:       ISComplement(pcbddc->is_R_local,0,pcis->n,&is_aux);
4160:     }
4161: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4162:     oldpin = pcbddc->local_mat->boundtocpu;
4163: #endif
4164:     MatBindToCPU(pcbddc->local_mat,PETSC_TRUE);
4165:     MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);
4166:     MatCreateSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);
4167:     PetscObjectBaseTypeCompare((PetscObject)A_VR,MATSEQAIJ,&isaij);
4168:     if (!isaij) { /* TODO REMOVE: MatMatMult(A_VR,A_RRmA_RV) below may raise an error */
4169:       MatConvert(A_VR,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_VR);
4170:     }
4171:     MatCreateSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);
4172: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4173:     MatBindToCPU(pcbddc->local_mat,oldpin);
4174: #endif
4175:     ISDestroy(&is_aux);
4176:   }

4178:   /* Matrix of coarse basis functions (local) */
4179:   if (pcbddc->coarse_phi_B) {
4180:     PetscInt on_B,on_primal,on_D=n_D;
4181:     if (pcbddc->coarse_phi_D) {
4182:       MatGetSize(pcbddc->coarse_phi_D,&on_D,NULL);
4183:     }
4184:     MatGetSize(pcbddc->coarse_phi_B,&on_B,&on_primal);
4185:     if (on_B != n_B || on_primal != pcbddc->local_primal_size || on_D != n_D) {
4186:       PetscScalar *marray;

4188:       MatDenseGetArray(pcbddc->coarse_phi_B,&marray);
4189:       PetscFree(marray);
4190:       MatDestroy(&pcbddc->coarse_phi_B);
4191:       MatDestroy(&pcbddc->coarse_psi_B);
4192:       MatDestroy(&pcbddc->coarse_phi_D);
4193:       MatDestroy(&pcbddc->coarse_psi_D);
4194:     }
4195:   }

4197:   if (!pcbddc->coarse_phi_B) {
4198:     PetscScalar *marr;

4200:     /* memory size */
4201:     n = n_B*pcbddc->local_primal_size;
4202:     if (pcbddc->switch_static || pcbddc->dbg_flag) n += n_D*pcbddc->local_primal_size;
4203:     if (!pcbddc->symmetric_primal) n *= 2;
4204:     PetscCalloc1(n,&marr);
4205:     MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marr,&pcbddc->coarse_phi_B);
4206:     marr += n_B*pcbddc->local_primal_size;
4207:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
4208:       MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marr,&pcbddc->coarse_phi_D);
4209:       marr += n_D*pcbddc->local_primal_size;
4210:     }
4211:     if (!pcbddc->symmetric_primal) {
4212:       MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marr,&pcbddc->coarse_psi_B);
4213:       marr += n_B*pcbddc->local_primal_size;
4214:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4215:         MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marr,&pcbddc->coarse_psi_D);
4216:       }
4217:     } else {
4218:       PetscObjectReference((PetscObject)pcbddc->coarse_phi_B);
4219:       pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
4220:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4221:         PetscObjectReference((PetscObject)pcbddc->coarse_phi_D);
4222:         pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
4223:       }
4224:     }
4225:   }

4227:   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
4228:   p0_lidx_I = NULL;
4229:   if (pcbddc->benign_n && (pcbddc->switch_static || pcbddc->dbg_flag)) {
4230:     const PetscInt *idxs;

4232:     ISGetIndices(pcis->is_I_local,&idxs);
4233:     PetscMalloc1(pcbddc->benign_n,&p0_lidx_I);
4234:     for (i=0;i<pcbddc->benign_n;i++) {
4235:       PetscFindInt(pcbddc->benign_p0_lidx[i],pcis->n-pcis->n_B,idxs,&p0_lidx_I[i]);
4236:     }
4237:     ISRestoreIndices(pcis->is_I_local,&idxs);
4238:   }

4240:   /* vertices */
4241:   if (n_vertices) {
4242:     PetscBool restoreavr = PETSC_FALSE;

4244:     MatConvert(A_VV,MATDENSE,MAT_INPLACE_MATRIX,&A_VV);

4246:     if (n_R) {
4247:       Mat               A_RRmA_RV,A_RV_bcorr=NULL,S_VVt; /* S_VVt with LDA=N */
4248:       PetscBLASInt      B_N,B_one = 1;
4249:       const PetscScalar *x;
4250:       PetscScalar       *y;

4252:       MatScale(A_RV,m_one);
4253:       if (need_benign_correction) {
4254:         ISLocalToGlobalMapping RtoN;
4255:         IS                     is_p0;
4256:         PetscInt               *idxs_p0,n;

4258:         PetscMalloc1(pcbddc->benign_n,&idxs_p0);
4259:         ISLocalToGlobalMappingCreateIS(pcbddc->is_R_local,&RtoN);
4260:         ISGlobalToLocalMappingApply(RtoN,IS_GTOLM_DROP,pcbddc->benign_n,pcbddc->benign_p0_lidx,&n,idxs_p0);
4261:         if (n != pcbddc->benign_n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in R numbering for benign p0! %D != %D",n,pcbddc->benign_n);
4262:         ISLocalToGlobalMappingDestroy(&RtoN);
4263:         ISCreateGeneral(PETSC_COMM_SELF,n,idxs_p0,PETSC_OWN_POINTER,&is_p0);
4264:         MatCreateSubMatrix(A_RV,is_p0,NULL,MAT_INITIAL_MATRIX,&A_RV_bcorr);
4265:         ISDestroy(&is_p0);
4266:       }

4268:       MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,work,&A_RRmA_RV);
4269:       if (!sparserhs || need_benign_correction) {
4270:         if (lda_rhs == n_R) {
4271:           MatConvert(A_RV,MATDENSE,MAT_INPLACE_MATRIX,&A_RV);
4272:         } else {
4273:           PetscScalar    *av,*array;
4274:           const PetscInt *xadj,*adjncy;
4275:           PetscInt       n;
4276:           PetscBool      flg_row;

4278:           array = work+lda_rhs*n_vertices;
4279:           PetscArrayzero(array,lda_rhs*n_vertices);
4280:           MatConvert(A_RV,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_RV);
4281:           MatGetRowIJ(A_RV,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
4282:           MatSeqAIJGetArray(A_RV,&av);
4283:           for (i=0;i<n;i++) {
4284:             PetscInt j;
4285:             for (j=xadj[i];j<xadj[i+1];j++) array[lda_rhs*adjncy[j]+i] = av[j];
4286:           }
4287:           MatRestoreRowIJ(A_RV,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
4288:           MatDestroy(&A_RV);
4289:           MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,array,&A_RV);
4290:         }
4291:         if (need_benign_correction) {
4292:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4293:           PetscScalar        *marr;

4295:           MatDenseGetArray(A_RV,&marr);
4296:           /* need \Phi^T A_RV = (I+L)A_RV, L given by

4298:                  | 0 0  0 | (V)
4299:              L = | 0 0 -1 | (P-p0)
4300:                  | 0 0 -1 | (p0)

4302:           */
4303:           for (i=0;i<reuse_solver->benign_n;i++) {
4304:             const PetscScalar *vals;
4305:             const PetscInt    *idxs,*idxs_zero;
4306:             PetscInt          n,j,nz;

4308:             ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i],&nz);
4309:             ISGetIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
4310:             MatGetRow(A_RV_bcorr,i,&n,&idxs,&vals);
4311:             for (j=0;j<n;j++) {
4312:               PetscScalar val = vals[j];
4313:               PetscInt    k,col = idxs[j];
4314:               for (k=0;k<nz;k++) marr[idxs_zero[k]+lda_rhs*col] -= val;
4315:             }
4316:             MatRestoreRow(A_RV_bcorr,i,&n,&idxs,&vals);
4317:             ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
4318:           }
4319:           MatDenseRestoreArray(A_RV,&marr);
4320:         }
4321:         PetscObjectReference((PetscObject)A_RV);
4322:         Brhs = A_RV;
4323:       } else {
4324:         Mat tA_RVT,A_RVT;

4326:         if (!pcbddc->symmetric_primal) {
4327:           /* A_RV already scaled by -1 */
4328:           MatTranspose(A_RV,MAT_INITIAL_MATRIX,&A_RVT);
4329:         } else {
4330:           restoreavr = PETSC_TRUE;
4331:           MatScale(A_VR,-1.0);
4332:           PetscObjectReference((PetscObject)A_VR);
4333:           A_RVT = A_VR;
4334:         }
4335:         if (lda_rhs != n_R) {
4336:           PetscScalar *aa;
4337:           PetscInt    r,*ii,*jj;
4338:           PetscBool   done;

4340:           MatGetRowIJ(A_RVT,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
4341:           if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"GetRowIJ failed");
4342:           MatSeqAIJGetArray(A_RVT,&aa);
4343:           MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,n_vertices,lda_rhs,ii,jj,aa,&tA_RVT);
4344:           MatRestoreRowIJ(A_RVT,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
4345:           if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"RestoreRowIJ failed");
4346:         } else {
4347:           PetscObjectReference((PetscObject)A_RVT);
4348:           tA_RVT = A_RVT;
4349:         }
4350:         MatCreateTranspose(tA_RVT,&Brhs);
4351:         MatDestroy(&tA_RVT);
4352:         MatDestroy(&A_RVT);
4353:       }
4354:       if (F) {
4355:         /* need to correct the rhs */
4356:         if (need_benign_correction) {
4357:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4358:           PetscScalar        *marr;

4360:           MatDenseGetArray(Brhs,&marr);
4361:           if (lda_rhs != n_R) {
4362:             for (i=0;i<n_vertices;i++) {
4363:               VecPlaceArray(dummy_vec,marr+i*lda_rhs);
4364:               PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_FALSE,PETSC_TRUE);
4365:               VecResetArray(dummy_vec);
4366:             }
4367:           } else {
4368:             for (i=0;i<n_vertices;i++) {
4369:               VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
4370:               PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_FALSE,PETSC_TRUE);
4371:               VecResetArray(pcbddc->vec1_R);
4372:             }
4373:           }
4374:           MatDenseRestoreArray(Brhs,&marr);
4375:         }
4376:         MatMatSolve(F,Brhs,A_RRmA_RV);
4377:         if (restoreavr) {
4378:           MatScale(A_VR,-1.0);
4379:         }
4380:         /* need to correct the solution */
4381:         if (need_benign_correction) {
4382:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4383:           PetscScalar        *marr;

4385:           MatDenseGetArray(A_RRmA_RV,&marr);
4386:           if (lda_rhs != n_R) {
4387:             for (i=0;i<n_vertices;i++) {
4388:               VecPlaceArray(dummy_vec,marr+i*lda_rhs);
4389:               PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_TRUE,PETSC_TRUE);
4390:               VecResetArray(dummy_vec);
4391:             }
4392:           } else {
4393:             for (i=0;i<n_vertices;i++) {
4394:               VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
4395:               PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_TRUE,PETSC_TRUE);
4396:               VecResetArray(pcbddc->vec1_R);
4397:             }
4398:           }
4399:           MatDenseRestoreArray(A_RRmA_RV,&marr);
4400:         }
4401:       } else {
4402:         MatDenseGetArray(Brhs,&y);
4403:         for (i=0;i<n_vertices;i++) {
4404:           VecPlaceArray(pcbddc->vec1_R,y+i*lda_rhs);
4405:           VecPlaceArray(pcbddc->vec2_R,work+i*lda_rhs);
4406:           KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
4407:           KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
4408:           VecResetArray(pcbddc->vec1_R);
4409:           VecResetArray(pcbddc->vec2_R);
4410:         }
4411:         MatDenseRestoreArray(Brhs,&y);
4412:       }
4413:       MatDestroy(&A_RV);
4414:       MatDestroy(&Brhs);
4415:       /* S_VV and S_CV */
4416:       if (n_constraints) {
4417:         Mat B;

4419:         PetscArrayzero(work+lda_rhs*n_vertices,n_B*n_vertices);
4420:         for (i=0;i<n_vertices;i++) {
4421:           VecPlaceArray(pcbddc->vec1_R,work+i*lda_rhs);
4422:           VecPlaceArray(pcis->vec1_B,work+lda_rhs*n_vertices+i*n_B);
4423:           VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4424:           VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4425:           VecResetArray(pcis->vec1_B);
4426:           VecResetArray(pcbddc->vec1_R);
4427:         }
4428:         MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_vertices,work+lda_rhs*n_vertices,&B);
4429:         /* Reuse dense S_C = pcbddc->local_auxmat1 * B */
4430:         MatProductCreateWithMat(pcbddc->local_auxmat1,B,NULL,S_CV);
4431:         MatProductSetType(S_CV,MATPRODUCT_AB);
4432:         MatProductSetFromOptions(S_CV);
4433:         MatProductSymbolic(S_CV);
4434:         MatProductNumeric(S_CV);
4435:         MatProductClear(S_CV);

4437:         MatDestroy(&B);
4438:         MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,work+lda_rhs*n_vertices,&B);
4439:         /* Reuse B = local_auxmat2_R * S_CV */
4440:         MatProductCreateWithMat(local_auxmat2_R,S_CV,NULL,B);
4441:         MatProductSetType(B,MATPRODUCT_AB);
4442:         MatProductSetFromOptions(B);
4443:         MatProductSymbolic(B);
4444:         MatProductNumeric(B);

4446:         MatScale(S_CV,m_one);
4447:         PetscBLASIntCast(lda_rhs*n_vertices,&B_N);
4448:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,work+lda_rhs*n_vertices,&B_one,work,&B_one));
4449:         MatDestroy(&B);
4450:       }
4451:       if (lda_rhs != n_R) {
4452:         MatDestroy(&A_RRmA_RV);
4453:         MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&A_RRmA_RV);
4454:         MatDenseSetLDA(A_RRmA_RV,lda_rhs);
4455:       }
4456:       MatMatMult(A_VR,A_RRmA_RV,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VVt);
4457:       /* need A_VR * \Phi * A_RRmA_RV = A_VR * (I+L)^T * A_RRmA_RV, L given as before */
4458:       if (need_benign_correction) {
4459:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4460:         PetscScalar        *marr,*sums;

4462:         PetscMalloc1(n_vertices,&sums);
4463:         MatDenseGetArray(S_VVt,&marr);
4464:         for (i=0;i<reuse_solver->benign_n;i++) {
4465:           const PetscScalar *vals;
4466:           const PetscInt    *idxs,*idxs_zero;
4467:           PetscInt          n,j,nz;

4469:           ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i],&nz);
4470:           ISGetIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
4471:           for (j=0;j<n_vertices;j++) {
4472:             PetscInt k;
4473:             sums[j] = 0.;
4474:             for (k=0;k<nz;k++) sums[j] += work[idxs_zero[k]+j*lda_rhs];
4475:           }
4476:           MatGetRow(A_RV_bcorr,i,&n,&idxs,&vals);
4477:           for (j=0;j<n;j++) {
4478:             PetscScalar val = vals[j];
4479:             PetscInt k;
4480:             for (k=0;k<n_vertices;k++) {
4481:               marr[idxs[j]+k*n_vertices] += val*sums[k];
4482:             }
4483:           }
4484:           MatRestoreRow(A_RV_bcorr,i,&n,&idxs,&vals);
4485:           ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
4486:         }
4487:         PetscFree(sums);
4488:         MatDenseRestoreArray(S_VVt,&marr);
4489:         MatDestroy(&A_RV_bcorr);
4490:       }
4491:       MatDestroy(&A_RRmA_RV);
4492:       PetscBLASIntCast(n_vertices*n_vertices,&B_N);
4493:       MatDenseGetArrayRead(A_VV,&x);
4494:       MatDenseGetArray(S_VVt,&y);
4495:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,x,&B_one,y,&B_one));
4496:       MatDenseRestoreArrayRead(A_VV,&x);
4497:       MatDenseRestoreArray(S_VVt,&y);
4498:       MatCopy(S_VVt,S_VV,SAME_NONZERO_PATTERN);
4499:       MatDestroy(&S_VVt);
4500:     } else {
4501:       MatCopy(A_VV,S_VV,SAME_NONZERO_PATTERN);
4502:     }
4503:     MatDestroy(&A_VV);

4505:     /* coarse basis functions */
4506:     for (i=0;i<n_vertices;i++) {
4507:       PetscScalar *y;

4509:       VecPlaceArray(pcbddc->vec1_R,work+lda_rhs*i);
4510:       MatDenseGetArray(pcbddc->coarse_phi_B,&y);
4511:       VecPlaceArray(pcis->vec1_B,y+n_B*i);
4512:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4513:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4514:       y[n_B*i+idx_V_B[i]] = 1.0;
4515:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);
4516:       VecResetArray(pcis->vec1_B);

4518:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4519:         PetscInt j;

4521:         MatDenseGetArray(pcbddc->coarse_phi_D,&y);
4522:         VecPlaceArray(pcis->vec1_D,y+n_D*i);
4523:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4524:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4525:         VecResetArray(pcis->vec1_D);
4526:         for (j=0;j<pcbddc->benign_n;j++) y[n_D*i+p0_lidx_I[j]] = 0.0;
4527:         MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);
4528:       }
4529:       VecResetArray(pcbddc->vec1_R);
4530:     }
4531:     /* if n_R == 0 the object is not destroyed */
4532:     MatDestroy(&A_RV);
4533:   }
4534:   VecDestroy(&dummy_vec);

4536:   if (n_constraints) {
4537:     Mat B;

4539:     MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,work,&B);
4540:     MatScale(S_CC,m_one);
4541:     MatProductCreateWithMat(local_auxmat2_R,S_CC,NULL,B);
4542:     MatProductSetType(B,MATPRODUCT_AB);
4543:     MatProductSetFromOptions(B);
4544:     MatProductSymbolic(B);
4545:     MatProductNumeric(B);

4547:     MatScale(S_CC,m_one);
4548:     if (n_vertices) {
4549:       if (isCHOL || need_benign_correction) { /* if we can solve the interior problem with cholesky, we should also be fine with transposing here */
4550:         MatTranspose(S_CV,MAT_REUSE_MATRIX,&S_VC);
4551:       } else {
4552:         Mat S_VCt;

4554:         if (lda_rhs != n_R) {
4555:           MatDestroy(&B);
4556:           MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work,&B);
4557:           MatDenseSetLDA(B,lda_rhs);
4558:         }
4559:         MatMatMult(A_VR,B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VCt);
4560:         MatCopy(S_VCt,S_VC,SAME_NONZERO_PATTERN);
4561:         MatDestroy(&S_VCt);
4562:       }
4563:     }
4564:     MatDestroy(&B);
4565:     /* coarse basis functions */
4566:     for (i=0;i<n_constraints;i++) {
4567:       PetscScalar *y;

4569:       VecPlaceArray(pcbddc->vec1_R,work+lda_rhs*i);
4570:       MatDenseGetArray(pcbddc->coarse_phi_B,&y);
4571:       VecPlaceArray(pcis->vec1_B,y+n_B*(i+n_vertices));
4572:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4573:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4574:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);
4575:       VecResetArray(pcis->vec1_B);
4576:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4577:         PetscInt j;

4579:         MatDenseGetArray(pcbddc->coarse_phi_D,&y);
4580:         VecPlaceArray(pcis->vec1_D,y+n_D*(i+n_vertices));
4581:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4582:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4583:         VecResetArray(pcis->vec1_D);
4584:         for (j=0;j<pcbddc->benign_n;j++) y[n_D*i+p0_lidx_I[j]] = 0.0;
4585:         MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);
4586:       }
4587:       VecResetArray(pcbddc->vec1_R);
4588:     }
4589:   }
4590:   if (n_constraints) {
4591:     MatDestroy(&local_auxmat2_R);
4592:   }
4593:   PetscFree(p0_lidx_I);

4595:   /* coarse matrix entries relative to B_0 */
4596:   if (pcbddc->benign_n) {
4597:     Mat               B0_B,B0_BPHI;
4598:     IS                is_dummy;
4599:     const PetscScalar *data;
4600:     PetscInt          j;

4602:     ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy);
4603:     MatCreateSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
4604:     ISDestroy(&is_dummy);
4605:     MatMatMult(B0_B,pcbddc->coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&B0_BPHI);
4606:     MatConvert(B0_BPHI,MATSEQDENSE,MAT_INPLACE_MATRIX,&B0_BPHI);
4607:     MatDenseGetArrayRead(B0_BPHI,&data);
4608:     for (j=0;j<pcbddc->benign_n;j++) {
4609:       PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
4610:       for (i=0;i<pcbddc->local_primal_size;i++) {
4611:         coarse_submat_vals[primal_idx*pcbddc->local_primal_size+i] = data[i*pcbddc->benign_n+j];
4612:         coarse_submat_vals[i*pcbddc->local_primal_size+primal_idx] = data[i*pcbddc->benign_n+j];
4613:       }
4614:     }
4615:     MatDenseRestoreArrayRead(B0_BPHI,&data);
4616:     MatDestroy(&B0_B);
4617:     MatDestroy(&B0_BPHI);
4618:   }

4620:   /* compute other basis functions for non-symmetric problems */
4621:   if (!pcbddc->symmetric_primal) {
4622:     Mat         B_V=NULL,B_C=NULL;
4623:     PetscScalar *marray;

4625:     if (n_constraints) {
4626:       Mat S_CCT,C_CRT;

4628:       MatTranspose(C_CR,MAT_INITIAL_MATRIX,&C_CRT);
4629:       MatTranspose(S_CC,MAT_INITIAL_MATRIX,&S_CCT);
4630:       MatMatMult(C_CRT,S_CCT,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B_C);
4631:       MatDestroy(&S_CCT);
4632:       if (n_vertices) {
4633:         Mat S_VCT;

4635:         MatTranspose(S_VC,MAT_INITIAL_MATRIX,&S_VCT);
4636:         MatMatMult(C_CRT,S_VCT,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B_V);
4637:         MatDestroy(&S_VCT);
4638:       }
4639:       MatDestroy(&C_CRT);
4640:     } else {
4641:       MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,NULL,&B_V);
4642:     }
4643:     if (n_vertices && n_R) {
4644:       PetscScalar    *av,*marray;
4645:       const PetscInt *xadj,*adjncy;
4646:       PetscInt       n;
4647:       PetscBool      flg_row;

4649:       /* B_V = B_V - A_VR^T */
4650:       MatConvert(A_VR,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_VR);
4651:       MatGetRowIJ(A_VR,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
4652:       MatSeqAIJGetArray(A_VR,&av);
4653:       MatDenseGetArray(B_V,&marray);
4654:       for (i=0;i<n;i++) {
4655:         PetscInt j;
4656:         for (j=xadj[i];j<xadj[i+1];j++) marray[i*n_R + adjncy[j]] -= av[j];
4657:       }
4658:       MatDenseRestoreArray(B_V,&marray);
4659:       MatRestoreRowIJ(A_VR,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
4660:       MatDestroy(&A_VR);
4661:     }

4663:     /* currently there's no support for MatTransposeMatSolve(F,B,X) */
4664:     if (n_vertices) {
4665:       MatDenseGetArray(B_V,&marray);
4666:       for (i=0;i<n_vertices;i++) {
4667:         VecPlaceArray(pcbddc->vec1_R,marray+i*n_R);
4668:         VecPlaceArray(pcbddc->vec2_R,work+i*n_R);
4669:         KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
4670:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
4671:         VecResetArray(pcbddc->vec1_R);
4672:         VecResetArray(pcbddc->vec2_R);
4673:       }
4674:       MatDenseRestoreArray(B_V,&marray);
4675:     }
4676:     if (B_C) {
4677:       MatDenseGetArray(B_C,&marray);
4678:       for (i=n_vertices;i<n_constraints+n_vertices;i++) {
4679:         VecPlaceArray(pcbddc->vec1_R,marray+(i-n_vertices)*n_R);
4680:         VecPlaceArray(pcbddc->vec2_R,work+i*n_R);
4681:         KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
4682:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
4683:         VecResetArray(pcbddc->vec1_R);
4684:         VecResetArray(pcbddc->vec2_R);
4685:       }
4686:       MatDenseRestoreArray(B_C,&marray);
4687:     }
4688:     /* coarse basis functions */
4689:     for (i=0;i<pcbddc->local_primal_size;i++) {
4690:       PetscScalar *y;

4692:       VecPlaceArray(pcbddc->vec1_R,work+i*n_R);
4693:       MatDenseGetArray(pcbddc->coarse_psi_B,&y);
4694:       VecPlaceArray(pcis->vec1_B,y+n_B*i);
4695:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4696:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4697:       if (i<n_vertices) {
4698:         y[n_B*i+idx_V_B[i]] = 1.0;
4699:       }
4700:       MatDenseRestoreArray(pcbddc->coarse_psi_B,&y);
4701:       VecResetArray(pcis->vec1_B);

4703:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4704:         MatDenseGetArray(pcbddc->coarse_psi_D,&y);
4705:         VecPlaceArray(pcis->vec1_D,y+n_D*i);
4706:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4707:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4708:         VecResetArray(pcis->vec1_D);
4709:         MatDenseRestoreArray(pcbddc->coarse_psi_D,&y);
4710:       }
4711:       VecResetArray(pcbddc->vec1_R);
4712:     }
4713:     MatDestroy(&B_V);
4714:     MatDestroy(&B_C);
4715:   }

4717:   /* free memory */
4718:   PetscFree(idx_V_B);
4719:   MatDestroy(&S_VV);
4720:   MatDestroy(&S_CV);
4721:   MatDestroy(&S_VC);
4722:   MatDestroy(&S_CC);
4723:   PetscFree(work);
4724:   if (n_vertices) {
4725:     MatDestroy(&A_VR);
4726:   }
4727:   if (n_constraints) {
4728:     MatDestroy(&C_CR);
4729:   }
4730:   PetscLogEventEnd(PC_BDDC_CorrectionSetUp[pcbddc->current_level],pc,0,0,0);

4732:   /* Checking coarse_sub_mat and coarse basis functios */
4733:   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
4734:   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
4735:   if (pcbddc->dbg_flag) {
4736:     Mat         coarse_sub_mat;
4737:     Mat         AUXMAT,TM1,TM2,TM3,TM4;
4738:     Mat         coarse_phi_D,coarse_phi_B;
4739:     Mat         coarse_psi_D,coarse_psi_B;
4740:     Mat         A_II,A_BB,A_IB,A_BI;
4741:     Mat         C_B,CPHI;
4742:     IS          is_dummy;
4743:     Vec         mones;
4744:     MatType     checkmattype=MATSEQAIJ;
4745:     PetscReal   real_value;

4747:     if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
4748:       Mat A;
4749:       PCBDDCBenignProject(pc,NULL,NULL,&A);
4750:       MatCreateSubMatrix(A,pcis->is_I_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&A_II);
4751:       MatCreateSubMatrix(A,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&A_IB);
4752:       MatCreateSubMatrix(A,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&A_BI);
4753:       MatCreateSubMatrix(A,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&A_BB);
4754:       MatDestroy(&A);
4755:     } else {
4756:       MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);
4757:       MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);
4758:       MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);
4759:       MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);
4760:     }
4761:     MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);
4762:     MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);
4763:     if (!pcbddc->symmetric_primal) {
4764:       MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);
4765:       MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);
4766:     }
4767:     MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);

4769:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
4770:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat computation (symmetric %d)\n",pcbddc->symmetric_primal);
4771:     PetscViewerFlush(pcbddc->dbg_viewer);
4772:     if (!pcbddc->symmetric_primal) {
4773:       MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4774:       MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);
4775:       MatDestroy(&AUXMAT);
4776:       MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4777:       MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);
4778:       MatDestroy(&AUXMAT);
4779:       MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4780:       MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);
4781:       MatDestroy(&AUXMAT);
4782:       MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4783:       MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);
4784:       MatDestroy(&AUXMAT);
4785:     } else {
4786:       MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);
4787:       MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);
4788:       MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4789:       MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);
4790:       MatDestroy(&AUXMAT);
4791:       MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4792:       MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);
4793:       MatDestroy(&AUXMAT);
4794:     }
4795:     MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);
4796:     MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);
4797:     MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);
4798:     MatConvert(TM1,MATSEQDENSE,MAT_INPLACE_MATRIX,&TM1);
4799:     if (pcbddc->benign_n) {
4800:       Mat               B0_B,B0_BPHI;
4801:       const PetscScalar *data2;
4802:       PetscScalar       *data;
4803:       PetscInt          j;

4805:       ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy);
4806:       MatCreateSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
4807:       MatMatMult(B0_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&B0_BPHI);
4808:       MatConvert(B0_BPHI,MATSEQDENSE,MAT_INPLACE_MATRIX,&B0_BPHI);
4809:       MatDenseGetArray(TM1,&data);
4810:       MatDenseGetArrayRead(B0_BPHI,&data2);
4811:       for (j=0;j<pcbddc->benign_n;j++) {
4812:         PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
4813:         for (i=0;i<pcbddc->local_primal_size;i++) {
4814:           data[primal_idx*pcbddc->local_primal_size+i] += data2[i*pcbddc->benign_n+j];
4815:           data[i*pcbddc->local_primal_size+primal_idx] += data2[i*pcbddc->benign_n+j];
4816:         }
4817:       }
4818:       MatDenseRestoreArray(TM1,&data);
4819:       MatDenseRestoreArrayRead(B0_BPHI,&data2);
4820:       MatDestroy(&B0_B);
4821:       ISDestroy(&is_dummy);
4822:       MatDestroy(&B0_BPHI);
4823:     }
4824: #if 0
4825:   {
4826:     PetscViewer viewer;
4827:     char filename[256];
4828:     sprintf(filename,"details_local_coarse_mat%d_level%d.m",PetscGlobalRank,pcbddc->current_level);
4829:     PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);
4830:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
4831:     PetscObjectSetName((PetscObject)coarse_sub_mat,"computed");
4832:     MatView(coarse_sub_mat,viewer);
4833:     PetscObjectSetName((PetscObject)TM1,"projected");
4834:     MatView(TM1,viewer);
4835:     if (pcbddc->coarse_phi_B) {
4836:       PetscObjectSetName((PetscObject)pcbddc->coarse_phi_B,"phi_B");
4837:       MatView(pcbddc->coarse_phi_B,viewer);
4838:     }
4839:     if (pcbddc->coarse_phi_D) {
4840:       PetscObjectSetName((PetscObject)pcbddc->coarse_phi_D,"phi_D");
4841:       MatView(pcbddc->coarse_phi_D,viewer);
4842:     }
4843:     if (pcbddc->coarse_psi_B) {
4844:       PetscObjectSetName((PetscObject)pcbddc->coarse_psi_B,"psi_B");
4845:       MatView(pcbddc->coarse_psi_B,viewer);
4846:     }
4847:     if (pcbddc->coarse_psi_D) {
4848:       PetscObjectSetName((PetscObject)pcbddc->coarse_psi_D,"psi_D");
4849:       MatView(pcbddc->coarse_psi_D,viewer);
4850:     }
4851:     PetscObjectSetName((PetscObject)pcbddc->local_mat,"A");
4852:     MatView(pcbddc->local_mat,viewer);
4853:     PetscObjectSetName((PetscObject)pcbddc->ConstraintMatrix,"C");
4854:     MatView(pcbddc->ConstraintMatrix,viewer);
4855:     PetscObjectSetName((PetscObject)pcis->is_I_local,"I");
4856:     ISView(pcis->is_I_local,viewer);
4857:     PetscObjectSetName((PetscObject)pcis->is_B_local,"B");
4858:     ISView(pcis->is_B_local,viewer);
4859:     PetscObjectSetName((PetscObject)pcbddc->is_R_local,"R");
4860:     ISView(pcbddc->is_R_local,viewer);
4861:     PetscViewerDestroy(&viewer);
4862:   }
4863: #endif
4864:     MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);
4865:     MatNorm(TM1,NORM_FROBENIUS,&real_value);
4866:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
4867:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d          matrix error % 1.14e\n",PetscGlobalRank,real_value);

4869:     /* check constraints */
4870:     ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size-pcbddc->benign_n,0,1,&is_dummy);
4871:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);
4872:     if (!pcbddc->benign_n) { /* TODO: add benign case */
4873:       MatMatMult(C_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&CPHI);
4874:     } else {
4875:       PetscScalar *data;
4876:       Mat         tmat;
4877:       MatDenseGetArray(pcbddc->coarse_phi_B,&data);
4878:       MatCreateSeqDense(PETSC_COMM_SELF,pcis->n_B,pcbddc->local_primal_size-pcbddc->benign_n,data,&tmat);
4879:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&data);
4880:       MatMatMult(C_B,tmat,MAT_INITIAL_MATRIX,1.0,&CPHI);
4881:       MatDestroy(&tmat);
4882:     }
4883:     MatCreateVecs(CPHI,&mones,NULL);
4884:     VecSet(mones,-1.0);
4885:     MatDiagonalSet(CPHI,mones,ADD_VALUES);
4886:     MatNorm(CPHI,NORM_FROBENIUS,&real_value);
4887:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d phi constraints error % 1.14e\n",PetscGlobalRank,real_value);
4888:     if (!pcbddc->symmetric_primal) {
4889:       MatMatMult(C_B,coarse_psi_B,MAT_REUSE_MATRIX,1.0,&CPHI);
4890:       VecSet(mones,-1.0);
4891:       MatDiagonalSet(CPHI,mones,ADD_VALUES);
4892:       MatNorm(CPHI,NORM_FROBENIUS,&real_value);
4893:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d psi constraints error % 1.14e\n",PetscGlobalRank,real_value);
4894:     }
4895:     MatDestroy(&C_B);
4896:     MatDestroy(&CPHI);
4897:     ISDestroy(&is_dummy);
4898:     VecDestroy(&mones);
4899:     PetscViewerFlush(pcbddc->dbg_viewer);
4900:     MatDestroy(&A_II);
4901:     MatDestroy(&A_BB);
4902:     MatDestroy(&A_IB);
4903:     MatDestroy(&A_BI);
4904:     MatDestroy(&TM1);
4905:     MatDestroy(&TM2);
4906:     MatDestroy(&TM3);
4907:     MatDestroy(&TM4);
4908:     MatDestroy(&coarse_phi_D);
4909:     MatDestroy(&coarse_phi_B);
4910:     if (!pcbddc->symmetric_primal) {
4911:       MatDestroy(&coarse_psi_D);
4912:       MatDestroy(&coarse_psi_B);
4913:     }
4914:     MatDestroy(&coarse_sub_mat);
4915:   }
4916:   /* FINAL CUDA support (we cannot currently mix viennacl and cuda vectors */
4917:   {
4918:     PetscBool gpu;

4920:     PetscObjectTypeCompare((PetscObject)pcis->vec1_N,VECSEQCUDA,&gpu);
4921:     if (gpu) {
4922:       if (pcbddc->local_auxmat1) {
4923:         MatConvert(pcbddc->local_auxmat1,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->local_auxmat1);
4924:       }
4925:       if (pcbddc->local_auxmat2) {
4926:         MatConvert(pcbddc->local_auxmat2,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->local_auxmat2);
4927:       }
4928:       if (pcbddc->coarse_phi_B) {
4929:         MatConvert(pcbddc->coarse_phi_B,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_phi_B);
4930:       }
4931:       if (pcbddc->coarse_phi_D) {
4932:         MatConvert(pcbddc->coarse_phi_D,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_phi_D);
4933:       }
4934:       if (pcbddc->coarse_psi_B) {
4935:         MatConvert(pcbddc->coarse_psi_B,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_psi_B);
4936:       }
4937:       if (pcbddc->coarse_psi_D) {
4938:         MatConvert(pcbddc->coarse_psi_D,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_psi_D);
4939:       }
4940:     }
4941:   }
4942:   /* get back data */
4943:   *coarse_submat_vals_n = coarse_submat_vals;
4944:   return(0);
4945: }

4947: PetscErrorCode MatCreateSubMatrixUnsorted(Mat A, IS isrow, IS iscol, Mat* B)
4948: {
4949:   Mat            *work_mat;
4950:   IS             isrow_s,iscol_s;
4951:   PetscBool      rsorted,csorted;
4952:   PetscInt       rsize,*idxs_perm_r=NULL,csize,*idxs_perm_c=NULL;

4956:   ISSorted(isrow,&rsorted);
4957:   ISSorted(iscol,&csorted);
4958:   ISGetLocalSize(isrow,&rsize);
4959:   ISGetLocalSize(iscol,&csize);

4961:   if (!rsorted) {
4962:     const PetscInt *idxs;
4963:     PetscInt *idxs_sorted,i;

4965:     PetscMalloc1(rsize,&idxs_perm_r);
4966:     PetscMalloc1(rsize,&idxs_sorted);
4967:     for (i=0;i<rsize;i++) {
4968:       idxs_perm_r[i] = i;
4969:     }
4970:     ISGetIndices(isrow,&idxs);
4971:     PetscSortIntWithPermutation(rsize,idxs,idxs_perm_r);
4972:     for (i=0;i<rsize;i++) {
4973:       idxs_sorted[i] = idxs[idxs_perm_r[i]];
4974:     }
4975:     ISRestoreIndices(isrow,&idxs);
4976:     ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_sorted,PETSC_OWN_POINTER,&isrow_s);
4977:   } else {
4978:     PetscObjectReference((PetscObject)isrow);
4979:     isrow_s = isrow;
4980:   }

4982:   if (!csorted) {
4983:     if (isrow == iscol) {
4984:       PetscObjectReference((PetscObject)isrow_s);
4985:       iscol_s = isrow_s;
4986:     } else {
4987:       const PetscInt *idxs;
4988:       PetscInt       *idxs_sorted,i;

4990:       PetscMalloc1(csize,&idxs_perm_c);
4991:       PetscMalloc1(csize,&idxs_sorted);
4992:       for (i=0;i<csize;i++) {
4993:         idxs_perm_c[i] = i;
4994:       }
4995:       ISGetIndices(iscol,&idxs);
4996:       PetscSortIntWithPermutation(csize,idxs,idxs_perm_c);
4997:       for (i=0;i<csize;i++) {
4998:         idxs_sorted[i] = idxs[idxs_perm_c[i]];
4999:       }
5000:       ISRestoreIndices(iscol,&idxs);
5001:       ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_sorted,PETSC_OWN_POINTER,&iscol_s);
5002:     }
5003:   } else {
5004:     PetscObjectReference((PetscObject)iscol);
5005:     iscol_s = iscol;
5006:   }

5008:   MatCreateSubMatrices(A,1,&isrow_s,&iscol_s,MAT_INITIAL_MATRIX,&work_mat);

5010:   if (!rsorted || !csorted) {
5011:     Mat      new_mat;
5012:     IS       is_perm_r,is_perm_c;

5014:     if (!rsorted) {
5015:       PetscInt *idxs_r,i;
5016:       PetscMalloc1(rsize,&idxs_r);
5017:       for (i=0;i<rsize;i++) {
5018:         idxs_r[idxs_perm_r[i]] = i;
5019:       }
5020:       PetscFree(idxs_perm_r);
5021:       ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_r,PETSC_OWN_POINTER,&is_perm_r);
5022:     } else {
5023:       ISCreateStride(PETSC_COMM_SELF,rsize,0,1,&is_perm_r);
5024:     }
5025:     ISSetPermutation(is_perm_r);

5027:     if (!csorted) {
5028:       if (isrow_s == iscol_s) {
5029:         PetscObjectReference((PetscObject)is_perm_r);
5030:         is_perm_c = is_perm_r;
5031:       } else {
5032:         PetscInt *idxs_c,i;
5033:         if (!idxs_perm_c) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Permutation array not present");
5034:         PetscMalloc1(csize,&idxs_c);
5035:         for (i=0;i<csize;i++) {
5036:           idxs_c[idxs_perm_c[i]] = i;
5037:         }
5038:         PetscFree(idxs_perm_c);
5039:         ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_c,PETSC_OWN_POINTER,&is_perm_c);
5040:       }
5041:     } else {
5042:       ISCreateStride(PETSC_COMM_SELF,csize,0,1,&is_perm_c);
5043:     }
5044:     ISSetPermutation(is_perm_c);

5046:     MatPermute(work_mat[0],is_perm_r,is_perm_c,&new_mat);
5047:     MatDestroy(&work_mat[0]);
5048:     work_mat[0] = new_mat;
5049:     ISDestroy(&is_perm_r);
5050:     ISDestroy(&is_perm_c);
5051:   }

5053:   PetscObjectReference((PetscObject)work_mat[0]);
5054:   *B = work_mat[0];
5055:   MatDestroyMatrices(1,&work_mat);
5056:   ISDestroy(&isrow_s);
5057:   ISDestroy(&iscol_s);
5058:   return(0);
5059: }

5061: PetscErrorCode PCBDDCComputeLocalMatrix(PC pc, Mat ChangeOfBasisMatrix)
5062: {
5063:   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
5064:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
5065:   Mat            new_mat,lA;
5066:   IS             is_local,is_global;
5067:   PetscInt       local_size;
5068:   PetscBool      isseqaij;

5072:   MatDestroy(&pcbddc->local_mat);
5073:   MatGetSize(matis->A,&local_size,NULL);
5074:   ISCreateStride(PetscObjectComm((PetscObject)matis->A),local_size,0,1,&is_local);
5075:   ISLocalToGlobalMappingApplyIS(pc->pmat->rmap->mapping,is_local,&is_global);
5076:   ISDestroy(&is_local);
5077:   MatCreateSubMatrixUnsorted(ChangeOfBasisMatrix,is_global,is_global,&new_mat);
5078:   ISDestroy(&is_global);

5080:   if (pcbddc->dbg_flag) {
5081:     Vec       x,x_change;
5082:     PetscReal error;

5084:     MatCreateVecs(ChangeOfBasisMatrix,&x,&x_change);
5085:     VecSetRandom(x,NULL);
5086:     MatMult(ChangeOfBasisMatrix,x,x_change);
5087:     VecScatterBegin(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);
5088:     VecScatterEnd(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);
5089:     MatMult(new_mat,matis->x,matis->y);
5090:     if (!pcbddc->change_interior) {
5091:       const PetscScalar *x,*y,*v;
5092:       PetscReal         lerror = 0.;
5093:       PetscInt          i;

5095:       VecGetArrayRead(matis->x,&x);
5096:       VecGetArrayRead(matis->y,&y);
5097:       VecGetArrayRead(matis->counter,&v);
5098:       for (i=0;i<local_size;i++)
5099:         if (PetscRealPart(v[i]) < 1.5 && PetscAbsScalar(x[i]-y[i]) > lerror)
5100:           lerror = PetscAbsScalar(x[i]-y[i]);
5101:       VecRestoreArrayRead(matis->x,&x);
5102:       VecRestoreArrayRead(matis->y,&y);
5103:       VecRestoreArrayRead(matis->counter,&v);
5104:       MPIU_Allreduce(&lerror,&error,1,MPIU_REAL,MPI_MAX,PetscObjectComm((PetscObject)pc));
5105:       if (error > PETSC_SMALL) {
5106:         if (!pcbddc->user_ChangeOfBasisMatrix || pcbddc->current_level) {
5107:           SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on I: %1.6e",error);
5108:         } else {
5109:           SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_USER,"Error global vs local change on I: %1.6e",error);
5110:         }
5111:       }
5112:     }
5113:     VecScatterBegin(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);
5114:     VecScatterEnd(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);
5115:     VecAXPY(x,-1.0,x_change);
5116:     VecNorm(x,NORM_INFINITY,&error);
5117:     if (error > PETSC_SMALL) {
5118:       if (!pcbddc->user_ChangeOfBasisMatrix || pcbddc->current_level) {
5119:         SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on N: %1.6e",error);
5120:       } else {
5121:         SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_USER,"Error global vs local change on N: %1.6e",error);
5122:       }
5123:     }
5124:     VecDestroy(&x);
5125:     VecDestroy(&x_change);
5126:   }

5128:   /* lA is present if we are setting up an inner BDDC for a saddle point FETI-DP */
5129:   PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);

5131:   /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
5132:   PetscObjectBaseTypeCompare((PetscObject)matis->A,MATSEQAIJ,&isseqaij);
5133:   if (isseqaij) {
5134:     MatDestroy(&pcbddc->local_mat);
5135:     MatPtAP(matis->A,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);
5136:     if (lA) {
5137:       Mat work;
5138:       MatPtAP(lA,new_mat,MAT_INITIAL_MATRIX,2.0,&work);
5139:       PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject)work);
5140:       MatDestroy(&work);
5141:     }
5142:   } else {
5143:     Mat work_mat;

5145:     MatDestroy(&pcbddc->local_mat);
5146:     MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);
5147:     MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);
5148:     MatDestroy(&work_mat);
5149:     if (lA) {
5150:       Mat work;
5151:       MatConvert(lA,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);
5152:       MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&work);
5153:       PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject)work);
5154:       MatDestroy(&work);
5155:     }
5156:   }
5157:   if (matis->A->symmetric_set) {
5158:     MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);
5159: #if !defined(PETSC_USE_COMPLEX)
5160:     MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);
5161: #endif
5162:   }
5163:   MatDestroy(&new_mat);
5164:   return(0);
5165: }

5167: PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
5168: {
5169:   PC_IS*          pcis = (PC_IS*)(pc->data);
5170:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
5171:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5172:   PetscInt        *idx_R_local=NULL;
5173:   PetscInt        n_vertices,i,j,n_R,n_D,n_B;
5174:   PetscInt        vbs,bs;
5175:   PetscBT         bitmask=NULL;
5176:   PetscErrorCode  ierr;

5179:   /*
5180:     No need to setup local scatters if
5181:       - primal space is unchanged
5182:         AND
5183:       - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
5184:         AND
5185:       - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
5186:   */
5187:   if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) {
5188:     return(0);
5189:   }
5190:   /* destroy old objects */
5191:   ISDestroy(&pcbddc->is_R_local);
5192:   VecScatterDestroy(&pcbddc->R_to_B);
5193:   VecScatterDestroy(&pcbddc->R_to_D);
5194:   /* Set Non-overlapping dimensions */
5195:   n_B = pcis->n_B;
5196:   n_D = pcis->n - n_B;
5197:   n_vertices = pcbddc->n_vertices;

5199:   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */

5201:   /* create auxiliary bitmask and allocate workspace */
5202:   if (!sub_schurs || !sub_schurs->reuse_solver) {
5203:     PetscMalloc1(pcis->n-n_vertices,&idx_R_local);
5204:     PetscBTCreate(pcis->n,&bitmask);
5205:     for (i=0;i<n_vertices;i++) {
5206:       PetscBTSet(bitmask,pcbddc->local_primal_ref_node[i]);
5207:     }

5209:     for (i=0, n_R=0; i<pcis->n; i++) {
5210:       if (!PetscBTLookup(bitmask,i)) {
5211:         idx_R_local[n_R++] = i;
5212:       }
5213:     }
5214:   } else { /* A different ordering (already computed) is present if we are reusing the Schur solver */
5215:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5217:     ISGetIndices(reuse_solver->is_R,(const PetscInt**)&idx_R_local);
5218:     ISGetLocalSize(reuse_solver->is_R,&n_R);
5219:   }

5221:   /* Block code */
5222:   vbs = 1;
5223:   MatGetBlockSize(pcbddc->local_mat,&bs);
5224:   if (bs>1 && !(n_vertices%bs)) {
5225:     PetscBool is_blocked = PETSC_TRUE;
5226:     PetscInt  *vary;
5227:     if (!sub_schurs || !sub_schurs->reuse_solver) {
5228:       PetscMalloc1(pcis->n/bs,&vary);
5229:       PetscArrayzero(vary,pcis->n/bs);
5230:       /* Verify that the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
5231:       /* it is ok to check this way since local_primal_ref_node are always sorted by local numbering and idx_R_local is obtained as a complement */
5232:       for (i=0; i<n_vertices; i++) vary[pcbddc->local_primal_ref_node[i]/bs]++;
5233:       for (i=0; i<pcis->n/bs; i++) {
5234:         if (vary[i]!=0 && vary[i]!=bs) {
5235:           is_blocked = PETSC_FALSE;
5236:           break;
5237:         }
5238:       }
5239:       PetscFree(vary);
5240:     } else {
5241:       /* Verify directly the R set */
5242:       for (i=0; i<n_R/bs; i++) {
5243:         PetscInt j,node=idx_R_local[bs*i];
5244:         for (j=1; j<bs; j++) {
5245:           if (node != idx_R_local[bs*i+j]-j) {
5246:             is_blocked = PETSC_FALSE;
5247:             break;
5248:           }
5249:         }
5250:       }
5251:     }
5252:     if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
5253:       vbs = bs;
5254:       for (i=0;i<n_R/vbs;i++) {
5255:         idx_R_local[i] = idx_R_local[vbs*i]/vbs;
5256:       }
5257:     }
5258:   }
5259:   ISCreateBlock(PETSC_COMM_SELF,vbs,n_R/vbs,idx_R_local,PETSC_COPY_VALUES,&pcbddc->is_R_local);
5260:   if (sub_schurs && sub_schurs->reuse_solver) {
5261:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5263:     ISRestoreIndices(reuse_solver->is_R,(const PetscInt**)&idx_R_local);
5264:     ISDestroy(&reuse_solver->is_R);
5265:     PetscObjectReference((PetscObject)pcbddc->is_R_local);
5266:     reuse_solver->is_R = pcbddc->is_R_local;
5267:   } else {
5268:     PetscFree(idx_R_local);
5269:   }

5271:   /* print some info if requested */
5272:   if (pcbddc->dbg_flag) {
5273:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
5274:     PetscViewerFlush(pcbddc->dbg_viewer);
5275:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
5276:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);
5277:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %D, dirichlet_size = %D, boundary_size = %D\n",pcis->n,n_D,n_B);
5278:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"r_size = %D, v_size = %D, constraints = %D, local_primal_size = %D\n",n_R,n_vertices,pcbddc->local_primal_size-n_vertices-pcbddc->benign_n,pcbddc->local_primal_size);
5279:     PetscViewerFlush(pcbddc->dbg_viewer);
5280:   }

5282:   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
5283:   if (!sub_schurs || !sub_schurs->reuse_solver) {
5284:     IS       is_aux1,is_aux2;
5285:     PetscInt *aux_array1,*aux_array2,*is_indices,*idx_R_local;

5287:     ISGetIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);
5288:     PetscMalloc1(pcis->n_B-n_vertices,&aux_array1);
5289:     PetscMalloc1(pcis->n_B-n_vertices,&aux_array2);
5290:     ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);
5291:     for (i=0; i<n_D; i++) {
5292:       PetscBTSet(bitmask,is_indices[i]);
5293:     }
5294:     ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);
5295:     for (i=0, j=0; i<n_R; i++) {
5296:       if (!PetscBTLookup(bitmask,idx_R_local[i])) {
5297:         aux_array1[j++] = i;
5298:       }
5299:     }
5300:     ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);
5301:     ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);
5302:     for (i=0, j=0; i<n_B; i++) {
5303:       if (!PetscBTLookup(bitmask,is_indices[i])) {
5304:         aux_array2[j++] = i;
5305:       }
5306:     }
5307:     ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);
5308:     ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);
5309:     VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);
5310:     ISDestroy(&is_aux1);
5311:     ISDestroy(&is_aux2);

5313:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
5314:       PetscMalloc1(n_D,&aux_array1);
5315:       for (i=0, j=0; i<n_R; i++) {
5316:         if (PetscBTLookup(bitmask,idx_R_local[i])) {
5317:           aux_array1[j++] = i;
5318:         }
5319:       }
5320:       ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);
5321:       VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);
5322:       ISDestroy(&is_aux1);
5323:     }
5324:     PetscBTDestroy(&bitmask);
5325:     ISRestoreIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);
5326:   } else {
5327:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
5328:     IS                 tis;
5329:     PetscInt           schur_size;

5331:     ISGetLocalSize(reuse_solver->is_B,&schur_size);
5332:     ISCreateStride(PETSC_COMM_SELF,schur_size,n_D,1,&tis);
5333:     VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_B,reuse_solver->is_B,&pcbddc->R_to_B);
5334:     ISDestroy(&tis);
5335:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
5336:       ISCreateStride(PETSC_COMM_SELF,n_D,0,1,&tis);
5337:       VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);
5338:       ISDestroy(&tis);
5339:     }
5340:   }
5341:   return(0);
5342: }

5344: static PetscErrorCode MatNullSpacePropagateAny_Private(Mat A, IS is, Mat B)
5345: {
5346:   MatNullSpace   NullSpace;
5347:   Mat            dmat;
5348:   const Vec      *nullvecs;
5349:   Vec            v,v2,*nullvecs2;
5350:   VecScatter     sct = NULL;
5351:   PetscContainer c;
5352:   PetscScalar    *ddata;
5353:   PetscInt       k,nnsp_size,bsiz,bsiz2,n,N,bs;
5354:   PetscBool      nnsp_has_cnst;

5358:   if (!is && !B) { /* MATIS */
5359:     Mat_IS* matis = (Mat_IS*)A->data;

5361:     if (!B) {
5362:       MatISGetLocalMat(A,&B);
5363:     }
5364:     sct  = matis->cctx;
5365:     PetscObjectReference((PetscObject)sct);
5366:   } else {
5367:     MatGetNullSpace(B,&NullSpace);
5368:     if (!NullSpace) {
5369:       MatGetNearNullSpace(B,&NullSpace);
5370:     }
5371:     if (NullSpace) return(0);
5372:   }
5373:   MatGetNullSpace(A,&NullSpace);
5374:   if (!NullSpace) {
5375:     MatGetNearNullSpace(A,&NullSpace);
5376:   }
5377:   if (!NullSpace) return(0);

5379:   MatCreateVecs(A,&v,NULL);
5380:   MatCreateVecs(B,&v2,NULL);
5381:   if (!sct) {
5382:     VecScatterCreate(v,is,v2,NULL,&sct);
5383:   }
5384:   MatNullSpaceGetVecs(NullSpace,&nnsp_has_cnst,&nnsp_size,(const Vec**)&nullvecs);
5385:   bsiz = bsiz2 = nnsp_size+!!nnsp_has_cnst;
5386:   PetscMalloc1(bsiz,&nullvecs2);
5387:   VecGetBlockSize(v2,&bs);
5388:   VecGetSize(v2,&N);
5389:   VecGetLocalSize(v2,&n);
5390:   PetscMalloc1(n*bsiz,&ddata);
5391:   for (k=0;k<nnsp_size;k++) {
5392:     VecCreateMPIWithArray(PetscObjectComm((PetscObject)B),bs,n,N,ddata + n*k,&nullvecs2[k]);
5393:     VecScatterBegin(sct,nullvecs[k],nullvecs2[k],INSERT_VALUES,SCATTER_FORWARD);
5394:     VecScatterEnd(sct,nullvecs[k],nullvecs2[k],INSERT_VALUES,SCATTER_FORWARD);
5395:   }
5396:   if (nnsp_has_cnst) {
5397:     VecCreateMPIWithArray(PetscObjectComm((PetscObject)B),bs,n,N,ddata + n*nnsp_size,&nullvecs2[nnsp_size]);
5398:     VecSet(nullvecs2[nnsp_size],1.0);
5399:   }
5400:   PCBDDCOrthonormalizeVecs(&bsiz2,nullvecs2);
5401:   MatNullSpaceCreate(PetscObjectComm((PetscObject)B),PETSC_FALSE,bsiz2,nullvecs2,&NullSpace);

5403:   MatCreateDense(PetscObjectComm((PetscObject)B),n,PETSC_DECIDE,N,bsiz2,ddata,&dmat);
5404:   PetscContainerCreate(PetscObjectComm((PetscObject)B),&c);
5405:   PetscContainerSetPointer(c,ddata);
5406:   PetscContainerSetUserDestroy(c,PetscContainerUserDestroyDefault);
5407:   PetscObjectCompose((PetscObject)dmat,"_PBDDC_Null_dmat_arr",(PetscObject)c);
5408:   PetscContainerDestroy(&c);
5409:   PetscObjectCompose((PetscObject)NullSpace,"_PBDDC_Null_dmat",(PetscObject)dmat);
5410:   MatDestroy(&dmat);

5412:   for (k=0;k<bsiz;k++) {
5413:     VecDestroy(&nullvecs2[k]);
5414:   }
5415:   PetscFree(nullvecs2);
5416:   MatSetNearNullSpace(B,NullSpace);
5417:   MatNullSpaceDestroy(&NullSpace);
5418:   VecDestroy(&v);
5419:   VecDestroy(&v2);
5420:   VecScatterDestroy(&sct);
5421:   return(0);
5422: }

5424: PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, PetscBool dirichlet, PetscBool neumann)
5425: {
5426:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
5427:   PC_IS          *pcis = (PC_IS*)pc->data;
5428:   PC             pc_temp;
5429:   Mat            A_RR;
5430:   MatNullSpace   nnsp;
5431:   MatReuse       reuse;
5432:   PetscScalar    m_one = -1.0;
5433:   PetscReal      value;
5434:   PetscInt       n_D,n_R;
5435:   PetscBool      issbaij,opts;
5437:   void           (*f)(void) = NULL;
5438:   char           dir_prefix[256],neu_prefix[256],str_level[16];
5439:   size_t         len;

5442:   PetscLogEventBegin(PC_BDDC_LocalSolvers[pcbddc->current_level],pc,0,0,0);
5443:   /* approximate solver, propagate NearNullSpace if needed */
5444:   if (!pc->setupcalled && (pcbddc->NullSpace_corr[0] || pcbddc->NullSpace_corr[2])) {
5445:     MatNullSpace gnnsp1,gnnsp2;
5446:     PetscBool    lhas,ghas;

5448:     MatGetNearNullSpace(pcbddc->local_mat,&nnsp);
5449:     MatGetNearNullSpace(pc->pmat,&gnnsp1);
5450:     MatGetNullSpace(pc->pmat,&gnnsp2);
5451:     lhas = nnsp ? PETSC_TRUE : PETSC_FALSE;
5452:     MPIU_Allreduce(&lhas,&ghas,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
5453:     if (!ghas && (gnnsp1 || gnnsp2)) {
5454:       MatNullSpacePropagateAny_Private(pc->pmat,NULL,NULL);
5455:     }
5456:   }

5458:   /* compute prefixes */
5459:   PetscStrcpy(dir_prefix,"");
5460:   PetscStrcpy(neu_prefix,"");
5461:   if (!pcbddc->current_level) {
5462:     PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,sizeof(dir_prefix));
5463:     PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,sizeof(neu_prefix));
5464:     PetscStrlcat(dir_prefix,"pc_bddc_dirichlet_",sizeof(dir_prefix));
5465:     PetscStrlcat(neu_prefix,"pc_bddc_neumann_",sizeof(neu_prefix));
5466:   } else {
5467:     PetscSNPrintf(str_level,sizeof(str_level),"l%d_",(int)(pcbddc->current_level));
5468:     PetscStrlen(((PetscObject)pc)->prefix,&len);
5469:     len -= 15; /* remove "pc_bddc_coarse_" */
5470:     if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
5471:     if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
5472:     /* Nonstandard use of PetscStrncpy() to only copy a portion of the input string */
5473:     PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,len+1);
5474:     PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len+1);
5475:     PetscStrlcat(dir_prefix,"pc_bddc_dirichlet_",sizeof(dir_prefix));
5476:     PetscStrlcat(neu_prefix,"pc_bddc_neumann_",sizeof(neu_prefix));
5477:     PetscStrlcat(dir_prefix,str_level,sizeof(dir_prefix));
5478:     PetscStrlcat(neu_prefix,str_level,sizeof(neu_prefix));
5479:   }

5481:   /* DIRICHLET PROBLEM */
5482:   if (dirichlet) {
5483:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5484:     if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
5485:       if (!sub_schurs || !sub_schurs->reuse_solver) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented");
5486:       if (pcbddc->dbg_flag) {
5487:         Mat    A_IIn;

5489:         PCBDDCBenignProject(pc,pcis->is_I_local,pcis->is_I_local,&A_IIn);
5490:         MatDestroy(&pcis->A_II);
5491:         pcis->A_II = A_IIn;
5492:       }
5493:     }
5494:     if (pcbddc->local_mat->symmetric_set) {
5495:       MatSetOption(pcis->A_II,MAT_SYMMETRIC,pcbddc->local_mat->symmetric);
5496:     }
5497:     /* Matrix for Dirichlet problem is pcis->A_II */
5498:     n_D  = pcis->n - pcis->n_B;
5499:     opts = PETSC_FALSE;
5500:     if (!pcbddc->ksp_D) { /* create object if not yet build */
5501:       opts = PETSC_TRUE;
5502:       KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);
5503:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);
5504:       /* default */
5505:       KSPSetType(pcbddc->ksp_D,KSPPREONLY);
5506:       KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);
5507:       PetscObjectTypeCompare((PetscObject)pcis->pA_II,MATSEQSBAIJ,&issbaij);
5508:       KSPGetPC(pcbddc->ksp_D,&pc_temp);
5509:       if (issbaij) {
5510:         PCSetType(pc_temp,PCCHOLESKY);
5511:       } else {
5512:         PCSetType(pc_temp,PCLU);
5513:       }
5514:       KSPSetErrorIfNotConverged(pcbddc->ksp_D,pc->erroriffailure);
5515:     }
5516:     MatSetOptionsPrefix(pcis->pA_II,((PetscObject)pcbddc->ksp_D)->prefix);
5517:     KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->pA_II);
5518:     /* Allow user's customization */
5519:     if (opts) {
5520:       KSPSetFromOptions(pcbddc->ksp_D);
5521:     }
5522:     MatGetNearNullSpace(pcis->pA_II,&nnsp);
5523:     if (pcbddc->NullSpace_corr[0] && !nnsp) { /* approximate solver, propagate NearNullSpace */
5524:       MatNullSpacePropagateAny_Private(pcbddc->local_mat,pcis->is_I_local,pcis->pA_II);
5525:     }
5526:     MatGetNearNullSpace(pcis->pA_II,&nnsp);
5527:     KSPGetPC(pcbddc->ksp_D,&pc_temp);
5528:     PetscObjectQueryFunction((PetscObject)pc_temp,"PCSetCoordinates_C",&f);
5529:     if (f && pcbddc->mat_graph->cloc && !nnsp) {
5530:       PetscReal      *coords = pcbddc->mat_graph->coords,*scoords;
5531:       const PetscInt *idxs;
5532:       PetscInt       cdim = pcbddc->mat_graph->cdim,nl,i,d;

5534:       ISGetLocalSize(pcis->is_I_local,&nl);
5535:       ISGetIndices(pcis->is_I_local,&idxs);
5536:       PetscMalloc1(nl*cdim,&scoords);
5537:       for (i=0;i<nl;i++) {
5538:         for (d=0;d<cdim;d++) {
5539:           scoords[i*cdim+d] = coords[idxs[i]*cdim+d];
5540:         }
5541:       }
5542:       ISRestoreIndices(pcis->is_I_local,&idxs);
5543:       PCSetCoordinates(pc_temp,cdim,nl,scoords);
5544:       PetscFree(scoords);
5545:     }
5546:     if (sub_schurs && sub_schurs->reuse_solver) {
5547:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5549:       KSPSetPC(pcbddc->ksp_D,reuse_solver->interior_solver);
5550:     }

5552:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
5553:     if (!n_D) {
5554:       KSPGetPC(pcbddc->ksp_D,&pc_temp);
5555:       PCSetType(pc_temp,PCNONE);
5556:     }
5557:     KSPSetUp(pcbddc->ksp_D);
5558:     /* set ksp_D into pcis data */
5559:     PetscObjectReference((PetscObject)pcbddc->ksp_D);
5560:     KSPDestroy(&pcis->ksp_D);
5561:     pcis->ksp_D = pcbddc->ksp_D;
5562:   }

5564:   /* NEUMANN PROBLEM */
5565:   A_RR = NULL;
5566:   if (neumann) {
5567:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5568:     PetscInt        ibs,mbs;
5569:     PetscBool       issbaij, reuse_neumann_solver;
5570:     Mat_IS*         matis = (Mat_IS*)pc->pmat->data;

5572:     reuse_neumann_solver = PETSC_FALSE;
5573:     if (sub_schurs && sub_schurs->reuse_solver) {
5574:       IS iP;

5576:       reuse_neumann_solver = PETSC_TRUE;
5577:       PetscObjectQuery((PetscObject)sub_schurs->A,"__KSPFETIDP_iP",(PetscObject*)&iP);
5578:       if (iP) reuse_neumann_solver = PETSC_FALSE;
5579:     }
5580:     /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
5581:     ISGetSize(pcbddc->is_R_local,&n_R);
5582:     if (pcbddc->ksp_R) { /* already created ksp */
5583:       PetscInt nn_R;
5584:       KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);
5585:       PetscObjectReference((PetscObject)A_RR);
5586:       MatGetSize(A_RR,&nn_R,NULL);
5587:       if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
5588:         KSPReset(pcbddc->ksp_R);
5589:         MatDestroy(&A_RR);
5590:         reuse = MAT_INITIAL_MATRIX;
5591:       } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
5592:         if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
5593:           MatDestroy(&A_RR);
5594:           reuse = MAT_INITIAL_MATRIX;
5595:         } else { /* safe to reuse the matrix */
5596:           reuse = MAT_REUSE_MATRIX;
5597:         }
5598:       }
5599:       /* last check */
5600:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
5601:         MatDestroy(&A_RR);
5602:         reuse = MAT_INITIAL_MATRIX;
5603:       }
5604:     } else { /* first time, so we need to create the matrix */
5605:       reuse = MAT_INITIAL_MATRIX;
5606:     }
5607:     /* convert pcbddc->local_mat if needed later in PCBDDCSetUpCorrection
5608:        TODO: Get Rid of these conversions */
5609:     MatGetBlockSize(pcbddc->local_mat,&mbs);
5610:     ISGetBlockSize(pcbddc->is_R_local,&ibs);
5611:     PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);
5612:     if (ibs != mbs) { /* need to convert to SEQAIJ to extract any submatrix with is_R_local */
5613:       if (matis->A == pcbddc->local_mat) {
5614:         MatDestroy(&pcbddc->local_mat);
5615:         MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
5616:       } else {
5617:         MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
5618:       }
5619:     } else if (issbaij) { /* need to convert to BAIJ to get offdiagonal blocks */
5620:       if (matis->A == pcbddc->local_mat) {
5621:         MatDestroy(&pcbddc->local_mat);
5622:         MatConvert(matis->A,mbs > 1 ? MATSEQBAIJ : MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
5623:       } else {
5624:         MatConvert(pcbddc->local_mat,mbs > 1 ? MATSEQBAIJ : MATSEQAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
5625:       }
5626:     }
5627:     /* extract A_RR */
5628:     if (reuse_neumann_solver) {
5629:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5631:       if (pcbddc->dbg_flag) { /* we need A_RR to test the solver later */
5632:         MatDestroy(&A_RR);
5633:         if (reuse_solver->benign_n) { /* we are not using the explicit change of basis on the pressures */
5634:           PCBDDCBenignProject(pc,pcbddc->is_R_local,pcbddc->is_R_local,&A_RR);
5635:         } else {
5636:           MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_RR);
5637:         }
5638:       } else {
5639:         MatDestroy(&A_RR);
5640:         PCGetOperators(reuse_solver->correction_solver,&A_RR,NULL);
5641:         PetscObjectReference((PetscObject)A_RR);
5642:       }
5643:     } else { /* we have to build the neumann solver, so we need to extract the relevant matrix */
5644:       MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);
5645:     }
5646:     if (pcbddc->local_mat->symmetric_set) {
5647:       MatSetOption(A_RR,MAT_SYMMETRIC,pcbddc->local_mat->symmetric);
5648:     }
5649:     opts = PETSC_FALSE;
5650:     if (!pcbddc->ksp_R) { /* create object if not present */
5651:       opts = PETSC_TRUE;
5652:       KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);
5653:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);
5654:       /* default */
5655:       KSPSetType(pcbddc->ksp_R,KSPPREONLY);
5656:       KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);
5657:       KSPGetPC(pcbddc->ksp_R,&pc_temp);
5658:       PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);
5659:       if (issbaij) {
5660:         PCSetType(pc_temp,PCCHOLESKY);
5661:       } else {
5662:         PCSetType(pc_temp,PCLU);
5663:       }
5664:       KSPSetErrorIfNotConverged(pcbddc->ksp_R,pc->erroriffailure);
5665:     }
5666:     KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);
5667:     MatSetOptionsPrefix(A_RR,((PetscObject)pcbddc->ksp_R)->prefix);
5668:     if (opts) { /* Allow user's customization once */
5669:       KSPSetFromOptions(pcbddc->ksp_R);
5670:     }
5671:     MatGetNearNullSpace(A_RR,&nnsp);
5672:     if (pcbddc->NullSpace_corr[2] && !nnsp) { /* approximate solver, propagate NearNullSpace */
5673:       MatNullSpacePropagateAny_Private(pcbddc->local_mat,pcbddc->is_R_local,A_RR);
5674:     }
5675:     MatGetNearNullSpace(A_RR,&nnsp);
5676:     KSPGetPC(pcbddc->ksp_R,&pc_temp);
5677:     PetscObjectQueryFunction((PetscObject)pc_temp,"PCSetCoordinates_C",&f);
5678:     if (f && pcbddc->mat_graph->cloc && !nnsp) {
5679:       PetscReal      *coords = pcbddc->mat_graph->coords,*scoords;
5680:       const PetscInt *idxs;
5681:       PetscInt       cdim = pcbddc->mat_graph->cdim,nl,i,d;

5683:       ISGetLocalSize(pcbddc->is_R_local,&nl);
5684:       ISGetIndices(pcbddc->is_R_local,&idxs);
5685:       PetscMalloc1(nl*cdim,&scoords);
5686:       for (i=0;i<nl;i++) {
5687:         for (d=0;d<cdim;d++) {
5688:           scoords[i*cdim+d] = coords[idxs[i]*cdim+d];
5689:         }
5690:       }
5691:       ISRestoreIndices(pcbddc->is_R_local,&idxs);
5692:       PCSetCoordinates(pc_temp,cdim,nl,scoords);
5693:       PetscFree(scoords);
5694:     }

5696:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
5697:     if (!n_R) {
5698:       KSPGetPC(pcbddc->ksp_R,&pc_temp);
5699:       PCSetType(pc_temp,PCNONE);
5700:     }
5701:     /* Reuse solver if it is present */
5702:     if (reuse_neumann_solver) {
5703:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5705:       KSPSetPC(pcbddc->ksp_R,reuse_solver->correction_solver);
5706:     }
5707:     KSPSetUp(pcbddc->ksp_R);
5708:   }

5710:   if (pcbddc->dbg_flag) {
5711:     PetscViewerFlush(pcbddc->dbg_viewer);
5712:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
5713:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
5714:   }
5715:   PetscLogEventEnd(PC_BDDC_LocalSolvers[pcbddc->current_level],pc,0,0,0);

5717:   /* adapt Dirichlet and Neumann solvers if a nullspace correction has been requested */
5718:   if (pcbddc->NullSpace_corr[0]) {
5719:     PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);
5720:   }
5721:   if (dirichlet && pcbddc->NullSpace_corr[0] && !pcbddc->switch_static) {
5722:     PCBDDCNullSpaceAssembleCorrection(pc,PETSC_TRUE,pcbddc->NullSpace_corr[1]);
5723:   }
5724:   if (neumann && pcbddc->NullSpace_corr[2]) {
5725:     PCBDDCNullSpaceAssembleCorrection(pc,PETSC_FALSE,pcbddc->NullSpace_corr[3]);
5726:   }
5727:   /* check Dirichlet and Neumann solvers */
5728:   if (pcbddc->dbg_flag) {
5729:     if (dirichlet) { /* Dirichlet */
5730:       VecSetRandom(pcis->vec1_D,NULL);
5731:       MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);
5732:       KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);
5733:       KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);
5734:       VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);
5735:       VecNorm(pcis->vec1_D,NORM_INFINITY,&value);
5736:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve (%s) = % 1.14e \n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_D))->prefix,value);
5737:       PetscViewerFlush(pcbddc->dbg_viewer);
5738:     }
5739:     if (neumann) { /* Neumann */
5740:       VecSetRandom(pcbddc->vec1_R,NULL);
5741:       MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);
5742:       KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);
5743:       KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
5744:       VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);
5745:       VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);
5746:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann solve (%s) = % 1.14e\n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_R))->prefix,value);
5747:       PetscViewerFlush(pcbddc->dbg_viewer);
5748:     }
5749:   }
5750:   /* free Neumann problem's matrix */
5751:   MatDestroy(&A_RR);
5752:   return(0);
5753: }

5755: static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec inout_B, Vec inout_D, PetscBool applytranspose)
5756: {
5757:   PetscErrorCode  ierr;
5758:   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
5759:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5760:   PetscBool       reuse_solver = sub_schurs ? ( sub_schurs->reuse_solver ? PETSC_TRUE : PETSC_FALSE) : PETSC_FALSE;

5763:   if (!reuse_solver) {
5764:     VecSet(pcbddc->vec1_R,0.);
5765:   }
5766:   if (!pcbddc->switch_static) {
5767:     if (applytranspose && pcbddc->local_auxmat1) {
5768:       MatMultTranspose(pcbddc->local_auxmat2,inout_B,pcbddc->vec1_C);
5769:       MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);
5770:     }
5771:     if (!reuse_solver) {
5772:       VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5773:       VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5774:     } else {
5775:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5777:       VecScatterBegin(reuse_solver->correction_scatter_B,inout_B,reuse_solver->rhs_B,INSERT_VALUES,SCATTER_FORWARD);
5778:       VecScatterEnd(reuse_solver->correction_scatter_B,inout_B,reuse_solver->rhs_B,INSERT_VALUES,SCATTER_FORWARD);
5779:     }
5780:   } else {
5781:     VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5782:     VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5783:     VecScatterBegin(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5784:     VecScatterEnd(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5785:     if (applytranspose && pcbddc->local_auxmat1) {
5786:       MatMultTranspose(pcbddc->local_auxmat2,pcbddc->vec1_R,pcbddc->vec1_C);
5787:       MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);
5788:       VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5789:       VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5790:     }
5791:   }
5792:   PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][1],pc,0,0,0);
5793:   if (!reuse_solver || pcbddc->switch_static) {
5794:     if (applytranspose) {
5795:       KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);
5796:     } else {
5797:       KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);
5798:     }
5799:     KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec1_R);
5800:   } else {
5801:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5803:     if (applytranspose) {
5804:       MatFactorSolveSchurComplementTranspose(reuse_solver->F,reuse_solver->rhs_B,reuse_solver->sol_B);
5805:     } else {
5806:       MatFactorSolveSchurComplement(reuse_solver->F,reuse_solver->rhs_B,reuse_solver->sol_B);
5807:     }
5808:   }
5809:   PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][1],pc,0,0,0);
5810:   VecSet(inout_B,0.);
5811:   if (!pcbddc->switch_static) {
5812:     if (!reuse_solver) {
5813:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5814:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5815:     } else {
5816:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5818:       VecScatterBegin(reuse_solver->correction_scatter_B,reuse_solver->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);
5819:       VecScatterEnd(reuse_solver->correction_scatter_B,reuse_solver->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);
5820:     }
5821:     if (!applytranspose && pcbddc->local_auxmat1) {
5822:       MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);
5823:       MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,inout_B,inout_B);
5824:     }
5825:   } else {
5826:     VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5827:     VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5828:     VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
5829:     VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
5830:     if (!applytranspose && pcbddc->local_auxmat1) {
5831:       MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);
5832:       MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);
5833:     }
5834:     VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5835:     VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5836:     VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
5837:     VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
5838:   }
5839:   return(0);
5840: }

5842: /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
5843: PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
5844: {
5846:   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
5847:   PC_IS*            pcis = (PC_IS*)  (pc->data);
5848:   const PetscScalar zero = 0.0;

5851:   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
5852:   if (!pcbddc->benign_apply_coarse_only) {
5853:     if (applytranspose) {
5854:       MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);
5855:       if (pcbddc->switch_static) { MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P); }
5856:     } else {
5857:       MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);
5858:       if (pcbddc->switch_static) { MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P); }
5859:     }
5860:   } else {
5861:     VecSet(pcbddc->vec1_P,zero);
5862:   }

5864:   /* add p0 to the last value of vec1_P holding the coarse dof relative to p0 */
5865:   if (pcbddc->benign_n) {
5866:     PetscScalar *array;
5867:     PetscInt    j;

5869:     VecGetArray(pcbddc->vec1_P,&array);
5870:     for (j=0;j<pcbddc->benign_n;j++) array[pcbddc->local_primal_size-pcbddc->benign_n+j] += pcbddc->benign_p0[j];
5871:     VecRestoreArray(pcbddc->vec1_P,&array);
5872:   }

5874:   /* start communications from local primal nodes to rhs of coarse solver */
5875:   VecSet(pcbddc->coarse_vec,zero);
5876:   PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);
5877:   PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);

5879:   /* Coarse solution -> rhs and sol updated inside PCBDDCScattarCoarseDataBegin/End */
5880:   if (pcbddc->coarse_ksp) {
5881:     Mat          coarse_mat;
5882:     Vec          rhs,sol;
5883:     MatNullSpace nullsp;
5884:     PetscBool    isbddc = PETSC_FALSE;

5886:     if (pcbddc->benign_have_null) {
5887:       PC        coarse_pc;

5889:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
5890:       PetscObjectTypeCompare((PetscObject)coarse_pc,PCBDDC,&isbddc);
5891:       /* we need to propagate to coarser levels the need for a possible benign correction */
5892:       if (isbddc && pcbddc->benign_apply_coarse_only && !pcbddc->benign_skip_correction) {
5893:         PC_BDDC* coarsepcbddc = (PC_BDDC*)(coarse_pc->data);
5894:         coarsepcbddc->benign_skip_correction = PETSC_FALSE;
5895:         coarsepcbddc->benign_apply_coarse_only = PETSC_TRUE;
5896:       }
5897:     }
5898:     KSPGetRhs(pcbddc->coarse_ksp,&rhs);
5899:     KSPGetSolution(pcbddc->coarse_ksp,&sol);
5900:     KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);
5901:     if (applytranspose) {
5902:       if (pcbddc->benign_apply_coarse_only) SETERRQ(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),PETSC_ERR_SUP,"Not yet implemented");
5903:       PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][2],pc,0,0,0);
5904:       KSPSolveTranspose(pcbddc->coarse_ksp,rhs,sol);
5905:       PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][2],pc,0,0,0);
5906:       KSPCheckSolve(pcbddc->coarse_ksp,pc,sol);
5907:       MatGetTransposeNullSpace(coarse_mat,&nullsp);
5908:       if (nullsp) {
5909:         MatNullSpaceRemove(nullsp,sol);
5910:       }
5911:     } else {
5912:       MatGetNullSpace(coarse_mat,&nullsp);
5913:       if (pcbddc->benign_apply_coarse_only && isbddc) { /* need just to apply the coarse preconditioner during presolve */
5914:         PC        coarse_pc;

5916:         if (nullsp) {
5917:           MatNullSpaceRemove(nullsp,rhs);
5918:         }
5919:         KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
5920:         PCPreSolve(coarse_pc,pcbddc->coarse_ksp);
5921:         PCBDDCBenignRemoveInterior(coarse_pc,rhs,sol);
5922:         PCPostSolve(coarse_pc,pcbddc->coarse_ksp);
5923:       } else {
5924:         PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][2],pc,0,0,0);
5925:         KSPSolve(pcbddc->coarse_ksp,rhs,sol);
5926:         PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][2],pc,0,0,0);
5927:         KSPCheckSolve(pcbddc->coarse_ksp,pc,sol);
5928:         if (nullsp) {
5929:           MatNullSpaceRemove(nullsp,sol);
5930:         }
5931:       }
5932:     }
5933:     /* we don't need the benign correction at coarser levels anymore */
5934:     if (pcbddc->benign_have_null && isbddc) {
5935:       PC        coarse_pc;
5936:       PC_BDDC*  coarsepcbddc;

5938:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
5939:       coarsepcbddc = (PC_BDDC*)(coarse_pc->data);
5940:       coarsepcbddc->benign_skip_correction = PETSC_TRUE;
5941:       coarsepcbddc->benign_apply_coarse_only = PETSC_FALSE;
5942:     }
5943:   }

5945:   /* Local solution on R nodes */
5946:   if (pcis->n && !pcbddc->benign_apply_coarse_only) {
5947:     PCBDDCSolveSubstructureCorrection(pc,pcis->vec1_B,pcis->vec1_D,applytranspose);
5948:   }
5949:   /* communications from coarse sol to local primal nodes */
5950:   PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);
5951:   PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);

5953:   /* Sum contributions from the two levels */
5954:   if (!pcbddc->benign_apply_coarse_only) {
5955:     if (applytranspose) {
5956:       MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);
5957:       if (pcbddc->switch_static) { MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D); }
5958:     } else {
5959:       MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);
5960:       if (pcbddc->switch_static) { MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D); }
5961:     }
5962:     /* store p0 */
5963:     if (pcbddc->benign_n) {
5964:       PetscScalar *array;
5965:       PetscInt    j;

5967:       VecGetArray(pcbddc->vec1_P,&array);
5968:       for (j=0;j<pcbddc->benign_n;j++) pcbddc->benign_p0[j] = array[pcbddc->local_primal_size-pcbddc->benign_n+j];
5969:       VecRestoreArray(pcbddc->vec1_P,&array);
5970:     }
5971:   } else { /* expand the coarse solution */
5972:     if (applytranspose) {
5973:       MatMult(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B);
5974:     } else {
5975:       MatMult(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B);
5976:     }
5977:   }
5978:   return(0);
5979: }

5981: PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
5982: {
5983:   PC_BDDC*          pcbddc = (PC_BDDC*)(pc->data);
5984:   Vec               from,to;
5985:   const PetscScalar *array;
5986:   PetscErrorCode    ierr;

5989:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
5990:     from = pcbddc->coarse_vec;
5991:     to = pcbddc->vec1_P;
5992:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
5993:       Vec tvec;

5995:       KSPGetRhs(pcbddc->coarse_ksp,&tvec);
5996:       VecResetArray(tvec);
5997:       KSPGetSolution(pcbddc->coarse_ksp,&tvec);
5998:       VecGetArrayRead(tvec,&array);
5999:       VecPlaceArray(from,array);
6000:       VecRestoreArrayRead(tvec,&array);
6001:     }
6002:   } else { /* from local to global -> put data in coarse right hand side */
6003:     from = pcbddc->vec1_P;
6004:     to = pcbddc->coarse_vec;
6005:   }
6006:   VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);
6007:   return(0);
6008: }

6010: PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
6011: {
6012:   PC_BDDC*          pcbddc = (PC_BDDC*)(pc->data);
6013:   Vec               from,to;
6014:   const PetscScalar *array;
6015:   PetscErrorCode    ierr;

6018:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
6019:     from = pcbddc->coarse_vec;
6020:     to = pcbddc->vec1_P;
6021:   } else { /* from local to global -> put data in coarse right hand side */
6022:     from = pcbddc->vec1_P;
6023:     to = pcbddc->coarse_vec;
6024:   }
6025:   VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);
6026:   if (smode == SCATTER_FORWARD) {
6027:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
6028:       Vec tvec;

6030:       KSPGetRhs(pcbddc->coarse_ksp,&tvec);
6031:       VecGetArrayRead(to,&array);
6032:       VecPlaceArray(tvec,array);
6033:       VecRestoreArrayRead(to,&array);
6034:     }
6035:   } else {
6036:     if (pcbddc->coarse_ksp) { /* restore array of pcbddc->coarse_vec */
6037:      VecResetArray(from);
6038:     }
6039:   }
6040:   return(0);
6041: }

6043: PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
6044: {
6045:   PetscErrorCode    ierr;
6046:   PC_IS*            pcis = (PC_IS*)(pc->data);
6047:   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
6048:   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
6049:   /* one and zero */
6050:   PetscScalar       one=1.0,zero=0.0;
6051:   /* space to store constraints and their local indices */
6052:   PetscScalar       *constraints_data;
6053:   PetscInt          *constraints_idxs,*constraints_idxs_B;
6054:   PetscInt          *constraints_idxs_ptr,*constraints_data_ptr;
6055:   PetscInt          *constraints_n;
6056:   /* iterators */
6057:   PetscInt          i,j,k,total_counts,total_counts_cc,cum;
6058:   /* BLAS integers */
6059:   PetscBLASInt      lwork,lierr;
6060:   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
6061:   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
6062:   /* reuse */
6063:   PetscInt          olocal_primal_size,olocal_primal_size_cc;
6064:   PetscInt          *olocal_primal_ref_node,*olocal_primal_ref_mult;
6065:   /* change of basis */
6066:   PetscBool         qr_needed;
6067:   PetscBT           change_basis,qr_needed_idx;
6068:   /* auxiliary stuff */
6069:   PetscInt          *nnz,*is_indices;
6070:   PetscInt          ncc;
6071:   /* some quantities */
6072:   PetscInt          n_vertices,total_primal_vertices,valid_constraints;
6073:   PetscInt          size_of_constraint,max_size_of_constraint=0,max_constraints,temp_constraints;
6074:   PetscReal         tol; /* tolerance for retaining eigenmodes */

6077:   tol  = PetscSqrtReal(PETSC_SMALL);
6078:   /* Destroy Mat objects computed previously */
6079:   MatDestroy(&pcbddc->ChangeOfBasisMatrix);
6080:   MatDestroy(&pcbddc->ConstraintMatrix);
6081:   MatDestroy(&pcbddc->switch_static_change);
6082:   /* save info on constraints from previous setup (if any) */
6083:   olocal_primal_size = pcbddc->local_primal_size;
6084:   olocal_primal_size_cc = pcbddc->local_primal_size_cc;
6085:   PetscMalloc2(olocal_primal_size_cc,&olocal_primal_ref_node,olocal_primal_size_cc,&olocal_primal_ref_mult);
6086:   PetscArraycpy(olocal_primal_ref_node,pcbddc->local_primal_ref_node,olocal_primal_size_cc);
6087:   PetscArraycpy(olocal_primal_ref_mult,pcbddc->local_primal_ref_mult,olocal_primal_size_cc);
6088:   PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);
6089:   PetscFree(pcbddc->primal_indices_local_idxs);

6091:   if (!pcbddc->adaptive_selection) {
6092:     IS           ISForVertices,*ISForFaces,*ISForEdges;
6093:     MatNullSpace nearnullsp;
6094:     const Vec    *nearnullvecs;
6095:     Vec          *localnearnullsp;
6096:     PetscScalar  *array;
6097:     PetscInt     n_ISForFaces,n_ISForEdges,nnsp_size;
6098:     PetscBool    nnsp_has_cnst;
6099:     /* LAPACK working arrays for SVD or POD */
6100:     PetscBool    skip_lapack,boolforchange;
6101:     PetscScalar  *work;
6102:     PetscReal    *singular_vals;
6103: #if defined(PETSC_USE_COMPLEX)
6104:     PetscReal    *rwork;
6105: #endif
6106:     PetscScalar  *temp_basis = NULL,*correlation_mat = NULL;
6107:     PetscBLASInt dummy_int=1;
6108:     PetscScalar  dummy_scalar=1.;
6109:     PetscBool    use_pod = PETSC_FALSE;

6111:     /* MKL SVD with same input gives different results on different processes! */
6112: #if defined(PETSC_MISSING_LAPACK_GESVD) || defined(PETSC_HAVE_MKL)
6113:     use_pod = PETSC_TRUE;
6114: #endif
6115:     /* Get index sets for faces, edges and vertices from graph */
6116:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
6117:     /* print some info */
6118:     if (pcbddc->dbg_flag && (!pcbddc->sub_schurs || pcbddc->sub_schurs_rebuild)) {
6119:       PetscInt nv;

6121:       PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);
6122:       ISGetSize(ISForVertices,&nv);
6123:       PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
6124:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
6125:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%D)\n",PetscGlobalRank,nv,pcbddc->use_vertices);
6126:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%D)\n",PetscGlobalRank,n_ISForEdges,pcbddc->use_edges);
6127:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%D)\n",PetscGlobalRank,n_ISForFaces,pcbddc->use_faces);
6128:       PetscViewerFlush(pcbddc->dbg_viewer);
6129:       PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);
6130:     }

6132:     /* free unneeded index sets */
6133:     if (!pcbddc->use_vertices) {
6134:       ISDestroy(&ISForVertices);
6135:     }
6136:     if (!pcbddc->use_edges) {
6137:       for (i=0;i<n_ISForEdges;i++) {
6138:         ISDestroy(&ISForEdges[i]);
6139:       }
6140:       PetscFree(ISForEdges);
6141:       n_ISForEdges = 0;
6142:     }
6143:     if (!pcbddc->use_faces) {
6144:       for (i=0;i<n_ISForFaces;i++) {
6145:         ISDestroy(&ISForFaces[i]);
6146:       }
6147:       PetscFree(ISForFaces);
6148:       n_ISForFaces = 0;
6149:     }

6151:     /* check if near null space is attached to global mat */
6152:     if (pcbddc->use_nnsp) {
6153:       MatGetNearNullSpace(pc->pmat,&nearnullsp);
6154:     } else nearnullsp = NULL;

6156:     if (nearnullsp) {
6157:       MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);
6158:       /* remove any stored info */
6159:       MatNullSpaceDestroy(&pcbddc->onearnullspace);
6160:       PetscFree(pcbddc->onearnullvecs_state);
6161:       /* store information for BDDC solver reuse */
6162:       PetscObjectReference((PetscObject)nearnullsp);
6163:       pcbddc->onearnullspace = nearnullsp;
6164:       PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);
6165:       for (i=0;i<nnsp_size;i++) {
6166:         PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);
6167:       }
6168:     } else { /* if near null space is not provided BDDC uses constants by default */
6169:       nnsp_size = 0;
6170:       nnsp_has_cnst = PETSC_TRUE;
6171:     }
6172:     /* get max number of constraints on a single cc */
6173:     max_constraints = nnsp_size;
6174:     if (nnsp_has_cnst) max_constraints++;

6176:     /*
6177:          Evaluate maximum storage size needed by the procedure
6178:          - Indices for connected component i stored at "constraints_idxs + constraints_idxs_ptr[i]"
6179:          - Values for constraints on connected component i stored at "constraints_data + constraints_data_ptr[i]"
6180:          There can be multiple constraints per connected component
6181:                                                                                                                                                            */
6182:     n_vertices = 0;
6183:     if (ISForVertices) {
6184:       ISGetSize(ISForVertices,&n_vertices);
6185:     }
6186:     ncc = n_vertices+n_ISForFaces+n_ISForEdges;
6187:     PetscMalloc3(ncc+1,&constraints_idxs_ptr,ncc+1,&constraints_data_ptr,ncc,&constraints_n);

6189:     total_counts = n_ISForFaces+n_ISForEdges;
6190:     total_counts *= max_constraints;
6191:     total_counts += n_vertices;
6192:     PetscBTCreate(total_counts,&change_basis);

6194:     total_counts = 0;
6195:     max_size_of_constraint = 0;
6196:     for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
6197:       IS used_is;
6198:       if (i<n_ISForEdges) {
6199:         used_is = ISForEdges[i];
6200:       } else {
6201:         used_is = ISForFaces[i-n_ISForEdges];
6202:       }
6203:       ISGetSize(used_is,&j);
6204:       total_counts += j;
6205:       max_size_of_constraint = PetscMax(j,max_size_of_constraint);
6206:     }
6207:     PetscMalloc3(total_counts*max_constraints+n_vertices,&constraints_data,total_counts+n_vertices,&constraints_idxs,total_counts+n_vertices,&constraints_idxs_B);

6209:     /* get local part of global near null space vectors */
6210:     PetscMalloc1(nnsp_size,&localnearnullsp);
6211:     for (k=0;k<nnsp_size;k++) {
6212:       VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);
6213:       VecScatterBegin(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);
6214:       VecScatterEnd(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);
6215:     }

6217:     /* whether or not to skip lapack calls */
6218:     skip_lapack = PETSC_TRUE;
6219:     if (n_ISForFaces+n_ISForEdges && max_constraints > 1 && !pcbddc->use_nnsp_true) skip_lapack = PETSC_FALSE;

6221:     /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
6222:     if (!skip_lapack) {
6223:       PetscScalar temp_work;

6225:       if (use_pod) {
6226:         /* Proper Orthogonal Decomposition (POD) using the snapshot method */
6227:         PetscMalloc1(max_constraints*max_constraints,&correlation_mat);
6228:         PetscMalloc1(max_constraints,&singular_vals);
6229:         PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);
6230: #if defined(PETSC_USE_COMPLEX)
6231:         PetscMalloc1(3*max_constraints,&rwork);
6232: #endif
6233:         /* now we evaluate the optimal workspace using query with lwork=-1 */
6234:         PetscBLASIntCast(max_constraints,&Blas_N);
6235:         PetscBLASIntCast(max_constraints,&Blas_LDA);
6236:         lwork = -1;
6237:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6238: #if !defined(PETSC_USE_COMPLEX)
6239:         PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
6240: #else
6241:         PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
6242: #endif
6243:         PetscFPTrapPop();
6244:         if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
6245:       } else {
6246: #if !defined(PETSC_MISSING_LAPACK_GESVD)
6247:         /* SVD */
6248:         PetscInt max_n,min_n;
6249:         max_n = max_size_of_constraint;
6250:         min_n = max_constraints;
6251:         if (max_size_of_constraint < max_constraints) {
6252:           min_n = max_size_of_constraint;
6253:           max_n = max_constraints;
6254:         }
6255:         PetscMalloc1(min_n,&singular_vals);
6256: #if defined(PETSC_USE_COMPLEX)
6257:         PetscMalloc1(5*min_n,&rwork);
6258: #endif
6259:         /* now we evaluate the optimal workspace using query with lwork=-1 */
6260:         lwork = -1;
6261:         PetscBLASIntCast(max_n,&Blas_M);
6262:         PetscBLASIntCast(min_n,&Blas_N);
6263:         PetscBLASIntCast(max_n,&Blas_LDA);
6264:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6265: #if !defined(PETSC_USE_COMPLEX)
6266:         PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&constraints_data[0],&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,&lierr));
6267: #else
6268:         PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,&constraints_data[0],&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,&temp_work,&lwork,rwork,&lierr));
6269: #endif
6270:         PetscFPTrapPop();
6271:         if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
6272: #else
6273:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"This should not happen");
6274: #endif /* on missing GESVD */
6275:       }
6276:       /* Allocate optimal workspace */
6277:       PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);
6278:       PetscMalloc1(lwork,&work);
6279:     }
6280:     /* Now we can loop on constraining sets */
6281:     total_counts = 0;
6282:     constraints_idxs_ptr[0] = 0;
6283:     constraints_data_ptr[0] = 0;
6284:     /* vertices */
6285:     if (n_vertices) {
6286:       ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);
6287:       PetscArraycpy(constraints_idxs,is_indices,n_vertices);
6288:       for (i=0;i<n_vertices;i++) {
6289:         constraints_n[total_counts] = 1;
6290:         constraints_data[total_counts] = 1.0;
6291:         constraints_idxs_ptr[total_counts+1] = constraints_idxs_ptr[total_counts]+1;
6292:         constraints_data_ptr[total_counts+1] = constraints_data_ptr[total_counts]+1;
6293:         total_counts++;
6294:       }
6295:       ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);
6296:       n_vertices = total_counts;
6297:     }

6299:     /* edges and faces */
6300:     total_counts_cc = total_counts;
6301:     for (ncc=0;ncc<n_ISForEdges+n_ISForFaces;ncc++) {
6302:       IS        used_is;
6303:       PetscBool idxs_copied = PETSC_FALSE;

6305:       if (ncc<n_ISForEdges) {
6306:         used_is = ISForEdges[ncc];
6307:         boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
6308:       } else {
6309:         used_is = ISForFaces[ncc-n_ISForEdges];
6310:         boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
6311:       }
6312:       temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */

6314:       ISGetSize(used_is,&size_of_constraint);
6315:       ISGetIndices(used_is,(const PetscInt**)&is_indices);
6316:       /* change of basis should not be performed on local periodic nodes */
6317:       if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
6318:       if (nnsp_has_cnst) {
6319:         PetscScalar quad_value;

6321:         PetscArraycpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint);
6322:         idxs_copied = PETSC_TRUE;

6324:         if (!pcbddc->use_nnsp_true) {
6325:           quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
6326:         } else {
6327:           quad_value = 1.0;
6328:         }
6329:         for (j=0;j<size_of_constraint;j++) {
6330:           constraints_data[constraints_data_ptr[total_counts_cc]+j] = quad_value;
6331:         }
6332:         temp_constraints++;
6333:         total_counts++;
6334:       }
6335:       for (k=0;k<nnsp_size;k++) {
6336:         PetscReal real_value;
6337:         PetscScalar *ptr_to_data;

6339:         VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
6340:         ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]+temp_constraints*size_of_constraint];
6341:         for (j=0;j<size_of_constraint;j++) {
6342:           ptr_to_data[j] = array[is_indices[j]];
6343:         }
6344:         VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
6345:         /* check if array is null on the connected component */
6346:         PetscBLASIntCast(size_of_constraint,&Blas_N);
6347:         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,ptr_to_data,&Blas_one));
6348:         if (real_value > tol*size_of_constraint) { /* keep indices and values */
6349:           temp_constraints++;
6350:           total_counts++;
6351:           if (!idxs_copied) {
6352:             PetscArraycpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint);
6353:             idxs_copied = PETSC_TRUE;
6354:           }
6355:         }
6356:       }
6357:       ISRestoreIndices(used_is,(const PetscInt**)&is_indices);
6358:       valid_constraints = temp_constraints;
6359:       if (!pcbddc->use_nnsp_true && temp_constraints) {
6360:         if (temp_constraints == 1) { /* just normalize the constraint */
6361:           PetscScalar norm,*ptr_to_data;

6363:           ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];
6364:           PetscBLASIntCast(size_of_constraint,&Blas_N);
6365:           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,ptr_to_data,&Blas_one,ptr_to_data,&Blas_one));
6366:           norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
6367:           PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,ptr_to_data,&Blas_one));
6368:         } else { /* perform SVD */
6369:           PetscScalar *ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];

6371:           if (use_pod) {
6372:             /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
6373:                POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
6374:                -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
6375:                   the constraints basis will differ (by a complex factor with absolute value equal to 1)
6376:                   from that computed using LAPACKgesvd
6377:                -> This is due to a different computation of eigenvectors in LAPACKheev
6378:                -> The quality of the POD-computed basis will be the same */
6379:             PetscArrayzero(correlation_mat,temp_constraints*temp_constraints);
6380:             /* Store upper triangular part of correlation matrix */
6381:             PetscBLASIntCast(size_of_constraint,&Blas_N);
6382:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6383:             for (j=0;j<temp_constraints;j++) {
6384:               for (k=0;k<j+1;k++) {
6385:                 PetscStackCallBLAS("BLASdot",correlation_mat[j*temp_constraints+k] = BLASdot_(&Blas_N,ptr_to_data+k*size_of_constraint,&Blas_one,ptr_to_data+j*size_of_constraint,&Blas_one));
6386:               }
6387:             }
6388:             /* compute eigenvalues and eigenvectors of correlation matrix */
6389:             PetscBLASIntCast(temp_constraints,&Blas_N);
6390:             PetscBLASIntCast(temp_constraints,&Blas_LDA);
6391: #if !defined(PETSC_USE_COMPLEX)
6392:             PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
6393: #else
6394:             PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
6395: #endif
6396:             PetscFPTrapPop();
6397:             if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
6398:             /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
6399:             j = 0;
6400:             while (j < temp_constraints && singular_vals[j]/singular_vals[temp_constraints-1] < tol) j++;
6401:             total_counts = total_counts-j;
6402:             valid_constraints = temp_constraints-j;
6403:             /* scale and copy POD basis into used quadrature memory */
6404:             PetscBLASIntCast(size_of_constraint,&Blas_M);
6405:             PetscBLASIntCast(temp_constraints,&Blas_N);
6406:             PetscBLASIntCast(temp_constraints,&Blas_K);
6407:             PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6408:             PetscBLASIntCast(temp_constraints,&Blas_LDB);
6409:             PetscBLASIntCast(size_of_constraint,&Blas_LDC);
6410:             if (j<temp_constraints) {
6411:               PetscInt ii;
6412:               for (k=j;k<temp_constraints;k++) singular_vals[k] = 1.0/PetscSqrtReal(singular_vals[k]);
6413:               PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6414:               PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Blas_M,&Blas_N,&Blas_K,&one,ptr_to_data,&Blas_LDA,correlation_mat,&Blas_LDB,&zero,temp_basis,&Blas_LDC));
6415:               PetscFPTrapPop();
6416:               for (k=0;k<temp_constraints-j;k++) {
6417:                 for (ii=0;ii<size_of_constraint;ii++) {
6418:                   ptr_to_data[k*size_of_constraint+ii] = singular_vals[temp_constraints-1-k]*temp_basis[(temp_constraints-1-k)*size_of_constraint+ii];
6419:                 }
6420:               }
6421:             }
6422:           } else {
6423: #if !defined(PETSC_MISSING_LAPACK_GESVD)
6424:             PetscBLASIntCast(size_of_constraint,&Blas_M);
6425:             PetscBLASIntCast(temp_constraints,&Blas_N);
6426:             PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6427:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6428: #if !defined(PETSC_USE_COMPLEX)
6429:             PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,ptr_to_data,&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,&lierr));
6430: #else
6431:             PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&Blas_M,&Blas_N,ptr_to_data,&Blas_LDA,singular_vals,&dummy_scalar,&dummy_int,&dummy_scalar,&dummy_int,work,&lwork,rwork,&lierr));
6432: #endif
6433:             if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
6434:             PetscFPTrapPop();
6435:             /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
6436:             k = temp_constraints;
6437:             if (k > size_of_constraint) k = size_of_constraint;
6438:             j = 0;
6439:             while (j < k && singular_vals[k-j-1]/singular_vals[0] < tol) j++;
6440:             valid_constraints = k-j;
6441:             total_counts = total_counts-temp_constraints+valid_constraints;
6442: #else
6443:             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"This should not happen");
6444: #endif /* on missing GESVD */
6445:           }
6446:         }
6447:       }
6448:       /* update pointers information */
6449:       if (valid_constraints) {
6450:         constraints_n[total_counts_cc] = valid_constraints;
6451:         constraints_idxs_ptr[total_counts_cc+1] = constraints_idxs_ptr[total_counts_cc]+size_of_constraint;
6452:         constraints_data_ptr[total_counts_cc+1] = constraints_data_ptr[total_counts_cc]+size_of_constraint*valid_constraints;
6453:         /* set change_of_basis flag */
6454:         if (boolforchange) {
6455:           PetscBTSet(change_basis,total_counts_cc);
6456:         }
6457:         total_counts_cc++;
6458:       }
6459:     }
6460:     /* free workspace */
6461:     if (!skip_lapack) {
6462:       PetscFree(work);
6463: #if defined(PETSC_USE_COMPLEX)
6464:       PetscFree(rwork);
6465: #endif
6466:       PetscFree(singular_vals);
6467:       PetscFree(correlation_mat);
6468:       PetscFree(temp_basis);
6469:     }
6470:     for (k=0;k<nnsp_size;k++) {
6471:       VecDestroy(&localnearnullsp[k]);
6472:     }
6473:     PetscFree(localnearnullsp);
6474:     /* free index sets of faces, edges and vertices */
6475:     for (i=0;i<n_ISForFaces;i++) {
6476:       ISDestroy(&ISForFaces[i]);
6477:     }
6478:     if (n_ISForFaces) {
6479:       PetscFree(ISForFaces);
6480:     }
6481:     for (i=0;i<n_ISForEdges;i++) {
6482:       ISDestroy(&ISForEdges[i]);
6483:     }
6484:     if (n_ISForEdges) {
6485:       PetscFree(ISForEdges);
6486:     }
6487:     ISDestroy(&ISForVertices);
6488:   } else {
6489:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

6491:     total_counts = 0;
6492:     n_vertices = 0;
6493:     if (sub_schurs->is_vertices && pcbddc->use_vertices) {
6494:       ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);
6495:     }
6496:     max_constraints = 0;
6497:     total_counts_cc = 0;
6498:     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
6499:       total_counts += pcbddc->adaptive_constraints_n[i];
6500:       if (pcbddc->adaptive_constraints_n[i]) total_counts_cc++;
6501:       max_constraints = PetscMax(max_constraints,pcbddc->adaptive_constraints_n[i]);
6502:     }
6503:     constraints_idxs_ptr = pcbddc->adaptive_constraints_idxs_ptr;
6504:     constraints_data_ptr = pcbddc->adaptive_constraints_data_ptr;
6505:     constraints_idxs = pcbddc->adaptive_constraints_idxs;
6506:     constraints_data = pcbddc->adaptive_constraints_data;
6507:     /* constraints_n differs from pcbddc->adaptive_constraints_n */
6508:     PetscMalloc1(total_counts_cc,&constraints_n);
6509:     total_counts_cc = 0;
6510:     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
6511:       if (pcbddc->adaptive_constraints_n[i]) {
6512:         constraints_n[total_counts_cc++] = pcbddc->adaptive_constraints_n[i];
6513:       }
6514:     }

6516:     max_size_of_constraint = 0;
6517:     for (i=0;i<total_counts_cc;i++) max_size_of_constraint = PetscMax(max_size_of_constraint,constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i]);
6518:     PetscMalloc1(constraints_idxs_ptr[total_counts_cc],&constraints_idxs_B);
6519:     /* Change of basis */
6520:     PetscBTCreate(total_counts_cc,&change_basis);
6521:     if (pcbddc->use_change_of_basis) {
6522:       for (i=0;i<sub_schurs->n_subs;i++) {
6523:         if (PetscBTLookup(sub_schurs->is_edge,i) || pcbddc->use_change_on_faces) {
6524:           PetscBTSet(change_basis,i+n_vertices);
6525:         }
6526:       }
6527:     }
6528:   }
6529:   pcbddc->local_primal_size = total_counts;
6530:   PetscMalloc1(pcbddc->local_primal_size+pcbddc->benign_n,&pcbddc->primal_indices_local_idxs);

6532:   /* map constraints_idxs in boundary numbering */
6533:   ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,constraints_idxs_ptr[total_counts_cc],constraints_idxs,&i,constraints_idxs_B);
6534:   if (i != constraints_idxs_ptr[total_counts_cc]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for constraints indices %D != %D",constraints_idxs_ptr[total_counts_cc],i);

6536:   /* Create constraint matrix */
6537:   MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);
6538:   MatSetType(pcbddc->ConstraintMatrix,MATAIJ);
6539:   MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);

6541:   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
6542:   /* determine if a QR strategy is needed for change of basis */
6543:   qr_needed = pcbddc->use_qr_single;
6544:   PetscBTCreate(total_counts_cc,&qr_needed_idx);
6545:   total_primal_vertices=0;
6546:   pcbddc->local_primal_size_cc = 0;
6547:   for (i=0;i<total_counts_cc;i++) {
6548:     size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
6549:     if (size_of_constraint == 1 && pcbddc->mat_graph->custom_minimal_size) {
6550:       pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]];
6551:       pcbddc->local_primal_size_cc += 1;
6552:     } else if (PetscBTLookup(change_basis,i)) {
6553:       for (k=0;k<constraints_n[i];k++) {
6554:         pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]+k];
6555:       }
6556:       pcbddc->local_primal_size_cc += constraints_n[i];
6557:       if (constraints_n[i] > 1 || pcbddc->use_qr_single) {
6558:         PetscBTSet(qr_needed_idx,i);
6559:         qr_needed = PETSC_TRUE;
6560:       }
6561:     } else {
6562:       pcbddc->local_primal_size_cc += 1;
6563:     }
6564:   }
6565:   /* note that the local variable n_vertices used below stores the number of pointwise constraints */
6566:   pcbddc->n_vertices = total_primal_vertices;
6567:   /* permute indices in order to have a sorted set of vertices */
6568:   PetscSortInt(total_primal_vertices,pcbddc->primal_indices_local_idxs);
6569:   PetscMalloc2(pcbddc->local_primal_size_cc+pcbddc->benign_n,&pcbddc->local_primal_ref_node,pcbddc->local_primal_size_cc+pcbddc->benign_n,&pcbddc->local_primal_ref_mult);
6570:   PetscArraycpy(pcbddc->local_primal_ref_node,pcbddc->primal_indices_local_idxs,total_primal_vertices);
6571:   for (i=0;i<total_primal_vertices;i++) pcbddc->local_primal_ref_mult[i] = 1;

6573:   /* nonzero structure of constraint matrix */
6574:   /* and get reference dof for local constraints */
6575:   PetscMalloc1(pcbddc->local_primal_size,&nnz);
6576:   for (i=0;i<total_primal_vertices;i++) nnz[i] = 1;

6578:   j = total_primal_vertices;
6579:   total_counts = total_primal_vertices;
6580:   cum = total_primal_vertices;
6581:   for (i=n_vertices;i<total_counts_cc;i++) {
6582:     if (!PetscBTLookup(change_basis,i)) {
6583:       pcbddc->local_primal_ref_node[cum] = constraints_idxs[constraints_idxs_ptr[i]];
6584:       pcbddc->local_primal_ref_mult[cum] = constraints_n[i];
6585:       cum++;
6586:       size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
6587:       for (k=0;k<constraints_n[i];k++) {
6588:         pcbddc->primal_indices_local_idxs[total_counts++] = constraints_idxs[constraints_idxs_ptr[i]+k];
6589:         nnz[j+k] = size_of_constraint;
6590:       }
6591:       j += constraints_n[i];
6592:     }
6593:   }
6594:   MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);
6595:   MatSetOption(pcbddc->ConstraintMatrix,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
6596:   PetscFree(nnz);

6598:   /* set values in constraint matrix */
6599:   for (i=0;i<total_primal_vertices;i++) {
6600:     MatSetValue(pcbddc->ConstraintMatrix,i,pcbddc->local_primal_ref_node[i],1.0,INSERT_VALUES);
6601:   }
6602:   total_counts = total_primal_vertices;
6603:   for (i=n_vertices;i<total_counts_cc;i++) {
6604:     if (!PetscBTLookup(change_basis,i)) {
6605:       PetscInt *cols;

6607:       size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
6608:       cols = constraints_idxs+constraints_idxs_ptr[i];
6609:       for (k=0;k<constraints_n[i];k++) {
6610:         PetscInt    row = total_counts+k;
6611:         PetscScalar *vals;

6613:         vals = constraints_data+constraints_data_ptr[i]+k*size_of_constraint;
6614:         MatSetValues(pcbddc->ConstraintMatrix,1,&row,size_of_constraint,cols,vals,INSERT_VALUES);
6615:       }
6616:       total_counts += constraints_n[i];
6617:     }
6618:   }
6619:   /* assembling */
6620:   MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);
6621:   MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);
6622:   MatViewFromOptions(pcbddc->ConstraintMatrix,(PetscObject)pc,"-pc_bddc_constraint_mat_view");

6624:   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
6625:   if (pcbddc->use_change_of_basis) {
6626:     /* dual and primal dofs on a single cc */
6627:     PetscInt     dual_dofs,primal_dofs;
6628:     /* working stuff for GEQRF */
6629:     PetscScalar  *qr_basis = NULL,*qr_tau = NULL,*qr_work = NULL,lqr_work_t;
6630:     PetscBLASInt lqr_work;
6631:     /* working stuff for UNGQR */
6632:     PetscScalar  *gqr_work = NULL,lgqr_work_t=0.0;
6633:     PetscBLASInt lgqr_work;
6634:     /* working stuff for TRTRS */
6635:     PetscScalar  *trs_rhs = NULL;
6636:     PetscBLASInt Blas_NRHS;
6637:     /* pointers for values insertion into change of basis matrix */
6638:     PetscInt     *start_rows,*start_cols;
6639:     PetscScalar  *start_vals;
6640:     /* working stuff for values insertion */
6641:     PetscBT      is_primal;
6642:     PetscInt     *aux_primal_numbering_B;
6643:     /* matrix sizes */
6644:     PetscInt     global_size,local_size;
6645:     /* temporary change of basis */
6646:     Mat          localChangeOfBasisMatrix;
6647:     /* extra space for debugging */
6648:     PetscScalar  *dbg_work = NULL;

6650:     /* local temporary change of basis acts on local interfaces -> dimension is n_B x n_B */
6651:     MatCreate(PETSC_COMM_SELF,&localChangeOfBasisMatrix);
6652:     MatSetType(localChangeOfBasisMatrix,MATAIJ);
6653:     MatSetSizes(localChangeOfBasisMatrix,pcis->n,pcis->n,pcis->n,pcis->n);
6654:     /* nonzeros for local mat */
6655:     PetscMalloc1(pcis->n,&nnz);
6656:     if (!pcbddc->benign_change || pcbddc->fake_change) {
6657:       for (i=0;i<pcis->n;i++) nnz[i]=1;
6658:     } else {
6659:       const PetscInt *ii;
6660:       PetscInt       n;
6661:       PetscBool      flg_row;
6662:       MatGetRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,NULL,&flg_row);
6663:       for (i=0;i<n;i++) nnz[i] = ii[i+1]-ii[i];
6664:       MatRestoreRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,NULL,&flg_row);
6665:     }
6666:     for (i=n_vertices;i<total_counts_cc;i++) {
6667:       if (PetscBTLookup(change_basis,i)) {
6668:         size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
6669:         if (PetscBTLookup(qr_needed_idx,i)) {
6670:           for (j=0;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = size_of_constraint;
6671:         } else {
6672:           nnz[constraints_idxs[constraints_idxs_ptr[i]]] = size_of_constraint;
6673:           for (j=1;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = 2;
6674:         }
6675:       }
6676:     }
6677:     MatSeqAIJSetPreallocation(localChangeOfBasisMatrix,0,nnz);
6678:     MatSetOption(localChangeOfBasisMatrix,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
6679:     PetscFree(nnz);
6680:     /* Set interior change in the matrix */
6681:     if (!pcbddc->benign_change || pcbddc->fake_change) {
6682:       for (i=0;i<pcis->n;i++) {
6683:         MatSetValue(localChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);
6684:       }
6685:     } else {
6686:       const PetscInt *ii,*jj;
6687:       PetscScalar    *aa;
6688:       PetscInt       n;
6689:       PetscBool      flg_row;
6690:       MatGetRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&jj,&flg_row);
6691:       MatSeqAIJGetArray(pcbddc->benign_change,&aa);
6692:       for (i=0;i<n;i++) {
6693:         MatSetValues(localChangeOfBasisMatrix,1,&i,ii[i+1]-ii[i],jj+ii[i],aa+ii[i],INSERT_VALUES);
6694:       }
6695:       MatSeqAIJRestoreArray(pcbddc->benign_change,&aa);
6696:       MatRestoreRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&jj,&flg_row);
6697:     }

6699:     if (pcbddc->dbg_flag) {
6700:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
6701:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);
6702:     }

6704:     /* Now we loop on the constraints which need a change of basis */
6705:     /*
6706:        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
6707:        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)

6709:        Basic blocks of change of basis matrix T computed by

6711:           - Using the following block transformation if there is only a primal dof on the cc (and -pc_bddc_use_qr_single is not specified)

6713:             | 1        0   ...        0         s_1/S |
6714:             | 0        1   ...        0         s_2/S |
6715:             |              ...                        |
6716:             | 0        ...            1     s_{n-1}/S |
6717:             | -s_1/s_n ...    -s_{n-1}/s_n      s_n/S |

6719:             with S = \sum_{i=1}^n s_i^2
6720:             NOTE: in the above example, the primal dof is the last one of the edge in LOCAL ordering
6721:                   in the current implementation, the primal dof is the first one of the edge in GLOBAL ordering

6723:           - QR decomposition of constraints otherwise
6724:     */
6725:     if (qr_needed && max_size_of_constraint) {
6726:       /* space to store Q */
6727:       PetscMalloc1(max_size_of_constraint*max_size_of_constraint,&qr_basis);
6728:       /* array to store scaling factors for reflectors */
6729:       PetscMalloc1(max_constraints,&qr_tau);
6730:       /* first we issue queries for optimal work */
6731:       PetscBLASIntCast(max_size_of_constraint,&Blas_M);
6732:       PetscBLASIntCast(max_constraints,&Blas_N);
6733:       PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);
6734:       lqr_work = -1;
6735:       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
6736:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
6737:       PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);
6738:       PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);
6739:       lgqr_work = -1;
6740:       PetscBLASIntCast(max_size_of_constraint,&Blas_M);
6741:       PetscBLASIntCast(max_size_of_constraint,&Blas_N);
6742:       PetscBLASIntCast(max_constraints,&Blas_K);
6743:       PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);
6744:       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
6745:       PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
6746:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to ORGQR/UNGQR Lapack routine %d",(int)lierr);
6747:       PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);
6748:       PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);
6749:       /* array to store rhs and solution of triangular solver */
6750:       PetscMalloc1(max_constraints*max_constraints,&trs_rhs);
6751:       /* allocating workspace for check */
6752:       if (pcbddc->dbg_flag) {
6753:         PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&dbg_work);
6754:       }
6755:     }
6756:     /* array to store whether a node is primal or not */
6757:     PetscBTCreate(pcis->n_B,&is_primal);
6758:     PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);
6759:     ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,pcbddc->local_primal_ref_node,&i,aux_primal_numbering_B);
6760:     if (i != total_primal_vertices) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for BDDC vertices! %D != %D",total_primal_vertices,i);
6761:     for (i=0;i<total_primal_vertices;i++) {
6762:       PetscBTSet(is_primal,aux_primal_numbering_B[i]);
6763:     }
6764:     PetscFree(aux_primal_numbering_B);

6766:     /* loop on constraints and see whether or not they need a change of basis and compute it */
6767:     for (total_counts=n_vertices;total_counts<total_counts_cc;total_counts++) {
6768:       size_of_constraint = constraints_idxs_ptr[total_counts+1]-constraints_idxs_ptr[total_counts];
6769:       if (PetscBTLookup(change_basis,total_counts)) {
6770:         /* get constraint info */
6771:         primal_dofs = constraints_n[total_counts];
6772:         dual_dofs = size_of_constraint-primal_dofs;

6774:         if (pcbddc->dbg_flag) {
6775:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraints %D: %D need a change of basis (size %D)\n",total_counts,primal_dofs,size_of_constraint);
6776:         }

6778:         if (PetscBTLookup(qr_needed_idx,total_counts)) { /* QR */

6780:           /* copy quadrature constraints for change of basis check */
6781:           if (pcbddc->dbg_flag) {
6782:             PetscArraycpy(dbg_work,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);
6783:           }
6784:           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
6785:           PetscArraycpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);

6787:           /* compute QR decomposition of constraints */
6788:           PetscBLASIntCast(size_of_constraint,&Blas_M);
6789:           PetscBLASIntCast(primal_dofs,&Blas_N);
6790:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6791:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6792:           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
6793:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
6794:           PetscFPTrapPop();

6796:           /* explicitly compute R^-T */
6797:           PetscArrayzero(trs_rhs,primal_dofs*primal_dofs);
6798:           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
6799:           PetscBLASIntCast(primal_dofs,&Blas_N);
6800:           PetscBLASIntCast(primal_dofs,&Blas_NRHS);
6801:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6802:           PetscBLASIntCast(primal_dofs,&Blas_LDB);
6803:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6804:           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
6805:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
6806:           PetscFPTrapPop();

6808:           /* explicitly compute all columns of Q (Q = [Q1 | Q2]) overwriting QR factorization in qr_basis */
6809:           PetscBLASIntCast(size_of_constraint,&Blas_M);
6810:           PetscBLASIntCast(size_of_constraint,&Blas_N);
6811:           PetscBLASIntCast(primal_dofs,&Blas_K);
6812:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6813:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6814:           PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
6815:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in ORGQR/UNGQR Lapack routine %d",(int)lierr);
6816:           PetscFPTrapPop();

6818:           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
6819:              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
6820:              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
6821:           PetscBLASIntCast(size_of_constraint,&Blas_M);
6822:           PetscBLASIntCast(primal_dofs,&Blas_N);
6823:           PetscBLASIntCast(primal_dofs,&Blas_K);
6824:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6825:           PetscBLASIntCast(primal_dofs,&Blas_LDB);
6826:           PetscBLASIntCast(size_of_constraint,&Blas_LDC);
6827:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6828:           PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&Blas_M,&Blas_N,&Blas_K,&one,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&zero,constraints_data+constraints_data_ptr[total_counts],&Blas_LDC));
6829:           PetscFPTrapPop();
6830:           PetscArraycpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);

6832:           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
6833:           start_rows = &constraints_idxs[constraints_idxs_ptr[total_counts]];
6834:           /* insert cols for primal dofs */
6835:           for (j=0;j<primal_dofs;j++) {
6836:             start_vals = &qr_basis[j*size_of_constraint];
6837:             start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+j];
6838:             MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);
6839:           }
6840:           /* insert cols for dual dofs */
6841:           for (j=0,k=0;j<dual_dofs;k++) {
6842:             if (!PetscBTLookup(is_primal,constraints_idxs_B[constraints_idxs_ptr[total_counts]+k])) {
6843:               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
6844:               start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+k];
6845:               MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);
6846:               j++;
6847:             }
6848:           }

6850:           /* check change of basis */
6851:           if (pcbddc->dbg_flag) {
6852:             PetscInt   ii,jj;
6853:             PetscBool valid_qr=PETSC_TRUE;
6854:             PetscBLASIntCast(primal_dofs,&Blas_M);
6855:             PetscBLASIntCast(size_of_constraint,&Blas_N);
6856:             PetscBLASIntCast(size_of_constraint,&Blas_K);
6857:             PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6858:             PetscBLASIntCast(size_of_constraint,&Blas_LDB);
6859:             PetscBLASIntCast(primal_dofs,&Blas_LDC);
6860:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6861:             PetscStackCallBLAS("BLASgemm",BLASgemm_("T","N",&Blas_M,&Blas_N,&Blas_K,&one,dbg_work,&Blas_LDA,qr_basis,&Blas_LDB,&zero,&dbg_work[size_of_constraint*primal_dofs],&Blas_LDC));
6862:             PetscFPTrapPop();
6863:             for (jj=0;jj<size_of_constraint;jj++) {
6864:               for (ii=0;ii<primal_dofs;ii++) {
6865:                 if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
6866:                 if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-(PetscReal)1) > 1.e-12) valid_qr = PETSC_FALSE;
6867:               }
6868:             }
6869:             if (!valid_qr) {
6870:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");
6871:               for (jj=0;jj<size_of_constraint;jj++) {
6872:                 for (ii=0;ii<primal_dofs;ii++) {
6873:                   if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
6874:                     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %D is not orthogonal to constraint %D (%1.14e)!\n",jj,ii,PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
6875:                   }
6876:                   if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-(PetscReal)1) > 1.e-12) {
6877:                     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\tQr basis function %D is not unitary w.r.t constraint %D (%1.14e)!\n",jj,ii,PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]));
6878:                   }
6879:                 }
6880:               }
6881:             } else {
6882:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");
6883:             }
6884:           }
6885:         } else { /* simple transformation block */
6886:           PetscInt    row,col;
6887:           PetscScalar val,norm;

6889:           PetscBLASIntCast(size_of_constraint,&Blas_N);
6890:           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,constraints_data+constraints_data_ptr[total_counts],&Blas_one,constraints_data+constraints_data_ptr[total_counts],&Blas_one));
6891:           for (j=0;j<size_of_constraint;j++) {
6892:             PetscInt row_B = constraints_idxs_B[constraints_idxs_ptr[total_counts]+j];
6893:             row = constraints_idxs[constraints_idxs_ptr[total_counts]+j];
6894:             if (!PetscBTLookup(is_primal,row_B)) {
6895:               col = constraints_idxs[constraints_idxs_ptr[total_counts]];
6896:               MatSetValue(localChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);
6897:               MatSetValue(localChangeOfBasisMatrix,row,col,constraints_data[constraints_data_ptr[total_counts]+j]/norm,INSERT_VALUES);
6898:             } else {
6899:               for (k=0;k<size_of_constraint;k++) {
6900:                 col = constraints_idxs[constraints_idxs_ptr[total_counts]+k];
6901:                 if (row != col) {
6902:                   val = -constraints_data[constraints_data_ptr[total_counts]+k]/constraints_data[constraints_data_ptr[total_counts]];
6903:                 } else {
6904:                   val = constraints_data[constraints_data_ptr[total_counts]]/norm;
6905:                 }
6906:                 MatSetValue(localChangeOfBasisMatrix,row,col,val,INSERT_VALUES);
6907:               }
6908:             }
6909:           }
6910:           if (pcbddc->dbg_flag) {
6911:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");
6912:           }
6913:         }
6914:       } else {
6915:         if (pcbddc->dbg_flag) {
6916:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %D does not need a change of basis (size %D)\n",total_counts,size_of_constraint);
6917:         }
6918:       }
6919:     }

6921:     /* free workspace */
6922:     if (qr_needed) {
6923:       if (pcbddc->dbg_flag) {
6924:         PetscFree(dbg_work);
6925:       }
6926:       PetscFree(trs_rhs);
6927:       PetscFree(qr_tau);
6928:       PetscFree(qr_work);
6929:       PetscFree(gqr_work);
6930:       PetscFree(qr_basis);
6931:     }
6932:     PetscBTDestroy(&is_primal);
6933:     MatAssemblyBegin(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);
6934:     MatAssemblyEnd(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);

6936:     /* assembling of global change of variable */
6937:     if (!pcbddc->fake_change) {
6938:       Mat      tmat;
6939:       PetscInt bs;

6941:       VecGetSize(pcis->vec1_global,&global_size);
6942:       VecGetLocalSize(pcis->vec1_global,&local_size);
6943:       MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&tmat);
6944:       MatISSetLocalMat(tmat,localChangeOfBasisMatrix);
6945:       MatAssemblyBegin(tmat,MAT_FINAL_ASSEMBLY);
6946:       MatAssemblyEnd(tmat,MAT_FINAL_ASSEMBLY);
6947:       MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->ChangeOfBasisMatrix);
6948:       MatSetType(pcbddc->ChangeOfBasisMatrix,MATAIJ);
6949:       MatGetBlockSize(pc->pmat,&bs);
6950:       MatSetBlockSize(pcbddc->ChangeOfBasisMatrix,bs);
6951:       MatSetSizes(pcbddc->ChangeOfBasisMatrix,local_size,local_size,global_size,global_size);
6952:       MatISSetMPIXAIJPreallocation_Private(tmat,pcbddc->ChangeOfBasisMatrix,PETSC_TRUE);
6953:       MatConvert(tmat,MATAIJ,MAT_REUSE_MATRIX,&pcbddc->ChangeOfBasisMatrix);
6954:       MatDestroy(&tmat);
6955:       VecSet(pcis->vec1_global,0.0);
6956:       VecSet(pcis->vec1_N,1.0);
6957:       VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
6958:       VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
6959:       VecReciprocal(pcis->vec1_global);
6960:       MatDiagonalScale(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,NULL);

6962:       /* check */
6963:       if (pcbddc->dbg_flag) {
6964:         PetscReal error;
6965:         Vec       x,x_change;

6967:         VecDuplicate(pcis->vec1_global,&x);
6968:         VecDuplicate(pcis->vec1_global,&x_change);
6969:         VecSetRandom(x,NULL);
6970:         VecCopy(x,pcis->vec1_global);
6971:         VecScatterBegin(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
6972:         VecScatterEnd(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
6973:         MatMult(localChangeOfBasisMatrix,pcis->vec1_N,pcis->vec2_N);
6974:         VecScatterBegin(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);
6975:         VecScatterEnd(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);
6976:         MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);
6977:         VecAXPY(x,-1.0,x_change);
6978:         VecNorm(x,NORM_INFINITY,&error);
6979:         if (error > PETSC_SMALL) {
6980:           SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on N: %1.6e",error);
6981:         }
6982:         VecDestroy(&x);
6983:         VecDestroy(&x_change);
6984:       }
6985:       /* adapt sub_schurs computed (if any) */
6986:       if (pcbddc->use_deluxe_scaling) {
6987:         PCBDDCSubSchurs sub_schurs=pcbddc->sub_schurs;

6989:         if (pcbddc->use_change_of_basis && pcbddc->adaptive_userdefined) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot mix automatic change of basis, adaptive selection and user-defined constraints");
6990:         if (sub_schurs && sub_schurs->S_Ej_all) {
6991:           Mat                    S_new,tmat;
6992:           IS                     is_all_N,is_V_Sall = NULL;

6994:           ISLocalToGlobalMappingApplyIS(pcis->BtoNmap,sub_schurs->is_Ej_all,&is_all_N);
6995:           MatCreateSubMatrix(localChangeOfBasisMatrix,is_all_N,is_all_N,MAT_INITIAL_MATRIX,&tmat);
6996:           if (pcbddc->deluxe_zerorows) {
6997:             ISLocalToGlobalMapping NtoSall;
6998:             IS                     is_V;
6999:             ISCreateGeneral(PETSC_COMM_SELF,pcbddc->n_vertices,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&is_V);
7000:             ISLocalToGlobalMappingCreateIS(is_all_N,&NtoSall);
7001:             ISGlobalToLocalMappingApplyIS(NtoSall,IS_GTOLM_DROP,is_V,&is_V_Sall);
7002:             ISLocalToGlobalMappingDestroy(&NtoSall);
7003:             ISDestroy(&is_V);
7004:           }
7005:           ISDestroy(&is_all_N);
7006:           MatPtAP(sub_schurs->S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);
7007:           MatDestroy(&sub_schurs->S_Ej_all);
7008:           PetscObjectReference((PetscObject)S_new);
7009:           if (pcbddc->deluxe_zerorows) {
7010:             const PetscScalar *array;
7011:             const PetscInt    *idxs_V,*idxs_all;
7012:             PetscInt          i,n_V;

7014:             MatZeroRowsColumnsIS(S_new,is_V_Sall,1.,NULL,NULL);
7015:             ISGetLocalSize(is_V_Sall,&n_V);
7016:             ISGetIndices(is_V_Sall,&idxs_V);
7017:             ISGetIndices(sub_schurs->is_Ej_all,&idxs_all);
7018:             VecGetArrayRead(pcis->D,&array);
7019:             for (i=0;i<n_V;i++) {
7020:               PetscScalar val;
7021:               PetscInt    idx;

7023:               idx = idxs_V[i];
7024:               val = array[idxs_all[idxs_V[i]]];
7025:               MatSetValue(S_new,idx,idx,val,INSERT_VALUES);
7026:             }
7027:             MatAssemblyBegin(S_new,MAT_FINAL_ASSEMBLY);
7028:             MatAssemblyEnd(S_new,MAT_FINAL_ASSEMBLY);
7029:             VecRestoreArrayRead(pcis->D,&array);
7030:             ISRestoreIndices(sub_schurs->is_Ej_all,&idxs_all);
7031:             ISRestoreIndices(is_V_Sall,&idxs_V);
7032:           }
7033:           sub_schurs->S_Ej_all = S_new;
7034:           MatDestroy(&S_new);
7035:           if (sub_schurs->sum_S_Ej_all) {
7036:             MatPtAP(sub_schurs->sum_S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);
7037:             MatDestroy(&sub_schurs->sum_S_Ej_all);
7038:             PetscObjectReference((PetscObject)S_new);
7039:             if (pcbddc->deluxe_zerorows) {
7040:               MatZeroRowsColumnsIS(S_new,is_V_Sall,1.,NULL,NULL);
7041:             }
7042:             sub_schurs->sum_S_Ej_all = S_new;
7043:             MatDestroy(&S_new);
7044:           }
7045:           ISDestroy(&is_V_Sall);
7046:           MatDestroy(&tmat);
7047:         }
7048:         /* destroy any change of basis context in sub_schurs */
7049:         if (sub_schurs && sub_schurs->change) {
7050:           PetscInt i;

7052:           for (i=0;i<sub_schurs->n_subs;i++) {
7053:             KSPDestroy(&sub_schurs->change[i]);
7054:           }
7055:           PetscFree(sub_schurs->change);
7056:         }
7057:       }
7058:       if (pcbddc->switch_static) { /* need to save the local change */
7059:         pcbddc->switch_static_change = localChangeOfBasisMatrix;
7060:       } else {
7061:         MatDestroy(&localChangeOfBasisMatrix);
7062:       }
7063:       /* determine if any process has changed the pressures locally */
7064:       pcbddc->change_interior = pcbddc->benign_have_null;
7065:     } else { /* fake change (get back change of basis into ConstraintMatrix and info on qr) */
7066:       MatDestroy(&pcbddc->ConstraintMatrix);
7067:       pcbddc->ConstraintMatrix = localChangeOfBasisMatrix;
7068:       pcbddc->use_qr_single = qr_needed;
7069:     }
7070:   } else if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->benign_saddle_point) {
7071:     if (!pcbddc->benign_have_null && pcbddc->user_ChangeOfBasisMatrix) {
7072:       PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);
7073:       pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
7074:     } else {
7075:       Mat benign_global = NULL;
7076:       if (pcbddc->benign_have_null) {
7077:         Mat M;

7079:         pcbddc->change_interior = PETSC_TRUE;
7080:         VecCopy(matis->counter,pcis->vec1_N);
7081:         VecReciprocal(pcis->vec1_N);
7082:         MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&benign_global);
7083:         if (pcbddc->benign_change) {
7084:           MatDuplicate(pcbddc->benign_change,MAT_COPY_VALUES,&M);
7085:           MatDiagonalScale(M,pcis->vec1_N,NULL);
7086:         } else {
7087:           MatCreateSeqAIJ(PETSC_COMM_SELF,pcis->n,pcis->n,1,NULL,&M);
7088:           MatDiagonalSet(M,pcis->vec1_N,INSERT_VALUES);
7089:         }
7090:         MatISSetLocalMat(benign_global,M);
7091:         MatDestroy(&M);
7092:         MatAssemblyBegin(benign_global,MAT_FINAL_ASSEMBLY);
7093:         MatAssemblyEnd(benign_global,MAT_FINAL_ASSEMBLY);
7094:       }
7095:       if (pcbddc->user_ChangeOfBasisMatrix) {
7096:         MatMatMult(pcbddc->user_ChangeOfBasisMatrix,benign_global,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->ChangeOfBasisMatrix);
7097:         MatDestroy(&benign_global);
7098:       } else if (pcbddc->benign_have_null) {
7099:         pcbddc->ChangeOfBasisMatrix = benign_global;
7100:       }
7101:     }
7102:     if (pcbddc->switch_static && pcbddc->ChangeOfBasisMatrix) { /* need to save the local change */
7103:       IS             is_global;
7104:       const PetscInt *gidxs;

7106:       ISLocalToGlobalMappingGetIndices(pc->pmat->rmap->mapping,&gidxs);
7107:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcis->n,gidxs,PETSC_COPY_VALUES,&is_global);
7108:       ISLocalToGlobalMappingRestoreIndices(pc->pmat->rmap->mapping,&gidxs);
7109:       MatCreateSubMatrixUnsorted(pcbddc->ChangeOfBasisMatrix,is_global,is_global,&pcbddc->switch_static_change);
7110:       ISDestroy(&is_global);
7111:     }
7112:   }
7113:   if (!pcbddc->fake_change && pcbddc->ChangeOfBasisMatrix && !pcbddc->work_change) {
7114:     VecDuplicate(pcis->vec1_global,&pcbddc->work_change);
7115:   }

7117:   if (!pcbddc->fake_change) {
7118:     /* add pressure dofs to set of primal nodes for numbering purposes */
7119:     for (i=0;i<pcbddc->benign_n;i++) {
7120:       pcbddc->local_primal_ref_node[pcbddc->local_primal_size_cc] = pcbddc->benign_p0_lidx[i];
7121:       pcbddc->primal_indices_local_idxs[pcbddc->local_primal_size] = pcbddc->benign_p0_lidx[i];
7122:       pcbddc->local_primal_ref_mult[pcbddc->local_primal_size_cc] = 1;
7123:       pcbddc->local_primal_size_cc++;
7124:       pcbddc->local_primal_size++;
7125:     }

7127:     /* check if a new primal space has been introduced (also take into account benign trick) */
7128:     pcbddc->new_primal_space_local = PETSC_TRUE;
7129:     if (olocal_primal_size == pcbddc->local_primal_size) {
7130:       PetscArraycmp(pcbddc->local_primal_ref_node,olocal_primal_ref_node,olocal_primal_size_cc,&pcbddc->new_primal_space_local);
7131:       pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
7132:       if (!pcbddc->new_primal_space_local) {
7133:         PetscArraycmp(pcbddc->local_primal_ref_mult,olocal_primal_ref_mult,olocal_primal_size_cc,&pcbddc->new_primal_space_local);
7134:         pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
7135:       }
7136:     }
7137:     /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
7138:     MPIU_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
7139:   }
7140:   PetscFree2(olocal_primal_ref_node,olocal_primal_ref_mult);

7142:   /* flush dbg viewer */
7143:   if (pcbddc->dbg_flag) {
7144:     PetscViewerFlush(pcbddc->dbg_viewer);
7145:   }

7147:   /* free workspace */
7148:   PetscBTDestroy(&qr_needed_idx);
7149:   PetscBTDestroy(&change_basis);
7150:   if (!pcbddc->adaptive_selection) {
7151:     PetscFree3(constraints_idxs_ptr,constraints_data_ptr,constraints_n);
7152:     PetscFree3(constraints_data,constraints_idxs,constraints_idxs_B);
7153:   } else {
7154:     PetscFree5(pcbddc->adaptive_constraints_n,
7155:                       pcbddc->adaptive_constraints_idxs_ptr,
7156:                       pcbddc->adaptive_constraints_data_ptr,
7157:                       pcbddc->adaptive_constraints_idxs,
7158:                       pcbddc->adaptive_constraints_data);
7159:     PetscFree(constraints_n);
7160:     PetscFree(constraints_idxs_B);
7161:   }
7162:   return(0);
7163: }

7165: PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
7166: {
7167:   ISLocalToGlobalMapping map;
7168:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
7169:   Mat_IS                 *matis  = (Mat_IS*)pc->pmat->data;
7170:   PetscInt               i,N;
7171:   PetscBool              rcsr = PETSC_FALSE;
7172:   PetscErrorCode         ierr;

7175:   if (pcbddc->recompute_topography) {
7176:     pcbddc->graphanalyzed = PETSC_FALSE;
7177:     /* Reset previously computed graph */
7178:     PCBDDCGraphReset(pcbddc->mat_graph);
7179:     /* Init local Graph struct */
7180:     MatGetSize(pc->pmat,&N,NULL);
7181:     MatGetLocalToGlobalMapping(pc->pmat,&map,NULL);
7182:     PCBDDCGraphInit(pcbddc->mat_graph,map,N,pcbddc->graphmaxcount);

7184:     if (pcbddc->user_primal_vertices_local && !pcbddc->user_primal_vertices) {
7185:       PCBDDCConsistencyCheckIS(pc,MPI_LOR,&pcbddc->user_primal_vertices_local);
7186:     }
7187:     /* Check validity of the csr graph passed in by the user */
7188:     if (pcbddc->mat_graph->nvtxs_csr && pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid size of local CSR graph! Found %D, expected %D",pcbddc->mat_graph->nvtxs_csr,pcbddc->mat_graph->nvtxs);

7190:     /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
7191:     if (!pcbddc->mat_graph->xadj && pcbddc->use_local_adj) {
7192:       PetscInt  *xadj,*adjncy;
7193:       PetscInt  nvtxs;
7194:       PetscBool flg_row=PETSC_FALSE;

7196:       MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
7197:       if (flg_row) {
7198:         PCBDDCSetLocalAdjacencyGraph(pc,nvtxs,xadj,adjncy,PETSC_COPY_VALUES);
7199:         pcbddc->computed_rowadj = PETSC_TRUE;
7200:       }
7201:       MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
7202:       rcsr = PETSC_TRUE;
7203:     }
7204:     if (pcbddc->dbg_flag) {
7205:       PetscViewerFlush(pcbddc->dbg_viewer);
7206:     }

7208:     if (pcbddc->mat_graph->cdim && !pcbddc->mat_graph->cloc) {
7209:       PetscReal    *lcoords;
7210:       PetscInt     n;
7211:       MPI_Datatype dimrealtype;

7213:       /* TODO: support for blocked */
7214:       if (pcbddc->mat_graph->cnloc != pc->pmat->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_USER,"Invalid number of local coordinates! Got %D, expected %D",pcbddc->mat_graph->cnloc,pc->pmat->rmap->n);
7215:       MatGetLocalSize(matis->A,&n,NULL);
7216:       PetscMalloc1(pcbddc->mat_graph->cdim*n,&lcoords);
7217:       MPI_Type_contiguous(pcbddc->mat_graph->cdim,MPIU_REAL,&dimrealtype);
7218:       MPI_Type_commit(&dimrealtype);
7219:       PetscSFBcastBegin(matis->sf,dimrealtype,pcbddc->mat_graph->coords,lcoords,MPI_REPLACE);
7220:       PetscSFBcastEnd(matis->sf,dimrealtype,pcbddc->mat_graph->coords,lcoords,MPI_REPLACE);
7221:       MPI_Type_free(&dimrealtype);
7222:       PetscFree(pcbddc->mat_graph->coords);

7224:       pcbddc->mat_graph->coords = lcoords;
7225:       pcbddc->mat_graph->cloc   = PETSC_TRUE;
7226:       pcbddc->mat_graph->cnloc  = n;
7227:     }
7228:     if (pcbddc->mat_graph->cnloc && pcbddc->mat_graph->cnloc != pcbddc->mat_graph->nvtxs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_USER,"Invalid number of local subdomain coordinates! Got %D, expected %D",pcbddc->mat_graph->cnloc,pcbddc->mat_graph->nvtxs);
7229:     pcbddc->mat_graph->active_coords = (PetscBool)(pcbddc->corner_selection && pcbddc->mat_graph->cdim && !pcbddc->corner_selected);

7231:     /* Setup of Graph */
7232:     pcbddc->mat_graph->commsizelimit = 0; /* don't use the COMM_SELF variant of the graph */
7233:     PCBDDCGraphSetUp(pcbddc->mat_graph,pcbddc->vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices_local);

7235:     /* attach info on disconnected subdomains if present */
7236:     if (pcbddc->n_local_subs) {
7237:       PetscInt *local_subs,n,totn;

7239:       MatGetLocalSize(matis->A,&n,NULL);
7240:       PetscMalloc1(n,&local_subs);
7241:       for (i=0;i<n;i++) local_subs[i] = pcbddc->n_local_subs;
7242:       for (i=0;i<pcbddc->n_local_subs;i++) {
7243:         const PetscInt *idxs;
7244:         PetscInt       nl,j;

7246:         ISGetLocalSize(pcbddc->local_subs[i],&nl);
7247:         ISGetIndices(pcbddc->local_subs[i],&idxs);
7248:         for (j=0;j<nl;j++) local_subs[idxs[j]] = i;
7249:         ISRestoreIndices(pcbddc->local_subs[i],&idxs);
7250:       }
7251:       for (i=0,totn=0;i<n;i++) totn = PetscMax(totn,local_subs[i]);
7252:       pcbddc->mat_graph->n_local_subs = totn + 1;
7253:       pcbddc->mat_graph->local_subs = local_subs;
7254:     }
7255:   }

7257:   if (!pcbddc->graphanalyzed) {
7258:     /* Graph's connected components analysis */
7259:     PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);
7260:     pcbddc->graphanalyzed = PETSC_TRUE;
7261:     pcbddc->corner_selected = pcbddc->corner_selection;
7262:   }
7263:   if (rcsr) pcbddc->mat_graph->nvtxs_csr = 0;
7264:   return(0);
7265: }

7267: PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt *nio, Vec vecs[])
7268: {
7269:   PetscInt       i,j,n;
7270:   PetscScalar    *alphas;
7271:   PetscReal      norm,*onorms;

7275:   n = *nio;
7276:   if (!n) return(0);
7277:   PetscMalloc2(n,&alphas,n,&onorms);
7278:   VecNormalize(vecs[0],&norm);
7279:   if (norm < PETSC_SMALL) {
7280:     onorms[0] = 0.0;
7281:     VecSet(vecs[0],0.0);
7282:   } else {
7283:     onorms[0] = norm;
7284:   }

7286:   for (i=1;i<n;i++) {
7287:     VecMDot(vecs[i],i,vecs,alphas);
7288:     for (j=0;j<i;j++) alphas[j] = PetscConj(-alphas[j]);
7289:     VecMAXPY(vecs[i],i,alphas,vecs);
7290:     VecNormalize(vecs[i],&norm);
7291:     if (norm < PETSC_SMALL) {
7292:       onorms[i] = 0.0;
7293:       VecSet(vecs[i],0.0);
7294:     } else {
7295:       onorms[i] = norm;
7296:     }
7297:   }
7298:   /* push nonzero vectors at the beginning */
7299:   for (i=0;i<n;i++) {
7300:     if (onorms[i] == 0.0) {
7301:       for (j=i+1;j<n;j++) {
7302:         if (onorms[j] != 0.0) {
7303:           VecCopy(vecs[j],vecs[i]);
7304:           onorms[j] = 0.0;
7305:         }
7306:       }
7307:     }
7308:   }
7309:   for (i=0,*nio=0;i<n;i++) *nio += onorms[i] != 0.0 ? 1 : 0;
7310:   PetscFree2(alphas,onorms);
7311:   return(0);
7312: }

7314: PetscErrorCode PCBDDCMatISGetSubassemblingPattern(Mat mat, PetscInt *n_subdomains, PetscInt redprocs, IS* is_sends, PetscBool *have_void)
7315: {
7316:   Mat            A;
7317:   PetscInt       n_neighs,*neighs,*n_shared,**shared;
7318:   PetscMPIInt    size,rank,color;
7319:   PetscInt       *xadj,*adjncy;
7320:   PetscInt       *adjncy_wgt,*v_wgt,*ranks_send_to_idx;
7321:   PetscInt       im_active,active_procs,N,n,i,j,threshold = 2;
7322:   PetscInt       void_procs,*procs_candidates = NULL;
7323:   PetscInt       xadj_count,*count;
7324:   PetscBool      ismatis,use_vwgt=PETSC_FALSE;
7325:   PetscSubcomm   psubcomm;
7326:   MPI_Comm       subcomm;

7331:   PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);
7332:   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",PETSC_FUNCTION_NAME);
7335:   if (*n_subdomains <=0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Invalid number of subdomains requested %D",*n_subdomains);

7337:   if (have_void) *have_void = PETSC_FALSE;
7338:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
7339:   MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);
7340:   MatISGetLocalMat(mat,&A);
7341:   MatGetLocalSize(A,&n,NULL);
7342:   im_active = !!n;
7343:   MPIU_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)mat));
7344:   void_procs = size - active_procs;
7345:   /* get ranks of of non-active processes in mat communicator */
7346:   if (void_procs) {
7347:     PetscInt ncand;

7349:     if (have_void) *have_void = PETSC_TRUE;
7350:     PetscMalloc1(size,&procs_candidates);
7351:     MPI_Allgather(&im_active,1,MPIU_INT,procs_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)mat));
7352:     for (i=0,ncand=0;i<size;i++) {
7353:       if (!procs_candidates[i]) {
7354:         procs_candidates[ncand++] = i;
7355:       }
7356:     }
7357:     /* force n_subdomains to be not greater that the number of non-active processes */
7358:     *n_subdomains = PetscMin(void_procs,*n_subdomains);
7359:   }

7361:   /* number of subdomains requested greater than active processes or matrix size -> just shift the matrix
7362:      number of subdomains requested 1 -> send to rank-0 or first candidate in voids  */
7363:   MatGetSize(mat,&N,NULL);
7364:   if (active_procs < *n_subdomains || *n_subdomains == 1 || N <= *n_subdomains) {
7365:     PetscInt issize,isidx,dest;
7366:     if (*n_subdomains == 1) dest = 0;
7367:     else dest = rank;
7368:     if (im_active) {
7369:       issize = 1;
7370:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7371:         isidx = procs_candidates[dest];
7372:       } else {
7373:         isidx = dest;
7374:       }
7375:     } else {
7376:       issize = 0;
7377:       isidx = -1;
7378:     }
7379:     if (*n_subdomains != 1) *n_subdomains = active_procs;
7380:     ISCreateGeneral(PetscObjectComm((PetscObject)mat),issize,&isidx,PETSC_COPY_VALUES,is_sends);
7381:     PetscFree(procs_candidates);
7382:     return(0);
7383:   }
7384:   PetscOptionsGetBool(NULL,NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);
7385:   PetscOptionsGetInt(NULL,NULL,"-matis_partitioning_threshold",&threshold,NULL);
7386:   threshold = PetscMax(threshold,2);

7388:   /* Get info on mapping */
7389:   ISLocalToGlobalMappingGetInfo(mat->rmap->mapping,&n_neighs,&neighs,&n_shared,&shared);

7391:   /* build local CSR graph of subdomains' connectivity */
7392:   PetscMalloc1(2,&xadj);
7393:   xadj[0] = 0;
7394:   xadj[1] = PetscMax(n_neighs-1,0);
7395:   PetscMalloc1(xadj[1],&adjncy);
7396:   PetscMalloc1(xadj[1],&adjncy_wgt);
7397:   PetscCalloc1(n,&count);
7398:   for (i=1;i<n_neighs;i++)
7399:     for (j=0;j<n_shared[i];j++)
7400:       count[shared[i][j]] += 1;

7402:   xadj_count = 0;
7403:   for (i=1;i<n_neighs;i++) {
7404:     for (j=0;j<n_shared[i];j++) {
7405:       if (count[shared[i][j]] < threshold) {
7406:         adjncy[xadj_count] = neighs[i];
7407:         adjncy_wgt[xadj_count] = n_shared[i];
7408:         xadj_count++;
7409:         break;
7410:       }
7411:     }
7412:   }
7413:   xadj[1] = xadj_count;
7414:   PetscFree(count);
7415:   ISLocalToGlobalMappingRestoreInfo(mat->rmap->mapping,&n_neighs,&neighs,&n_shared,&shared);
7416:   PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);

7418:   PetscMalloc1(1,&ranks_send_to_idx);

7420:   /* Restrict work on active processes only */
7421:   PetscMPIIntCast(im_active,&color);
7422:   if (void_procs) {
7423:     PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&psubcomm);
7424:     PetscSubcommSetNumber(psubcomm,2); /* 2 groups, active process and not active processes */
7425:     PetscSubcommSetTypeGeneral(psubcomm,color,rank);
7426:     subcomm = PetscSubcommChild(psubcomm);
7427:   } else {
7428:     psubcomm = NULL;
7429:     subcomm = PetscObjectComm((PetscObject)mat);
7430:   }

7432:   v_wgt = NULL;
7433:   if (!color) {
7434:     PetscFree(xadj);
7435:     PetscFree(adjncy);
7436:     PetscFree(adjncy_wgt);
7437:   } else {
7438:     Mat             subdomain_adj;
7439:     IS              new_ranks,new_ranks_contig;
7440:     MatPartitioning partitioner;
7441:     PetscInt        rstart=0,rend=0;
7442:     PetscInt        *is_indices,*oldranks;
7443:     PetscMPIInt     size;
7444:     PetscBool       aggregate;

7446:     MPI_Comm_size(subcomm,&size);
7447:     if (void_procs) {
7448:       PetscInt prank = rank;
7449:       PetscMalloc1(size,&oldranks);
7450:       MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm);
7451:       for (i=0;i<xadj[1];i++) {
7452:         PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);
7453:       }
7454:       PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);
7455:     } else {
7456:       oldranks = NULL;
7457:     }
7458:     aggregate = ((redprocs > 0 && redprocs < size) ? PETSC_TRUE : PETSC_FALSE);
7459:     if (aggregate) { /* TODO: all this part could be made more efficient */
7460:       PetscInt    lrows,row,ncols,*cols;
7461:       PetscMPIInt nrank;
7462:       PetscScalar *vals;

7464:       MPI_Comm_rank(subcomm,&nrank);
7465:       lrows = 0;
7466:       if (nrank<redprocs) {
7467:         lrows = size/redprocs;
7468:         if (nrank<size%redprocs) lrows++;
7469:       }
7470:       MatCreateAIJ(subcomm,lrows,lrows,size,size,50,NULL,50,NULL,&subdomain_adj);
7471:       MatGetOwnershipRange(subdomain_adj,&rstart,&rend);
7472:       MatSetOption(subdomain_adj,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
7473:       MatSetOption(subdomain_adj,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
7474:       row = nrank;
7475:       ncols = xadj[1]-xadj[0];
7476:       cols = adjncy;
7477:       PetscMalloc1(ncols,&vals);
7478:       for (i=0;i<ncols;i++) vals[i] = adjncy_wgt[i];
7479:       MatSetValues(subdomain_adj,1,&row,ncols,cols,vals,INSERT_VALUES);
7480:       MatAssemblyBegin(subdomain_adj,MAT_FINAL_ASSEMBLY);
7481:       MatAssemblyEnd(subdomain_adj,MAT_FINAL_ASSEMBLY);
7482:       PetscFree(xadj);
7483:       PetscFree(adjncy);
7484:       PetscFree(adjncy_wgt);
7485:       PetscFree(vals);
7486:       if (use_vwgt) {
7487:         Vec               v;
7488:         const PetscScalar *array;
7489:         PetscInt          nl;

7491:         MatCreateVecs(subdomain_adj,&v,NULL);
7492:         VecSetValue(v,row,(PetscScalar)n,INSERT_VALUES);
7493:         VecAssemblyBegin(v);
7494:         VecAssemblyEnd(v);
7495:         VecGetLocalSize(v,&nl);
7496:         VecGetArrayRead(v,&array);
7497:         PetscMalloc1(nl,&v_wgt);
7498:         for (i=0;i<nl;i++) v_wgt[i] = (PetscInt)PetscRealPart(array[i]);
7499:         VecRestoreArrayRead(v,&array);
7500:         VecDestroy(&v);
7501:       }
7502:     } else {
7503:       MatCreateMPIAdj(subcomm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);
7504:       if (use_vwgt) {
7505:         PetscMalloc1(1,&v_wgt);
7506:         v_wgt[0] = n;
7507:       }
7508:     }
7509:     /* MatView(subdomain_adj,0); */

7511:     /* Partition */
7512:     MatPartitioningCreate(subcomm,&partitioner);
7513: #if defined(PETSC_HAVE_PTSCOTCH)
7514:     MatPartitioningSetType(partitioner,MATPARTITIONINGPTSCOTCH);
7515: #elif defined(PETSC_HAVE_PARMETIS)
7516:     MatPartitioningSetType(partitioner,MATPARTITIONINGPARMETIS);
7517: #else
7518:     MatPartitioningSetType(partitioner,MATPARTITIONINGAVERAGE);
7519: #endif
7520:     MatPartitioningSetAdjacency(partitioner,subdomain_adj);
7521:     if (v_wgt) {
7522:       MatPartitioningSetVertexWeights(partitioner,v_wgt);
7523:     }
7524:     *n_subdomains = PetscMin((PetscInt)size,*n_subdomains);
7525:     MatPartitioningSetNParts(partitioner,*n_subdomains);
7526:     MatPartitioningSetFromOptions(partitioner);
7527:     MatPartitioningApply(partitioner,&new_ranks);
7528:     /* MatPartitioningView(partitioner,0); */

7530:     /* renumber new_ranks to avoid "holes" in new set of processors */
7531:     ISRenumber(new_ranks,NULL,NULL,&new_ranks_contig);
7532:     ISDestroy(&new_ranks);
7533:     ISGetIndices(new_ranks_contig,(const PetscInt**)&is_indices);
7534:     if (!aggregate) {
7535:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7536:         if (PetscUnlikelyDebug(!oldranks)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
7537:         ranks_send_to_idx[0] = procs_candidates[oldranks[is_indices[0]]];
7538:       } else if (oldranks) {
7539:         ranks_send_to_idx[0] = oldranks[is_indices[0]];
7540:       } else {
7541:         ranks_send_to_idx[0] = is_indices[0];
7542:       }
7543:     } else {
7544:       PetscInt    idx = 0;
7545:       PetscMPIInt tag;
7546:       MPI_Request *reqs;

7548:       PetscObjectGetNewTag((PetscObject)subdomain_adj,&tag);
7549:       PetscMalloc1(rend-rstart,&reqs);
7550:       for (i=rstart;i<rend;i++) {
7551:         MPI_Isend(is_indices+i-rstart,1,MPIU_INT,i,tag,subcomm,&reqs[i-rstart]);
7552:       }
7553:       MPI_Recv(&idx,1,MPIU_INT,MPI_ANY_SOURCE,tag,subcomm,MPI_STATUS_IGNORE);
7554:       MPI_Waitall(rend-rstart,reqs,MPI_STATUSES_IGNORE);
7555:       PetscFree(reqs);
7556:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7557:         if (PetscUnlikelyDebug(!oldranks)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
7558:         ranks_send_to_idx[0] = procs_candidates[oldranks[idx]];
7559:       } else if (oldranks) {
7560:         ranks_send_to_idx[0] = oldranks[idx];
7561:       } else {
7562:         ranks_send_to_idx[0] = idx;
7563:       }
7564:     }
7565:     ISRestoreIndices(new_ranks_contig,(const PetscInt**)&is_indices);
7566:     /* clean up */
7567:     PetscFree(oldranks);
7568:     ISDestroy(&new_ranks_contig);
7569:     MatDestroy(&subdomain_adj);
7570:     MatPartitioningDestroy(&partitioner);
7571:   }
7572:   PetscSubcommDestroy(&psubcomm);
7573:   PetscFree(procs_candidates);

7575:   /* assemble parallel IS for sends */
7576:   i = 1;
7577:   if (!color) i=0;
7578:   ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,is_sends);
7579:   return(0);
7580: }

7582: typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;

7584: PetscErrorCode PCBDDCMatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, PetscBool restrict_full, PetscBool reuse, Mat *mat_n, PetscInt nis, IS isarray[], PetscInt nvecs, Vec nnsp_vec[])
7585: {
7586:   Mat                    local_mat;
7587:   IS                     is_sends_internal;
7588:   PetscInt               rows,cols,new_local_rows;
7589:   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals,buf_size_vecs;
7590:   PetscBool              ismatis,isdense,newisdense,destroy_mat;
7591:   ISLocalToGlobalMapping l2gmap;
7592:   PetscInt*              l2gmap_indices;
7593:   const PetscInt*        is_indices;
7594:   MatType                new_local_type;
7595:   /* buffers */
7596:   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
7597:   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
7598:   PetscInt               *recv_buffer_idxs_local;
7599:   PetscScalar            *ptr_vals,*recv_buffer_vals;
7600:   const PetscScalar      *send_buffer_vals;
7601:   PetscScalar            *ptr_vecs,*send_buffer_vecs,*recv_buffer_vecs;
7602:   /* MPI */
7603:   MPI_Comm               comm,comm_n;
7604:   PetscSubcomm           subcomm;
7605:   PetscMPIInt            n_sends,n_recvs,size;
7606:   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
7607:   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
7608:   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,tag_vecs,source_dest;
7609:   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals,*send_req_vecs;
7610:   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals,*recv_req_vecs;
7611:   PetscErrorCode         ierr;

7615:   PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);
7616:   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",PETSC_FUNCTION_NAME);
7623:   if (nvecs) {
7624:     if (nvecs > 1) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Just 1 vector supported");
7626:   }
7627:   /* further checks */
7628:   MatISGetLocalMat(mat,&local_mat);
7629:   PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);
7630:   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
7631:   MatGetSize(local_mat,&rows,&cols);
7632:   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
7633:   if (reuse && *mat_n) {
7634:     PetscInt mrows,mcols,mnrows,mncols;
7636:     PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);
7637:     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
7638:     MatGetSize(mat,&mrows,&mcols);
7639:     MatGetSize(*mat_n,&mnrows,&mncols);
7640:     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
7641:     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
7642:   }
7643:   MatGetBlockSize(local_mat,&bs);

7646:   /* prepare IS for sending if not provided */
7647:   if (!is_sends) {
7648:     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
7649:     PCBDDCMatISGetSubassemblingPattern(mat,&n_subdomains,0,&is_sends_internal,NULL);
7650:   } else {
7651:     PetscObjectReference((PetscObject)is_sends);
7652:     is_sends_internal = is_sends;
7653:   }

7655:   /* get comm */
7656:   PetscObjectGetComm((PetscObject)mat,&comm);

7658:   /* compute number of sends */
7659:   ISGetLocalSize(is_sends_internal,&i);
7660:   PetscMPIIntCast(i,&n_sends);

7662:   /* compute number of receives */
7663:   MPI_Comm_size(comm,&size);
7664:   PetscMalloc1(size,&iflags);
7665:   PetscArrayzero(iflags,size);
7666:   ISGetIndices(is_sends_internal,&is_indices);
7667:   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
7668:   PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);
7669:   PetscFree(iflags);

7671:   /* restrict comm if requested */
7672:   subcomm = NULL;
7673:   destroy_mat = PETSC_FALSE;
7674:   if (restrict_comm) {
7675:     PetscMPIInt color,subcommsize;

7677:     color = 0;
7678:     if (restrict_full) {
7679:       if (!n_recvs) color = 1; /* processes not receiving anything will not partecipate in new comm (full restriction) */
7680:     } else {
7681:       if (!n_recvs && n_sends) color = 1; /* just those processes that are sending but not receiving anything will not partecipate in new comm */
7682:     }
7683:     MPIU_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);
7684:     subcommsize = size - subcommsize;
7685:     /* check if reuse has been requested */
7686:     if (reuse) {
7687:       if (*mat_n) {
7688:         PetscMPIInt subcommsize2;
7689:         MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);
7690:         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
7691:         comm_n = PetscObjectComm((PetscObject)*mat_n);
7692:       } else {
7693:         comm_n = PETSC_COMM_SELF;
7694:       }
7695:     } else { /* MAT_INITIAL_MATRIX */
7696:       PetscMPIInt rank;

7698:       MPI_Comm_rank(comm,&rank);
7699:       PetscSubcommCreate(comm,&subcomm);
7700:       PetscSubcommSetNumber(subcomm,2);
7701:       PetscSubcommSetTypeGeneral(subcomm,color,rank);
7702:       comm_n = PetscSubcommChild(subcomm);
7703:     }
7704:     /* flag to destroy *mat_n if not significative */
7705:     if (color) destroy_mat = PETSC_TRUE;
7706:   } else {
7707:     comm_n = comm;
7708:   }

7710:   /* prepare send/receive buffers */
7711:   PetscMalloc1(size,&ilengths_idxs);
7712:   PetscArrayzero(ilengths_idxs,size);
7713:   PetscMalloc1(size,&ilengths_vals);
7714:   PetscArrayzero(ilengths_vals,size);
7715:   if (nis) {
7716:     PetscCalloc1(size,&ilengths_idxs_is);
7717:   }

7719:   /* Get data from local matrices */
7720:   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Subassembling of AIJ local matrices not yet implemented");
7721:     /* TODO: See below some guidelines on how to prepare the local buffers */
7722:     /*
7723:        send_buffer_vals should contain the raw values of the local matrix
7724:        send_buffer_idxs should contain:
7725:        - MatType_PRIVATE type
7726:        - PetscInt        size_of_l2gmap
7727:        - PetscInt        global_row_indices[size_of_l2gmap]
7728:        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
7729:     */
7730:   else {
7731:     MatDenseGetArrayRead(local_mat,&send_buffer_vals);
7732:     ISLocalToGlobalMappingGetSize(mat->rmap->mapping,&i);
7733:     PetscMalloc1(i+2,&send_buffer_idxs);
7734:     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
7735:     send_buffer_idxs[1] = i;
7736:     ISLocalToGlobalMappingGetIndices(mat->rmap->mapping,(const PetscInt**)&ptr_idxs);
7737:     PetscArraycpy(&send_buffer_idxs[2],ptr_idxs,i);
7738:     ISLocalToGlobalMappingRestoreIndices(mat->rmap->mapping,(const PetscInt**)&ptr_idxs);
7739:     PetscMPIIntCast(i,&len);
7740:     for (i=0;i<n_sends;i++) {
7741:       ilengths_vals[is_indices[i]] = len*len;
7742:       ilengths_idxs[is_indices[i]] = len+2;
7743:     }
7744:   }
7745:   PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);
7746:   /* additional is (if any) */
7747:   if (nis) {
7748:     PetscMPIInt psum;
7749:     PetscInt j;
7750:     for (j=0,psum=0;j<nis;j++) {
7751:       PetscInt plen;
7752:       ISGetLocalSize(isarray[j],&plen);
7753:       PetscMPIIntCast(plen,&len);
7754:       psum += len+1; /* indices + lenght */
7755:     }
7756:     PetscMalloc1(psum,&send_buffer_idxs_is);
7757:     for (j=0,psum=0;j<nis;j++) {
7758:       PetscInt plen;
7759:       const PetscInt *is_array_idxs;
7760:       ISGetLocalSize(isarray[j],&plen);
7761:       send_buffer_idxs_is[psum] = plen;
7762:       ISGetIndices(isarray[j],&is_array_idxs);
7763:       PetscArraycpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen);
7764:       ISRestoreIndices(isarray[j],&is_array_idxs);
7765:       psum += plen+1; /* indices + lenght */
7766:     }
7767:     for (i=0;i<n_sends;i++) {
7768:       ilengths_idxs_is[is_indices[i]] = psum;
7769:     }
7770:     PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);
7771:   }
7772:   MatISRestoreLocalMat(mat,&local_mat);

7774:   buf_size_idxs = 0;
7775:   buf_size_vals = 0;
7776:   buf_size_idxs_is = 0;
7777:   buf_size_vecs = 0;
7778:   for (i=0;i<n_recvs;i++) {
7779:     buf_size_idxs += (PetscInt)olengths_idxs[i];
7780:     buf_size_vals += (PetscInt)olengths_vals[i];
7781:     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
7782:     if (nvecs) buf_size_vecs += (PetscInt)olengths_idxs[i];
7783:   }
7784:   PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);
7785:   PetscMalloc1(buf_size_vals,&recv_buffer_vals);
7786:   PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);
7787:   PetscMalloc1(buf_size_vecs,&recv_buffer_vecs);

7789:   /* get new tags for clean communications */
7790:   PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);
7791:   PetscObjectGetNewTag((PetscObject)mat,&tag_vals);
7792:   PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);
7793:   PetscObjectGetNewTag((PetscObject)mat,&tag_vecs);

7795:   /* allocate for requests */
7796:   PetscMalloc1(n_sends,&send_req_idxs);
7797:   PetscMalloc1(n_sends,&send_req_vals);
7798:   PetscMalloc1(n_sends,&send_req_idxs_is);
7799:   PetscMalloc1(n_sends,&send_req_vecs);
7800:   PetscMalloc1(n_recvs,&recv_req_idxs);
7801:   PetscMalloc1(n_recvs,&recv_req_vals);
7802:   PetscMalloc1(n_recvs,&recv_req_idxs_is);
7803:   PetscMalloc1(n_recvs,&recv_req_vecs);

7805:   /* communications */
7806:   ptr_idxs = recv_buffer_idxs;
7807:   ptr_vals = recv_buffer_vals;
7808:   ptr_idxs_is = recv_buffer_idxs_is;
7809:   ptr_vecs = recv_buffer_vecs;
7810:   for (i=0;i<n_recvs;i++) {
7811:     source_dest = onodes[i];
7812:     MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);
7813:     MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);
7814:     ptr_idxs += olengths_idxs[i];
7815:     ptr_vals += olengths_vals[i];
7816:     if (nis) {
7817:       source_dest = onodes_is[i];
7818:       MPI_Irecv(ptr_idxs_is,olengths_idxs_is[i],MPIU_INT,source_dest,tag_idxs_is,comm,&recv_req_idxs_is[i]);
7819:       ptr_idxs_is += olengths_idxs_is[i];
7820:     }
7821:     if (nvecs) {
7822:       source_dest = onodes[i];
7823:       MPI_Irecv(ptr_vecs,olengths_idxs[i]-2,MPIU_SCALAR,source_dest,tag_vecs,comm,&recv_req_vecs[i]);
7824:       ptr_vecs += olengths_idxs[i]-2;
7825:     }
7826:   }
7827:   for (i=0;i<n_sends;i++) {
7828:     PetscMPIIntCast(is_indices[i],&source_dest);
7829:     MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);
7830:     MPI_Isend((PetscScalar*)send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);
7831:     if (nis) {
7832:       MPI_Isend(send_buffer_idxs_is,ilengths_idxs_is[source_dest],MPIU_INT,source_dest,tag_idxs_is,comm,&send_req_idxs_is[i]);
7833:     }
7834:     if (nvecs) {
7835:       VecGetArray(nnsp_vec[0],&send_buffer_vecs);
7836:       MPI_Isend(send_buffer_vecs,ilengths_idxs[source_dest]-2,MPIU_SCALAR,source_dest,tag_vecs,comm,&send_req_vecs[i]);
7837:     }
7838:   }
7839:   ISRestoreIndices(is_sends_internal,&is_indices);
7840:   ISDestroy(&is_sends_internal);

7842:   /* assemble new l2g map */
7843:   MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);
7844:   ptr_idxs = recv_buffer_idxs;
7845:   new_local_rows = 0;
7846:   for (i=0;i<n_recvs;i++) {
7847:     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
7848:     ptr_idxs += olengths_idxs[i];
7849:   }
7850:   PetscMalloc1(new_local_rows,&l2gmap_indices);
7851:   ptr_idxs = recv_buffer_idxs;
7852:   new_local_rows = 0;
7853:   for (i=0;i<n_recvs;i++) {
7854:     PetscArraycpy(&l2gmap_indices[new_local_rows],ptr_idxs+2,*(ptr_idxs+1));
7855:     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
7856:     ptr_idxs += olengths_idxs[i];
7857:   }
7858:   PetscSortRemoveDupsInt(&new_local_rows,l2gmap_indices);
7859:   ISLocalToGlobalMappingCreate(comm_n,1,new_local_rows,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);
7860:   PetscFree(l2gmap_indices);

7862:   /* infer new local matrix type from received local matrices type */
7863:   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
7864:   /* it also assumes that if the block size is set, than it is the same among all local matrices (see checks at the beginning of the function) */
7865:   if (n_recvs) {
7866:     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
7867:     ptr_idxs = recv_buffer_idxs;
7868:     for (i=0;i<n_recvs;i++) {
7869:       if ((PetscInt)new_local_type_private != *ptr_idxs) {
7870:         new_local_type_private = MATAIJ_PRIVATE;
7871:         break;
7872:       }
7873:       ptr_idxs += olengths_idxs[i];
7874:     }
7875:     switch (new_local_type_private) {
7876:       case MATDENSE_PRIVATE:
7877:         new_local_type = MATSEQAIJ;
7878:         bs = 1;
7879:         break;
7880:       case MATAIJ_PRIVATE:
7881:         new_local_type = MATSEQAIJ;
7882:         bs = 1;
7883:         break;
7884:       case MATBAIJ_PRIVATE:
7885:         new_local_type = MATSEQBAIJ;
7886:         break;
7887:       case MATSBAIJ_PRIVATE:
7888:         new_local_type = MATSEQSBAIJ;
7889:         break;
7890:       default:
7891:         SETERRQ2(comm,PETSC_ERR_SUP,"Unsupported private type %d in %s",new_local_type_private,PETSC_FUNCTION_NAME);
7892:     }
7893:   } else { /* by default, new_local_type is seqaij */
7894:     new_local_type = MATSEQAIJ;
7895:     bs = 1;
7896:   }

7898:   /* create MATIS object if needed */
7899:   if (!reuse) {
7900:     MatGetSize(mat,&rows,&cols);
7901:     MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,NULL,mat_n);
7902:   } else {
7903:     /* it also destroys the local matrices */
7904:     if (*mat_n) {
7905:       MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);
7906:     } else { /* this is a fake object */
7907:       MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,NULL,mat_n);
7908:     }
7909:   }
7910:   MatISGetLocalMat(*mat_n,&local_mat);
7911:   MatSetType(local_mat,new_local_type);

7913:   MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);

7915:   /* Global to local map of received indices */
7916:   PetscMalloc1(buf_size_idxs,&recv_buffer_idxs_local); /* needed for values insertion */
7917:   ISGlobalToLocalMappingApply(l2gmap,IS_GTOLM_MASK,buf_size_idxs,recv_buffer_idxs,&i,recv_buffer_idxs_local);
7918:   ISLocalToGlobalMappingDestroy(&l2gmap);

7920:   /* restore attributes -> type of incoming data and its size */
7921:   buf_size_idxs = 0;
7922:   for (i=0;i<n_recvs;i++) {
7923:     recv_buffer_idxs_local[buf_size_idxs] = recv_buffer_idxs[buf_size_idxs];
7924:     recv_buffer_idxs_local[buf_size_idxs+1] = recv_buffer_idxs[buf_size_idxs+1];
7925:     buf_size_idxs += (PetscInt)olengths_idxs[i];
7926:   }
7927:   PetscFree(recv_buffer_idxs);

7929:   /* set preallocation */
7930:   PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&newisdense);
7931:   if (!newisdense) {
7932:     PetscInt *new_local_nnz=NULL;

7934:     ptr_idxs = recv_buffer_idxs_local;
7935:     if (n_recvs) {
7936:       PetscCalloc1(new_local_rows,&new_local_nnz);
7937:     }
7938:     for (i=0;i<n_recvs;i++) {
7939:       PetscInt j;
7940:       if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
7941:         for (j=0;j<*(ptr_idxs+1);j++) {
7942:           new_local_nnz[*(ptr_idxs+2+j)] += *(ptr_idxs+1);
7943:         }
7944:       } else {
7945:         /* TODO */
7946:       }
7947:       ptr_idxs += olengths_idxs[i];
7948:     }
7949:     if (new_local_nnz) {
7950:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMin(new_local_nnz[i],new_local_rows);
7951:       MatSeqAIJSetPreallocation(local_mat,0,new_local_nnz);
7952:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] /= bs;
7953:       MatSeqBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);
7954:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMax(new_local_nnz[i]-i,0);
7955:       MatSeqSBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);
7956:     } else {
7957:       MatSetUp(local_mat);
7958:     }
7959:     PetscFree(new_local_nnz);
7960:   } else {
7961:     MatSetUp(local_mat);
7962:   }

7964:   /* set values */
7965:   ptr_vals = recv_buffer_vals;
7966:   ptr_idxs = recv_buffer_idxs_local;
7967:   for (i=0;i<n_recvs;i++) {
7968:     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
7969:       MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);
7970:       MatSetValues(local_mat,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);
7971:       MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);
7972:       MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);
7973:       MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);
7974:     } else {
7975:       /* TODO */
7976:     }
7977:     ptr_idxs += olengths_idxs[i];
7978:     ptr_vals += olengths_vals[i];
7979:   }
7980:   MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);
7981:   MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);
7982:   MatISRestoreLocalMat(*mat_n,&local_mat);
7983:   MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);
7984:   MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);
7985:   PetscFree(recv_buffer_vals);

7987: #if 0
7988:   if (!restrict_comm) { /* check */
7989:     Vec       lvec,rvec;
7990:     PetscReal infty_error;

7992:     MatCreateVecs(mat,&rvec,&lvec);
7993:     VecSetRandom(rvec,NULL);
7994:     MatMult(mat,rvec,lvec);
7995:     VecScale(lvec,-1.0);
7996:     MatMultAdd(*mat_n,rvec,lvec,lvec);
7997:     VecNorm(lvec,NORM_INFINITY,&infty_error);
7998:     PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
7999:     VecDestroy(&rvec);
8000:     VecDestroy(&lvec);
8001:   }
8002: #endif

8004:   /* assemble new additional is (if any) */
8005:   if (nis) {
8006:     PetscInt **temp_idxs,*count_is,j,psum;

8008:     MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);
8009:     PetscCalloc1(nis,&count_is);
8010:     ptr_idxs = recv_buffer_idxs_is;
8011:     psum = 0;
8012:     for (i=0;i<n_recvs;i++) {
8013:       for (j=0;j<nis;j++) {
8014:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
8015:         count_is[j] += plen; /* increment counting of buffer for j-th IS */
8016:         psum += plen;
8017:         ptr_idxs += plen+1; /* shift pointer to received data */
8018:       }
8019:     }
8020:     PetscMalloc1(nis,&temp_idxs);
8021:     PetscMalloc1(psum,&temp_idxs[0]);
8022:     for (i=1;i<nis;i++) {
8023:       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
8024:     }
8025:     PetscArrayzero(count_is,nis);
8026:     ptr_idxs = recv_buffer_idxs_is;
8027:     for (i=0;i<n_recvs;i++) {
8028:       for (j=0;j<nis;j++) {
8029:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
8030:         PetscArraycpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen);
8031:         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
8032:         ptr_idxs += plen+1; /* shift pointer to received data */
8033:       }
8034:     }
8035:     for (i=0;i<nis;i++) {
8036:       ISDestroy(&isarray[i]);
8037:       PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);
8038:       ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);
8039:     }
8040:     PetscFree(count_is);
8041:     PetscFree(temp_idxs[0]);
8042:     PetscFree(temp_idxs);
8043:   }
8044:   /* free workspace */
8045:   PetscFree(recv_buffer_idxs_is);
8046:   MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);
8047:   PetscFree(send_buffer_idxs);
8048:   MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);
8049:   if (isdense) {
8050:     MatISGetLocalMat(mat,&local_mat);
8051:     MatDenseRestoreArrayRead(local_mat,&send_buffer_vals);
8052:     MatISRestoreLocalMat(mat,&local_mat);
8053:   } else {
8054:     /* PetscFree(send_buffer_vals); */
8055:   }
8056:   if (nis) {
8057:     MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);
8058:     PetscFree(send_buffer_idxs_is);
8059:   }

8061:   if (nvecs) {
8062:     MPI_Waitall(n_recvs,recv_req_vecs,MPI_STATUSES_IGNORE);
8063:     MPI_Waitall(n_sends,send_req_vecs,MPI_STATUSES_IGNORE);
8064:     VecRestoreArray(nnsp_vec[0],&send_buffer_vecs);
8065:     VecDestroy(&nnsp_vec[0]);
8066:     VecCreate(comm_n,&nnsp_vec[0]);
8067:     VecSetSizes(nnsp_vec[0],new_local_rows,PETSC_DECIDE);
8068:     VecSetType(nnsp_vec[0],VECSTANDARD);
8069:     /* set values */
8070:     ptr_vals = recv_buffer_vecs;
8071:     ptr_idxs = recv_buffer_idxs_local;
8072:     VecGetArray(nnsp_vec[0],&send_buffer_vecs);
8073:     for (i=0;i<n_recvs;i++) {
8074:       PetscInt j;
8075:       for (j=0;j<*(ptr_idxs+1);j++) {
8076:         send_buffer_vecs[*(ptr_idxs+2+j)] += *(ptr_vals + j);
8077:       }
8078:       ptr_idxs += olengths_idxs[i];
8079:       ptr_vals += olengths_idxs[i]-2;
8080:     }
8081:     VecRestoreArray(nnsp_vec[0],&send_buffer_vecs);
8082:     VecAssemblyBegin(nnsp_vec[0]);
8083:     VecAssemblyEnd(nnsp_vec[0]);
8084:   }

8086:   PetscFree(recv_buffer_vecs);
8087:   PetscFree(recv_buffer_idxs_local);
8088:   PetscFree(recv_req_idxs);
8089:   PetscFree(recv_req_vals);
8090:   PetscFree(recv_req_vecs);
8091:   PetscFree(recv_req_idxs_is);
8092:   PetscFree(send_req_idxs);
8093:   PetscFree(send_req_vals);
8094:   PetscFree(send_req_vecs);
8095:   PetscFree(send_req_idxs_is);
8096:   PetscFree(ilengths_vals);
8097:   PetscFree(ilengths_idxs);
8098:   PetscFree(olengths_vals);
8099:   PetscFree(olengths_idxs);
8100:   PetscFree(onodes);
8101:   if (nis) {
8102:     PetscFree(ilengths_idxs_is);
8103:     PetscFree(olengths_idxs_is);
8104:     PetscFree(onodes_is);
8105:   }
8106:   PetscSubcommDestroy(&subcomm);
8107:   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
8108:     MatDestroy(mat_n);
8109:     for (i=0;i<nis;i++) {
8110:       ISDestroy(&isarray[i]);
8111:     }
8112:     if (nvecs) { /* need to match VecDestroy nnsp_vec called in the other code path */
8113:       VecDestroy(&nnsp_vec[0]);
8114:     }
8115:     *mat_n = NULL;
8116:   }
8117:   return(0);
8118: }

8120: /* temporary hack into ksp private data structure */
8121: #include <petsc/private/kspimpl.h>

8123: PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
8124: {
8125:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
8126:   PC_IS                  *pcis = (PC_IS*)pc->data;
8127:   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
8128:   Mat                    coarsedivudotp = NULL;
8129:   Mat                    coarseG,t_coarse_mat_is;
8130:   MatNullSpace           CoarseNullSpace = NULL;
8131:   ISLocalToGlobalMapping coarse_islg;
8132:   IS                     coarse_is,*isarray,corners;
8133:   PetscInt               i,im_active=-1,active_procs=-1;
8134:   PetscInt               nis,nisdofs,nisneu,nisvert;
8135:   PetscInt               coarse_eqs_per_proc;
8136:   PC                     pc_temp;
8137:   PCType                 coarse_pc_type;
8138:   KSPType                coarse_ksp_type;
8139:   PetscBool              multilevel_requested,multilevel_allowed;
8140:   PetscBool              coarse_reuse;
8141:   PetscInt               ncoarse,nedcfield;
8142:   PetscBool              compute_vecs = PETSC_FALSE;
8143:   PetscScalar            *array;
8144:   MatReuse               coarse_mat_reuse;
8145:   PetscBool              restr, full_restr, have_void;
8146:   PetscMPIInt            size;
8147:   PetscErrorCode         ierr;

8150:   PetscLogEventBegin(PC_BDDC_CoarseSetUp[pcbddc->current_level],pc,0,0,0);
8151:   /* Assign global numbering to coarse dofs */
8152:   if (pcbddc->new_primal_space || pcbddc->coarse_size == -1) { /* a new primal space is present or it is the first initialization, so recompute global numbering */
8153:     PetscInt ocoarse_size;
8154:     compute_vecs = PETSC_TRUE;

8156:     pcbddc->new_primal_space = PETSC_TRUE;
8157:     ocoarse_size = pcbddc->coarse_size;
8158:     PetscFree(pcbddc->global_primal_indices);
8159:     PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);
8160:     /* see if we can avoid some work */
8161:     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
8162:       /* if the coarse size is different or we are using adaptive selection, better to not reuse the coarse matrix */
8163:       if (ocoarse_size != pcbddc->coarse_size || pcbddc->adaptive_selection) {
8164:         KSPReset(pcbddc->coarse_ksp);
8165:         coarse_reuse = PETSC_FALSE;
8166:       } else { /* we can safely reuse already computed coarse matrix */
8167:         coarse_reuse = PETSC_TRUE;
8168:       }
8169:     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
8170:       coarse_reuse = PETSC_FALSE;
8171:     }
8172:     /* reset any subassembling information */
8173:     if (!coarse_reuse || pcbddc->recompute_topography) {
8174:       ISDestroy(&pcbddc->coarse_subassembling);
8175:     }
8176:   } else { /* primal space is unchanged, so we can reuse coarse matrix */
8177:     coarse_reuse = PETSC_TRUE;
8178:   }
8179:   if (coarse_reuse && pcbddc->coarse_ksp) {
8180:     KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);
8181:     PetscObjectReference((PetscObject)coarse_mat);
8182:     coarse_mat_reuse = MAT_REUSE_MATRIX;
8183:   } else {
8184:     coarse_mat = NULL;
8185:     coarse_mat_reuse = MAT_INITIAL_MATRIX;
8186:   }

8188:   /* creates temporary l2gmap and IS for coarse indexes */
8189:   ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);
8190:   ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);

8192:   /* creates temporary MATIS object for coarse matrix */
8193:   MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_submat_dense);
8194:   MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,NULL,&t_coarse_mat_is);
8195:   MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);
8196:   MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);
8197:   MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);
8198:   MatDestroy(&coarse_submat_dense);

8200:   /* count "active" (i.e. with positive local size) and "void" processes */
8201:   im_active = !!(pcis->n);
8202:   MPIU_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));

8204:   /* determine number of processes partecipating to coarse solver and compute subassembling pattern */
8205:   /* restr : whether we want to exclude senders (which are not receivers) from the subassembling pattern */
8206:   /* full_restr : just use the receivers from the subassembling pattern */
8207:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
8208:   coarse_mat_is        = NULL;
8209:   multilevel_allowed   = PETSC_FALSE;
8210:   multilevel_requested = PETSC_FALSE;
8211:   coarse_eqs_per_proc  = PetscMin(PetscMax(pcbddc->coarse_size,1),pcbddc->coarse_eqs_per_proc);
8212:   if (coarse_eqs_per_proc < 0) coarse_eqs_per_proc = pcbddc->coarse_size;
8213:   if (pcbddc->current_level < pcbddc->max_levels) multilevel_requested = PETSC_TRUE;
8214:   if (pcbddc->coarse_size <= pcbddc->coarse_eqs_limit) multilevel_requested = PETSC_FALSE;
8215:   if (multilevel_requested) {
8216:     ncoarse    = active_procs/pcbddc->coarsening_ratio;
8217:     restr      = PETSC_FALSE;
8218:     full_restr = PETSC_FALSE;
8219:   } else {
8220:     ncoarse    = pcbddc->coarse_size/coarse_eqs_per_proc + !!(pcbddc->coarse_size%coarse_eqs_per_proc);
8221:     restr      = PETSC_TRUE;
8222:     full_restr = PETSC_TRUE;
8223:   }
8224:   if (!pcbddc->coarse_size || size == 1) multilevel_allowed = multilevel_requested = restr = full_restr = PETSC_FALSE;
8225:   ncoarse = PetscMax(1,ncoarse);
8226:   if (!pcbddc->coarse_subassembling) {
8227:     if (pcbddc->coarsening_ratio > 1) {
8228:       if (multilevel_requested) {
8229:         PCBDDCMatISGetSubassemblingPattern(pc->pmat,&ncoarse,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling,&have_void);
8230:       } else {
8231:         PCBDDCMatISGetSubassemblingPattern(t_coarse_mat_is,&ncoarse,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling,&have_void);
8232:       }
8233:     } else {
8234:       PetscMPIInt rank;

8236:       MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
8237:       have_void = (active_procs == (PetscInt)size) ? PETSC_FALSE : PETSC_TRUE;
8238:       ISCreateStride(PetscObjectComm((PetscObject)pc),1,rank,1,&pcbddc->coarse_subassembling);
8239:     }
8240:   } else { /* if a subassembling pattern exists, then we can reuse the coarse ksp and compute the number of process involved */
8241:     PetscInt    psum;
8242:     if (pcbddc->coarse_ksp) psum = 1;
8243:     else psum = 0;
8244:     MPIU_Allreduce(&psum,&ncoarse,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
8245:     have_void = ncoarse < size ? PETSC_TRUE : PETSC_FALSE;
8246:   }
8247:   /* determine if we can go multilevel */
8248:   if (multilevel_requested) {
8249:     if (ncoarse > 1) multilevel_allowed = PETSC_TRUE; /* found enough processes */
8250:     else restr = full_restr = PETSC_TRUE; /* 1 subdomain, use a direct solver */
8251:   }
8252:   if (multilevel_allowed && have_void) restr = PETSC_TRUE;

8254:   /* dump subassembling pattern */
8255:   if (pcbddc->dbg_flag && multilevel_allowed) {
8256:     ISView(pcbddc->coarse_subassembling,pcbddc->dbg_viewer);
8257:   }
8258:   /* compute dofs splitting and neumann boundaries for coarse dofs */
8259:   nedcfield = -1;
8260:   corners = NULL;
8261:   if (multilevel_allowed && !coarse_reuse && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal || pcbddc->nedclocal || pcbddc->corner_selected)) { /* protects from unneeded computations */
8262:     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
8263:     const PetscInt         *idxs;
8264:     ISLocalToGlobalMapping tmap;

8266:     /* create map between primal indices (in local representative ordering) and local primal numbering */
8267:     ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);
8268:     /* allocate space for temporary storage */
8269:     PetscMalloc1(pcbddc->local_primal_size,&tidxs);
8270:     PetscMalloc1(pcbddc->local_primal_size,&tidxs2);
8271:     /* allocate for IS array */
8272:     nisdofs = pcbddc->n_ISForDofsLocal;
8273:     if (pcbddc->nedclocal) {
8274:       if (pcbddc->nedfield > -1) {
8275:         nedcfield = pcbddc->nedfield;
8276:       } else {
8277:         nedcfield = 0;
8278:         if (nisdofs) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen (%D)",nisdofs);
8279:         nisdofs = 1;
8280:       }
8281:     }
8282:     nisneu = !!pcbddc->NeumannBoundariesLocal;
8283:     nisvert = 0; /* nisvert is not used */
8284:     nis = nisdofs + nisneu + nisvert;
8285:     PetscMalloc1(nis,&isarray);
8286:     /* dofs splitting */
8287:     for (i=0;i<nisdofs;i++) {
8288:       /* ISView(pcbddc->ISForDofsLocal[i],0); */
8289:       if (nedcfield != i) {
8290:         ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);
8291:         ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);
8292:         ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
8293:         ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);
8294:       } else {
8295:         ISGetLocalSize(pcbddc->nedclocal,&tsize);
8296:         ISGetIndices(pcbddc->nedclocal,&idxs);
8297:         ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
8298:         if (tsize != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Failed when mapping coarse nedelec field! %D != %D",tsize,nout);
8299:         ISRestoreIndices(pcbddc->nedclocal,&idxs);
8300:       }
8301:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
8302:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);
8303:       /* ISView(isarray[i],0); */
8304:     }
8305:     /* neumann boundaries */
8306:     if (pcbddc->NeumannBoundariesLocal) {
8307:       /* ISView(pcbddc->NeumannBoundariesLocal,0); */
8308:       ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);
8309:       ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);
8310:       ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
8311:       ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);
8312:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
8313:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);
8314:       /* ISView(isarray[nisdofs],0); */
8315:     }
8316:     /* coordinates */
8317:     if (pcbddc->corner_selected) {
8318:       PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&corners);
8319:       ISGetLocalSize(corners,&tsize);
8320:       ISGetIndices(corners,&idxs);
8321:       ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
8322:       if (tsize != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Failed when mapping corners! %D != %D",tsize,nout);
8323:       ISRestoreIndices(corners,&idxs);
8324:       PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&corners);
8325:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
8326:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&corners);
8327:     }
8328:     PetscFree(tidxs);
8329:     PetscFree(tidxs2);
8330:     ISLocalToGlobalMappingDestroy(&tmap);
8331:   } else {
8332:     nis = 0;
8333:     nisdofs = 0;
8334:     nisneu = 0;
8335:     nisvert = 0;
8336:     isarray = NULL;
8337:   }
8338:   /* destroy no longer needed map */
8339:   ISLocalToGlobalMappingDestroy(&coarse_islg);

8341:   /* subassemble */
8342:   if (multilevel_allowed) {
8343:     Vec       vp[1];
8344:     PetscInt  nvecs = 0;
8345:     PetscBool reuse,reuser;

8347:     if (coarse_mat) reuse = PETSC_TRUE;
8348:     else reuse = PETSC_FALSE;
8349:     MPIU_Allreduce(&reuse,&reuser,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
8350:     vp[0] = NULL;
8351:     if (pcbddc->benign_have_null) { /* propagate no-net-flux quadrature to coarser level */
8352:       VecCreate(PetscObjectComm((PetscObject)pc),&vp[0]);
8353:       VecSetSizes(vp[0],pcbddc->local_primal_size,PETSC_DECIDE);
8354:       VecSetType(vp[0],VECSTANDARD);
8355:       nvecs = 1;

8357:       if (pcbddc->divudotp) {
8358:         Mat      B,loc_divudotp;
8359:         Vec      v,p;
8360:         IS       dummy;
8361:         PetscInt np;

8363:         MatISGetLocalMat(pcbddc->divudotp,&loc_divudotp);
8364:         MatGetSize(loc_divudotp,&np,NULL);
8365:         ISCreateStride(PETSC_COMM_SELF,np,0,1,&dummy);
8366:         MatCreateSubMatrix(loc_divudotp,dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B);
8367:         MatCreateVecs(B,&v,&p);
8368:         VecSet(p,1.);
8369:         MatMultTranspose(B,p,v);
8370:         VecDestroy(&p);
8371:         MatDestroy(&B);
8372:         VecGetArray(vp[0],&array);
8373:         VecPlaceArray(pcbddc->vec1_P,array);
8374:         VecRestoreArray(vp[0],&array);
8375:         MatMultTranspose(pcbddc->coarse_phi_B,v,pcbddc->vec1_P);
8376:         VecResetArray(pcbddc->vec1_P);
8377:         ISDestroy(&dummy);
8378:         VecDestroy(&v);
8379:       }
8380:     }
8381:     if (reuser) {
8382:       PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_TRUE,&coarse_mat,nis,isarray,nvecs,vp);
8383:     } else {
8384:       PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_FALSE,&coarse_mat_is,nis,isarray,nvecs,vp);
8385:     }
8386:     if (vp[0]) { /* vp[0] could have been placed on a different set of processes */
8387:       PetscScalar       *arraym;
8388:       const PetscScalar *arrayv;
8389:       PetscInt          nl;
8390:       VecGetLocalSize(vp[0],&nl);
8391:       MatCreateSeqDense(PETSC_COMM_SELF,1,nl,NULL,&coarsedivudotp);
8392:       MatDenseGetArray(coarsedivudotp,&arraym);
8393:       VecGetArrayRead(vp[0],&arrayv);
8394:       PetscArraycpy(arraym,arrayv,nl);
8395:       VecRestoreArrayRead(vp[0],&arrayv);
8396:       MatDenseRestoreArray(coarsedivudotp,&arraym);
8397:       VecDestroy(&vp[0]);
8398:     } else {
8399:       MatCreateSeqAIJ(PETSC_COMM_SELF,0,0,1,NULL,&coarsedivudotp);
8400:     }
8401:   } else {
8402:     PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_FALSE,&coarse_mat_is,0,NULL,0,NULL);
8403:   }
8404:   if (coarse_mat_is || coarse_mat) {
8405:     if (!multilevel_allowed) {
8406:       MatConvert(coarse_mat_is,MATAIJ,coarse_mat_reuse,&coarse_mat);
8407:     } else {
8408:       /* if this matrix is present, it means we are not reusing the coarse matrix */
8409:       if (coarse_mat_is) {
8410:         if (coarse_mat) SETERRQ(PetscObjectComm((PetscObject)coarse_mat_is),PETSC_ERR_PLIB,"This should not happen");
8411:         PetscObjectReference((PetscObject)coarse_mat_is);
8412:         coarse_mat = coarse_mat_is;
8413:       }
8414:     }
8415:   }
8416:   MatDestroy(&t_coarse_mat_is);
8417:   MatDestroy(&coarse_mat_is);

8419:   /* create local to global scatters for coarse problem */
8420:   if (compute_vecs) {
8421:     PetscInt lrows;
8422:     VecDestroy(&pcbddc->coarse_vec);
8423:     if (coarse_mat) {
8424:       MatGetLocalSize(coarse_mat,&lrows,NULL);
8425:     } else {
8426:       lrows = 0;
8427:     }
8428:     VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);
8429:     VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);
8430:     VecSetType(pcbddc->coarse_vec,coarse_mat ? coarse_mat->defaultvectype : VECSTANDARD);
8431:     VecScatterDestroy(&pcbddc->coarse_loc_to_glob);
8432:     VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);
8433:   }
8434:   ISDestroy(&coarse_is);

8436:   /* set defaults for coarse KSP and PC */
8437:   if (multilevel_allowed) {
8438:     coarse_ksp_type = KSPRICHARDSON;
8439:     coarse_pc_type  = PCBDDC;
8440:   } else {
8441:     coarse_ksp_type = KSPPREONLY;
8442:     coarse_pc_type  = PCREDUNDANT;
8443:   }

8445:   /* print some info if requested */
8446:   if (pcbddc->dbg_flag) {
8447:     if (!multilevel_allowed) {
8448:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
8449:       if (multilevel_requested) {
8450:         PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Not enough active processes on level %D (active processes %D, coarsening ratio %D)\n",pcbddc->current_level,active_procs,pcbddc->coarsening_ratio);
8451:       } else if (pcbddc->max_levels) {
8452:         PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%D)\n",pcbddc->max_levels);
8453:       }
8454:       PetscViewerFlush(pcbddc->dbg_viewer);
8455:     }
8456:   }

8458:   /* communicate coarse discrete gradient */
8459:   coarseG = NULL;
8460:   if (pcbddc->nedcG && multilevel_allowed) {
8461:     MPI_Comm ccomm;
8462:     if (coarse_mat) {
8463:       ccomm = PetscObjectComm((PetscObject)coarse_mat);
8464:     } else {
8465:       ccomm = MPI_COMM_NULL;
8466:     }
8467:     MatMPIAIJRestrict(pcbddc->nedcG,ccomm,&coarseG);
8468:   }

8470:   /* create the coarse KSP object only once with defaults */
8471:   if (coarse_mat) {
8472:     PetscBool   isredundant,isbddc,force,valid;
8473:     PetscViewer dbg_viewer = NULL;

8475:     if (pcbddc->dbg_flag) {
8476:       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat));
8477:       PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);
8478:     }
8479:     if (!pcbddc->coarse_ksp) {
8480:       char   prefix[256],str_level[16];
8481:       size_t len;

8483:       KSPCreate(PetscObjectComm((PetscObject)coarse_mat),&pcbddc->coarse_ksp);
8484:       KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,pc->erroriffailure);
8485:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);
8486:       KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);
8487:       KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);
8488:       KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);
8489:       KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);
8490:       KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
8491:       /* TODO is this logic correct? should check for coarse_mat type */
8492:       PCSetType(pc_temp,coarse_pc_type);
8493:       /* prefix */
8494:       PetscStrcpy(prefix,"");
8495:       PetscStrcpy(str_level,"");
8496:       if (!pcbddc->current_level) {
8497:         PetscStrncpy(prefix,((PetscObject)pc)->prefix,sizeof(prefix));
8498:         PetscStrlcat(prefix,"pc_bddc_coarse_",sizeof(prefix));
8499:       } else {
8500:         PetscStrlen(((PetscObject)pc)->prefix,&len);
8501:         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
8502:         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
8503:         /* Nonstandard use of PetscStrncpy() to copy only a portion of the string */
8504:         PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);
8505:         PetscSNPrintf(str_level,sizeof(str_level),"l%d_",(int)(pcbddc->current_level));
8506:         PetscStrlcat(prefix,str_level,sizeof(prefix));
8507:       }
8508:       KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);
8509:       /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
8510:       PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);
8511:       PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);
8512:       PCBDDCSetLevels(pc_temp,pcbddc->max_levels);
8513:       /* allow user customization */
8514:       KSPSetFromOptions(pcbddc->coarse_ksp);
8515:       /* get some info after set from options */
8516:       KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
8517:       /* multilevel cannot be done with coarse PC different from BDDC, NN, HPDDM, unless forced to */
8518:       force = PETSC_FALSE;
8519:       PetscOptionsGetBool(NULL,((PetscObject)pc_temp)->prefix,"-pc_type_forced",&force,NULL);
8520:       PetscObjectTypeCompareAny((PetscObject)pc_temp,&valid,PCBDDC,PCNN,PCHPDDM,"");
8521:       PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);
8522:       if (multilevel_allowed && !force && !valid) {
8523:         isbddc = PETSC_TRUE;
8524:         PCSetType(pc_temp,PCBDDC);
8525:         PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);
8526:         PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);
8527:         PCBDDCSetLevels(pc_temp,pcbddc->max_levels);
8528:         if (pc_temp->ops->setfromoptions) { /* need to setfromoptions again, skipping the pc_type */
8529:           PetscObjectOptionsBegin((PetscObject)pc_temp);
8530:           (*pc_temp->ops->setfromoptions)(PetscOptionsObject,pc_temp);
8531:           PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)pc_temp);
8532:           PetscOptionsEnd();
8533:           pc_temp->setfromoptionscalled++;
8534:         }
8535:       }
8536:     }
8537:     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
8538:     KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
8539:     if (nisdofs) {
8540:       PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);
8541:       for (i=0;i<nisdofs;i++) {
8542:         ISDestroy(&isarray[i]);
8543:       }
8544:     }
8545:     if (nisneu) {
8546:       PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);
8547:       ISDestroy(&isarray[nisdofs]);
8548:     }
8549:     if (nisvert) {
8550:       PCBDDCSetPrimalVerticesIS(pc_temp,isarray[nis-1]);
8551:       ISDestroy(&isarray[nis-1]);
8552:     }
8553:     if (coarseG) {
8554:       PCBDDCSetDiscreteGradient(pc_temp,coarseG,1,nedcfield,PETSC_FALSE,PETSC_TRUE);
8555:     }

8557:     /* get some info after set from options */
8558:     PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);

8560:     /* multilevel can only be requested via -pc_bddc_levels or PCBDDCSetLevels */
8561:     if (isbddc && !multilevel_allowed) {
8562:       PCSetType(pc_temp,coarse_pc_type);
8563:     }
8564:     /* multilevel cannot be done with coarse PC different from BDDC, NN, HPDDM, unless forced to */
8565:     force = PETSC_FALSE;
8566:     PetscOptionsGetBool(NULL,((PetscObject)pc_temp)->prefix,"-pc_type_forced",&force,NULL);
8567:     PetscObjectTypeCompareAny((PetscObject)pc_temp,&valid,PCBDDC,PCNN,PCHPDDM,"");
8568:     if (multilevel_requested && multilevel_allowed && !valid && !force) {
8569:       PCSetType(pc_temp,PCBDDC);
8570:     }
8571:     PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);
8572:     if (isredundant) {
8573:       KSP inner_ksp;
8574:       PC  inner_pc;

8576:       PCRedundantGetKSP(pc_temp,&inner_ksp);
8577:       KSPGetPC(inner_ksp,&inner_pc);
8578:     }

8580:     /* parameters which miss an API */
8581:     PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);
8582:     if (isbddc) {
8583:       PC_BDDC* pcbddc_coarse = (PC_BDDC*)pc_temp->data;

8585:       pcbddc_coarse->detect_disconnected = PETSC_TRUE;
8586:       pcbddc_coarse->coarse_eqs_per_proc = pcbddc->coarse_eqs_per_proc;
8587:       pcbddc_coarse->coarse_eqs_limit    = pcbddc->coarse_eqs_limit;
8588:       pcbddc_coarse->benign_saddle_point = pcbddc->benign_have_null;
8589:       if (pcbddc_coarse->benign_saddle_point) {
8590:         Mat                    coarsedivudotp_is;
8591:         ISLocalToGlobalMapping l2gmap,rl2g,cl2g;
8592:         IS                     row,col;
8593:         const PetscInt         *gidxs;
8594:         PetscInt               n,st,M,N;

8596:         MatGetSize(coarsedivudotp,&n,NULL);
8597:         MPI_Scan(&n,&st,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)coarse_mat));
8598:         st   = st-n;
8599:         ISCreateStride(PetscObjectComm((PetscObject)coarse_mat),1,st,1,&row);
8600:         MatGetLocalToGlobalMapping(coarse_mat,&l2gmap,NULL);
8601:         ISLocalToGlobalMappingGetSize(l2gmap,&n);
8602:         ISLocalToGlobalMappingGetIndices(l2gmap,&gidxs);
8603:         ISCreateGeneral(PetscObjectComm((PetscObject)coarse_mat),n,gidxs,PETSC_COPY_VALUES,&col);
8604:         ISLocalToGlobalMappingRestoreIndices(l2gmap,&gidxs);
8605:         ISLocalToGlobalMappingCreateIS(row,&rl2g);
8606:         ISLocalToGlobalMappingCreateIS(col,&cl2g);
8607:         ISGetSize(row,&M);
8608:         MatGetSize(coarse_mat,&N,NULL);
8609:         ISDestroy(&row);
8610:         ISDestroy(&col);
8611:         MatCreate(PetscObjectComm((PetscObject)coarse_mat),&coarsedivudotp_is);
8612:         MatSetType(coarsedivudotp_is,MATIS);
8613:         MatSetSizes(coarsedivudotp_is,PETSC_DECIDE,PETSC_DECIDE,M,N);
8614:         MatSetLocalToGlobalMapping(coarsedivudotp_is,rl2g,cl2g);
8615:         ISLocalToGlobalMappingDestroy(&rl2g);
8616:         ISLocalToGlobalMappingDestroy(&cl2g);
8617:         MatISSetLocalMat(coarsedivudotp_is,coarsedivudotp);
8618:         MatDestroy(&coarsedivudotp);
8619:         PCBDDCSetDivergenceMat(pc_temp,coarsedivudotp_is,PETSC_FALSE,NULL);
8620:         MatDestroy(&coarsedivudotp_is);
8621:         pcbddc_coarse->adaptive_userdefined = PETSC_TRUE;
8622:         if (pcbddc->adaptive_threshold[0] == 0.0) pcbddc_coarse->deluxe_zerorows = PETSC_TRUE;
8623:       }
8624:     }

8626:     /* propagate symmetry info of coarse matrix */
8627:     MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);
8628:     if (pc->pmat->symmetric_set) {
8629:       MatSetOption(coarse_mat,MAT_SYMMETRIC,pc->pmat->symmetric);
8630:     }
8631:     if (pc->pmat->hermitian_set) {
8632:       MatSetOption(coarse_mat,MAT_HERMITIAN,pc->pmat->hermitian);
8633:     }
8634:     if (pc->pmat->spd_set) {
8635:       MatSetOption(coarse_mat,MAT_SPD,pc->pmat->spd);
8636:     }
8637:     if (pcbddc->benign_saddle_point && !pcbddc->benign_have_null) {
8638:       MatSetOption(coarse_mat,MAT_SPD,PETSC_TRUE);
8639:     }
8640:     /* set operators */
8641:     MatViewFromOptions(coarse_mat,(PetscObject)pc,"-pc_bddc_coarse_mat_view");
8642:     MatSetOptionsPrefix(coarse_mat,((PetscObject)pcbddc->coarse_ksp)->prefix);
8643:     KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);
8644:     if (pcbddc->dbg_flag) {
8645:       PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);
8646:     }
8647:   }
8648:   MatDestroy(&coarseG);
8649:   PetscFree(isarray);
8650: #if 0
8651:   {
8652:     PetscViewer viewer;
8653:     char filename[256];
8654:     sprintf(filename,"coarse_mat_level%d.m",pcbddc->current_level);
8655:     PetscViewerASCIIOpen(PetscObjectComm((PetscObject)coarse_mat),filename,&viewer);
8656:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
8657:     MatView(coarse_mat,viewer);
8658:     PetscViewerPopFormat(viewer);
8659:     PetscViewerDestroy(&viewer);
8660:   }
8661: #endif

8663:   if (corners) {
8664:     Vec            gv;
8665:     IS             is;
8666:     const PetscInt *idxs;
8667:     PetscInt       i,d,N,n,cdim = pcbddc->mat_graph->cdim;
8668:     PetscScalar    *coords;

8670:     if (!pcbddc->mat_graph->cloc) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing local coordinates");
8671:     VecGetSize(pcbddc->coarse_vec,&N);
8672:     VecGetLocalSize(pcbddc->coarse_vec,&n);
8673:     VecCreate(PetscObjectComm((PetscObject)pcbddc->coarse_vec),&gv);
8674:     VecSetBlockSize(gv,cdim);
8675:     VecSetSizes(gv,n*cdim,N*cdim);
8676:     VecSetType(gv,VECSTANDARD);
8677:     VecSetFromOptions(gv);
8678:     VecSet(gv,PETSC_MAX_REAL); /* we only propagate coordinates from vertices constraints */

8680:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&is);
8681:     ISGetLocalSize(is,&n);
8682:     ISGetIndices(is,&idxs);
8683:     PetscMalloc1(n*cdim,&coords);
8684:     for (i=0;i<n;i++) {
8685:       for (d=0;d<cdim;d++) {
8686:         coords[cdim*i+d] = pcbddc->mat_graph->coords[cdim*idxs[i]+d];
8687:       }
8688:     }
8689:     ISRestoreIndices(is,&idxs);
8690:     PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&is);

8692:     ISGetLocalSize(corners,&n);
8693:     ISGetIndices(corners,&idxs);
8694:     VecSetValuesBlocked(gv,n,idxs,coords,INSERT_VALUES);
8695:     ISRestoreIndices(corners,&idxs);
8696:     PetscFree(coords);
8697:     VecAssemblyBegin(gv);
8698:     VecAssemblyEnd(gv);
8699:     VecGetArray(gv,&coords);
8700:     if (pcbddc->coarse_ksp) {
8701:       PC        coarse_pc;
8702:       PetscBool isbddc;

8704:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
8705:       PetscObjectTypeCompare((PetscObject)coarse_pc,PCBDDC,&isbddc);
8706:       if (isbddc) { /* coarse coordinates have PETSC_MAX_REAL, specific for BDDC */
8707:         PetscReal *realcoords;

8709:         VecGetLocalSize(gv,&n);
8710: #if defined(PETSC_USE_COMPLEX)
8711:         PetscMalloc1(n,&realcoords);
8712:         for (i=0;i<n;i++) realcoords[i] = PetscRealPart(coords[i]);
8713: #else
8714:         realcoords = coords;
8715: #endif
8716:         PCSetCoordinates(coarse_pc,cdim,n/cdim,realcoords);
8717: #if defined(PETSC_USE_COMPLEX)
8718:         PetscFree(realcoords);
8719: #endif
8720:       }
8721:     }
8722:     VecRestoreArray(gv,&coords);
8723:     VecDestroy(&gv);
8724:   }
8725:   ISDestroy(&corners);

8727:   if (pcbddc->coarse_ksp) {
8728:     Vec crhs,csol;

8730:     KSPGetSolution(pcbddc->coarse_ksp,&csol);
8731:     KSPGetRhs(pcbddc->coarse_ksp,&crhs);
8732:     if (!csol) {
8733:       MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);
8734:     }
8735:     if (!crhs) {
8736:       MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));
8737:     }
8738:   }
8739:   MatDestroy(&coarsedivudotp);

8741:   /* compute null space for coarse solver if the benign trick has been requested */
8742:   if (pcbddc->benign_null) {

8744:     VecSet(pcbddc->vec1_P,0.);
8745:     for (i=0;i<pcbddc->benign_n;i++) {
8746:       VecSetValue(pcbddc->vec1_P,pcbddc->local_primal_size-pcbddc->benign_n+i,1.0,INSERT_VALUES);
8747:     }
8748:     VecAssemblyBegin(pcbddc->vec1_P);
8749:     VecAssemblyEnd(pcbddc->vec1_P);
8750:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,INSERT_VALUES,SCATTER_FORWARD);
8751:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,INSERT_VALUES,SCATTER_FORWARD);
8752:     if (coarse_mat) {
8753:       Vec         nullv;
8754:       PetscScalar *array,*array2;
8755:       PetscInt    nl;

8757:       MatCreateVecs(coarse_mat,&nullv,NULL);
8758:       VecGetLocalSize(nullv,&nl);
8759:       VecGetArrayRead(pcbddc->coarse_vec,(const PetscScalar**)&array);
8760:       VecGetArray(nullv,&array2);
8761:       PetscArraycpy(array2,array,nl);
8762:       VecRestoreArray(nullv,&array2);
8763:       VecRestoreArrayRead(pcbddc->coarse_vec,(const PetscScalar**)&array);
8764:       VecNormalize(nullv,NULL);
8765:       MatNullSpaceCreate(PetscObjectComm((PetscObject)coarse_mat),PETSC_FALSE,1,&nullv,&CoarseNullSpace);
8766:       VecDestroy(&nullv);
8767:     }
8768:   }
8769:   PetscLogEventEnd(PC_BDDC_CoarseSetUp[pcbddc->current_level],pc,0,0,0);

8771:   PetscLogEventBegin(PC_BDDC_CoarseSolver[pcbddc->current_level],pc,0,0,0);
8772:   if (pcbddc->coarse_ksp) {
8773:     PetscBool ispreonly;

8775:     if (CoarseNullSpace) {
8776:       PetscBool isnull;
8777:       MatNullSpaceTest(CoarseNullSpace,coarse_mat,&isnull);
8778:       if (isnull) {
8779:         MatSetNullSpace(coarse_mat,CoarseNullSpace);
8780:       }
8781:       /* TODO: add local nullspaces (if any) */
8782:     }
8783:     /* setup coarse ksp */
8784:     KSPSetUp(pcbddc->coarse_ksp);
8785:     /* Check coarse problem if in debug mode or if solving with an iterative method */
8786:     PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);
8787:     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates)) {
8788:       KSP       check_ksp;
8789:       KSPType   check_ksp_type;
8790:       PC        check_pc;
8791:       Vec       check_vec,coarse_vec;
8792:       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
8793:       PetscInt  its;
8794:       PetscBool compute_eigs;
8795:       PetscReal *eigs_r,*eigs_c;
8796:       PetscInt  neigs;
8797:       const char *prefix;

8799:       /* Create ksp object suitable for estimation of extreme eigenvalues */
8800:       KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);
8801:       PetscObjectIncrementTabLevel((PetscObject)check_ksp,(PetscObject)pcbddc->coarse_ksp,0);
8802:       KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,PETSC_FALSE);
8803:       KSPSetOperators(check_ksp,coarse_mat,coarse_mat);
8804:       KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);
8805:       /* prevent from setup unneeded object */
8806:       KSPGetPC(check_ksp,&check_pc);
8807:       PCSetType(check_pc,PCNONE);
8808:       if (ispreonly) {
8809:         check_ksp_type = KSPPREONLY;
8810:         compute_eigs = PETSC_FALSE;
8811:       } else {
8812:         check_ksp_type = KSPGMRES;
8813:         compute_eigs = PETSC_TRUE;
8814:       }
8815:       KSPSetType(check_ksp,check_ksp_type);
8816:       KSPSetComputeSingularValues(check_ksp,compute_eigs);
8817:       KSPSetComputeEigenvalues(check_ksp,compute_eigs);
8818:       KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);
8819:       KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);
8820:       KSPSetOptionsPrefix(check_ksp,prefix);
8821:       KSPAppendOptionsPrefix(check_ksp,"check_");
8822:       KSPSetFromOptions(check_ksp);
8823:       KSPSetUp(check_ksp);
8824:       KSPGetPC(pcbddc->coarse_ksp,&check_pc);
8825:       KSPSetPC(check_ksp,check_pc);
8826:       /* create random vec */
8827:       MatCreateVecs(coarse_mat,&coarse_vec,&check_vec);
8828:       VecSetRandom(check_vec,NULL);
8829:       MatMult(coarse_mat,check_vec,coarse_vec);
8830:       /* solve coarse problem */
8831:       KSPSolve(check_ksp,coarse_vec,coarse_vec);
8832:       KSPCheckSolve(check_ksp,pc,coarse_vec);
8833:       /* set eigenvalue estimation if preonly has not been requested */
8834:       if (compute_eigs) {
8835:         PetscMalloc1(pcbddc->coarse_size+1,&eigs_r);
8836:         PetscMalloc1(pcbddc->coarse_size+1,&eigs_c);
8837:         KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);
8838:         if (neigs) {
8839:           lambda_max = eigs_r[neigs-1];
8840:           lambda_min = eigs_r[0];
8841:           if (pcbddc->use_coarse_estimates) {
8842:             if (lambda_max>=lambda_min) { /* using PETSC_SMALL since lambda_max == lambda_min is not allowed by KSPChebyshevSetEigenvalues */
8843:               KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max+PETSC_SMALL,lambda_min);
8844:               KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));
8845:             }
8846:           }
8847:         }
8848:       }

8850:       /* check coarse problem residual error */
8851:       if (pcbddc->dbg_flag) {
8852:         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
8853:         PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));
8854:         VecAXPY(check_vec,-1.0,coarse_vec);
8855:         VecNorm(check_vec,NORM_INFINITY,&infty_error);
8856:         MatMult(coarse_mat,check_vec,coarse_vec);
8857:         VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);
8858:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (use estimates %d)\n",pcbddc->use_coarse_estimates);
8859:         PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);
8860:         PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);
8861:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);
8862:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);
8863:         if (CoarseNullSpace) {
8864:           PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem is singular\n");
8865:         }
8866:         if (compute_eigs) {
8867:           PetscReal          lambda_max_s,lambda_min_s;
8868:           KSPConvergedReason reason;
8869:           KSPGetType(check_ksp,&check_ksp_type);
8870:           KSPGetIterationNumber(check_ksp,&its);
8871:           KSPGetConvergedReason(check_ksp,&reason);
8872:           KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);
8873:           PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem eigenvalues (estimated with %d iterations of %s, conv reason %d): %1.6e %1.6e (%1.6e %1.6e)\n",its,check_ksp_type,reason,lambda_min,lambda_max,lambda_min_s,lambda_max_s);
8874:           for (i=0;i<neigs;i++) {
8875:             PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);
8876:           }
8877:         }
8878:         PetscViewerFlush(dbg_viewer);
8879:         PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));
8880:       }
8881:       VecDestroy(&check_vec);
8882:       VecDestroy(&coarse_vec);
8883:       KSPDestroy(&check_ksp);
8884:       if (compute_eigs) {
8885:         PetscFree(eigs_r);
8886:         PetscFree(eigs_c);
8887:       }
8888:     }
8889:   }
8890:   MatNullSpaceDestroy(&CoarseNullSpace);
8891:   /* print additional info */
8892:   if (pcbddc->dbg_flag) {
8893:     /* waits until all processes reaches this point */
8894:     PetscBarrier((PetscObject)pc);
8895:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %D\n",pcbddc->current_level);
8896:     PetscViewerFlush(pcbddc->dbg_viewer);
8897:   }

8899:   /* free memory */
8900:   MatDestroy(&coarse_mat);
8901:   PetscLogEventEnd(PC_BDDC_CoarseSolver[pcbddc->current_level],pc,0,0,0);
8902:   return(0);
8903: }

8905: PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
8906: {
8907:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
8908:   PC_IS*         pcis = (PC_IS*)pc->data;
8909:   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
8910:   IS             subset,subset_mult,subset_n;
8911:   PetscInt       local_size,coarse_size=0;
8912:   PetscInt       *local_primal_indices=NULL;
8913:   const PetscInt *t_local_primal_indices;

8917:   /* Compute global number of coarse dofs */
8918:   if (pcbddc->local_primal_size && !pcbddc->local_primal_ref_node) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"BDDC ConstraintsSetUp should be called first");
8919:   ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&subset_n);
8920:   ISLocalToGlobalMappingApplyIS(pcis->mapping,subset_n,&subset);
8921:   ISDestroy(&subset_n);
8922:   ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_mult,PETSC_COPY_VALUES,&subset_mult);
8923:   ISRenumber(subset,subset_mult,&coarse_size,&subset_n);
8924:   ISDestroy(&subset);
8925:   ISDestroy(&subset_mult);
8926:   ISGetLocalSize(subset_n,&local_size);
8927:   if (local_size != pcbddc->local_primal_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid number of local primal indices computed %D != %D",local_size,pcbddc->local_primal_size);
8928:   PetscMalloc1(local_size,&local_primal_indices);
8929:   ISGetIndices(subset_n,&t_local_primal_indices);
8930:   PetscArraycpy(local_primal_indices,t_local_primal_indices,local_size);
8931:   ISRestoreIndices(subset_n,&t_local_primal_indices);
8932:   ISDestroy(&subset_n);

8934:   /* check numbering */
8935:   if (pcbddc->dbg_flag) {
8936:     PetscScalar coarsesum,*array,*array2;
8937:     PetscInt    i;
8938:     PetscBool   set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;

8940:     PetscViewerFlush(pcbddc->dbg_viewer);
8941:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
8942:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");
8943:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
8944:     /* counter */
8945:     VecSet(pcis->vec1_global,0.0);
8946:     VecSet(pcis->vec1_N,1.0);
8947:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8948:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8949:     VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);
8950:     VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);
8951:     VecSet(pcis->vec1_N,0.0);
8952:     for (i=0;i<pcbddc->local_primal_size;i++) {
8953:       VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);
8954:     }
8955:     VecAssemblyBegin(pcis->vec1_N);
8956:     VecAssemblyEnd(pcis->vec1_N);
8957:     VecSet(pcis->vec1_global,0.0);
8958:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8959:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8960:     VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
8961:     VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
8962:     VecGetArray(pcis->vec1_N,&array);
8963:     VecGetArray(pcis->vec2_N,&array2);
8964:     for (i=0;i<pcis->n;i++) {
8965:       if (array[i] != 0.0 && array[i] != array2[i]) {
8966:         PetscInt owned = (PetscInt)PetscRealPart(array[i]),gi;
8967:         PetscInt neigh = (PetscInt)PetscRealPart(array2[i]);
8968:         set_error = PETSC_TRUE;
8969:         ISLocalToGlobalMappingApply(pcis->mapping,1,&i,&gi);
8970:         PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %D (gid %D) owned by %D processes instead of %D!\n",PetscGlobalRank,i,gi,owned,neigh);
8971:       }
8972:     }
8973:     VecRestoreArray(pcis->vec2_N,&array2);
8974:     MPIU_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
8975:     PetscViewerFlush(pcbddc->dbg_viewer);
8976:     for (i=0;i<pcis->n;i++) {
8977:       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
8978:     }
8979:     VecRestoreArray(pcis->vec1_N,&array);
8980:     VecSet(pcis->vec1_global,0.0);
8981:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8982:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8983:     VecSum(pcis->vec1_global,&coarsesum);
8984:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %D (%lf)\n",coarse_size,PetscRealPart(coarsesum));
8985:     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
8986:       PetscInt *gidxs;

8988:       PetscMalloc1(pcbddc->local_primal_size,&gidxs);
8989:       ISLocalToGlobalMappingApply(pcis->mapping,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,gidxs);
8990:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");
8991:       PetscViewerFlush(pcbddc->dbg_viewer);
8992:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);
8993:       for (i=0;i<pcbddc->local_primal_size;i++) {
8994:         PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_primal_indices[%D]=%D (%D,%D)\n",i,local_primal_indices[i],pcbddc->primal_indices_local_idxs[i],gidxs[i]);
8995:       }
8996:       PetscViewerFlush(pcbddc->dbg_viewer);
8997:       PetscFree(gidxs);
8998:     }
8999:     PetscViewerFlush(pcbddc->dbg_viewer);
9000:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
9001:     if (set_error_reduced) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
9002:   }

9004:   /* get back data */
9005:   *coarse_size_n = coarse_size;
9006:   *local_primal_indices_n = local_primal_indices;
9007:   return(0);
9008: }

9010: PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
9011: {
9012:   IS             localis_t;
9013:   PetscInt       i,lsize,*idxs,n;
9014:   PetscScalar    *vals;

9018:   /* get indices in local ordering exploiting local to global map */
9019:   ISGetLocalSize(globalis,&lsize);
9020:   PetscMalloc1(lsize,&vals);
9021:   for (i=0;i<lsize;i++) vals[i] = 1.0;
9022:   ISGetIndices(globalis,(const PetscInt**)&idxs);
9023:   VecSet(gwork,0.0);
9024:   VecSet(lwork,0.0);
9025:   if (idxs) { /* multilevel guard */
9026:     VecSetOption(gwork,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);
9027:     VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);
9028:   }
9029:   VecAssemblyBegin(gwork);
9030:   ISRestoreIndices(globalis,(const PetscInt**)&idxs);
9031:   PetscFree(vals);
9032:   VecAssemblyEnd(gwork);
9033:   /* now compute set in local ordering */
9034:   VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);
9035:   VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);
9036:   VecGetArrayRead(lwork,(const PetscScalar**)&vals);
9037:   VecGetSize(lwork,&n);
9038:   for (i=0,lsize=0;i<n;i++) {
9039:     if (PetscRealPart(vals[i]) > 0.5) {
9040:       lsize++;
9041:     }
9042:   }
9043:   PetscMalloc1(lsize,&idxs);
9044:   for (i=0,lsize=0;i<n;i++) {
9045:     if (PetscRealPart(vals[i]) > 0.5) {
9046:       idxs[lsize++] = i;
9047:     }
9048:   }
9049:   VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);
9050:   ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);
9051:   *localis = localis_t;
9052:   return(0);
9053: }

9055: PetscErrorCode PCBDDCSetUpSubSchurs(PC pc)
9056: {
9057:   PC_IS               *pcis=(PC_IS*)pc->data;
9058:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
9059:   PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
9060:   Mat                 S_j;
9061:   PetscInt            *used_xadj,*used_adjncy;
9062:   PetscBool           free_used_adj;
9063:   PetscErrorCode      ierr;

9066:   PetscLogEventBegin(PC_BDDC_Schurs[pcbddc->current_level],pc,0,0,0);
9067:   /* decide the adjacency to be used for determining internal problems for local schur on subsets */
9068:   free_used_adj = PETSC_FALSE;
9069:   if (pcbddc->sub_schurs_layers == -1) {
9070:     used_xadj = NULL;
9071:     used_adjncy = NULL;
9072:   } else {
9073:     if (pcbddc->sub_schurs_use_useradj && pcbddc->mat_graph->xadj) {
9074:       used_xadj = pcbddc->mat_graph->xadj;
9075:       used_adjncy = pcbddc->mat_graph->adjncy;
9076:     } else if (pcbddc->computed_rowadj) {
9077:       used_xadj = pcbddc->mat_graph->xadj;
9078:       used_adjncy = pcbddc->mat_graph->adjncy;
9079:     } else {
9080:       PetscBool      flg_row=PETSC_FALSE;
9081:       const PetscInt *xadj,*adjncy;
9082:       PetscInt       nvtxs;

9084:       MatGetRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);
9085:       if (flg_row) {
9086:         PetscMalloc2(nvtxs+1,&used_xadj,xadj[nvtxs],&used_adjncy);
9087:         PetscArraycpy(used_xadj,xadj,nvtxs+1);
9088:         PetscArraycpy(used_adjncy,adjncy,xadj[nvtxs]);
9089:         free_used_adj = PETSC_TRUE;
9090:       } else {
9091:         pcbddc->sub_schurs_layers = -1;
9092:         used_xadj = NULL;
9093:         used_adjncy = NULL;
9094:       }
9095:       MatRestoreRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);
9096:     }
9097:   }

9099:   /* setup sub_schurs data */
9100:   MatCreateSchurComplement(pcis->A_II,pcis->pA_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);
9101:   if (!sub_schurs->schur_explicit) {
9102:     /* pcbddc->ksp_D up to date only if not using MatFactor with Schur complement support */
9103:     MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);
9104:     PCBDDCSubSchursSetUp(sub_schurs,NULL,S_j,PETSC_FALSE,used_xadj,used_adjncy,pcbddc->sub_schurs_layers,NULL,pcbddc->adaptive_selection,PETSC_FALSE,PETSC_FALSE,0,NULL,NULL,NULL,NULL);
9105:   } else {
9106:     Mat       change = NULL;
9107:     Vec       scaling = NULL;
9108:     IS        change_primal = NULL, iP;
9109:     PetscInt  benign_n;
9110:     PetscBool reuse_solvers = (PetscBool)!pcbddc->use_change_of_basis;
9111:     PetscBool need_change = PETSC_FALSE;
9112:     PetscBool discrete_harmonic = PETSC_FALSE;

9114:     if (!pcbddc->use_vertices && reuse_solvers) {
9115:       PetscInt n_vertices;

9117:       ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);
9118:       reuse_solvers = (PetscBool)!n_vertices;
9119:     }
9120:     if (!pcbddc->benign_change_explicit) {
9121:       benign_n = pcbddc->benign_n;
9122:     } else {
9123:       benign_n = 0;
9124:     }
9125:     /* sub_schurs->change is a local object; instead, PCBDDCConstraintsSetUp and the quantities used in the test below are logically collective on pc.
9126:        We need a global reduction to avoid possible deadlocks.
9127:        We assume that sub_schurs->change is created once, and then reused for different solves, unless the topography has been recomputed */
9128:     if (pcbddc->adaptive_userdefined || (pcbddc->deluxe_zerorows && !pcbddc->use_change_of_basis)) {
9129:       PetscBool have_loc_change = (PetscBool)(!!sub_schurs->change);
9130:       MPIU_Allreduce(&have_loc_change,&need_change,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
9131:       need_change = (PetscBool)(!need_change);
9132:     }
9133:     /* If the user defines additional constraints, we import them here.
9134:        We need to compute the change of basis according to the quadrature weights attached to pmat via MatSetNearNullSpace, and this could not be done (at the moment) without some hacking */
9135:     if (need_change) {
9136:       PC_IS   *pcisf;
9137:       PC_BDDC *pcbddcf;
9138:       PC      pcf;

9140:       if (pcbddc->sub_schurs_rebuild) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot compute change of basis with a different graph");
9141:       PCCreate(PetscObjectComm((PetscObject)pc),&pcf);
9142:       PCSetOperators(pcf,pc->mat,pc->pmat);
9143:       PCSetType(pcf,PCBDDC);

9145:       /* hacks */
9146:       pcisf                        = (PC_IS*)pcf->data;
9147:       pcisf->is_B_local            = pcis->is_B_local;
9148:       pcisf->vec1_N                = pcis->vec1_N;
9149:       pcisf->BtoNmap               = pcis->BtoNmap;
9150:       pcisf->n                     = pcis->n;
9151:       pcisf->n_B                   = pcis->n_B;
9152:       pcbddcf                      = (PC_BDDC*)pcf->data;
9153:       PetscFree(pcbddcf->mat_graph);
9154:       pcbddcf->mat_graph           = pcbddc->mat_graph;
9155:       pcbddcf->use_faces           = PETSC_TRUE;
9156:       pcbddcf->use_change_of_basis = PETSC_TRUE;
9157:       pcbddcf->use_change_on_faces = PETSC_TRUE;
9158:       pcbddcf->use_qr_single       = PETSC_TRUE;
9159:       pcbddcf->fake_change         = PETSC_TRUE;

9161:       /* setup constraints so that we can get information on primal vertices and change of basis (in local numbering) */
9162:       PCBDDCConstraintsSetUp(pcf);
9163:       sub_schurs->change_with_qr = pcbddcf->use_qr_single;
9164:       ISCreateGeneral(PETSC_COMM_SELF,pcbddcf->n_vertices,pcbddcf->local_primal_ref_node,PETSC_COPY_VALUES,&change_primal);
9165:       change = pcbddcf->ConstraintMatrix;
9166:       pcbddcf->ConstraintMatrix = NULL;

9168:       /* free unneeded memory allocated in PCBDDCConstraintsSetUp */
9169:       PetscFree(pcbddcf->sub_schurs);
9170:       MatNullSpaceDestroy(&pcbddcf->onearnullspace);
9171:       PetscFree2(pcbddcf->local_primal_ref_node,pcbddcf->local_primal_ref_mult);
9172:       PetscFree(pcbddcf->primal_indices_local_idxs);
9173:       PetscFree(pcbddcf->onearnullvecs_state);
9174:       PetscFree(pcf->data);
9175:       pcf->ops->destroy = NULL;
9176:       pcf->ops->reset   = NULL;
9177:       PCDestroy(&pcf);
9178:     }
9179:     if (!pcbddc->use_deluxe_scaling) scaling = pcis->D;

9181:     PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_iP",(PetscObject*)&iP);
9182:     if (iP) {
9183:       PetscOptionsBegin(PetscObjectComm((PetscObject)iP),sub_schurs->prefix,"BDDC sub_schurs options","PC");
9184:       PetscOptionsBool("-sub_schurs_discrete_harmonic",NULL,NULL,discrete_harmonic,&discrete_harmonic,NULL);
9185:       PetscOptionsEnd();
9186:     }
9187:     if (discrete_harmonic) {
9188:       Mat A;
9189:       MatDuplicate(pcbddc->local_mat,MAT_COPY_VALUES,&A);
9190:       MatZeroRowsColumnsIS(A,iP,1.0,NULL,NULL);
9191:       PetscObjectCompose((PetscObject)A,"__KSPFETIDP_iP",(PetscObject)iP);
9192:       PCBDDCSubSchursSetUp(sub_schurs,A,S_j,pcbddc->sub_schurs_exact_schur,used_xadj,used_adjncy,pcbddc->sub_schurs_layers,scaling,pcbddc->adaptive_selection,reuse_solvers,pcbddc->benign_saddle_point,benign_n,pcbddc->benign_p0_lidx,pcbddc->benign_zerodiag_subs,change,change_primal);
9193:       MatDestroy(&A);
9194:     } else {
9195:       PCBDDCSubSchursSetUp(sub_schurs,pcbddc->local_mat,S_j,pcbddc->sub_schurs_exact_schur,used_xadj,used_adjncy,pcbddc->sub_schurs_layers,scaling,pcbddc->adaptive_selection,reuse_solvers,pcbddc->benign_saddle_point,benign_n,pcbddc->benign_p0_lidx,pcbddc->benign_zerodiag_subs,change,change_primal);
9196:     }
9197:     MatDestroy(&change);
9198:     ISDestroy(&change_primal);
9199:   }
9200:   MatDestroy(&S_j);

9202:   /* free adjacency */
9203:   if (free_used_adj) {
9204:     PetscFree2(used_xadj,used_adjncy);
9205:   }
9206:   PetscLogEventEnd(PC_BDDC_Schurs[pcbddc->current_level],pc,0,0,0);
9207:   return(0);
9208: }

9210: PetscErrorCode PCBDDCInitSubSchurs(PC pc)
9211: {
9212:   PC_IS               *pcis=(PC_IS*)pc->data;
9213:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
9214:   PCBDDCGraph         graph;
9215:   PetscErrorCode      ierr;

9218:   /* attach interface graph for determining subsets */
9219:   if (pcbddc->sub_schurs_rebuild) { /* in case rebuild has been requested, it uses a graph generated only by the neighbouring information */
9220:     IS       verticesIS,verticescomm;
9221:     PetscInt vsize,*idxs;

9223:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);
9224:     ISGetSize(verticesIS,&vsize);
9225:     ISGetIndices(verticesIS,(const PetscInt**)&idxs);
9226:     ISCreateGeneral(PetscObjectComm((PetscObject)pc),vsize,idxs,PETSC_COPY_VALUES,&verticescomm);
9227:     ISRestoreIndices(verticesIS,(const PetscInt**)&idxs);
9228:     PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);
9229:     PCBDDCGraphCreate(&graph);
9230:     PCBDDCGraphInit(graph,pcbddc->mat_graph->l2gmap,pcbddc->mat_graph->nvtxs_global,pcbddc->graphmaxcount);
9231:     PCBDDCGraphSetUp(graph,pcbddc->mat_graph->custom_minimal_size,NULL,pcbddc->DirichletBoundariesLocal,0,NULL,verticescomm);
9232:     ISDestroy(&verticescomm);
9233:     PCBDDCGraphComputeConnectedComponents(graph);
9234:   } else {
9235:     graph = pcbddc->mat_graph;
9236:   }
9237:   /* print some info */
9238:   if (pcbddc->dbg_flag && !pcbddc->sub_schurs_rebuild) {
9239:     IS       vertices;
9240:     PetscInt nv,nedges,nfaces;
9241:     PCBDDCGraphASCIIView(graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);
9242:     PCBDDCGraphGetCandidatesIS(graph,&nfaces,NULL,&nedges,NULL,&vertices);
9243:     ISGetSize(vertices,&nv);
9244:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
9245:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
9246:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%D)\n",PetscGlobalRank,(int)nv,pcbddc->use_vertices);
9247:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%D)\n",PetscGlobalRank,(int)nedges,pcbddc->use_edges);
9248:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%D)\n",PetscGlobalRank,(int)nfaces,pcbddc->use_faces);
9249:     PetscViewerFlush(pcbddc->dbg_viewer);
9250:     PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);
9251:     PCBDDCGraphRestoreCandidatesIS(graph,&nfaces,NULL,&nedges,NULL,&vertices);
9252:   }

9254:   /* sub_schurs init */
9255:   if (!pcbddc->sub_schurs) {
9256:     PCBDDCSubSchursCreate(&pcbddc->sub_schurs);
9257:   }
9258:   PCBDDCSubSchursInit(pcbddc->sub_schurs,((PetscObject)pc)->prefix,pcis->is_I_local,pcis->is_B_local,graph,pcis->BtoNmap,pcbddc->sub_schurs_rebuild);

9260:   /* free graph struct */
9261:   if (pcbddc->sub_schurs_rebuild) {
9262:     PCBDDCGraphDestroy(&graph);
9263:   }
9264:   return(0);
9265: }

9267: PetscErrorCode PCBDDCCheckOperator(PC pc)
9268: {
9269:   PC_IS               *pcis=(PC_IS*)pc->data;
9270:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
9271:   PetscErrorCode      ierr;

9274:   if (pcbddc->n_vertices == pcbddc->local_primal_size) {
9275:     IS             zerodiag = NULL;
9276:     Mat            S_j,B0_B=NULL;
9277:     Vec            dummy_vec=NULL,vec_check_B,vec_scale_P;
9278:     PetscScalar    *p0_check,*array,*array2;
9279:     PetscReal      norm;
9280:     PetscInt       i;

9282:     /* B0 and B0_B */
9283:     if (zerodiag) {
9284:       IS       dummy;

9286:       ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&dummy);
9287:       MatCreateSubMatrix(pcbddc->benign_B0,dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
9288:       MatCreateVecs(B0_B,NULL,&dummy_vec);
9289:       ISDestroy(&dummy);
9290:     }
9291:     /* I need a primal vector to scale primal nodes since BDDC sums contibutions */
9292:     VecDuplicate(pcbddc->vec1_P,&vec_scale_P);
9293:     VecSet(pcbddc->vec1_P,1.0);
9294:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
9295:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
9296:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);
9297:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);
9298:     VecReciprocal(vec_scale_P);
9299:     /* S_j */
9300:     MatCreateSchurComplement(pcis->A_II,pcis->pA_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);
9301:     MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);

9303:     /* mimic vector in \widetilde{W}_\Gamma */
9304:     VecSetRandom(pcis->vec1_N,NULL);
9305:     /* continuous in primal space */
9306:     VecSetRandom(pcbddc->coarse_vec,NULL);
9307:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
9308:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
9309:     VecGetArray(pcbddc->vec1_P,&array);
9310:     PetscCalloc1(pcbddc->benign_n,&p0_check);
9311:     for (i=0;i<pcbddc->benign_n;i++) p0_check[i] = array[pcbddc->local_primal_size-pcbddc->benign_n+i];
9312:     VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);
9313:     VecRestoreArray(pcbddc->vec1_P,&array);
9314:     VecAssemblyBegin(pcis->vec1_N);
9315:     VecAssemblyEnd(pcis->vec1_N);
9316:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
9317:     VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
9318:     VecDuplicate(pcis->vec2_B,&vec_check_B);
9319:     VecCopy(pcis->vec2_B,vec_check_B);

9321:     /* assemble rhs for coarse problem */
9322:     /* widetilde{S}_\Gamma w_\Gamma + \widetilde{B0}^T_B p0 */
9323:     /* local with Schur */
9324:     MatMult(S_j,pcis->vec2_B,pcis->vec1_B);
9325:     if (zerodiag) {
9326:       VecGetArray(dummy_vec,&array);
9327:       for (i=0;i<pcbddc->benign_n;i++) array[i] = p0_check[i];
9328:       VecRestoreArray(dummy_vec,&array);
9329:       MatMultTransposeAdd(B0_B,dummy_vec,pcis->vec1_B,pcis->vec1_B);
9330:     }
9331:     /* sum on primal nodes the local contributions */
9332:     VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);
9333:     VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);
9334:     VecGetArray(pcis->vec1_N,&array);
9335:     VecGetArray(pcbddc->vec1_P,&array2);
9336:     for (i=0;i<pcbddc->local_primal_size;i++) array2[i] = array[pcbddc->local_primal_ref_node[i]];
9337:     VecRestoreArray(pcbddc->vec1_P,&array2);
9338:     VecRestoreArray(pcis->vec1_N,&array);
9339:     VecSet(pcbddc->coarse_vec,0.);
9340:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
9341:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
9342:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
9343:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
9344:     VecGetArray(pcbddc->vec1_P,&array);
9345:     /* scale primal nodes (BDDC sums contibutions) */
9346:     VecPointwiseMult(pcbddc->vec1_P,vec_scale_P,pcbddc->vec1_P);
9347:     VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);
9348:     VecRestoreArray(pcbddc->vec1_P,&array);
9349:     VecAssemblyBegin(pcis->vec1_N);
9350:     VecAssemblyEnd(pcis->vec1_N);
9351:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
9352:     VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
9353:     /* global: \widetilde{B0}_B w_\Gamma */
9354:     if (zerodiag) {
9355:       MatMult(B0_B,pcis->vec2_B,dummy_vec);
9356:       VecGetArray(dummy_vec,&array);
9357:       for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = array[i];
9358:       VecRestoreArray(dummy_vec,&array);
9359:     }
9360:     /* BDDC */
9361:     VecSet(pcis->vec1_D,0.);
9362:     PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);

9364:     VecCopy(pcis->vec1_B,pcis->vec2_B);
9365:     VecAXPY(pcis->vec1_B,-1.0,vec_check_B);
9366:     VecNorm(pcis->vec1_B,NORM_INFINITY,&norm);
9367:     PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC local error is %1.4e\n",PetscGlobalRank,norm);
9368:     for (i=0;i<pcbddc->benign_n;i++) {
9369:       PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC p0[%D] error is %1.4e\n",PetscGlobalRank,i,PetscAbsScalar(pcbddc->benign_p0[i]-p0_check[i]));
9370:     }
9371:     PetscFree(p0_check);
9372:     VecDestroy(&vec_scale_P);
9373:     VecDestroy(&vec_check_B);
9374:     VecDestroy(&dummy_vec);
9375:     MatDestroy(&S_j);
9376:     MatDestroy(&B0_B);
9377:   }
9378:   return(0);
9379: }

9381: #include <../src/mat/impls/aij/mpi/mpiaij.h>
9382: PetscErrorCode MatMPIAIJRestrict(Mat A, MPI_Comm ccomm, Mat *B)
9383: {
9384:   Mat            At;
9385:   IS             rows;
9386:   PetscInt       rst,ren;
9388:   PetscLayout    rmap;

9391:   rst = ren = 0;
9392:   if (ccomm != MPI_COMM_NULL) {
9393:     PetscLayoutCreate(ccomm,&rmap);
9394:     PetscLayoutSetSize(rmap,A->rmap->N);
9395:     PetscLayoutSetBlockSize(rmap,1);
9396:     PetscLayoutSetUp(rmap);
9397:     PetscLayoutGetRange(rmap,&rst,&ren);
9398:   }
9399:   ISCreateStride(PetscObjectComm((PetscObject)A),ren-rst,rst,1,&rows);
9400:   MatCreateSubMatrix(A,rows,NULL,MAT_INITIAL_MATRIX,&At);
9401:   ISDestroy(&rows);

9403:   if (ccomm != MPI_COMM_NULL) {
9404:     Mat_MPIAIJ *a,*b;
9405:     IS         from,to;
9406:     Vec        gvec;
9407:     PetscInt   lsize;

9409:     MatCreate(ccomm,B);
9410:     MatSetSizes(*B,ren-rst,PETSC_DECIDE,PETSC_DECIDE,At->cmap->N);
9411:     MatSetType(*B,MATAIJ);
9412:     PetscLayoutDestroy(&((*B)->rmap));
9413:     PetscLayoutSetUp((*B)->cmap);
9414:     a    = (Mat_MPIAIJ*)At->data;
9415:     b    = (Mat_MPIAIJ*)(*B)->data;
9416:     MPI_Comm_size(ccomm,&b->size);
9417:     MPI_Comm_rank(ccomm,&b->rank);
9418:     PetscObjectReference((PetscObject)a->A);
9419:     PetscObjectReference((PetscObject)a->B);
9420:     b->A = a->A;
9421:     b->B = a->B;

9423:     b->donotstash      = a->donotstash;
9424:     b->roworiented     = a->roworiented;
9425:     b->rowindices      = NULL;
9426:     b->rowvalues       = NULL;
9427:     b->getrowactive    = PETSC_FALSE;

9429:     (*B)->rmap         = rmap;
9430:     (*B)->factortype   = A->factortype;
9431:     (*B)->assembled    = PETSC_TRUE;
9432:     (*B)->insertmode   = NOT_SET_VALUES;
9433:     (*B)->preallocated = PETSC_TRUE;

9435:     if (a->colmap) {
9436: #if defined(PETSC_USE_CTABLE)
9437:       PetscTableCreateCopy(a->colmap,&b->colmap);
9438: #else
9439:       PetscMalloc1(At->cmap->N,&b->colmap);
9440:       PetscLogObjectMemory((PetscObject)*B,At->cmap->N*sizeof(PetscInt));
9441:       PetscArraycpy(b->colmap,a->colmap,At->cmap->N);
9442: #endif
9443:     } else b->colmap = NULL;
9444:     if (a->garray) {
9445:       PetscInt len;
9446:       len  = a->B->cmap->n;
9447:       PetscMalloc1(len+1,&b->garray);
9448:       PetscLogObjectMemory((PetscObject)(*B),len*sizeof(PetscInt));
9449:       if (len) { PetscArraycpy(b->garray,a->garray,len); }
9450:     } else b->garray = NULL;

9452:     PetscObjectReference((PetscObject)a->lvec);
9453:     b->lvec = a->lvec;
9454:     PetscLogObjectParent((PetscObject)*B,(PetscObject)b->lvec);

9456:     /* cannot use VecScatterCopy */
9457:     VecGetLocalSize(b->lvec,&lsize);
9458:     ISCreateGeneral(ccomm,lsize,b->garray,PETSC_USE_POINTER,&from);
9459:     ISCreateStride(PETSC_COMM_SELF,lsize,0,1,&to);
9460:     MatCreateVecs(*B,&gvec,NULL);
9461:     VecScatterCreate(gvec,from,b->lvec,to,&b->Mvctx);
9462:     PetscLogObjectParent((PetscObject)*B,(PetscObject)b->Mvctx);
9463:     ISDestroy(&from);
9464:     ISDestroy(&to);
9465:     VecDestroy(&gvec);
9466:   }
9467:   MatDestroy(&At);
9468:   return(0);
9469: }