Actual source code: bddcprivate.c

petsc-3.12.0 2019-09-29
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  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: #if !defined(PETSC_USE_COMPLEX)
 18:   PetscScalar    *uwork,*data,*U, ds = 0.;
 19:   PetscReal      *sing;
 20:   PetscBLASInt   bM,bN,lwork,lierr,di = 1;
 21:   PetscInt       ulw,i,nr,nc,n;

 25: #if defined(PETSC_MISSING_LAPACK_GESVD)
 26:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"LAPACK _GESVD not available");
 27: #else
 28:   MatGetSize(A,&nr,&nc);
 29:   if (!nr || !nc) return(0);

 31:   /* workspace */
 32:   if (!work) {
 33:     ulw  = PetscMax(PetscMax(1,5*PetscMin(nr,nc)),3*PetscMin(nr,nc)+PetscMax(nr,nc));
 34:     PetscMalloc1(ulw,&uwork);
 35:   } else {
 36:     ulw   = lw;
 37:     uwork = work;
 38:   }
 39:   n = PetscMin(nr,nc);
 40:   if (!rwork) {
 41:     PetscMalloc1(n,&sing);
 42:   } else {
 43:     sing = rwork;
 44:   }

 46:   /* SVD */
 47:   PetscMalloc1(nr*nr,&U);
 48:   PetscBLASIntCast(nr,&bM);
 49:   PetscBLASIntCast(nc,&bN);
 50:   PetscBLASIntCast(ulw,&lwork);
 51:   MatDenseGetArray(A,&data);
 52:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
 53:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","N",&bM,&bN,data,&bM,sing,U,&bM,&ds,&di,uwork,&lwork,&lierr));
 54:   PetscFPTrapPop();
 55:   if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
 56:   MatDenseRestoreArray(A,&data);
 57:   for (i=0;i<n;i++) if (sing[i] < PETSC_SMALL) break;
 58:   if (!rwork) {
 59:     PetscFree(sing);
 60:   }
 61:   if (!work) {
 62:     PetscFree(uwork);
 63:   }
 64:   /* create B */
 65:   if (!range) {
 66:     MatCreateSeqDense(PETSC_COMM_SELF,nr,nr-i,NULL,B);
 67:     MatDenseGetArray(*B,&data);
 68:     PetscArraycpy(data,U+nr*i,(nr-i)*nr);
 69:   } else {
 70:     MatCreateSeqDense(PETSC_COMM_SELF,nr,i,NULL,B);
 71:     MatDenseGetArray(*B,&data);
 72:     PetscArraycpy(data,U,i*nr);
 73:   }
 74:   MatDenseRestoreArray(*B,&data);
 75:   PetscFree(U);
 76: #endif
 77: #else /* PETSC_USE_COMPLEX */
 79:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for complexes");
 80: #endif
 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: #if defined(PETSC_USE_DEBUG)
179:   PetscInt               *emarks;
180: #endif
181:   PetscBool              print,eerr,done,lrc[2],conforming,global,singular,setprimal;
182:   PetscErrorCode         ierr;

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

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

205:   /* Return if there are no edges in the decomposition and the problem is not singular */
206:   MatGetLocalToGlobalMapping(pc->pmat,&al2g,NULL);
207:   ISLocalToGlobalMappingGetSize(al2g,&n);
208:   PetscObjectGetComm((PetscObject)pc,&comm);
209:   if (!singular) {
210:     VecGetArrayRead(matis->counter,(const PetscScalar**)&vals);
211:     lrc[0] = PETSC_FALSE;
212:     for (i=0;i<n;i++) {
213:       if (PetscRealPart(vals[i]) > 2.) {
214:         lrc[0] = PETSC_TRUE;
215:         break;
216:       }
217:     }
218:     VecRestoreArrayRead(matis->counter,(const PetscScalar**)&vals);
219:     MPIU_Allreduce(&lrc[0],&lrc[1],1,MPIU_BOOL,MPI_LOR,comm);
220:     if (!lrc[1]) return(0);
221:   }

223:   /* Get Nedelec field */
224:   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);
225:   if (pcbddc->n_ISForDofsLocal && field >= 0) {
226:     PetscObjectReference((PetscObject)pcbddc->ISForDofsLocal[field]);
227:     nedfieldlocal = pcbddc->ISForDofsLocal[field];
228:     ISGetLocalSize(nedfieldlocal,&ne);
229:   } else if (!pcbddc->n_ISForDofsLocal && field != PETSC_DECIDE) {
230:     ne            = n;
231:     nedfieldlocal = NULL;
232:     global        = PETSC_TRUE;
233:   } else if (field == PETSC_DECIDE) {
234:     PetscInt rst,ren,*idx;

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

242:       MatGetRow(pcbddc->discretegradient,i,&nc,NULL,NULL);
243:       if (nc > 1) matis->sf_rootdata[i-rst] = 1;
244:       MatRestoreRow(pcbddc->discretegradient,i,&nc,NULL,NULL);
245:     }
246:     PetscSFBcastBegin(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata);
247:     PetscSFBcastEnd(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata);
248:     PetscMalloc1(n,&idx);
249:     for (i=0,ne=0;i<n;i++) if (matis->sf_leafdata[i]) idx[ne++] = i;
250:     ISCreateGeneral(comm,ne,idx,PETSC_OWN_POINTER,&nedfieldlocal);
251:   } else {
252:     SETERRQ(comm,PETSC_ERR_USER,"When multiple fields are present, the Nedelec field has to be specified");
253:   }

255:   /* Sanity checks */
256:   if (!order && !conforming) SETERRQ(comm,PETSC_ERR_SUP,"Variable order and non-conforming spaces are not supported at the same time");
257:   if (pcbddc->user_ChangeOfBasisMatrix) SETERRQ(comm,PETSC_ERR_SUP,"Cannot generate Nedelec support with user defined change of basis");
258:   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);

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

265:     PetscMalloc1(ne,&eidxs);
266:     VecGetArrayRead(matis->counter,(const PetscScalar**)&vals);
267:     if (nedfieldlocal) {
268:       ISGetIndices(nedfieldlocal,&idxs);
269:       for (i=0,cum=0;i<ne;i++) {
270:         if (PetscRealPart(vals[idxs[i]]) > 2.) {
271:           eidxs[cum++] = idxs[i];
272:         }
273:       }
274:       ISRestoreIndices(nedfieldlocal,&idxs);
275:     } else {
276:       for (i=0,cum=0;i<ne;i++) {
277:         if (PetscRealPart(vals[i]) > 2.) {
278:           eidxs[cum++] = i;
279:         }
280:       }
281:     }
282:     VecRestoreArrayRead(matis->counter,(const PetscScalar**)&vals);
283:     ISCreateGeneral(comm,cum,eidxs,PETSC_COPY_VALUES,&enedfieldlocal);
284:     PCBDDCSetPrimalVerticesLocalIS(pc,enedfieldlocal);
285:     PetscFree(eidxs);
286:     ISDestroy(&nedfieldlocal);
287:     ISDestroy(&enedfieldlocal);
288:     return(0);
289:   }

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

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

307:       ISRenumber(is,NULL,NULL,&gis);
308:       ISLocalToGlobalMappingCreateIS(gis,&el2g);
309:       ISDestroy(&gis);
310:     }
311:     ISDestroy(&is);
312:   } else {
313:     /* restore default */
314:     pcbddc->nedfield = -1;
315:     /* one ref for the destruction of al2g, one for el2g */
316:     PetscObjectReference((PetscObject)al2g);
317:     PetscObjectReference((PetscObject)al2g);
318:     el2g = al2g;
319:     fl2g = NULL;
320:   }

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

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

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

352:       PetscMalloc1(ne,&tbz);
353:       PetscSFBcastBegin(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata);
354:       PetscSFBcastEnd(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata);
355:       ISGetIndices(nedfieldlocal,&idxs);
356:       for (i=0,cum=0;i<ne;i++)
357:         if (matis->sf_leafdata[idxs[i]] == 1)
358:           tbz[cum++] = i;
359:       ISRestoreIndices(nedfieldlocal,&idxs);
360:       ISLocalToGlobalMappingApply(el2g,cum,tbz,tbz);
361:       MatZeroRows(G,cum,tbz,0.,NULL,NULL);
362:       PetscFree(tbz);
363:     }
364:   } else { /* we need the entire G to infer the nullspace */
365:     PetscObjectReference((PetscObject)pcbddc->discretegradient);
366:     G    = pcbddc->discretegradient;
367:   }

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

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

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

396:   if (print) {
397:     PetscObjectSetName((PetscObject)lG,"initial_lG");
398:     MatView(lG,NULL);
399:   }

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

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

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

438:     if (fl2g) {
439:       ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_MASK,pcbddc->NeumannBoundariesLocal,&is);
440:     } else {
441:       is = pcbddc->NeumannBoundariesLocal;
442:     }
443:     ISGetLocalSize(is,&cum);
444:     ISGetIndices(is,&idxs);
445:     for (i=0;i<cum;i++) {
446:       if (idxs[i] >= 0) {
447:         PetscBTSet(btb,idxs[i]);
448:       }
449:     }
450:     ISRestoreIndices(is,&idxs);
451:     if (fl2g) {
452:       ISDestroy(&is);
453:     }
454:   }

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

460:   /* need to remove coarse faces' dofs and coarse edges' dirichlet dofs
461:      for proper detection of coarse edges' endpoints */
462:   PetscBTCreate(ne,&btee);
463:   for (i=0;i<ne;i++) {
464:     if ((ecount[i] > 2 && !PetscBTLookup(btbd,i)) || (ecount[i] == 2 && PetscBTLookup(btb,i))) {
465:       PetscBTSet(btee,i);
466:     }
467:   }
468:   PetscMalloc1(ne,&marks);
469:   if (!conforming) {
470:     MatTranspose(lGe,MAT_INITIAL_MATRIX,&lGt);
471:     MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
472:   }
473:   MatGetRowIJ(lGe,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
474:   MatSeqAIJGetArray(lGe,&vals);
475:   cum  = 0;
476:   for (i=0;i<ne;i++) {
477:     /* eliminate rows corresponding to edge dofs belonging to coarse faces */
478:     if (!PetscBTLookup(btee,i)) {
479:       marks[cum++] = i;
480:       continue;
481:     }
482:     /* set badly connected edge dofs as primal */
483:     if (!conforming) {
484:       if (ii[i+1]-ii[i] != order + 1) { /* every row of G on the coarse edge should list order+1 nodal dofs */
485:         marks[cum++] = i;
486:         PetscBTSet(bte,i);
487:         for (j=ii[i];j<ii[i+1];j++) {
488:           PetscBTSet(btv,jj[j]);
489:         }
490:       } else {
491:         /* every edge dofs should be connected trough a certain number of nodal dofs
492:            to other edge dofs belonging to coarse edges
493:            - at most 2 endpoints
494:            - order-1 interior nodal dofs
495:            - no undefined nodal dofs (nconn < order)
496:         */
497:         PetscInt ends = 0,ints = 0, undef = 0;
498:         for (j=ii[i];j<ii[i+1];j++) {
499:           PetscInt v = jj[j],k;
500:           PetscInt nconn = iit[v+1]-iit[v];
501:           for (k=iit[v];k<iit[v+1];k++) if (!PetscBTLookup(btee,jjt[k])) nconn--;
502:           if (nconn > order) ends++;
503:           else if (nconn == order) ints++;
504:           else undef++;
505:         }
506:         if (undef || ends > 2 || ints != order -1) {
507:           marks[cum++] = i;
508:           PetscBTSet(bte,i);
509:           for (j=ii[i];j<ii[i+1];j++) {
510:             PetscBTSet(btv,jj[j]);
511:           }
512:         }
513:       }
514:     }
515:     /* We assume the order on the element edge is ii[i+1]-ii[i]-1 */
516:     if (!order && ii[i+1] != ii[i]) {
517:       PetscScalar val = 1./(ii[i+1]-ii[i]-1);
518:       for (j=ii[i];j<ii[i+1];j++) vals[j] = val;
519:     }
520:   }
521:   PetscBTDestroy(&btee);
522:   MatSeqAIJRestoreArray(lGe,&vals);
523:   MatRestoreRowIJ(lGe,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
524:   if (!conforming) {
525:     MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
526:     MatDestroy(&lGt);
527:   }
528:   MatZeroRows(lGe,cum,marks,0.,NULL,NULL);

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

546:       for (j=ii[i];j<ii[i+1];j++) vorder += PetscRealPart(vals[j]);
547:       test = PetscFloorReal(vorder+10.*PETSC_SQRT_MACHINE_EPSILON);
548:       if (vorder-test > PETSC_SQRT_MACHINE_EPSILON) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected value for vorder: %g (%D)",vorder,test);
549:       ord  = 1;
550:     }
551: #if defined(PETSC_USE_DEBUG)
552:     if (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);
553: #endif
554:     for (j=ii[i];j<ii[i+1] && sneighs;j++) {
555:       if (PetscBTLookup(btbd,jj[j])) {
556:         bdir = PETSC_TRUE;
557:         break;
558:       }
559:       if (vc != ecount[jj[j]]) {
560:         sneighs = PETSC_FALSE;
561:       } else {
562:         PetscInt k,*vn = vneighs[i], *en = eneighs[jj[j]];
563:         for (k=0;k<vc;k++) {
564:           if (vn[k] != en[k]) {
565:             sneighs = PETSC_FALSE;
566:             break;
567:           }
568:         }
569:       }
570:     }
571:     if (!sneighs || test >= 3*ord || bdir) { /* splitpoints */
572:       if (print) PetscPrintf(PETSC_COMM_SELF,"SPLITPOINT %D (%D %D %D)\n",i,!sneighs,test >= 3*ord,bdir);
573:       PetscBTSet(btv,i);
574:     } else if (test == ord) {
575:       if (order == 1 || (!order && ii[i+1]-ii[i] == 1)) {
576:         if (print) PetscPrintf(PETSC_COMM_SELF,"ENDPOINT %D\n",i);
577:         PetscBTSet(btv,i);
578:       } else {
579:         if (print) PetscPrintf(PETSC_COMM_SELF,"CORNER CANDIDATE %D\n",i);
580:         PetscBTSet(btvcand,i);
581:       }
582:     }
583:   }
584:   ISLocalToGlobalMappingRestoreNodeInfo(el2g,NULL,&ecount,&eneighs);
585:   ISLocalToGlobalMappingRestoreNodeInfo(vl2g,NULL,&vcount,&vneighs);
586:   PetscBTDestroy(&btbd);

588:   /* a candidate is valid if it is connected to another candidate via a non-primal edge dof */
589:   if (order != 1) {
590:     if (print) PetscPrintf(PETSC_COMM_SELF,"INSPECTING CANDIDATES\n");
591:     MatGetRowIJ(lGe,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
592:     for (i=0;i<nv;i++) {
593:       if (PetscBTLookup(btvcand,i)) {
594:         PetscBool found = PETSC_FALSE;
595:         for (j=ii[i];j<ii[i+1] && !found;j++) {
596:           PetscInt k,e = jj[j];
597:           if (PetscBTLookup(bte,e)) continue;
598:           for (k=iit[e];k<iit[e+1];k++) {
599:             PetscInt v = jjt[k];
600:             if (v != i && PetscBTLookup(btvcand,v)) {
601:               found = PETSC_TRUE;
602:               break;
603:             }
604:           }
605:         }
606:         if (!found) {
607:           if (print) PetscPrintf(PETSC_COMM_SELF,"  CANDIDATE %D CLEARED\n",i);
608:           PetscBTClear(btvcand,i);
609:         } else {
610:           if (print) PetscPrintf(PETSC_COMM_SELF,"  CANDIDATE %D ACCEPTED\n",i);
611:         }
612:       }
613:     }
614:     MatRestoreRowIJ(lGe,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
615:   }
616:   MatSeqAIJRestoreArray(lGt,&vals);
617:   MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
618:   MatDestroy(&lGe);

620:   /* Get the local G^T explicitly */
621:   MatDestroy(&lGt);
622:   MatTranspose(lG,MAT_INITIAL_MATRIX,&lGt);
623:   MatSetOption(lGt,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);

625:   /* Mark interior nodal dofs */
626:   ISLocalToGlobalMappingGetInfo(vl2g,&n_neigh,&neigh,&n_shared,&shared);
627:   PetscBTCreate(nv,&btvi);
628:   for (i=1;i<n_neigh;i++) {
629:     for (j=0;j<n_shared[i];j++) {
630:       PetscBTSet(btvi,shared[i][j]);
631:     }
632:   }
633:   ISLocalToGlobalMappingRestoreInfo(vl2g,&n_neigh,&neigh,&n_shared,&shared);

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

641:   if (print) {
642:     IS tbz;

644:     cum = 0;
645:     for (i=0;i<nv;i++)
646:       if (sfvleaves[i])
647:         vmarks[cum++] = i;

649:     ISCreateGeneral(PETSC_COMM_SELF,cum,vmarks,PETSC_COPY_VALUES,&tbz);
650:     PetscObjectSetName((PetscObject)tbz,"corners_to_be_zeroed_local");
651:     ISView(tbz,NULL);
652:     ISDestroy(&tbz);
653:   }

655:   PetscSFReduceBegin(sfv,MPIU_INT,sfvleaves,sfvroots,MPI_SUM);
656:   PetscSFReduceEnd(sfv,MPIU_INT,sfvleaves,sfvroots,MPI_SUM);
657:   PetscSFBcastBegin(sfv,MPIU_INT,sfvroots,sfvleaves);
658:   PetscSFBcastEnd(sfv,MPIU_INT,sfvroots,sfvleaves);

660:   /* Zero rows of lGt corresponding to identified corners
661:      and interior nodal dofs */
662:   cum = 0;
663:   for (i=0;i<nv;i++) {
664:     if (sfvleaves[i]) {
665:       vmarks[cum++] = i;
666:       PetscBTSet(btv,i);
667:     }
668:     if (!PetscBTLookup(btvi,i)) vmarks[cum++] = i;
669:   }
670:   PetscBTDestroy(&btvi);
671:   if (print) {
672:     IS tbz;

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

684:   /* Recompute G */
685:   MatDestroy(&lG);
686:   MatTranspose(lGt,MAT_INITIAL_MATRIX,&lG);
687:   if (print) {
688:     PetscObjectSetName((PetscObject)lG,"used_lG");
689:     MatView(lG,NULL);
690:     PetscObjectSetName((PetscObject)lGt,"used_lGt");
691:     MatView(lGt,NULL);
692:   }

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

712:   /* Compute edge connectivity */
713:   PetscObjectSetOptionsPrefix((PetscObject)lG,"econn_");
714:   MatMatMultSymbolic(lG,lGt,PETSC_DEFAULT,&conn);
715:   MatGetRowIJ(conn,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
716:   if (fl2g) {
717:     PetscBT   btf;
718:     PetscInt  *iia,*jja,*iiu,*jju;
719:     PetscBool rest = PETSC_FALSE,free = PETSC_FALSE;

721:     /* create CSR for all local dofs */
722:     PetscMalloc1(n+1,&iia);
723:     if (pcbddc->mat_graph->nvtxs_csr) { /* the user has passed in a CSR graph */
724:       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);
725:       iiu = pcbddc->mat_graph->xadj;
726:       jju = pcbddc->mat_graph->adjncy;
727:     } else if (pcbddc->use_local_adj) {
728:       rest = PETSC_TRUE;
729:       MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&i,(const PetscInt**)&iiu,(const PetscInt**)&jju,&done);
730:     } else {
731:       free   = PETSC_TRUE;
732:       PetscMalloc2(n+1,&iiu,n,&jju);
733:       iiu[0] = 0;
734:       for (i=0;i<n;i++) {
735:         iiu[i+1] = i+1;
736:         jju[i]   = -1;
737:       }
738:     }

740:     /* import sizes of CSR */
741:     iia[0] = 0;
742:     for (i=0;i<n;i++) iia[i+1] = iiu[i+1]-iiu[i];

744:     /* overwrite entries corresponding to the Nedelec field */
745:     PetscBTCreate(n,&btf);
746:     ISGetIndices(nedfieldlocal,&idxs);
747:     for (i=0;i<ne;i++) {
748:       PetscBTSet(btf,idxs[i]);
749:       iia[idxs[i]+1] = ii[i+1]-ii[i];
750:     }

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

755:     /* jja in CSR */
756:     PetscMalloc1(iia[n],&jja);
757:     for (i=0;i<n;i++)
758:       if (!PetscBTLookup(btf,i))
759:         for (j=0;j<iiu[i+1]-iiu[i];j++)
760:           jja[iia[i]+j] = jju[iiu[i]+j];

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

783:   /* Analyze interface for edge dofs */
784:   PCBDDCAnalyzeInterface(pc);
785:   pcbddc->mat_graph->twodim = PETSC_FALSE;

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

791:   if (fl2g) {
792:     ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_DROP,allprimals,&primals);
793:     PetscMalloc1(nee,&eedges);
794:     for (i=0;i<nee;i++) {
795:       ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_DROP,alleedges[i],&eedges[i]);
796:     }
797:   } else {
798:     eedges  = alleedges;
799:     primals = allprimals;
800:   }

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

813:   maxsize = 0;
814:   for (i=0;i<nee;i++) {
815:     PetscInt size,mark = i+1;

817:     ISGetLocalSize(eedges[i],&size);
818:     ISGetIndices(eedges[i],&idxs);
819:     for (j=0;j<size;j++) marks[idxs[j]] = mark;
820:     ISRestoreIndices(eedges[i],&idxs);
821:     maxsize = PetscMax(maxsize,size);
822:   }

824:   /* Find coarse edge endpoints */
825:   MatGetRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
826:   MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&iit,&jjt,&done);
827:   for (i=0;i<nee;i++) {
828:     PetscInt mark = i+1,size;

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

872:   /* Reset marked primal dofs */
873:   ISGetLocalSize(primals,&cum);
874:   ISGetIndices(primals,&idxs);
875:   for (i=0;i<cum;i++) marks[idxs[i]] = 0;
876:   ISRestoreIndices(primals,&idxs);

878:   /* Now use the initial lG */
879:   MatDestroy(&lG);
880:   MatDestroy(&lGt);
881:   lG   = lGinit;
882:   MatTranspose(lG,MAT_INITIAL_MATRIX,&lGt);

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

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

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

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

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

1030:     /* Mark again */
1031:     PetscArrayzero(marks,ne);
1032:     for (i=0;i<nee;i++) {
1033:       PetscInt size,mark = i+1;

1035:       ISGetLocalSize(eedges[i],&size);
1036:       ISGetIndices(eedges[i],&idxs);
1037:       for (j=0;j<size;j++) marks[idxs[j]] = mark;
1038:       ISRestoreIndices(eedges[i],&idxs);
1039:     }
1040:     if (print) {
1041:       PetscObjectSetName((PetscObject)primals,"obtained_primal_dofs_secondpass");
1042:       ISView(primals,NULL);
1043:     }

1045:     /* Recompute extended cols */
1046:     eerr = PETSC_FALSE;
1047:     for (i=0;i<nee;i++) {
1048:       PetscInt size;

1050:       cum  = 0;
1051:       ISGetLocalSize(eedges[i],&size);
1052:       if (!size && nedfieldlocal) continue;
1053:       if (!size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected zero sized edge %D",i);
1054:       ISGetIndices(eedges[i],&idxs);
1055:       for (j=0;j<size;j++) {
1056:         PetscInt k,ee = idxs[j];
1057:         for (k=ii[ee];k<ii[ee+1];k++) if (!PetscBTLookup(btv,jj[k])) extrow[cum++] = jj[k];
1058:       }
1059:       ISRestoreIndices(eedges[i],&idxs);
1060:       PetscSortRemoveDupsInt(&cum,extrow);
1061:       ISLocalToGlobalMappingApply(vl2g,cum,extrow,gidxs);
1062:       PetscSortIntWithArray(cum,gidxs,extrow);
1063:       ISCreateGeneral(PETSC_COMM_SELF,cum,extrow,PETSC_COPY_VALUES,&extcols[i]);
1064:       if (cum != size -1) {
1065:         if (print) {
1066:           PetscObjectSetName((PetscObject)eedges[i],"error_edge_secondpass");
1067:           ISView(eedges[i],NULL);
1068:           PetscObjectSetName((PetscObject)extcols[i],"error_extcol_secondpass");
1069:           ISView(extcols[i],NULL);
1070:         }
1071:         eerr = PETSC_TRUE;
1072:       }
1073:     }
1074:   }
1075:   MatRestoreRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1076:   PetscFree2(extrow,gidxs);
1077:   PetscBTDestroy(&bter);
1078:   if (print) { PCBDDCGraphASCIIView(pcbddc->mat_graph,5,PETSC_VIEWER_STDOUT_SELF); }
1079:   /* an error should not occur at this point */
1080:   if (eerr) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected SIZE OF EDGE > EXTCOL SECOND PASS");

1082:   /* Check the number of endpoints */
1083:   MatGetRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1084:   PetscMalloc1(2*nee,&corners);
1085:   PetscMalloc1(nee,&cedges);
1086:   for (i=0;i<nee;i++) {
1087:     PetscInt size, found = 0, gc[2];

1089:     /* init with defaults */
1090:     cedges[i] = corners[i*2] = corners[i*2+1] = -1;
1091:     ISGetLocalSize(eedges[i],&size);
1092:     if (!size && nedfieldlocal) continue;
1093:     if (!size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected zero sized edge %D",i);
1094:     ISGetIndices(eedges[i],&idxs);
1095:     PetscBTMemzero(nv,btvc);
1096:     for (j=0;j<size;j++) {
1097:       PetscInt k,ee = idxs[j];
1098:       for (k=ii[ee];k<ii[ee+1];k++) {
1099:         PetscInt vv = jj[k];
1100:         if (PetscBTLookup(btv,vv) && !PetscBTLookupSet(btvc,vv)) {
1101:           if (found == 2) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Found more then two corners for edge %D",i);
1102:           corners[i*2+found++] = vv;
1103:         }
1104:       }
1105:     }
1106:     if (found != 2) {
1107:       PetscInt e;
1108:       if (fl2g) {
1109:         ISLocalToGlobalMappingApply(fl2g,1,idxs,&e);
1110:       } else {
1111:         e = idxs[0];
1112:       }
1113:       SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Found %D corners for edge %D (astart %D, estart %D)",found,i,e,idxs[0]);
1114:     }

1116:     /* get primal dof index on this coarse edge */
1117:     ISLocalToGlobalMappingApply(vl2g,2,corners+2*i,gc);
1118:     if (gc[0] > gc[1]) {
1119:       PetscInt swap  = corners[2*i];
1120:       corners[2*i]   = corners[2*i+1];
1121:       corners[2*i+1] = swap;
1122:     }
1123:     cedges[i] = idxs[size-1];
1124:     ISRestoreIndices(eedges[i],&idxs);
1125:     if (print) PetscPrintf(PETSC_COMM_SELF,"EDGE %D: ce %D, corners (%D,%D)\n",i,cedges[i],corners[2*i],corners[2*i+1]);
1126:   }
1127:   MatRestoreRowIJ(lG,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1128:   PetscBTDestroy(&btvc);

1130: #if defined(PETSC_USE_DEBUG)
1131:   /* Inspects columns of lG (rows of lGt) and make sure the change of basis will
1132:      not interfere with neighbouring coarse edges */
1133:   PetscMalloc1(nee+1,&emarks);
1134:   MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1135:   for (i=0;i<nv;i++) {
1136:     PetscInt emax = 0,eemax = 0;

1138:     if (ii[i+1]==ii[i] || PetscBTLookup(btv,i)) continue;
1139:     PetscArrayzero(emarks,nee+1);
1140:     for (j=ii[i];j<ii[i+1];j++) emarks[marks[jj[j]]]++;
1141:     for (j=1;j<nee+1;j++) {
1142:       if (emax < emarks[j]) {
1143:         emax = emarks[j];
1144:         eemax = j;
1145:       }
1146:     }
1147:     /* not relevant for edges */
1148:     if (!eemax) continue;

1150:     for (j=ii[i];j<ii[i+1];j++) {
1151:       if (marks[jj[j]] && marks[jj[j]] != eemax) {
1152:         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]);
1153:       }
1154:     }
1155:   }
1156:   PetscFree(emarks);
1157:   MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1158: #endif

1160:   /* Compute extended rows indices for edge blocks of the change of basis */
1161:   MatGetRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1162:   MatSeqAIJGetMaxRowNonzeros(lGt,&extmem);
1163:   extmem *= maxsize;
1164:   PetscMalloc1(extmem*nee,&extrow);
1165:   PetscMalloc1(nee,&extrows);
1166:   PetscCalloc1(nee,&extrowcum);
1167:   for (i=0;i<nv;i++) {
1168:     PetscInt mark = 0,size,start;

1170:     if (ii[i+1]==ii[i] || PetscBTLookup(btv,i)) continue;
1171:     for (j=ii[i];j<ii[i+1];j++)
1172:       if (marks[jj[j]] && !mark)
1173:         mark = marks[jj[j]];

1175:     /* not relevant */
1176:     if (!mark) continue;

1178:     /* import extended row */
1179:     mark--;
1180:     start = mark*extmem+extrowcum[mark];
1181:     size = ii[i+1]-ii[i];
1182:     if (extrowcum[mark] + size > extmem) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not enough memory allocated %D > %D",extrowcum[mark] + size,extmem);
1183:     PetscArraycpy(extrow+start,jj+ii[i],size);
1184:     extrowcum[mark] += size;
1185:   }
1186:   MatRestoreRowIJ(lGt,0,PETSC_FALSE,PETSC_FALSE,&i,&ii,&jj,&done);
1187:   MatDestroy(&lGt);
1188:   PetscFree(marks);

1190:   /* Compress extrows */
1191:   cum  = 0;
1192:   for (i=0;i<nee;i++) {
1193:     PetscInt size = extrowcum[i],*start = extrow + i*extmem;
1194:     PetscSortRemoveDupsInt(&size,start);
1195:     ISCreateGeneral(PETSC_COMM_SELF,size,start,PETSC_USE_POINTER,&extrows[i]);
1196:     cum  = PetscMax(cum,size);
1197:   }
1198:   PetscFree(extrowcum);
1199:   PetscBTDestroy(&btv);
1200:   PetscBTDestroy(&btvcand);

1202:   /* Workspace for lapack inner calls and VecSetValues */
1203:   PetscMalloc2((5+cum+maxsize)*maxsize,&work,maxsize,&rwork);

1205:   /* Create change of basis matrix (preallocation can be improved) */
1206:   MatCreate(comm,&T);
1207:   MatSetSizes(T,pc->pmat->rmap->n,pc->pmat->rmap->n,
1208:                        pc->pmat->rmap->N,pc->pmat->rmap->N);
1209:   MatSetType(T,MATAIJ);
1210:   MatSeqAIJSetPreallocation(T,10,NULL);
1211:   MatMPIAIJSetPreallocation(T,10,NULL,10,NULL);
1212:   MatSetLocalToGlobalMapping(T,al2g,al2g);
1213:   MatSetOption(T,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
1214:   MatSetOption(T,MAT_ROW_ORIENTED,PETSC_FALSE);
1215:   ISLocalToGlobalMappingDestroy(&al2g);

1217:   /* Defaults to identity */
1218:   MatCreateVecs(pc->pmat,&tvec,NULL);
1219:   VecSet(tvec,1.0);
1220:   MatDiagonalSet(T,tvec,INSERT_VALUES);
1221:   VecDestroy(&tvec);

1223:   /* Create discrete gradient for the coarser level if needed */
1224:   MatDestroy(&pcbddc->nedcG);
1225:   ISDestroy(&pcbddc->nedclocal);
1226:   if (pcbddc->current_level < pcbddc->max_levels) {
1227:     ISLocalToGlobalMapping cel2g,cvl2g;
1228:     IS                     wis,gwis;
1229:     PetscInt               cnv,cne;

1231:     ISCreateGeneral(comm,nee,cedges,PETSC_COPY_VALUES,&wis);
1232:     if (fl2g) {
1233:       ISLocalToGlobalMappingApplyIS(fl2g,wis,&pcbddc->nedclocal);
1234:     } else {
1235:       PetscObjectReference((PetscObject)wis);
1236:       pcbddc->nedclocal = wis;
1237:     }
1238:     ISLocalToGlobalMappingApplyIS(el2g,wis,&gwis);
1239:     ISDestroy(&wis);
1240:     ISRenumber(gwis,NULL,&cne,&wis);
1241:     ISLocalToGlobalMappingCreateIS(wis,&cel2g);
1242:     ISDestroy(&wis);
1243:     ISDestroy(&gwis);

1245:     ISCreateGeneral(comm,2*nee,corners,PETSC_USE_POINTER,&wis);
1246:     ISLocalToGlobalMappingApplyIS(vl2g,wis,&gwis);
1247:     ISDestroy(&wis);
1248:     ISRenumber(gwis,NULL,&cnv,&wis);
1249:     ISLocalToGlobalMappingCreateIS(wis,&cvl2g);
1250:     ISDestroy(&wis);
1251:     ISDestroy(&gwis);

1253:     MatCreate(comm,&pcbddc->nedcG);
1254:     MatSetSizes(pcbddc->nedcG,PETSC_DECIDE,PETSC_DECIDE,cne,cnv);
1255:     MatSetType(pcbddc->nedcG,MATAIJ);
1256:     MatSeqAIJSetPreallocation(pcbddc->nedcG,2,NULL);
1257:     MatMPIAIJSetPreallocation(pcbddc->nedcG,2,NULL,2,NULL);
1258:     MatSetLocalToGlobalMapping(pcbddc->nedcG,cel2g,cvl2g);
1259:     ISLocalToGlobalMappingDestroy(&cel2g);
1260:     ISLocalToGlobalMappingDestroy(&cvl2g);
1261:   }
1262:   ISLocalToGlobalMappingDestroy(&vl2g);

1264: #if defined(PRINT_GDET)
1265:   inc = 0;
1266:   lev = pcbddc->current_level;
1267: #endif

1269:   /* Insert values in the change of basis matrix */
1270:   for (i=0;i<nee;i++) {
1271:     Mat         Gins = NULL, GKins = NULL;
1272:     IS          cornersis = NULL;
1273:     PetscScalar cvals[2];

1275:     if (pcbddc->nedcG) {
1276:       ISCreateGeneral(PETSC_COMM_SELF,2,corners+2*i,PETSC_USE_POINTER,&cornersis);
1277:     }
1278:     PCBDDCComputeNedelecChangeEdge(lG,eedges[i],extrows[i],extcols[i],cornersis,&Gins,&GKins,cvals,work,rwork);
1279:     if (Gins && GKins) {
1280:       const PetscScalar *data;
1281:       const PetscInt    *rows,*cols;
1282:       PetscInt          nrh,nch,nrc,ncc;

1284:       ISGetIndices(eedges[i],&cols);
1285:       /* H1 */
1286:       ISGetIndices(extrows[i],&rows);
1287:       MatGetSize(Gins,&nrh,&nch);
1288:       MatDenseGetArrayRead(Gins,&data);
1289:       MatSetValuesLocal(T,nrh,rows,nch,cols,data,INSERT_VALUES);
1290:       MatDenseRestoreArrayRead(Gins,&data);
1291:       ISRestoreIndices(extrows[i],&rows);
1292:       /* complement */
1293:       MatGetSize(GKins,&nrc,&ncc);
1294:       if (!ncc) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Constant function has not been generated for coarse edge %D",i);
1295:       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);
1296:       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);
1297:       MatDenseGetArrayRead(GKins,&data);
1298:       MatSetValuesLocal(T,nrc,cols,ncc,cols+nch,data,INSERT_VALUES);
1299:       MatDenseRestoreArrayRead(GKins,&data);

1301:       /* coarse discrete gradient */
1302:       if (pcbddc->nedcG) {
1303:         PetscInt cols[2];

1305:         cols[0] = 2*i;
1306:         cols[1] = 2*i+1;
1307:         MatSetValuesLocal(pcbddc->nedcG,1,&i,2,cols,cvals,INSERT_VALUES);
1308:       }
1309:       ISRestoreIndices(eedges[i],&cols);
1310:     }
1311:     ISDestroy(&extrows[i]);
1312:     ISDestroy(&extcols[i]);
1313:     ISDestroy(&cornersis);
1314:     MatDestroy(&Gins);
1315:     MatDestroy(&GKins);
1316:   }
1317:   ISLocalToGlobalMappingDestroy(&el2g);

1319:   /* Start assembling */
1320:   MatAssemblyBegin(T,MAT_FINAL_ASSEMBLY);
1321:   if (pcbddc->nedcG) {
1322:     MatAssemblyBegin(pcbddc->nedcG,MAT_FINAL_ASSEMBLY);
1323:   }

1325:   /* Free */
1326:   if (fl2g) {
1327:     ISDestroy(&primals);
1328:     for (i=0;i<nee;i++) {
1329:       ISDestroy(&eedges[i]);
1330:     }
1331:     PetscFree(eedges);
1332:   }

1334:   /* hack mat_graph with primal dofs on the coarse edges */
1335:   {
1336:     PCBDDCGraph graph   = pcbddc->mat_graph;
1337:     PetscInt    *oqueue = graph->queue;
1338:     PetscInt    *ocptr  = graph->cptr;
1339:     PetscInt    ncc,*idxs;

1341:     /* find first primal edge */
1342:     if (pcbddc->nedclocal) {
1343:       ISGetIndices(pcbddc->nedclocal,(const PetscInt**)&idxs);
1344:     } else {
1345:       if (fl2g) {
1346:         ISLocalToGlobalMappingApply(fl2g,nee,cedges,cedges);
1347:       }
1348:       idxs = cedges;
1349:     }
1350:     cum = 0;
1351:     while (cum < nee && cedges[cum] < 0) cum++;

1353:     /* adapt connected components */
1354:     PetscMalloc2(graph->nvtxs+1,&graph->cptr,ocptr[graph->ncc],&graph->queue);
1355:     graph->cptr[0] = 0;
1356:     for (i=0,ncc=0;i<graph->ncc;i++) {
1357:       PetscInt lc = ocptr[i+1]-ocptr[i];
1358:       if (cum != nee && oqueue[ocptr[i+1]-1] == cedges[cum]) { /* this cc has a primal dof */
1359:         graph->cptr[ncc+1] = graph->cptr[ncc]+1;
1360:         graph->queue[graph->cptr[ncc]] = cedges[cum];
1361:         ncc++;
1362:         lc--;
1363:         cum++;
1364:         while (cum < nee && cedges[cum] < 0) cum++;
1365:       }
1366:       graph->cptr[ncc+1] = graph->cptr[ncc] + lc;
1367:       for (j=0;j<lc;j++) graph->queue[graph->cptr[ncc]+j] = oqueue[ocptr[i]+j];
1368:       ncc++;
1369:     }
1370:     graph->ncc = ncc;
1371:     if (pcbddc->nedclocal) {
1372:       ISRestoreIndices(pcbddc->nedclocal,(const PetscInt**)&idxs);
1373:     }
1374:     PetscFree2(ocptr,oqueue);
1375:   }
1376:   ISLocalToGlobalMappingDestroy(&fl2g);
1377:   PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,&nee,&alleedges,&allprimals);
1378:   PCBDDCGraphResetCSR(pcbddc->mat_graph);
1379:   MatDestroy(&conn);

1381:   ISDestroy(&nedfieldlocal);
1382:   PetscFree(extrow);
1383:   PetscFree2(work,rwork);
1384:   PetscFree(corners);
1385:   PetscFree(cedges);
1386:   PetscFree(extrows);
1387:   PetscFree(extcols);
1388:   MatDestroy(&lG);

1390:   /* Complete assembling */
1391:   MatAssemblyEnd(T,MAT_FINAL_ASSEMBLY);
1392:   if (pcbddc->nedcG) {
1393:     MatAssemblyEnd(pcbddc->nedcG,MAT_FINAL_ASSEMBLY);
1394: #if 0
1395:     PetscObjectSetName((PetscObject)pcbddc->nedcG,"coarse_G");
1396:     MatView(pcbddc->nedcG,NULL);
1397: #endif
1398:   }

1400:   /* set change of basis */
1401:   PCBDDCSetChangeOfBasisMat(pc,T,singular);
1402:   MatDestroy(&T);

1404:   return(0);
1405: }

1407: /* the near-null space of BDDC carries information on quadrature weights,
1408:    and these can be collinear -> so cheat with MatNullSpaceCreate
1409:    and create a suitable set of basis vectors first */
1410: PetscErrorCode PCBDDCNullSpaceCreate(MPI_Comm comm, PetscBool has_const, PetscInt nvecs, Vec quad_vecs[], MatNullSpace *nnsp)
1411: {
1413:   PetscInt       i;

1416:   for (i=0;i<nvecs;i++) {
1417:     PetscInt first,last;

1419:     VecGetOwnershipRange(quad_vecs[i],&first,&last);
1420:     if (last-first < 2*nvecs && has_const) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented");
1421:     if (i>=first && i < last) {
1422:       PetscScalar *data;
1423:       VecGetArray(quad_vecs[i],&data);
1424:       if (!has_const) {
1425:         data[i-first] = 1.;
1426:       } else {
1427:         data[2*i-first] = 1./PetscSqrtReal(2.);
1428:         data[2*i-first+1] = -1./PetscSqrtReal(2.);
1429:       }
1430:       VecRestoreArray(quad_vecs[i],&data);
1431:     }
1432:     PetscObjectStateIncrease((PetscObject)quad_vecs[i]);
1433:   }
1434:   MatNullSpaceCreate(comm,has_const,nvecs,quad_vecs,nnsp);
1435:   for (i=0;i<nvecs;i++) { /* reset vectors */
1436:     PetscInt first,last;
1437:     VecLockReadPop(quad_vecs[i]);
1438:     VecGetOwnershipRange(quad_vecs[i],&first,&last);
1439:     if (i>=first && i < last) {
1440:       PetscScalar *data;
1441:       VecGetArray(quad_vecs[i],&data);
1442:       if (!has_const) {
1443:         data[i-first] = 0.;
1444:       } else {
1445:         data[2*i-first] = 0.;
1446:         data[2*i-first+1] = 0.;
1447:       }
1448:       VecRestoreArray(quad_vecs[i],&data);
1449:     }
1450:     PetscObjectStateIncrease((PetscObject)quad_vecs[i]);
1451:     VecLockReadPush(quad_vecs[i]);
1452:   }
1453:   return(0);
1454: }

1456: PetscErrorCode PCBDDCComputeNoNetFlux(Mat A, Mat divudotp, PetscBool transpose, IS vl2l, PCBDDCGraph graph, MatNullSpace *nnsp)
1457: {
1458:   Mat                    loc_divudotp;
1459:   Vec                    p,v,vins,quad_vec,*quad_vecs;
1460:   ISLocalToGlobalMapping map;
1461:   PetscScalar            *vals;
1462:   const PetscScalar      *array;
1463:   PetscInt               i,maxneighs,maxsize,*gidxs;
1464:   PetscInt               n_neigh,*neigh,*n_shared,**shared;
1465:   PetscMPIInt            rank;
1466:   PetscErrorCode         ierr;

1469:   ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
1470:   MPIU_Allreduce(&n_neigh,&maxneighs,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)A));
1471:   if (!maxneighs) {
1472:     ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
1473:     *nnsp = NULL;
1474:     return(0);
1475:   }
1476:   maxsize = 0;
1477:   for (i=0;i<n_neigh;i++) maxsize = PetscMax(n_shared[i],maxsize);
1478:   PetscMalloc2(maxsize,&gidxs,maxsize,&vals);
1479:   /* create vectors to hold quadrature weights */
1480:   MatCreateVecs(A,&quad_vec,NULL);
1481:   if (!transpose) {
1482:     MatGetLocalToGlobalMapping(A,&map,NULL);
1483:   } else {
1484:     MatGetLocalToGlobalMapping(A,NULL,&map);
1485:   }
1486:   VecDuplicateVecs(quad_vec,maxneighs,&quad_vecs);
1487:   VecDestroy(&quad_vec);
1488:   PCBDDCNullSpaceCreate(PetscObjectComm((PetscObject)A),PETSC_FALSE,maxneighs,quad_vecs,nnsp);
1489:   for (i=0;i<maxneighs;i++) {
1490:     VecLockReadPop(quad_vecs[i]);
1491:   }

1493:   /* compute local quad vec */
1494:   MatISGetLocalMat(divudotp,&loc_divudotp);
1495:   if (!transpose) {
1496:     MatCreateVecs(loc_divudotp,&v,&p);
1497:   } else {
1498:     MatCreateVecs(loc_divudotp,&p,&v);
1499:   }
1500:   VecSet(p,1.);
1501:   if (!transpose) {
1502:     MatMultTranspose(loc_divudotp,p,v);
1503:   } else {
1504:     MatMult(loc_divudotp,p,v);
1505:   }
1506:   if (vl2l) {
1507:     Mat        lA;
1508:     VecScatter sc;

1510:     MatISGetLocalMat(A,&lA);
1511:     MatCreateVecs(lA,&vins,NULL);
1512:     VecScatterCreate(v,NULL,vins,vl2l,&sc);
1513:     VecScatterBegin(sc,v,vins,INSERT_VALUES,SCATTER_FORWARD);
1514:     VecScatterEnd(sc,v,vins,INSERT_VALUES,SCATTER_FORWARD);
1515:     VecScatterDestroy(&sc);
1516:   } else {
1517:     vins = v;
1518:   }
1519:   VecGetArrayRead(vins,&array);
1520:   VecDestroy(&p);

1522:   /* insert in global quadrature vecs */
1523:   MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);
1524:   for (i=0;i<n_neigh;i++) {
1525:     const PetscInt    *idxs;
1526:     PetscInt          idx,nn,j;

1528:     idxs = shared[i];
1529:     nn   = n_shared[i];
1530:     for (j=0;j<nn;j++) vals[j] = array[idxs[j]];
1531:     PetscFindInt(rank,graph->count[idxs[0]],graph->neighbours_set[idxs[0]],&idx);
1532:     idx  = -(idx+1);
1533:     ISLocalToGlobalMappingApply(map,nn,idxs,gidxs);
1534:     VecSetValues(quad_vecs[idx],nn,gidxs,vals,INSERT_VALUES);
1535:   }
1536:   ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
1537:   VecRestoreArrayRead(vins,&array);
1538:   if (vl2l) {
1539:     VecDestroy(&vins);
1540:   }
1541:   VecDestroy(&v);
1542:   PetscFree2(gidxs,vals);

1544:   /* assemble near null space */
1545:   for (i=0;i<maxneighs;i++) {
1546:     VecAssemblyBegin(quad_vecs[i]);
1547:   }
1548:   for (i=0;i<maxneighs;i++) {
1549:     VecAssemblyEnd(quad_vecs[i]);
1550:     VecViewFromOptions(quad_vecs[i],NULL,"-pc_bddc_quad_vecs_view");
1551:     VecLockReadPush(quad_vecs[i]);
1552:   }
1553:   VecDestroyVecs(maxneighs,&quad_vecs);
1554:   return(0);
1555: }

1557: PetscErrorCode PCBDDCAddPrimalVerticesLocalIS(PC pc, IS primalv)
1558: {
1559:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

1563:   if (primalv) {
1564:     if (pcbddc->user_primal_vertices_local) {
1565:       IS list[2], newp;

1567:       list[0] = primalv;
1568:       list[1] = pcbddc->user_primal_vertices_local;
1569:       ISConcatenate(PetscObjectComm((PetscObject)pc),2,list,&newp);
1570:       ISSortRemoveDups(newp);
1571:       ISDestroy(&list[1]);
1572:       pcbddc->user_primal_vertices_local = newp;
1573:     } else {
1574:       PCBDDCSetPrimalVerticesLocalIS(pc,primalv);
1575:     }
1576:   }
1577:   return(0);
1578: }

1580: static PetscErrorCode func_coords_private(PetscInt dim, PetscReal t, const PetscReal X[], PetscInt Nf, PetscScalar *out, void *ctx)
1581: {
1582:   PetscInt f, *comp  = (PetscInt *)ctx;

1585:   for (f=0;f<Nf;f++) out[f] = X[*comp];
1586:   return(0);
1587: }

1589: PetscErrorCode PCBDDCComputeLocalTopologyInfo(PC pc)
1590: {
1592:   Vec            local,global;
1593:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
1594:   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
1595:   PetscBool      monolithic = PETSC_FALSE;

1598:   PetscOptionsBegin(PetscObjectComm((PetscObject)pc),((PetscObject)pc)->prefix,"BDDC topology options","PC");
1599:   PetscOptionsBool("-pc_bddc_monolithic","Discard any information on dofs splitting",NULL,monolithic,&monolithic,NULL);
1600:   PetscOptionsEnd();
1601:   /* need to convert from global to local topology information and remove references to information in global ordering */
1602:   MatCreateVecs(pc->pmat,&global,NULL);
1603:   MatCreateVecs(matis->A,&local,NULL);
1604:   VecPinToCPU(global,PETSC_TRUE);
1605:   VecPinToCPU(local,PETSC_TRUE);
1606:   if (monolithic) { /* just get block size to properly compute vertices */
1607:     if (pcbddc->vertex_size == 1) {
1608:       MatGetBlockSize(pc->pmat,&pcbddc->vertex_size);
1609:     }
1610:     goto boundary;
1611:   }

1613:   if (pcbddc->user_provided_isfordofs) {
1614:     if (pcbddc->n_ISForDofs) {
1615:       PetscInt i;

1617:       PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);
1618:       for (i=0;i<pcbddc->n_ISForDofs;i++) {
1619:         PetscInt bs;

1621:         PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);
1622:         ISGetBlockSize(pcbddc->ISForDofs[i],&bs);
1623:         ISSetBlockSize(pcbddc->ISForDofsLocal[i],bs);
1624:         ISDestroy(&pcbddc->ISForDofs[i]);
1625:       }
1626:       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
1627:       pcbddc->n_ISForDofs = 0;
1628:       PetscFree(pcbddc->ISForDofs);
1629:     }
1630:   } else {
1631:     if (!pcbddc->n_ISForDofsLocal) { /* field split not present */
1632:       DM dm;

1634:       MatGetDM(pc->pmat, &dm);
1635:       if (!dm) {
1636:         PCGetDM(pc, &dm);
1637:       }
1638:       if (dm) {
1639:         IS      *fields;
1640:         PetscInt nf,i;

1642:         DMCreateFieldDecomposition(dm,&nf,NULL,&fields,NULL);
1643:         PetscMalloc1(nf,&pcbddc->ISForDofsLocal);
1644:         for (i=0;i<nf;i++) {
1645:           PetscInt bs;

1647:           PCBDDCGlobalToLocal(matis->rctx,global,local,fields[i],&pcbddc->ISForDofsLocal[i]);
1648:           ISGetBlockSize(fields[i],&bs);
1649:           ISSetBlockSize(pcbddc->ISForDofsLocal[i],bs);
1650:           ISDestroy(&fields[i]);
1651:         }
1652:         PetscFree(fields);
1653:         pcbddc->n_ISForDofsLocal = nf;
1654:       } else { /* See if MATIS has fields attached by the conversion from MatNest */
1655:         PetscContainer   c;

1657:         PetscObjectQuery((PetscObject)pc->pmat,"_convert_nest_lfields",(PetscObject*)&c);
1658:         if (c) {
1659:           MatISLocalFields lf;
1660:           PetscContainerGetPointer(c,(void**)&lf);
1661:           PCBDDCSetDofsSplittingLocal(pc,lf->nr,lf->rf);
1662:         } else { /* fallback, create the default fields if bs > 1 */
1663:           PetscInt i, n = matis->A->rmap->n;
1664:           MatGetBlockSize(pc->pmat,&i);
1665:           if (i > 1) {
1666:             pcbddc->n_ISForDofsLocal = i;
1667:             PetscMalloc1(pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal);
1668:             for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1669:               ISCreateStride(PetscObjectComm((PetscObject)pc),n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);
1670:             }
1671:           }
1672:         }
1673:       }
1674:     } else {
1675:       PetscInt i;
1676:       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
1677:         PCBDDCConsistencyCheckIS(pc,MPI_LAND,&pcbddc->ISForDofsLocal[i]);
1678:       }
1679:     }
1680:   }

1682: boundary:
1683:   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) {
1684:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);
1685:   } else if (pcbddc->DirichletBoundariesLocal) {
1686:     PCBDDCConsistencyCheckIS(pc,MPI_LAND,&pcbddc->DirichletBoundariesLocal);
1687:   }
1688:   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) {
1689:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);
1690:   } else if (pcbddc->NeumannBoundariesLocal) {
1691:     PCBDDCConsistencyCheckIS(pc,MPI_LOR,&pcbddc->NeumannBoundariesLocal);
1692:   }
1693:   if (!pcbddc->user_primal_vertices_local && pcbddc->user_primal_vertices) {
1694:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->user_primal_vertices,&pcbddc->user_primal_vertices_local);
1695:   }
1696:   VecDestroy(&global);
1697:   VecDestroy(&local);
1698:   /* detect local disconnected subdomains if requested (use matis->A) */
1699:   if (pcbddc->detect_disconnected) {
1700:     IS        primalv = NULL;
1701:     PetscInt  i;
1702:     PetscBool filter = pcbddc->detect_disconnected_filter;

1704:     for (i=0;i<pcbddc->n_local_subs;i++) {
1705:       ISDestroy(&pcbddc->local_subs[i]);
1706:     }
1707:     PetscFree(pcbddc->local_subs);
1708:     PCBDDCDetectDisconnectedComponents(pc,filter,&pcbddc->n_local_subs,&pcbddc->local_subs,&primalv);
1709:     PCBDDCAddPrimalVerticesLocalIS(pc,primalv);
1710:     ISDestroy(&primalv);
1711:   }
1712:   /* early stage corner detection */
1713:   {
1714:     DM dm;

1716:     MatGetDM(pc->pmat,&dm);
1717:     if (!dm) {
1718:       PCGetDM(pc,&dm);
1719:     }
1720:     if (dm) {
1721:       PetscBool isda;

1723:       PetscObjectTypeCompare((PetscObject)dm,DMDA,&isda);
1724:       if (isda) {
1725:         ISLocalToGlobalMapping l2l;
1726:         IS                     corners;
1727:         Mat                    lA;
1728:         PetscBool              gl,lo;

1730:         {
1731:           Vec               cvec;
1732:           const PetscScalar *coords;
1733:           PetscInt          dof,n,cdim;
1734:           PetscBool         memc = PETSC_TRUE;

1736:           DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
1737:           DMGetCoordinates(dm,&cvec);
1738:           VecGetLocalSize(cvec,&n);
1739:           VecGetBlockSize(cvec,&cdim);
1740:           n   /= cdim;
1741:           PetscFree(pcbddc->mat_graph->coords);
1742:           PetscMalloc1(dof*n*cdim,&pcbddc->mat_graph->coords);
1743:           VecGetArrayRead(cvec,&coords);
1744: #if defined(PETSC_USE_COMPLEX)
1745:           memc = PETSC_FALSE;
1746: #endif
1747:           if (dof != 1) memc = PETSC_FALSE;
1748:           if (memc) {
1749:             PetscArraycpy(pcbddc->mat_graph->coords,coords,cdim*n*dof);
1750:           } else { /* BDDC graph does not use any blocked information, we need to replicate the data */
1751:             PetscReal *bcoords = pcbddc->mat_graph->coords;
1752:             PetscInt  i, b, d;

1754:             for (i=0;i<n;i++) {
1755:               for (b=0;b<dof;b++) {
1756:                 for (d=0;d<cdim;d++) {
1757:                   bcoords[i*dof*cdim + b*cdim + d] = PetscRealPart(coords[i*cdim+d]);
1758:                 }
1759:               }
1760:             }
1761:           }
1762:           VecRestoreArrayRead(cvec,&coords);
1763:           pcbddc->mat_graph->cdim  = cdim;
1764:           pcbddc->mat_graph->cnloc = dof*n;
1765:           pcbddc->mat_graph->cloc  = PETSC_FALSE;
1766:         }
1767:         DMDAGetSubdomainCornersIS(dm,&corners);
1768:         MatISGetLocalMat(pc->pmat,&lA);
1769:         MatGetLocalToGlobalMapping(lA,&l2l,NULL);
1770:         MatISRestoreLocalMat(pc->pmat,&lA);
1771:         lo   = (PetscBool)(l2l && corners);
1772:         MPIU_Allreduce(&lo,&gl,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));
1773:         if (gl) { /* From PETSc's DMDA */
1774:           const PetscInt    *idx;
1775:           PetscInt          dof,bs,*idxout,n;

1777:           DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
1778:           ISLocalToGlobalMappingGetBlockSize(l2l,&bs);
1779:           ISGetLocalSize(corners,&n);
1780:           ISGetIndices(corners,&idx);
1781:           if (bs == dof) {
1782:             PetscMalloc1(n,&idxout);
1783:             ISLocalToGlobalMappingApplyBlock(l2l,n,idx,idxout);
1784:           } else { /* the original DMDA local-to-local map have been modified */
1785:             PetscInt i,d;

1787:             PetscMalloc1(dof*n,&idxout);
1788:             for (i=0;i<n;i++) for (d=0;d<dof;d++) idxout[dof*i+d] = dof*idx[i]+d;
1789:             ISLocalToGlobalMappingApply(l2l,dof*n,idxout,idxout);

1791:             bs = 1;
1792:             n *= dof;
1793:           }
1794:           ISRestoreIndices(corners,&idx);
1795:           DMDARestoreSubdomainCornersIS(dm,&corners);
1796:           ISCreateBlock(PetscObjectComm((PetscObject)pc),bs,n,idxout,PETSC_OWN_POINTER,&corners);
1797:           PCBDDCAddPrimalVerticesLocalIS(pc,corners);
1798:           ISDestroy(&corners);
1799:           pcbddc->corner_selected  = PETSC_TRUE;
1800:           pcbddc->corner_selection = PETSC_TRUE;
1801:         }
1802:         if (corners) {
1803:           DMDARestoreSubdomainCornersIS(dm,&corners);
1804:         }
1805:       }
1806:     }
1807:   }
1808:   if (pcbddc->corner_selection && !pcbddc->mat_graph->cdim) {
1809:     DM dm;

1811:     MatGetDM(pc->pmat,&dm);
1812:     if (!dm) {
1813:       PCGetDM(pc,&dm);
1814:     }
1815:     if (dm) { /* this can get very expensive, I need to find a faster alternative */
1816:       Vec            vcoords;
1817:       PetscSection   section;
1818:       PetscReal      *coords;
1819:       PetscInt       d,cdim,nl,nf,**ctxs;
1820:       PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *);

1822:       DMGetCoordinateDim(dm,&cdim);
1823:       DMGetLocalSection(dm,&section);
1824:       PetscSectionGetNumFields(section,&nf);
1825:       DMCreateGlobalVector(dm,&vcoords);
1826:       VecGetLocalSize(vcoords,&nl);
1827:       PetscMalloc1(nl*cdim,&coords);
1828:       PetscMalloc2(nf,&funcs,nf,&ctxs);
1829:       PetscMalloc1(nf,&ctxs[0]);
1830:       for (d=0;d<nf;d++) funcs[d] = func_coords_private;
1831:       for (d=1;d<nf;d++) ctxs[d] = ctxs[d-1] + 1;
1832:       for (d=0;d<cdim;d++) {
1833:         PetscInt          i;
1834:         const PetscScalar *v;

1836:         for (i=0;i<nf;i++) ctxs[i][0] = d;
1837:         DMProjectFunction(dm,0.0,funcs,(void**)ctxs,INSERT_VALUES,vcoords);
1838:         VecGetArrayRead(vcoords,&v);
1839:         for (i=0;i<nl;i++) coords[i*cdim+d] = PetscRealPart(v[i]);
1840:         VecRestoreArrayRead(vcoords,&v);
1841:       }
1842:       VecDestroy(&vcoords);
1843:       PCSetCoordinates(pc,cdim,nl,coords);
1844:       PetscFree(coords);
1845:       PetscFree(ctxs[0]);
1846:       PetscFree2(funcs,ctxs);
1847:     }
1848:   }
1849:   return(0);
1850: }

1852: PetscErrorCode PCBDDCConsistencyCheckIS(PC pc, MPI_Op mop, IS *is)
1853: {
1854:   Mat_IS          *matis = (Mat_IS*)(pc->pmat->data);
1855:   PetscErrorCode  ierr;
1856:   IS              nis;
1857:   const PetscInt  *idxs;
1858:   PetscInt        i,nd,n = matis->A->rmap->n,*nidxs,nnd;
1859:   PetscBool       *ld;

1862:   if (mop != MPI_LAND && mop != MPI_LOR) SETERRQ(PetscObjectComm((PetscObject)(pc)),PETSC_ERR_SUP,"Supported are MPI_LAND and MPI_LOR");
1863:   if (mop == MPI_LAND) {
1864:     /* init rootdata with true */
1865:     ld   = (PetscBool*) matis->sf_rootdata;
1866:     for (i=0;i<pc->pmat->rmap->n;i++) ld[i] = PETSC_TRUE;
1867:   } else {
1868:     PetscArrayzero(matis->sf_rootdata,pc->pmat->rmap->n);
1869:   }
1870:   PetscArrayzero(matis->sf_leafdata,n);
1871:   ISGetLocalSize(*is,&nd);
1872:   ISGetIndices(*is,&idxs);
1873:   ld   = (PetscBool*) matis->sf_leafdata;
1874:   for (i=0;i<nd;i++)
1875:     if (-1 < idxs[i] && idxs[i] < n)
1876:       ld[idxs[i]] = PETSC_TRUE;
1877:   ISRestoreIndices(*is,&idxs);
1878:   PetscSFReduceBegin(matis->sf,MPIU_BOOL,matis->sf_leafdata,matis->sf_rootdata,mop);
1879:   PetscSFReduceEnd(matis->sf,MPIU_BOOL,matis->sf_leafdata,matis->sf_rootdata,mop);
1880:   PetscSFBcastBegin(matis->sf,MPIU_BOOL,matis->sf_rootdata,matis->sf_leafdata);
1881:   PetscSFBcastEnd(matis->sf,MPIU_BOOL,matis->sf_rootdata,matis->sf_leafdata);
1882:   if (mop == MPI_LAND) {
1883:     PetscMalloc1(nd,&nidxs);
1884:   } else {
1885:     PetscMalloc1(n,&nidxs);
1886:   }
1887:   for (i=0,nnd=0;i<n;i++)
1888:     if (ld[i])
1889:       nidxs[nnd++] = i;
1890:   ISCreateGeneral(PetscObjectComm((PetscObject)(*is)),nnd,nidxs,PETSC_OWN_POINTER,&nis);
1891:   ISDestroy(is);
1892:   *is  = nis;
1893:   return(0);
1894: }

1896: PetscErrorCode PCBDDCBenignRemoveInterior(PC pc,Vec r,Vec z)
1897: {
1898:   PC_IS             *pcis = (PC_IS*)(pc->data);
1899:   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);
1900:   PetscErrorCode    ierr;

1903:   if (!pcbddc->benign_have_null) {
1904:     return(0);
1905:   }
1906:   if (pcbddc->ChangeOfBasisMatrix) {
1907:     Vec swap;

1909:     MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);
1910:     swap = pcbddc->work_change;
1911:     pcbddc->work_change = r;
1912:     r = swap;
1913:   }
1914:   VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
1915:   VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
1916:   KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);
1917:   KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);
1918:   VecSet(z,0.);
1919:   VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
1920:   VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
1921:   if (pcbddc->ChangeOfBasisMatrix) {
1922:     pcbddc->work_change = r;
1923:     VecCopy(z,pcbddc->work_change);
1924:     MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);
1925:   }
1926:   return(0);
1927: }

1929: PetscErrorCode PCBDDCBenignMatMult_Private_Private(Mat A, Vec x, Vec y, PetscBool transpose)
1930: {
1931:   PCBDDCBenignMatMult_ctx ctx;
1932:   PetscErrorCode          ierr;
1933:   PetscBool               apply_right,apply_left,reset_x;

1936:   MatShellGetContext(A,&ctx);
1937:   if (transpose) {
1938:     apply_right = ctx->apply_left;
1939:     apply_left = ctx->apply_right;
1940:   } else {
1941:     apply_right = ctx->apply_right;
1942:     apply_left = ctx->apply_left;
1943:   }
1944:   reset_x = PETSC_FALSE;
1945:   if (apply_right) {
1946:     const PetscScalar *ax;
1947:     PetscInt          nl,i;

1949:     VecGetLocalSize(x,&nl);
1950:     VecGetArrayRead(x,&ax);
1951:     PetscArraycpy(ctx->work,ax,nl);
1952:     VecRestoreArrayRead(x,&ax);
1953:     for (i=0;i<ctx->benign_n;i++) {
1954:       PetscScalar    sum,val;
1955:       const PetscInt *idxs;
1956:       PetscInt       nz,j;
1957:       ISGetLocalSize(ctx->benign_zerodiag_subs[i],&nz);
1958:       ISGetIndices(ctx->benign_zerodiag_subs[i],&idxs);
1959:       sum = 0.;
1960:       if (ctx->apply_p0) {
1961:         val = ctx->work[idxs[nz-1]];
1962:         for (j=0;j<nz-1;j++) {
1963:           sum += ctx->work[idxs[j]];
1964:           ctx->work[idxs[j]] += val;
1965:         }
1966:       } else {
1967:         for (j=0;j<nz-1;j++) {
1968:           sum += ctx->work[idxs[j]];
1969:         }
1970:       }
1971:       ctx->work[idxs[nz-1]] -= sum;
1972:       ISRestoreIndices(ctx->benign_zerodiag_subs[i],&idxs);
1973:     }
1974:     VecPlaceArray(x,ctx->work);
1975:     reset_x = PETSC_TRUE;
1976:   }
1977:   if (transpose) {
1978:     MatMultTranspose(ctx->A,x,y);
1979:   } else {
1980:     MatMult(ctx->A,x,y);
1981:   }
1982:   if (reset_x) {
1983:     VecResetArray(x);
1984:   }
1985:   if (apply_left) {
1986:     PetscScalar *ay;
1987:     PetscInt    i;

1989:     VecGetArray(y,&ay);
1990:     for (i=0;i<ctx->benign_n;i++) {
1991:       PetscScalar    sum,val;
1992:       const PetscInt *idxs;
1993:       PetscInt       nz,j;
1994:       ISGetLocalSize(ctx->benign_zerodiag_subs[i],&nz);
1995:       ISGetIndices(ctx->benign_zerodiag_subs[i],&idxs);
1996:       val = -ay[idxs[nz-1]];
1997:       if (ctx->apply_p0) {
1998:         sum = 0.;
1999:         for (j=0;j<nz-1;j++) {
2000:           sum += ay[idxs[j]];
2001:           ay[idxs[j]] += val;
2002:         }
2003:         ay[idxs[nz-1]] += sum;
2004:       } else {
2005:         for (j=0;j<nz-1;j++) {
2006:           ay[idxs[j]] += val;
2007:         }
2008:         ay[idxs[nz-1]] = 0.;
2009:       }
2010:       ISRestoreIndices(ctx->benign_zerodiag_subs[i],&idxs);
2011:     }
2012:     VecRestoreArray(y,&ay);
2013:   }
2014:   return(0);
2015: }

2017: PetscErrorCode PCBDDCBenignMatMultTranspose_Private(Mat A, Vec x, Vec y)
2018: {

2022:   PCBDDCBenignMatMult_Private_Private(A,x,y,PETSC_TRUE);
2023:   return(0);
2024: }

2026: PetscErrorCode PCBDDCBenignMatMult_Private(Mat A, Vec x, Vec y)
2027: {

2031:   PCBDDCBenignMatMult_Private_Private(A,x,y,PETSC_FALSE);
2032:   return(0);
2033: }

2035: PetscErrorCode PCBDDCBenignShellMat(PC pc, PetscBool restore)
2036: {
2037:   PC_IS                   *pcis = (PC_IS*)pc->data;
2038:   PC_BDDC                 *pcbddc = (PC_BDDC*)pc->data;
2039:   PCBDDCBenignMatMult_ctx ctx;
2040:   PetscErrorCode          ierr;

2043:   if (!restore) {
2044:     Mat                A_IB,A_BI;
2045:     PetscScalar        *work;
2046:     PCBDDCReuseSolvers reuse = pcbddc->sub_schurs ? pcbddc->sub_schurs->reuse_solver : NULL;

2048:     if (pcbddc->benign_original_mat) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Benign original mat has not been restored");
2049:     if (!pcbddc->benign_change || !pcbddc->benign_n || pcbddc->benign_change_explicit) return(0);
2050:     PetscMalloc1(pcis->n,&work);
2051:     MatCreate(PETSC_COMM_SELF,&A_IB);
2052:     MatSetSizes(A_IB,pcis->n-pcis->n_B,pcis->n_B,PETSC_DECIDE,PETSC_DECIDE);
2053:     MatSetType(A_IB,MATSHELL);
2054:     MatShellSetOperation(A_IB,MATOP_MULT,(void (*)(void))PCBDDCBenignMatMult_Private);
2055:     MatShellSetOperation(A_IB,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCBenignMatMultTranspose_Private);
2056:     PetscNew(&ctx);
2057:     MatShellSetContext(A_IB,ctx);
2058:     ctx->apply_left = PETSC_TRUE;
2059:     ctx->apply_right = PETSC_FALSE;
2060:     ctx->apply_p0 = PETSC_FALSE;
2061:     ctx->benign_n = pcbddc->benign_n;
2062:     if (reuse) {
2063:       ctx->benign_zerodiag_subs = reuse->benign_zerodiag_subs;
2064:       ctx->free = PETSC_FALSE;
2065:     } else { /* TODO: could be optimized for successive solves */
2066:       ISLocalToGlobalMapping N_to_D;
2067:       PetscInt               i;

2069:       ISLocalToGlobalMappingCreateIS(pcis->is_I_local,&N_to_D);
2070:       PetscMalloc1(pcbddc->benign_n,&ctx->benign_zerodiag_subs);
2071:       for (i=0;i<pcbddc->benign_n;i++) {
2072:         ISGlobalToLocalMappingApplyIS(N_to_D,IS_GTOLM_DROP,pcbddc->benign_zerodiag_subs[i],&ctx->benign_zerodiag_subs[i]);
2073:       }
2074:       ISLocalToGlobalMappingDestroy(&N_to_D);
2075:       ctx->free = PETSC_TRUE;
2076:     }
2077:     ctx->A = pcis->A_IB;
2078:     ctx->work = work;
2079:     MatSetUp(A_IB);
2080:     MatAssemblyBegin(A_IB,MAT_FINAL_ASSEMBLY);
2081:     MatAssemblyEnd(A_IB,MAT_FINAL_ASSEMBLY);
2082:     pcis->A_IB = A_IB;

2084:     /* A_BI as A_IB^T */
2085:     MatCreateTranspose(A_IB,&A_BI);
2086:     pcbddc->benign_original_mat = pcis->A_BI;
2087:     pcis->A_BI = A_BI;
2088:   } else {
2089:     if (!pcbddc->benign_original_mat) {
2090:       return(0);
2091:     }
2092:     MatShellGetContext(pcis->A_IB,&ctx);
2093:     MatDestroy(&pcis->A_IB);
2094:     pcis->A_IB = ctx->A;
2095:     ctx->A = NULL;
2096:     MatDestroy(&pcis->A_BI);
2097:     pcis->A_BI = pcbddc->benign_original_mat;
2098:     pcbddc->benign_original_mat = NULL;
2099:     if (ctx->free) {
2100:       PetscInt i;
2101:       for (i=0;i<ctx->benign_n;i++) {
2102:         ISDestroy(&ctx->benign_zerodiag_subs[i]);
2103:       }
2104:       PetscFree(ctx->benign_zerodiag_subs);
2105:     }
2106:     PetscFree(ctx->work);
2107:     PetscFree(ctx);
2108:   }
2109:   return(0);
2110: }

2112: /* used just in bddc debug mode */
2113: PetscErrorCode PCBDDCBenignProject(PC pc, IS is1, IS is2, Mat *B)
2114: {
2115:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
2116:   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
2117:   Mat            An;

2121:   MatPtAP(matis->A,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&An);
2122:   MatZeroRowsColumns(An,pcbddc->benign_n,pcbddc->benign_p0_lidx,1.0,NULL,NULL);
2123:   if (is1) {
2124:     MatCreateSubMatrix(An,is1,is2,MAT_INITIAL_MATRIX,B);
2125:     MatDestroy(&An);
2126:   } else {
2127:     *B = An;
2128:   }
2129:   return(0);
2130: }

2132: /* TODO: add reuse flag */
2133: PetscErrorCode MatSeqAIJCompress(Mat A, Mat *B)
2134: {
2135:   Mat            Bt;
2136:   PetscScalar    *a,*bdata;
2137:   const PetscInt *ii,*ij;
2138:   PetscInt       m,n,i,nnz,*bii,*bij;
2139:   PetscBool      flg_row;

2143:   MatGetSize(A,&n,&m);
2144:   MatGetRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&ij,&flg_row);
2145:   MatSeqAIJGetArray(A,&a);
2146:   nnz = n;
2147:   for (i=0;i<ii[n];i++) {
2148:     if (PetscLikely(PetscAbsScalar(a[i]) > PETSC_SMALL)) nnz++;
2149:   }
2150:   PetscMalloc1(n+1,&bii);
2151:   PetscMalloc1(nnz,&bij);
2152:   PetscMalloc1(nnz,&bdata);
2153:   nnz = 0;
2154:   bii[0] = 0;
2155:   for (i=0;i<n;i++) {
2156:     PetscInt j;
2157:     for (j=ii[i];j<ii[i+1];j++) {
2158:       PetscScalar entry = a[j];
2159:       if (PetscLikely(PetscAbsScalar(entry) > PETSC_SMALL) || (n == m && ij[j] == i)) {
2160:         bij[nnz] = ij[j];
2161:         bdata[nnz] = entry;
2162:         nnz++;
2163:       }
2164:     }
2165:     bii[i+1] = nnz;
2166:   }
2167:   MatSeqAIJRestoreArray(A,&a);
2168:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),n,m,bii,bij,bdata,&Bt);
2169:   MatRestoreRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&ij,&flg_row);
2170:   {
2171:     Mat_SeqAIJ *b = (Mat_SeqAIJ*)(Bt->data);
2172:     b->free_a = PETSC_TRUE;
2173:     b->free_ij = PETSC_TRUE;
2174:   }
2175:   if (*B == A) {
2176:     MatDestroy(&A);
2177:   }
2178:   *B = Bt;
2179:   return(0);
2180: }

2182: PetscErrorCode PCBDDCDetectDisconnectedComponents(PC pc, PetscBool filter, PetscInt *ncc, IS* cc[], IS* primalv)
2183: {
2184:   Mat                    B = NULL;
2185:   DM                     dm;
2186:   IS                     is_dummy,*cc_n;
2187:   ISLocalToGlobalMapping l2gmap_dummy;
2188:   PCBDDCGraph            graph;
2189:   PetscInt               *xadj_filtered = NULL,*adjncy_filtered = NULL;
2190:   PetscInt               i,n;
2191:   PetscInt               *xadj,*adjncy;
2192:   PetscBool              isplex = PETSC_FALSE;
2193:   PetscErrorCode         ierr;

2196:   if (ncc) *ncc = 0;
2197:   if (cc) *cc = NULL;
2198:   if (primalv) *primalv = NULL;
2199:   PCBDDCGraphCreate(&graph);
2200:   MatGetDM(pc->pmat,&dm);
2201:   if (!dm) {
2202:     PCGetDM(pc,&dm);
2203:   }
2204:   if (dm) {
2205:     PetscObjectTypeCompare((PetscObject)dm,DMPLEX,&isplex);
2206:   }
2207:   if (filter) isplex = PETSC_FALSE;

2209:   if (isplex) { /* this code has been modified from plexpartition.c */
2210:     PetscInt       p, pStart, pEnd, a, adjSize, idx, size, nroots;
2211:     PetscInt      *adj = NULL;
2212:     IS             cellNumbering;
2213:     const PetscInt *cellNum;
2214:     PetscBool      useCone, useClosure;
2215:     PetscSection   section;
2216:     PetscSegBuffer adjBuffer;
2217:     PetscSF        sfPoint;

2221:     DMPlexGetHeightStratum(dm, 0, &pStart, &pEnd);
2222:     DMGetPointSF(dm, &sfPoint);
2223:     PetscSFGetGraph(sfPoint, &nroots, NULL, NULL, NULL);
2224:     /* Build adjacency graph via a section/segbuffer */
2225:     PetscSectionCreate(PetscObjectComm((PetscObject) dm), &section);
2226:     PetscSectionSetChart(section, pStart, pEnd);
2227:     PetscSegBufferCreate(sizeof(PetscInt),1000,&adjBuffer);
2228:     /* Always use FVM adjacency to create partitioner graph */
2229:     DMGetBasicAdjacency(dm, &useCone, &useClosure);
2230:     DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);
2231:     DMPlexGetCellNumbering(dm, &cellNumbering);
2232:     ISGetIndices(cellNumbering, &cellNum);
2233:     for (n = 0, p = pStart; p < pEnd; p++) {
2234:       /* Skip non-owned cells in parallel (ParMetis expects no overlap) */
2235:       if (nroots > 0) {if (cellNum[p] < 0) continue;}
2236:       adjSize = PETSC_DETERMINE;
2237:       DMPlexGetAdjacency(dm, p, &adjSize, &adj);
2238:       for (a = 0; a < adjSize; ++a) {
2239:         const PetscInt point = adj[a];
2240:         if (pStart <= point && point < pEnd) {
2241:           PetscInt *PETSC_RESTRICT pBuf;
2242:           PetscSectionAddDof(section, p, 1);
2243:           PetscSegBufferGetInts(adjBuffer, 1, &pBuf);
2244:           *pBuf = point;
2245:         }
2246:       }
2247:       n++;
2248:     }
2249:     DMSetBasicAdjacency(dm, useCone, useClosure);
2250:     /* Derive CSR graph from section/segbuffer */
2251:     PetscSectionSetUp(section);
2252:     PetscSectionGetStorageSize(section, &size);
2253:     PetscMalloc1(n+1, &xadj);
2254:     for (idx = 0, p = pStart; p < pEnd; p++) {
2255:       if (nroots > 0) {if (cellNum[p] < 0) continue;}
2256:       PetscSectionGetOffset(section, p, &(xadj[idx++]));
2257:     }
2258:     xadj[n] = size;
2259:     PetscSegBufferExtractAlloc(adjBuffer, &adjncy);
2260:     /* Clean up */
2261:     PetscSegBufferDestroy(&adjBuffer);
2262:     PetscSectionDestroy(&section);
2263:     PetscFree(adj);
2264:     graph->xadj = xadj;
2265:     graph->adjncy = adjncy;
2266:   } else {
2267:     Mat       A;
2268:     PetscBool isseqaij, flg_row;

2270:     MatISGetLocalMat(pc->pmat,&A);
2271:     if (!A->rmap->N || !A->cmap->N) {
2272:       PCBDDCGraphDestroy(&graph);
2273:       return(0);
2274:     }
2275:     PetscObjectBaseTypeCompare((PetscObject)A,MATSEQAIJ,&isseqaij);
2276:     if (!isseqaij && filter) {
2277:       PetscBool isseqdense;

2279:       PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&isseqdense);
2280:       if (!isseqdense) {
2281:         MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&B);
2282:       } else { /* TODO: rectangular case and LDA */
2283:         PetscScalar *array;
2284:         PetscReal   chop=1.e-6;

2286:         MatDuplicate(A,MAT_COPY_VALUES,&B);
2287:         MatDenseGetArray(B,&array);
2288:         MatGetSize(B,&n,NULL);
2289:         for (i=0;i<n;i++) {
2290:           PetscInt j;
2291:           for (j=i+1;j<n;j++) {
2292:             PetscReal thresh = chop*(PetscAbsScalar(array[i*(n+1)])+PetscAbsScalar(array[j*(n+1)]));
2293:             if (PetscAbsScalar(array[i*n+j]) < thresh) array[i*n+j] = 0.;
2294:             if (PetscAbsScalar(array[j*n+i]) < thresh) array[j*n+i] = 0.;
2295:           }
2296:         }
2297:         MatDenseRestoreArray(B,&array);
2298:         MatConvert(B,MATSEQAIJ,MAT_INPLACE_MATRIX,&B);
2299:       }
2300:     } else {
2301:       PetscObjectReference((PetscObject)A);
2302:       B = A;
2303:     }
2304:     MatGetRowIJ(B,0,PETSC_TRUE,PETSC_FALSE,&n,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);

2306:     /* if filter is true, then removes entries lower than PETSC_SMALL in magnitude */
2307:     if (filter) {
2308:       PetscScalar *data;
2309:       PetscInt    j,cum;

2311:       PetscCalloc2(n+1,&xadj_filtered,xadj[n],&adjncy_filtered);
2312:       MatSeqAIJGetArray(B,&data);
2313:       cum = 0;
2314:       for (i=0;i<n;i++) {
2315:         PetscInt t;

2317:         for (j=xadj[i];j<xadj[i+1];j++) {
2318:           if (PetscUnlikely(PetscAbsScalar(data[j]) < PETSC_SMALL)) {
2319:             continue;
2320:           }
2321:           adjncy_filtered[cum+xadj_filtered[i]++] = adjncy[j];
2322:         }
2323:         t = xadj_filtered[i];
2324:         xadj_filtered[i] = cum;
2325:         cum += t;
2326:       }
2327:       MatSeqAIJRestoreArray(B,&data);
2328:       graph->xadj = xadj_filtered;
2329:       graph->adjncy = adjncy_filtered;
2330:     } else {
2331:       graph->xadj = xadj;
2332:       graph->adjncy = adjncy;
2333:     }
2334:   }
2335:   /* compute local connected components using PCBDDCGraph */
2336:   ISCreateStride(PETSC_COMM_SELF,n,0,1,&is_dummy);
2337:   ISLocalToGlobalMappingCreateIS(is_dummy,&l2gmap_dummy);
2338:   ISDestroy(&is_dummy);
2339:   PCBDDCGraphInit(graph,l2gmap_dummy,n,PETSC_MAX_INT);
2340:   ISLocalToGlobalMappingDestroy(&l2gmap_dummy);
2341:   PCBDDCGraphSetUp(graph,1,NULL,NULL,0,NULL,NULL);
2342:   PCBDDCGraphComputeConnectedComponents(graph);

2344:   /* partial clean up */
2345:   PetscFree2(xadj_filtered,adjncy_filtered);
2346:   if (B) {
2347:     PetscBool flg_row;
2348:     MatRestoreRowIJ(B,0,PETSC_TRUE,PETSC_FALSE,&n,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
2349:     MatDestroy(&B);
2350:   }
2351:   if (isplex) {
2352:     PetscFree(xadj);
2353:     PetscFree(adjncy);
2354:   }

2356:   /* get back data */
2357:   if (isplex) {
2358:     if (ncc) *ncc = graph->ncc;
2359:     if (cc || primalv) {
2360:       Mat          A;
2361:       PetscBT      btv,btvt;
2362:       PetscSection subSection;
2363:       PetscInt     *ids,cum,cump,*cids,*pids;

2365:       DMPlexGetSubdomainSection(dm,&subSection);
2366:       MatISGetLocalMat(pc->pmat,&A);
2367:       PetscMalloc3(A->rmap->n,&ids,graph->ncc+1,&cids,A->rmap->n,&pids);
2368:       PetscBTCreate(A->rmap->n,&btv);
2369:       PetscBTCreate(A->rmap->n,&btvt);

2371:       cids[0] = 0;
2372:       for (i = 0, cump = 0, cum = 0; i < graph->ncc; i++) {
2373:         PetscInt j;

2375:         PetscBTMemzero(A->rmap->n,btvt);
2376:         for (j = graph->cptr[i]; j < graph->cptr[i+1]; j++) {
2377:           PetscInt k, size, *closure = NULL, cell = graph->queue[j];

2379:           DMPlexGetTransitiveClosure(dm,cell,PETSC_TRUE,&size,&closure);
2380:           for (k = 0; k < 2*size; k += 2) {
2381:             PetscInt s, pp, p = closure[k], off, dof, cdof;

2383:             PetscSectionGetConstraintDof(subSection,p,&cdof);
2384:             PetscSectionGetOffset(subSection,p,&off);
2385:             PetscSectionGetDof(subSection,p,&dof);
2386:             for (s = 0; s < dof-cdof; s++) {
2387:               if (PetscBTLookupSet(btvt,off+s)) continue;
2388:               if (!PetscBTLookup(btv,off+s)) {
2389:                 ids[cum++] = off+s;
2390:               } else { /* cross-vertex */
2391:                 pids[cump++] = off+s;
2392:               }
2393:             }
2394:             DMPlexGetTreeParent(dm,p,&pp,NULL);
2395:             if (pp != p) {
2396:               PetscSectionGetConstraintDof(subSection,pp,&cdof);
2397:               PetscSectionGetOffset(subSection,pp,&off);
2398:               PetscSectionGetDof(subSection,pp,&dof);
2399:               for (s = 0; s < dof-cdof; s++) {
2400:                 if (PetscBTLookupSet(btvt,off+s)) continue;
2401:                 if (!PetscBTLookup(btv,off+s)) {
2402:                   ids[cum++] = off+s;
2403:                 } else { /* cross-vertex */
2404:                   pids[cump++] = off+s;
2405:                 }
2406:               }
2407:             }
2408:           }
2409:           DMPlexRestoreTransitiveClosure(dm,cell,PETSC_TRUE,&size,&closure);
2410:         }
2411:         cids[i+1] = cum;
2412:         /* mark dofs as already assigned */
2413:         for (j = cids[i]; j < cids[i+1]; j++) {
2414:           PetscBTSet(btv,ids[j]);
2415:         }
2416:       }
2417:       if (cc) {
2418:         PetscMalloc1(graph->ncc,&cc_n);
2419:         for (i = 0; i < graph->ncc; i++) {
2420:           ISCreateGeneral(PETSC_COMM_SELF,cids[i+1]-cids[i],ids+cids[i],PETSC_COPY_VALUES,&cc_n[i]);
2421:         }
2422:         *cc = cc_n;
2423:       }
2424:       if (primalv) {
2425:         ISCreateGeneral(PetscObjectComm((PetscObject)pc),cump,pids,PETSC_COPY_VALUES,primalv);
2426:       }
2427:       PetscFree3(ids,cids,pids);
2428:       PetscBTDestroy(&btv);
2429:       PetscBTDestroy(&btvt);
2430:     }
2431:   } else {
2432:     if (ncc) *ncc = graph->ncc;
2433:     if (cc) {
2434:       PetscMalloc1(graph->ncc,&cc_n);
2435:       for (i=0;i<graph->ncc;i++) {
2436:         ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],graph->queue+graph->cptr[i],PETSC_COPY_VALUES,&cc_n[i]);
2437:       }
2438:       *cc = cc_n;
2439:     }
2440:   }
2441:   /* clean up graph */
2442:   graph->xadj = 0;
2443:   graph->adjncy = 0;
2444:   PCBDDCGraphDestroy(&graph);
2445:   return(0);
2446: }

2448: PetscErrorCode PCBDDCBenignCheck(PC pc, IS zerodiag)
2449: {
2450:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
2451:   PC_IS*         pcis = (PC_IS*)(pc->data);
2452:   IS             dirIS = NULL;
2453:   PetscInt       i;

2457:   PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);
2458:   if (zerodiag) {
2459:     Mat            A;
2460:     Vec            vec3_N;
2461:     PetscScalar    *vals;
2462:     const PetscInt *idxs;
2463:     PetscInt       nz,*count;

2465:     /* p0 */
2466:     VecSet(pcis->vec1_N,0.);
2467:     PetscMalloc1(pcis->n,&vals);
2468:     ISGetLocalSize(zerodiag,&nz);
2469:     ISGetIndices(zerodiag,&idxs);
2470:     for (i=0;i<nz;i++) vals[i] = 1.;
2471:     VecSetValues(pcis->vec1_N,nz,idxs,vals,INSERT_VALUES);
2472:     VecAssemblyBegin(pcis->vec1_N);
2473:     VecAssemblyEnd(pcis->vec1_N);
2474:     /* v_I */
2475:     VecSetRandom(pcis->vec2_N,NULL);
2476:     for (i=0;i<nz;i++) vals[i] = 0.;
2477:     VecSetValues(pcis->vec2_N,nz,idxs,vals,INSERT_VALUES);
2478:     ISRestoreIndices(zerodiag,&idxs);
2479:     ISGetIndices(pcis->is_B_local,&idxs);
2480:     for (i=0;i<pcis->n_B;i++) vals[i] = 0.;
2481:     VecSetValues(pcis->vec2_N,pcis->n_B,idxs,vals,INSERT_VALUES);
2482:     ISRestoreIndices(pcis->is_B_local,&idxs);
2483:     if (dirIS) {
2484:       PetscInt n;

2486:       ISGetLocalSize(dirIS,&n);
2487:       ISGetIndices(dirIS,&idxs);
2488:       for (i=0;i<n;i++) vals[i] = 0.;
2489:       VecSetValues(pcis->vec2_N,n,idxs,vals,INSERT_VALUES);
2490:       ISRestoreIndices(dirIS,&idxs);
2491:     }
2492:     VecAssemblyBegin(pcis->vec2_N);
2493:     VecAssemblyEnd(pcis->vec2_N);
2494:     VecDuplicate(pcis->vec1_N,&vec3_N);
2495:     VecSet(vec3_N,0.);
2496:     MatISGetLocalMat(pc->pmat,&A);
2497:     MatMult(A,pcis->vec1_N,vec3_N);
2498:     VecDot(vec3_N,pcis->vec2_N,&vals[0]);
2499:     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]));
2500:     PetscFree(vals);
2501:     VecDestroy(&vec3_N);

2503:     /* there should not be any pressure dofs lying on the interface */
2504:     PetscCalloc1(pcis->n,&count);
2505:     ISGetIndices(pcis->is_B_local,&idxs);
2506:     for (i=0;i<pcis->n_B;i++) count[idxs[i]]++;
2507:     ISRestoreIndices(pcis->is_B_local,&idxs);
2508:     ISGetIndices(zerodiag,&idxs);
2509:     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]);
2510:     ISRestoreIndices(zerodiag,&idxs);
2511:     PetscFree(count);
2512:   }
2513:   ISDestroy(&dirIS);

2515:   /* check PCBDDCBenignGetOrSetP0 */
2516:   VecSetRandom(pcis->vec1_global,NULL);
2517:   for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = -PetscGlobalRank-i;
2518:   PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_FALSE);
2519:   for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = 1;
2520:   PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_TRUE);
2521:   for (i=0;i<pcbddc->benign_n;i++) {
2522:     PetscInt val = PetscRealPart(pcbddc->benign_p0[i]);
2523:     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);
2524:   }
2525:   return(0);
2526: }

2528: PetscErrorCode PCBDDCBenignDetectSaddlePoint(PC pc, PetscBool reuse, IS *zerodiaglocal)
2529: {
2530:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
2531:   IS             pressures = NULL,zerodiag = NULL,*bzerodiag = NULL,zerodiag_save,*zerodiag_subs;
2532:   PetscInt       nz,n,benign_n,bsp = 1;
2533:   PetscInt       *interior_dofs,n_interior_dofs,nneu;
2534:   PetscBool      sorted,have_null,has_null_pressures,recompute_zerodiag,checkb;

2538:   if (reuse) goto project_b0;
2539:   PetscSFDestroy(&pcbddc->benign_sf);
2540:   MatDestroy(&pcbddc->benign_B0);
2541:   for (n=0;n<pcbddc->benign_n;n++) {
2542:     ISDestroy(&pcbddc->benign_zerodiag_subs[n]);
2543:   }
2544:   PetscFree(pcbddc->benign_zerodiag_subs);
2545:   has_null_pressures = PETSC_TRUE;
2546:   have_null = PETSC_TRUE;
2547:   /* if a local information on dofs is present, gets pressure dofs from command line (uses the last field is not provided)
2548:      Without local information, it uses only the zerodiagonal dofs (ok if the pressure block is all zero and it is a scalar field)
2549:      Checks if all the pressure dofs in each subdomain have a zero diagonal
2550:      If not, a change of basis on pressures is not needed
2551:      since the local Schur complements are already SPD
2552:   */
2553:   if (pcbddc->n_ISForDofsLocal) {
2554:     IS        iP = NULL;
2555:     PetscInt  p,*pp;
2556:     PetscBool flg;

2558:     PetscMalloc1(pcbddc->n_ISForDofsLocal,&pp);
2559:     n    = pcbddc->n_ISForDofsLocal;
2560:     PetscOptionsBegin(PetscObjectComm((PetscObject)pc),((PetscObject)pc)->prefix,"BDDC benign options","PC");
2561:     PetscOptionsIntArray("-pc_bddc_pressure_field","Field id for pressures",NULL,pp,&n,&flg);
2562:     PetscOptionsEnd();
2563:     if (!flg) {
2564:       n = 1;
2565:       pp[0] = pcbddc->n_ISForDofsLocal-1;
2566:     }

2568:     bsp = 0;
2569:     for (p=0;p<n;p++) {
2570:       PetscInt bs;

2572:       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]);
2573:       ISGetBlockSize(pcbddc->ISForDofsLocal[pp[p]],&bs);
2574:       bsp += bs;
2575:     }
2576:     PetscMalloc1(bsp,&bzerodiag);
2577:     bsp  = 0;
2578:     for (p=0;p<n;p++) {
2579:       const PetscInt *idxs;
2580:       PetscInt       b,bs,npl,*bidxs;

2582:       ISGetBlockSize(pcbddc->ISForDofsLocal[pp[p]],&bs);
2583:       ISGetLocalSize(pcbddc->ISForDofsLocal[pp[p]],&npl);
2584:       ISGetIndices(pcbddc->ISForDofsLocal[pp[p]],&idxs);
2585:       PetscMalloc1(npl/bs,&bidxs);
2586:       for (b=0;b<bs;b++) {
2587:         PetscInt i;

2589:         for (i=0;i<npl/bs;i++) bidxs[i] = idxs[bs*i+b];
2590:         ISCreateGeneral(PETSC_COMM_SELF,npl/bs,bidxs,PETSC_COPY_VALUES,&bzerodiag[bsp]);
2591:         bsp++;
2592:       }
2593:       PetscFree(bidxs);
2594:       ISRestoreIndices(pcbddc->ISForDofsLocal[pp[p]],&idxs);
2595:     }
2596:     ISConcatenate(PETSC_COMM_SELF,bsp,bzerodiag,&pressures);

2598:     /* remove zeroed out pressures if we are setting up a BDDC solver for a saddle-point FETI-DP */
2599:     PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP",(PetscObject*)&iP);
2600:     if (iP) {
2601:       IS newpressures;

2603:       ISDifference(pressures,iP,&newpressures);
2604:       ISDestroy(&pressures);
2605:       pressures = newpressures;
2606:     }
2607:     ISSorted(pressures,&sorted);
2608:     if (!sorted) {
2609:       ISSort(pressures);
2610:     }
2611:     PetscFree(pp);
2612:   }

2614:   /* pcis has not been setup yet, so get the local size from the subdomain matrix */
2615:   MatGetLocalSize(pcbddc->local_mat,&n,NULL);
2616:   if (!n) pcbddc->benign_change_explicit = PETSC_TRUE;
2617:   MatFindZeroDiagonals(pcbddc->local_mat,&zerodiag);
2618:   ISSorted(zerodiag,&sorted);
2619:   if (!sorted) {
2620:     ISSort(zerodiag);
2621:   }
2622:   PetscObjectReference((PetscObject)zerodiag);
2623:   zerodiag_save = zerodiag;
2624:   ISGetLocalSize(zerodiag,&nz);
2625:   if (!nz) {
2626:     if (n) have_null = PETSC_FALSE;
2627:     has_null_pressures = PETSC_FALSE;
2628:     ISDestroy(&zerodiag);
2629:   }
2630:   recompute_zerodiag = PETSC_FALSE;

2632:   /* in case disconnected subdomains info is present, split the pressures accordingly (otherwise the benign trick could fail) */
2633:   zerodiag_subs    = NULL;
2634:   benign_n         = 0;
2635:   n_interior_dofs  = 0;
2636:   interior_dofs    = NULL;
2637:   nneu             = 0;
2638:   if (pcbddc->NeumannBoundariesLocal) {
2639:     ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&nneu);
2640:   }
2641:   checkb = (PetscBool)(!pcbddc->NeumannBoundariesLocal || pcbddc->current_level);
2642:   if (checkb) { /* need to compute interior nodes */
2643:     PetscInt n,i,j;
2644:     PetscInt n_neigh,*neigh,*n_shared,**shared;
2645:     PetscInt *iwork;

2647:     ISLocalToGlobalMappingGetSize(pc->pmat->rmap->mapping,&n);
2648:     ISLocalToGlobalMappingGetInfo(pc->pmat->rmap->mapping,&n_neigh,&neigh,&n_shared,&shared);
2649:     PetscCalloc1(n,&iwork);
2650:     PetscMalloc1(n,&interior_dofs);
2651:     for (i=1;i<n_neigh;i++)
2652:       for (j=0;j<n_shared[i];j++)
2653:           iwork[shared[i][j]] += 1;
2654:     for (i=0;i<n;i++)
2655:       if (!iwork[i])
2656:         interior_dofs[n_interior_dofs++] = i;
2657:     PetscFree(iwork);
2658:     ISLocalToGlobalMappingRestoreInfo(pc->pmat->rmap->mapping,&n_neigh,&neigh,&n_shared,&shared);
2659:   }
2660:   if (has_null_pressures) {
2661:     IS             *subs;
2662:     PetscInt       nsubs,i,j,nl;
2663:     const PetscInt *idxs;
2664:     PetscScalar    *array;
2665:     Vec            *work;
2666:     Mat_IS*        matis = (Mat_IS*)(pc->pmat->data);

2668:     subs  = pcbddc->local_subs;
2669:     nsubs = pcbddc->n_local_subs;
2670:     /* 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) */
2671:     if (checkb) {
2672:       VecDuplicateVecs(matis->y,2,&work);
2673:       ISGetLocalSize(zerodiag,&nl);
2674:       ISGetIndices(zerodiag,&idxs);
2675:       /* work[0] = 1_p */
2676:       VecSet(work[0],0.);
2677:       VecGetArray(work[0],&array);
2678:       for (j=0;j<nl;j++) array[idxs[j]] = 1.;
2679:       VecRestoreArray(work[0],&array);
2680:       /* work[0] = 1_v */
2681:       VecSet(work[1],1.);
2682:       VecGetArray(work[1],&array);
2683:       for (j=0;j<nl;j++) array[idxs[j]] = 0.;
2684:       VecRestoreArray(work[1],&array);
2685:       ISRestoreIndices(zerodiag,&idxs);
2686:     }

2688:     if (nsubs > 1 || bsp > 1) {
2689:       IS       *is;
2690:       PetscInt b,totb;

2692:       totb  = bsp;
2693:       is    = bsp > 1 ? bzerodiag : &zerodiag;
2694:       nsubs = PetscMax(nsubs,1);
2695:       PetscCalloc1(nsubs*totb,&zerodiag_subs);
2696:       for (b=0;b<totb;b++) {
2697:         for (i=0;i<nsubs;i++) {
2698:           ISLocalToGlobalMapping l2g;
2699:           IS                     t_zerodiag_subs;
2700:           PetscInt               nl;

2702:           if (subs) {
2703:             ISLocalToGlobalMappingCreateIS(subs[i],&l2g);
2704:           } else {
2705:             IS tis;

2707:             MatGetLocalSize(pcbddc->local_mat,&nl,NULL);
2708:             ISCreateStride(PETSC_COMM_SELF,nl,0,1,&tis);
2709:             ISLocalToGlobalMappingCreateIS(tis,&l2g);
2710:             ISDestroy(&tis);
2711:           }
2712:           ISGlobalToLocalMappingApplyIS(l2g,IS_GTOLM_DROP,is[b],&t_zerodiag_subs);
2713:           ISGetLocalSize(t_zerodiag_subs,&nl);
2714:           if (nl) {
2715:             PetscBool valid = PETSC_TRUE;

2717:             if (checkb) {
2718:               VecSet(matis->x,0);
2719:               ISGetLocalSize(subs[i],&nl);
2720:               ISGetIndices(subs[i],&idxs);
2721:               VecGetArray(matis->x,&array);
2722:               for (j=0;j<nl;j++) array[idxs[j]] = 1.;
2723:               VecRestoreArray(matis->x,&array);
2724:               ISRestoreIndices(subs[i],&idxs);
2725:               VecPointwiseMult(matis->x,work[0],matis->x);
2726:               MatMult(matis->A,matis->x,matis->y);
2727:               VecPointwiseMult(matis->y,work[1],matis->y);
2728:               VecGetArray(matis->y,&array);
2729:               for (j=0;j<n_interior_dofs;j++) {
2730:                 if (PetscAbsScalar(array[interior_dofs[j]]) > PETSC_SMALL) {
2731:                   valid = PETSC_FALSE;
2732:                   break;
2733:                 }
2734:               }
2735:               VecRestoreArray(matis->y,&array);
2736:             }
2737:             if (valid && nneu) {
2738:               const PetscInt *idxs;
2739:               PetscInt       nzb;

2741:               ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);
2742:               ISGlobalToLocalMappingApply(l2g,IS_GTOLM_DROP,nneu,idxs,&nzb,NULL);
2743:               ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);
2744:               if (nzb) valid = PETSC_FALSE;
2745:             }
2746:             if (valid && pressures) {
2747:               IS       t_pressure_subs,tmp;
2748:               PetscInt i1,i2;

2750:               ISGlobalToLocalMappingApplyIS(l2g,IS_GTOLM_DROP,pressures,&t_pressure_subs);
2751:               ISEmbed(t_zerodiag_subs,t_pressure_subs,PETSC_TRUE,&tmp);
2752:               ISGetLocalSize(tmp,&i1);
2753:               ISGetLocalSize(t_zerodiag_subs,&i2);
2754:               if (i2 != i1) valid = PETSC_FALSE;
2755:               ISDestroy(&t_pressure_subs);
2756:               ISDestroy(&tmp);
2757:             }
2758:             if (valid) {
2759:               ISLocalToGlobalMappingApplyIS(l2g,t_zerodiag_subs,&zerodiag_subs[benign_n]);
2760:               benign_n++;
2761:             } else recompute_zerodiag = PETSC_TRUE;
2762:           }
2763:           ISDestroy(&t_zerodiag_subs);
2764:           ISLocalToGlobalMappingDestroy(&l2g);
2765:         }
2766:       }
2767:     } else { /* there's just one subdomain (or zero if they have not been detected */
2768:       PetscBool valid = PETSC_TRUE;

2770:       if (nneu) valid = PETSC_FALSE;
2771:       if (valid && pressures) {
2772:         ISEqual(pressures,zerodiag,&valid);
2773:       }
2774:       if (valid && checkb) {
2775:         MatMult(matis->A,work[0],matis->x);
2776:         VecPointwiseMult(matis->x,work[1],matis->x);
2777:         VecGetArray(matis->x,&array);
2778:         for (j=0;j<n_interior_dofs;j++) {
2779:           if (PetscAbsScalar(array[interior_dofs[j]]) > PETSC_SMALL) {
2780:             valid = PETSC_FALSE;
2781:             break;
2782:           }
2783:         }
2784:         VecRestoreArray(matis->x,&array);
2785:       }
2786:       if (valid) {
2787:         benign_n = 1;
2788:         PetscMalloc1(benign_n,&zerodiag_subs);
2789:         PetscObjectReference((PetscObject)zerodiag);
2790:         zerodiag_subs[0] = zerodiag;
2791:       }
2792:     }
2793:     if (checkb) {
2794:       VecDestroyVecs(2,&work);
2795:     }
2796:   }
2797:   PetscFree(interior_dofs);

2799:   if (!benign_n) {
2800:     PetscInt n;

2802:     ISDestroy(&zerodiag);
2803:     recompute_zerodiag = PETSC_FALSE;
2804:     MatGetLocalSize(pcbddc->local_mat,&n,NULL);
2805:     if (n) have_null = PETSC_FALSE;
2806:   }

2808:   /* final check for null pressures */
2809:   if (zerodiag && pressures) {
2810:     ISEqual(pressures,zerodiag,&have_null);
2811:   }

2813:   if (recompute_zerodiag) {
2814:     ISDestroy(&zerodiag);
2815:     if (benign_n == 1) {
2816:       PetscObjectReference((PetscObject)zerodiag_subs[0]);
2817:       zerodiag = zerodiag_subs[0];
2818:     } else {
2819:       PetscInt i,nzn,*new_idxs;

2821:       nzn = 0;
2822:       for (i=0;i<benign_n;i++) {
2823:         PetscInt ns;
2824:         ISGetLocalSize(zerodiag_subs[i],&ns);
2825:         nzn += ns;
2826:       }
2827:       PetscMalloc1(nzn,&new_idxs);
2828:       nzn = 0;
2829:       for (i=0;i<benign_n;i++) {
2830:         PetscInt ns,*idxs;
2831:         ISGetLocalSize(zerodiag_subs[i],&ns);
2832:         ISGetIndices(zerodiag_subs[i],(const PetscInt**)&idxs);
2833:         PetscArraycpy(new_idxs+nzn,idxs,ns);
2834:         ISRestoreIndices(zerodiag_subs[i],(const PetscInt**)&idxs);
2835:         nzn += ns;
2836:       }
2837:       PetscSortInt(nzn,new_idxs);
2838:       ISCreateGeneral(PETSC_COMM_SELF,nzn,new_idxs,PETSC_OWN_POINTER,&zerodiag);
2839:     }
2840:     have_null = PETSC_FALSE;
2841:   }

2843:   /* determines if the coarse solver will be singular or not */
2844:   MPIU_Allreduce(&have_null,&pcbddc->benign_null,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));

2846:   /* Prepare matrix to compute no-net-flux */
2847:   if (pcbddc->compute_nonetflux && !pcbddc->divudotp) {
2848:     Mat                    A,loc_divudotp;
2849:     ISLocalToGlobalMapping rl2g,cl2g,l2gmap;
2850:     IS                     row,col,isused = NULL;
2851:     PetscInt               M,N,n,st,n_isused;

2853:     if (pressures) {
2854:       isused = pressures;
2855:     } else {
2856:       isused = zerodiag_save;
2857:     }
2858:     MatGetLocalToGlobalMapping(pc->pmat,&l2gmap,NULL);
2859:     MatISGetLocalMat(pc->pmat,&A);
2860:     MatGetLocalSize(A,&n,NULL);
2861:     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");
2862:     n_isused = 0;
2863:     if (isused) {
2864:       ISGetLocalSize(isused,&n_isused);
2865:     }
2866:     MPI_Scan(&n_isused,&st,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
2867:     st = st-n_isused;
2868:     if (n) {
2869:       const PetscInt *gidxs;

2871:       MatCreateSubMatrix(A,isused,NULL,MAT_INITIAL_MATRIX,&loc_divudotp);
2872:       ISLocalToGlobalMappingGetIndices(l2gmap,&gidxs);
2873:       /* TODO: extend ISCreateStride with st = PETSC_DECIDE */
2874:       ISCreateStride(PetscObjectComm((PetscObject)pc),n_isused,st,1,&row);
2875:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),n,gidxs,PETSC_COPY_VALUES,&col);
2876:       ISLocalToGlobalMappingRestoreIndices(l2gmap,&gidxs);
2877:     } else {
2878:       MatCreateSeqAIJ(PETSC_COMM_SELF,0,0,1,NULL,&loc_divudotp);
2879:       ISCreateStride(PetscObjectComm((PetscObject)pc),n_isused,st,1,&row);
2880:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),0,NULL,PETSC_COPY_VALUES,&col);
2881:     }
2882:     MatGetSize(pc->pmat,NULL,&N);
2883:     ISGetSize(row,&M);
2884:     ISLocalToGlobalMappingCreateIS(row,&rl2g);
2885:     ISLocalToGlobalMappingCreateIS(col,&cl2g);
2886:     ISDestroy(&row);
2887:     ISDestroy(&col);
2888:     MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->divudotp);
2889:     MatSetType(pcbddc->divudotp,MATIS);
2890:     MatSetSizes(pcbddc->divudotp,PETSC_DECIDE,PETSC_DECIDE,M,N);
2891:     MatSetLocalToGlobalMapping(pcbddc->divudotp,rl2g,cl2g);
2892:     ISLocalToGlobalMappingDestroy(&rl2g);
2893:     ISLocalToGlobalMappingDestroy(&cl2g);
2894:     MatISSetLocalMat(pcbddc->divudotp,loc_divudotp);
2895:     MatDestroy(&loc_divudotp);
2896:     MatAssemblyBegin(pcbddc->divudotp,MAT_FINAL_ASSEMBLY);
2897:     MatAssemblyEnd(pcbddc->divudotp,MAT_FINAL_ASSEMBLY);
2898:   }
2899:   ISDestroy(&zerodiag_save);
2900:   ISDestroy(&pressures);
2901:   if (bzerodiag) {
2902:     PetscInt i;

2904:     for (i=0;i<bsp;i++) {
2905:       ISDestroy(&bzerodiag[i]);
2906:     }
2907:     PetscFree(bzerodiag);
2908:   }
2909:   pcbddc->benign_n = benign_n;
2910:   pcbddc->benign_zerodiag_subs = zerodiag_subs;

2912:   /* determines if the problem has subdomains with 0 pressure block */
2913:   have_null = (PetscBool)(!!pcbddc->benign_n);
2914:   MPIU_Allreduce(&have_null,&pcbddc->benign_have_null,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));

2916: project_b0:
2917:   MatGetLocalSize(pcbddc->local_mat,&n,NULL);
2918:   /* change of basis and p0 dofs */
2919:   if (pcbddc->benign_n) {
2920:     PetscInt i,s,*nnz;

2922:     /* local change of basis for pressures */
2923:     MatDestroy(&pcbddc->benign_change);
2924:     MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat),&pcbddc->benign_change);
2925:     MatSetType(pcbddc->benign_change,MATAIJ);
2926:     MatSetSizes(pcbddc->benign_change,n,n,PETSC_DECIDE,PETSC_DECIDE);
2927:     PetscMalloc1(n,&nnz);
2928:     for (i=0;i<n;i++) nnz[i] = 1; /* defaults to identity */
2929:     for (i=0;i<pcbddc->benign_n;i++) {
2930:       const PetscInt *idxs;
2931:       PetscInt       nzs,j;

2933:       ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nzs);
2934:       ISGetIndices(pcbddc->benign_zerodiag_subs[i],&idxs);
2935:       for (j=0;j<nzs-1;j++) nnz[idxs[j]] = 2; /* change on pressures */
2936:       nnz[idxs[nzs-1]] = nzs; /* last local pressure dof in subdomain */
2937:       ISRestoreIndices(pcbddc->benign_zerodiag_subs[i],&idxs);
2938:     }
2939:     MatSeqAIJSetPreallocation(pcbddc->benign_change,0,nnz);
2940:     MatSetOption(pcbddc->benign_change,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
2941:     PetscFree(nnz);
2942:     /* set identity by default */
2943:     for (i=0;i<n;i++) {
2944:       MatSetValue(pcbddc->benign_change,i,i,1.,INSERT_VALUES);
2945:     }
2946:     PetscFree3(pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx,pcbddc->benign_p0);
2947:     PetscMalloc3(pcbddc->benign_n,&pcbddc->benign_p0_lidx,pcbddc->benign_n,&pcbddc->benign_p0_gidx,pcbddc->benign_n,&pcbddc->benign_p0);
2948:     /* set change on pressures */
2949:     for (s=0;s<pcbddc->benign_n;s++) {
2950:       PetscScalar    *array;
2951:       const PetscInt *idxs;
2952:       PetscInt       nzs;

2954:       ISGetLocalSize(pcbddc->benign_zerodiag_subs[s],&nzs);
2955:       ISGetIndices(pcbddc->benign_zerodiag_subs[s],&idxs);
2956:       for (i=0;i<nzs-1;i++) {
2957:         PetscScalar vals[2];
2958:         PetscInt    cols[2];

2960:         cols[0] = idxs[i];
2961:         cols[1] = idxs[nzs-1];
2962:         vals[0] = 1.;
2963:         vals[1] = 1.;
2964:         MatSetValues(pcbddc->benign_change,1,cols,2,cols,vals,INSERT_VALUES);
2965:       }
2966:       PetscMalloc1(nzs,&array);
2967:       for (i=0;i<nzs-1;i++) array[i] = -1.;
2968:       array[nzs-1] = 1.;
2969:       MatSetValues(pcbddc->benign_change,1,idxs+nzs-1,nzs,idxs,array,INSERT_VALUES);
2970:       /* store local idxs for p0 */
2971:       pcbddc->benign_p0_lidx[s] = idxs[nzs-1];
2972:       ISRestoreIndices(pcbddc->benign_zerodiag_subs[s],&idxs);
2973:       PetscFree(array);
2974:     }
2975:     MatAssemblyBegin(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);
2976:     MatAssemblyEnd(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);

2978:     /* project if needed */
2979:     if (pcbddc->benign_change_explicit) {
2980:       Mat M;

2982:       MatPtAP(pcbddc->local_mat,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&M);
2983:       MatDestroy(&pcbddc->local_mat);
2984:       MatSeqAIJCompress(M,&pcbddc->local_mat);
2985:       MatDestroy(&M);
2986:     }
2987:     /* store global idxs for p0 */
2988:     ISLocalToGlobalMappingApply(pc->pmat->rmap->mapping,pcbddc->benign_n,pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx);
2989:   }
2990:   *zerodiaglocal = zerodiag;
2991:   return(0);
2992: }

2994: PetscErrorCode PCBDDCBenignGetOrSetP0(PC pc, Vec v, PetscBool get)
2995: {
2996:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
2997:   PetscScalar    *array;

3001:   if (!pcbddc->benign_sf) {
3002:     PetscSFCreate(PetscObjectComm((PetscObject)pc),&pcbddc->benign_sf);
3003:     PetscSFSetGraphLayout(pcbddc->benign_sf,pc->pmat->rmap,pcbddc->benign_n,NULL,PETSC_OWN_POINTER,pcbddc->benign_p0_gidx);
3004:   }
3005:   if (get) {
3006:     VecGetArrayRead(v,(const PetscScalar**)&array);
3007:     PetscSFBcastBegin(pcbddc->benign_sf,MPIU_SCALAR,array,pcbddc->benign_p0);
3008:     PetscSFBcastEnd(pcbddc->benign_sf,MPIU_SCALAR,array,pcbddc->benign_p0);
3009:     VecRestoreArrayRead(v,(const PetscScalar**)&array);
3010:   } else {
3011:     VecGetArray(v,&array);
3012:     PetscSFReduceBegin(pcbddc->benign_sf,MPIU_SCALAR,pcbddc->benign_p0,array,MPIU_REPLACE);
3013:     PetscSFReduceEnd(pcbddc->benign_sf,MPIU_SCALAR,pcbddc->benign_p0,array,MPIU_REPLACE);
3014:     VecRestoreArray(v,&array);
3015:   }
3016:   return(0);
3017: }

3019: PetscErrorCode PCBDDCBenignPopOrPushB0(PC pc, PetscBool pop)
3020: {
3021:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;

3025:   /* TODO: add error checking
3026:     - avoid nested pop (or push) calls.
3027:     - cannot push before pop.
3028:     - cannot call this if pcbddc->local_mat is NULL
3029:   */
3030:   if (!pcbddc->benign_n) {
3031:     return(0);
3032:   }
3033:   if (pop) {
3034:     if (pcbddc->benign_change_explicit) {
3035:       IS       is_p0;
3036:       MatReuse reuse;

3038:       /* extract B_0 */
3039:       reuse = MAT_INITIAL_MATRIX;
3040:       if (pcbddc->benign_B0) {
3041:         reuse = MAT_REUSE_MATRIX;
3042:       }
3043:       ISCreateGeneral(PETSC_COMM_SELF,pcbddc->benign_n,pcbddc->benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);
3044:       MatCreateSubMatrix(pcbddc->local_mat,is_p0,NULL,reuse,&pcbddc->benign_B0);
3045:       /* remove rows and cols from local problem */
3046:       MatSetOption(pcbddc->local_mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
3047:       MatSetOption(pcbddc->local_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
3048:       MatZeroRowsColumnsIS(pcbddc->local_mat,is_p0,1.0,NULL,NULL);
3049:       ISDestroy(&is_p0);
3050:     } else {
3051:       Mat_IS      *matis = (Mat_IS*)pc->pmat->data;
3052:       PetscScalar *vals;
3053:       PetscInt    i,n,*idxs_ins;

3055:       VecGetLocalSize(matis->y,&n);
3056:       PetscMalloc2(n,&idxs_ins,n,&vals);
3057:       if (!pcbddc->benign_B0) {
3058:         PetscInt *nnz;
3059:         MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat),&pcbddc->benign_B0);
3060:         MatSetType(pcbddc->benign_B0,MATAIJ);
3061:         MatSetSizes(pcbddc->benign_B0,pcbddc->benign_n,n,PETSC_DECIDE,PETSC_DECIDE);
3062:         PetscMalloc1(pcbddc->benign_n,&nnz);
3063:         for (i=0;i<pcbddc->benign_n;i++) {
3064:           ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nnz[i]);
3065:           nnz[i] = n - nnz[i];
3066:         }
3067:         MatSeqAIJSetPreallocation(pcbddc->benign_B0,0,nnz);
3068:         MatSetOption(pcbddc->benign_B0,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
3069:         PetscFree(nnz);
3070:       }

3072:       for (i=0;i<pcbddc->benign_n;i++) {
3073:         PetscScalar *array;
3074:         PetscInt    *idxs,j,nz,cum;

3076:         VecSet(matis->x,0.);
3077:         ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nz);
3078:         ISGetIndices(pcbddc->benign_zerodiag_subs[i],(const PetscInt**)&idxs);
3079:         for (j=0;j<nz;j++) vals[j] = 1.;
3080:         VecSetValues(matis->x,nz,idxs,vals,INSERT_VALUES);
3081:         VecAssemblyBegin(matis->x);
3082:         VecAssemblyEnd(matis->x);
3083:         VecSet(matis->y,0.);
3084:         MatMult(matis->A,matis->x,matis->y);
3085:         VecGetArray(matis->y,&array);
3086:         cum = 0;
3087:         for (j=0;j<n;j++) {
3088:           if (PetscUnlikely(PetscAbsScalar(array[j]) > PETSC_SMALL)) {
3089:             vals[cum] = array[j];
3090:             idxs_ins[cum] = j;
3091:             cum++;
3092:           }
3093:         }
3094:         MatSetValues(pcbddc->benign_B0,1,&i,cum,idxs_ins,vals,INSERT_VALUES);
3095:         VecRestoreArray(matis->y,&array);
3096:         ISRestoreIndices(pcbddc->benign_zerodiag_subs[i],(const PetscInt**)&idxs);
3097:       }
3098:       MatAssemblyBegin(pcbddc->benign_B0,MAT_FINAL_ASSEMBLY);
3099:       MatAssemblyEnd(pcbddc->benign_B0,MAT_FINAL_ASSEMBLY);
3100:       PetscFree2(idxs_ins,vals);
3101:     }
3102:   } else { /* push */
3103:     if (pcbddc->benign_change_explicit) {
3104:       PetscInt i;

3106:       for (i=0;i<pcbddc->benign_n;i++) {
3107:         PetscScalar *B0_vals;
3108:         PetscInt    *B0_cols,B0_ncol;

3110:         MatGetRow(pcbddc->benign_B0,i,&B0_ncol,(const PetscInt**)&B0_cols,(const PetscScalar**)&B0_vals);
3111:         MatSetValues(pcbddc->local_mat,1,pcbddc->benign_p0_lidx+i,B0_ncol,B0_cols,B0_vals,INSERT_VALUES);
3112:         MatSetValues(pcbddc->local_mat,B0_ncol,B0_cols,1,pcbddc->benign_p0_lidx+i,B0_vals,INSERT_VALUES);
3113:         MatSetValue(pcbddc->local_mat,pcbddc->benign_p0_lidx[i],pcbddc->benign_p0_lidx[i],0.0,INSERT_VALUES);
3114:         MatRestoreRow(pcbddc->benign_B0,i,&B0_ncol,(const PetscInt**)&B0_cols,(const PetscScalar**)&B0_vals);
3115:       }
3116:       MatAssemblyBegin(pcbddc->local_mat,MAT_FINAL_ASSEMBLY);
3117:       MatAssemblyEnd(pcbddc->local_mat,MAT_FINAL_ASSEMBLY);
3118:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot push B0!");
3119:   }
3120:   return(0);
3121: }

3123: PetscErrorCode PCBDDCAdaptiveSelection(PC pc)
3124: {
3125:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
3126:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
3127:   PetscBLASInt    B_dummyint,B_neigs,B_ierr,B_lwork;
3128:   PetscBLASInt    *B_iwork,*B_ifail;
3129:   PetscScalar     *work,lwork;
3130:   PetscScalar     *St,*S,*eigv;
3131:   PetscScalar     *Sarray,*Starray;
3132:   PetscReal       *eigs,thresh,lthresh,uthresh;
3133:   PetscInt        i,nmax,nmin,nv,cum,mss,cum2,cumarray,maxneigs;
3134:   PetscBool       allocated_S_St;
3135: #if defined(PETSC_USE_COMPLEX)
3136:   PetscReal       *rwork;
3137: #endif
3138:   PetscErrorCode  ierr;

3141:   if (!sub_schurs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Adaptive selection of constraints requires SubSchurs data");
3142:   if (!sub_schurs->schur_explicit) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS and/or MKL_CPARDISO");
3143:   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);
3144:   PetscLogEventBegin(PC_BDDC_AdaptiveSetUp[pcbddc->current_level],pc,0,0,0);

3146:   if (pcbddc->dbg_flag) {
3147:     PetscViewerFlush(pcbddc->dbg_viewer);
3148:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
3149:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check adaptive selection of constraints\n");
3150:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
3151:   }

3153:   if (pcbddc->dbg_flag) {
3154:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d cc %D (%d,%d).\n",PetscGlobalRank,sub_schurs->n_subs,sub_schurs->is_hermitian,sub_schurs->is_posdef);
3155:   }

3157:   /* max size of subsets */
3158:   mss = 0;
3159:   for (i=0;i<sub_schurs->n_subs;i++) {
3160:     PetscInt subset_size;

3162:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
3163:     mss = PetscMax(mss,subset_size);
3164:   }

3166:   /* min/max and threshold */
3167:   nmax = pcbddc->adaptive_nmax > 0 ? pcbddc->adaptive_nmax : mss;
3168:   nmin = pcbddc->adaptive_nmin > 0 ? pcbddc->adaptive_nmin : 0;
3169:   nmax = PetscMax(nmin,nmax);
3170:   allocated_S_St = PETSC_FALSE;
3171:   if (nmin || !sub_schurs->is_posdef) { /* XXX */
3172:     allocated_S_St = PETSC_TRUE;
3173:   }

3175:   /* allocate lapack workspace */
3176:   cum = cum2 = 0;
3177:   maxneigs = 0;
3178:   for (i=0;i<sub_schurs->n_subs;i++) {
3179:     PetscInt n,subset_size;

3181:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
3182:     n = PetscMin(subset_size,nmax);
3183:     cum += subset_size;
3184:     cum2 += subset_size*n;
3185:     maxneigs = PetscMax(maxneigs,n);
3186:   }
3187:   lwork = 0;
3188:   if (mss) {
3189:     if (sub_schurs->is_symmetric) {
3190:       PetscScalar  sdummy = 0.;
3191:       PetscBLASInt B_itype = 1;
3192:       PetscBLASInt B_N = mss, idummy = 0;
3193:       PetscReal    rdummy = 0.,zero = 0.0;
3194:       PetscReal    eps = 0.0; /* dlamch? */

3196:       B_lwork = -1;
3197:       /* some implementations may complain about NULL pointers, even if we are querying */
3198:       S = &sdummy;
3199:       St = &sdummy;
3200:       eigs = &rdummy;
3201:       eigv = &sdummy;
3202:       B_iwork = &idummy;
3203:       B_ifail = &idummy;
3204: #if defined(PETSC_USE_COMPLEX)
3205:       rwork = &rdummy;
3206: #endif
3207:       thresh = 1.0;
3208:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
3209: #if defined(PETSC_USE_COMPLEX)
3210:       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));
3211: #else
3212:       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));
3213: #endif
3214:       if (B_ierr != 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYGVX Lapack routine %d",(int)B_ierr);
3215:       PetscFPTrapPop();
3216:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented");
3217:   }

3219:   nv = 0;
3220:   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) */
3221:     ISGetLocalSize(sub_schurs->is_vertices,&nv);
3222:   }
3223:   PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);
3224:   if (allocated_S_St) {
3225:     PetscMalloc2(mss*mss,&S,mss*mss,&St);
3226:   }
3227:   PetscMalloc5(mss*mss,&eigv,mss,&eigs,B_lwork,&work,5*mss,&B_iwork,mss,&B_ifail);
3228: #if defined(PETSC_USE_COMPLEX)
3229:   PetscMalloc1(7*mss,&rwork);
3230: #endif
3231:   PetscMalloc5(nv+sub_schurs->n_subs,&pcbddc->adaptive_constraints_n,
3232:                       nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_idxs_ptr,
3233:                       nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_data_ptr,
3234:                       nv+cum,&pcbddc->adaptive_constraints_idxs,
3235:                       nv+cum2,&pcbddc->adaptive_constraints_data);
3236:   PetscArrayzero(pcbddc->adaptive_constraints_n,nv+sub_schurs->n_subs);

3238:   maxneigs = 0;
3239:   cum = cumarray = 0;
3240:   pcbddc->adaptive_constraints_idxs_ptr[0] = 0;
3241:   pcbddc->adaptive_constraints_data_ptr[0] = 0;
3242:   if (sub_schurs->is_vertices && pcbddc->use_vertices) {
3243:     const PetscInt *idxs;

3245:     ISGetIndices(sub_schurs->is_vertices,&idxs);
3246:     for (cum=0;cum<nv;cum++) {
3247:       pcbddc->adaptive_constraints_n[cum] = 1;
3248:       pcbddc->adaptive_constraints_idxs[cum] = idxs[cum];
3249:       pcbddc->adaptive_constraints_data[cum] = 1.0;
3250:       pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum]+1;
3251:       pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum]+1;
3252:     }
3253:     ISRestoreIndices(sub_schurs->is_vertices,&idxs);
3254:   }

3256:   if (mss) { /* multilevel */
3257:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);
3258:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);
3259:   }

3261:   lthresh = pcbddc->adaptive_threshold[0];
3262:   uthresh = pcbddc->adaptive_threshold[1];
3263:   for (i=0;i<sub_schurs->n_subs;i++) {
3264:     const PetscInt *idxs;
3265:     PetscReal      upper,lower;
3266:     PetscInt       j,subset_size,eigs_start = 0;
3267:     PetscBLASInt   B_N;
3268:     PetscBool      same_data = PETSC_FALSE;
3269:     PetscBool      scal = PETSC_FALSE;

3271:     if (pcbddc->use_deluxe_scaling) {
3272:       upper = PETSC_MAX_REAL;
3273:       lower = uthresh;
3274:     } else {
3275:       if (!sub_schurs->is_posdef) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented without deluxe scaling");
3276:       upper = 1./uthresh;
3277:       lower = 0.;
3278:     }
3279:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
3280:     ISGetIndices(sub_schurs->is_subs[i],&idxs);
3281:     PetscBLASIntCast(subset_size,&B_N);
3282:     /* this is experimental: we assume the dofs have been properly grouped to have
3283:        the diagonal blocks Schur complements either positive or negative definite (true for Stokes) */
3284:     if (!sub_schurs->is_posdef) {
3285:       Mat T;

3287:       for (j=0;j<subset_size;j++) {
3288:         if (PetscRealPart(*(Sarray+cumarray+j*(subset_size+1))) < 0.0) {
3289:           MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,Sarray+cumarray,&T);
3290:           MatScale(T,-1.0);
3291:           MatDestroy(&T);
3292:           MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,Starray+cumarray,&T);
3293:           MatScale(T,-1.0);
3294:           MatDestroy(&T);
3295:           if (sub_schurs->change_primal_sub) {
3296:             PetscInt       nz,k;
3297:             const PetscInt *idxs;

3299:             ISGetLocalSize(sub_schurs->change_primal_sub[i],&nz);
3300:             ISGetIndices(sub_schurs->change_primal_sub[i],&idxs);
3301:             for (k=0;k<nz;k++) {
3302:               *( Sarray + cumarray + idxs[k]*(subset_size+1)) *= -1.0;
3303:               *(Starray + cumarray + idxs[k]*(subset_size+1))  = 0.0;
3304:             }
3305:             ISRestoreIndices(sub_schurs->change_primal_sub[i],&idxs);
3306:           }
3307:           scal = PETSC_TRUE;
3308:           break;
3309:         }
3310:       }
3311:     }

3313:     if (allocated_S_St) { /* S and S_t should be copied since we could need them later */
3314:       if (sub_schurs->is_symmetric) {
3315:         PetscInt j,k;
3316:         if (sub_schurs->n_subs == 1) { /* zeroing memory to use PetscArraycmp() later */
3317:           PetscArrayzero(S,subset_size*subset_size);
3318:           PetscArrayzero(St,subset_size*subset_size);
3319:         }
3320:         for (j=0;j<subset_size;j++) {
3321:           for (k=j;k<subset_size;k++) {
3322:             S [j*subset_size+k] = Sarray [cumarray+j*subset_size+k];
3323:             St[j*subset_size+k] = Starray[cumarray+j*subset_size+k];
3324:           }
3325:         }
3326:       } else {
3327:         PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3328:         PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3329:       }
3330:     } else {
3331:       S = Sarray + cumarray;
3332:       St = Starray + cumarray;
3333:     }
3334:     /* see if we can save some work */
3335:     if (sub_schurs->n_subs == 1 && pcbddc->use_deluxe_scaling) {
3336:       PetscArraycmp(S,St,subset_size*subset_size,&same_data);
3337:     }

3339:     if (same_data && !sub_schurs->change) { /* there's no need of constraints here */
3340:       B_neigs = 0;
3341:     } else {
3342:       if (sub_schurs->is_symmetric) {
3343:         PetscBLASInt B_itype = 1;
3344:         PetscBLASInt B_IL, B_IU;
3345:         PetscReal    eps = -1.0; /* dlamch? */
3346:         PetscInt     nmin_s;
3347:         PetscBool    compute_range;

3349:         B_neigs = 0;
3350:         compute_range = (PetscBool)!same_data;
3351:         if (nmin >= subset_size) compute_range = PETSC_FALSE;

3353:         if (pcbddc->dbg_flag) {
3354:           PetscInt nc = 0;

3356:           if (sub_schurs->change_primal_sub) {
3357:             ISGetLocalSize(sub_schurs->change_primal_sub[i],&nc);
3358:           }
3359:           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);
3360:         }

3362:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
3363:         if (compute_range) {

3365:           /* ask for eigenvalues larger than thresh */
3366:           if (sub_schurs->is_posdef) {
3367: #if defined(PETSC_USE_COMPLEX)
3368:             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));
3369: #else
3370:             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));
3371: #endif
3372:             PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3373:           } else { /* no theory so far, but it works nicely */
3374:             PetscInt  recipe = 0,recipe_m = 1;
3375:             PetscReal bb[2];

3377:             PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe",&recipe,NULL);
3378:             switch (recipe) {
3379:             case 0:
3380:               if (scal) { bb[0] = PETSC_MIN_REAL; bb[1] = lthresh; }
3381:               else { bb[0] = uthresh; bb[1] = PETSC_MAX_REAL; }
3382: #if defined(PETSC_USE_COMPLEX)
3383:               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));
3384: #else
3385:               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));
3386: #endif
3387:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3388:               break;
3389:             case 1:
3390:               bb[0] = PETSC_MIN_REAL; bb[1] = lthresh*lthresh;
3391: #if defined(PETSC_USE_COMPLEX)
3392:               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));
3393: #else
3394:               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));
3395: #endif
3396:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3397:               if (!scal) {
3398:                 PetscBLASInt B_neigs2 = 0;

3400:                 bb[0] = PetscMax(lthresh*lthresh,uthresh); bb[1] = PETSC_MAX_REAL;
3401:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3402:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3403: #if defined(PETSC_USE_COMPLEX)
3404:                 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));
3405: #else
3406:                 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));
3407: #endif
3408:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3409:                 B_neigs += B_neigs2;
3410:               }
3411:               break;
3412:             case 2:
3413:               if (scal) {
3414:                 bb[0] = PETSC_MIN_REAL;
3415:                 bb[1] = 0;
3416: #if defined(PETSC_USE_COMPLEX)
3417:                 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));
3418: #else
3419:                 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));
3420: #endif
3421:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3422:               } else {
3423:                 PetscBLASInt B_neigs2 = 0;
3424:                 PetscBool    import = PETSC_FALSE;

3426:                 lthresh = PetscMax(lthresh,0.0);
3427:                 if (lthresh > 0.0) {
3428:                   bb[0] = PETSC_MIN_REAL;
3429:                   bb[1] = lthresh*lthresh;

3431:                   import = PETSC_TRUE;
3432: #if defined(PETSC_USE_COMPLEX)
3433:                   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));
3434: #else
3435:                   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));
3436: #endif
3437:                   PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3438:                 }
3439:                 bb[0] = PetscMax(lthresh*lthresh,uthresh);
3440:                 bb[1] = PETSC_MAX_REAL;
3441:                 if (import) {
3442:                   PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3443:                   PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3444:                 }
3445: #if defined(PETSC_USE_COMPLEX)
3446:                 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));
3447: #else
3448:                 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));
3449: #endif
3450:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3451:                 B_neigs += B_neigs2;
3452:               }
3453:               break;
3454:             case 3:
3455:               if (scal) {
3456:                 PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe3_min_scal",&recipe_m,NULL);
3457:               } else {
3458:                 PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe3_min",&recipe_m,NULL);
3459:               }
3460:               if (!scal) {
3461:                 bb[0] = uthresh;
3462:                 bb[1] = PETSC_MAX_REAL;
3463: #if defined(PETSC_USE_COMPLEX)
3464:                 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));
3465: #else
3466:                 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));
3467: #endif
3468:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3469:               }
3470:               if (recipe_m > 0 && B_N - B_neigs > 0) {
3471:                 PetscBLASInt B_neigs2 = 0;

3473:                 B_IL = 1;
3474:                 PetscBLASIntCast(PetscMin(recipe_m,B_N - B_neigs),&B_IU);
3475:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3476:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3477: #if defined(PETSC_USE_COMPLEX)
3478:                 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));
3479: #else
3480:                 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));
3481: #endif
3482:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3483:                 B_neigs += B_neigs2;
3484:               }
3485:               break;
3486:             case 4:
3487:               bb[0] = PETSC_MIN_REAL; bb[1] = lthresh;
3488: #if defined(PETSC_USE_COMPLEX)
3489:               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));
3490: #else
3491:               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));
3492: #endif
3493:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3494:               {
3495:                 PetscBLASInt B_neigs2 = 0;

3497:                 bb[0] = PetscMax(lthresh+PETSC_SMALL,uthresh); bb[1] = PETSC_MAX_REAL;
3498:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3499:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3500: #if defined(PETSC_USE_COMPLEX)
3501:                 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));
3502: #else
3503:                 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));
3504: #endif
3505:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3506:                 B_neigs += B_neigs2;
3507:               }
3508:               break;
3509:             case 5: /* same as before: first compute all eigenvalues, then filter */
3510: #if defined(PETSC_USE_COMPLEX)
3511:               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));
3512: #else
3513:               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));
3514: #endif
3515:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3516:               {
3517:                 PetscInt e,k,ne;
3518:                 for (e=0,ne=0;e<B_neigs;e++) {
3519:                   if (eigs[e] < lthresh || eigs[e] > uthresh) {
3520:                     for (k=0;k<B_N;k++) S[ne*B_N+k] = eigv[e*B_N+k];
3521:                     eigs[ne] = eigs[e];
3522:                     ne++;
3523:                   }
3524:                 }
3525:                 PetscArraycpy(eigv,S,B_N*ne);
3526:                 B_neigs = ne;
3527:               }
3528:               break;
3529:             default:
3530:               SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Unknown recipe %D",recipe);
3531:               break;
3532:             }
3533:           }
3534:         } else if (!same_data) { /* this is just to see all the eigenvalues */
3535:           B_IU = PetscMax(1,PetscMin(B_N,nmax));
3536:           B_IL = 1;
3537: #if defined(PETSC_USE_COMPLEX)
3538:           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));
3539: #else
3540:           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));
3541: #endif
3542:           PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3543:         } else { /* same_data is true, so just get the adaptive functional requested by the user */
3544:           PetscInt k;
3545:           if (!sub_schurs->change_primal_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
3546:           ISGetLocalSize(sub_schurs->change_primal_sub[i],&nmax);
3547:           PetscBLASIntCast(nmax,&B_neigs);
3548:           nmin = nmax;
3549:           PetscArrayzero(eigv,subset_size*nmax);
3550:           for (k=0;k<nmax;k++) {
3551:             eigs[k] = 1./PETSC_SMALL;
3552:             eigv[k*(subset_size+1)] = 1.0;
3553:           }
3554:         }
3555:         PetscFPTrapPop();
3556:         if (B_ierr) {
3557:           if (B_ierr < 0 ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
3558:           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);
3559:           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);
3560:         }

3562:         if (B_neigs > nmax) {
3563:           if (pcbddc->dbg_flag) {
3564:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, more than maximum required %D.\n",B_neigs,nmax);
3565:           }
3566:           if (pcbddc->use_deluxe_scaling) eigs_start = scal ? 0 : B_neigs-nmax;
3567:           B_neigs = nmax;
3568:         }

3570:         nmin_s = PetscMin(nmin,B_N);
3571:         if (B_neigs < nmin_s) {
3572:           PetscBLASInt B_neigs2 = 0;

3574:           if (pcbddc->use_deluxe_scaling) {
3575:             if (scal) {
3576:               B_IU = nmin_s;
3577:               B_IL = B_neigs + 1;
3578:             } else {
3579:               B_IL = B_N - nmin_s + 1;
3580:               B_IU = B_N - B_neigs;
3581:             }
3582:           } else {
3583:             B_IL = B_neigs + 1;
3584:             B_IU = nmin_s;
3585:           }
3586:           if (pcbddc->dbg_flag) {
3587:             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);
3588:           }
3589:           if (sub_schurs->is_symmetric) {
3590:             PetscInt j,k;
3591:             for (j=0;j<subset_size;j++) {
3592:               for (k=j;k<subset_size;k++) {
3593:                 S [j*subset_size+k] = Sarray [cumarray+j*subset_size+k];
3594:                 St[j*subset_size+k] = Starray[cumarray+j*subset_size+k];
3595:               }
3596:             }
3597:           } else {
3598:             PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
3599:             PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
3600:           }
3601:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
3602: #if defined(PETSC_USE_COMPLEX)
3603:           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));
3604: #else
3605:           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));
3606: #endif
3607:           PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
3608:           PetscFPTrapPop();
3609:           B_neigs += B_neigs2;
3610:         }
3611:         if (B_ierr) {
3612:           if (B_ierr < 0 ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
3613:           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);
3614:           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);
3615:         }
3616:         if (pcbddc->dbg_flag) {
3617:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Got %d eigs\n",B_neigs);
3618:           for (j=0;j<B_neigs;j++) {
3619:             if (eigs[j] == 0.0) {
3620:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     Inf\n");
3621:             } else {
3622:               if (pcbddc->use_deluxe_scaling) {
3623:                 PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",eigs[j+eigs_start]);
3624:               } else {
3625:                 PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",1./eigs[j+eigs_start]);
3626:               }
3627:             }
3628:           }
3629:         }
3630:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented");
3631:     }
3632:     /* change the basis back to the original one */
3633:     if (sub_schurs->change) {
3634:       Mat change,phi,phit;

3636:       if (pcbddc->dbg_flag > 2) {
3637:         PetscInt ii;
3638:         for (ii=0;ii<B_neigs;ii++) {
3639:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector (old basis) %d/%d (%d)\n",ii,B_neigs,B_N);
3640:           for (j=0;j<B_N;j++) {
3641: #if defined(PETSC_USE_COMPLEX)
3642:             PetscReal r = PetscRealPart(eigv[(ii+eigs_start)*subset_size+j]);
3643:             PetscReal c = PetscImaginaryPart(eigv[(ii+eigs_start)*subset_size+j]);
3644:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e + %1.4e i\n",r,c);
3645: #else
3646:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",eigv[(ii+eigs_start)*subset_size+j]);
3647: #endif
3648:           }
3649:         }
3650:       }
3651:       KSPGetOperators(sub_schurs->change[i],&change,NULL);
3652:       MatCreateSeqDense(PETSC_COMM_SELF,subset_size,B_neigs,eigv+eigs_start*subset_size,&phit);
3653:       MatMatMult(change,phit,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&phi);
3654:       MatCopy(phi,phit,SAME_NONZERO_PATTERN);
3655:       MatDestroy(&phit);
3656:       MatDestroy(&phi);
3657:     }
3658:     maxneigs = PetscMax(B_neigs,maxneigs);
3659:     pcbddc->adaptive_constraints_n[i+nv] = B_neigs;
3660:     if (B_neigs) {
3661:       PetscArraycpy(pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum],eigv+eigs_start*subset_size,B_neigs*subset_size);

3663:       if (pcbddc->dbg_flag > 1) {
3664:         PetscInt ii;
3665:         for (ii=0;ii<B_neigs;ii++) {
3666:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector %d/%d (%d)\n",ii,B_neigs,B_N);
3667:           for (j=0;j<B_N;j++) {
3668: #if defined(PETSC_USE_COMPLEX)
3669:             PetscReal r = PetscRealPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
3670:             PetscReal c = PetscImaginaryPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
3671:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e + %1.4e i\n",r,c);
3672: #else
3673:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
3674: #endif
3675:           }
3676:         }
3677:       }
3678:       PetscArraycpy(pcbddc->adaptive_constraints_idxs+pcbddc->adaptive_constraints_idxs_ptr[cum],idxs,subset_size);
3679:       pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum] + subset_size;
3680:       pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum] + subset_size*B_neigs;
3681:       cum++;
3682:     }
3683:     ISRestoreIndices(sub_schurs->is_subs[i],&idxs);
3684:     /* shift for next computation */
3685:     cumarray += subset_size*subset_size;
3686:   }
3687:   if (pcbddc->dbg_flag) {
3688:     PetscViewerFlush(pcbddc->dbg_viewer);
3689:   }

3691:   if (mss) {
3692:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);
3693:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);
3694:     /* destroy matrices (junk) */
3695:     MatDestroy(&sub_schurs->sum_S_Ej_inv_all);
3696:     MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);
3697:   }
3698:   if (allocated_S_St) {
3699:     PetscFree2(S,St);
3700:   }
3701:   PetscFree5(eigv,eigs,work,B_iwork,B_ifail);
3702: #if defined(PETSC_USE_COMPLEX)
3703:   PetscFree(rwork);
3704: #endif
3705:   if (pcbddc->dbg_flag) {
3706:     PetscInt maxneigs_r;
3707:     MPIU_Allreduce(&maxneigs,&maxneigs_r,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));
3708:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of constraints per cc %D\n",maxneigs_r);
3709:   }
3710:   PetscLogEventEnd(PC_BDDC_AdaptiveSetUp[pcbddc->current_level],pc,0,0,0);
3711:   return(0);
3712: }

3714: PetscErrorCode PCBDDCSetUpSolvers(PC pc)
3715: {
3716:   PetscScalar    *coarse_submat_vals;

3720:   /* Setup local scatters R_to_B and (optionally) R_to_D */
3721:   /* PCBDDCSetUpLocalWorkVectors should be called first! */
3722:   PCBDDCSetUpLocalScatters(pc);

3724:   /* Setup local neumann solver ksp_R */
3725:   /* PCBDDCSetUpLocalScatters should be called first! */
3726:   PCBDDCSetUpLocalSolvers(pc,PETSC_FALSE,PETSC_TRUE);

3728:   /*
3729:      Setup local correction and local part of coarse basis.
3730:      Gives back the dense local part of the coarse matrix in column major ordering
3731:   */
3732:   PCBDDCSetUpCorrection(pc,&coarse_submat_vals);

3734:   /* Compute total number of coarse nodes and setup coarse solver */
3735:   PCBDDCSetUpCoarseSolver(pc,coarse_submat_vals);

3737:   /* free */
3738:   PetscFree(coarse_submat_vals);
3739:   return(0);
3740: }

3742: PetscErrorCode PCBDDCResetCustomization(PC pc)
3743: {
3744:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

3748:   ISDestroy(&pcbddc->user_primal_vertices);
3749:   ISDestroy(&pcbddc->user_primal_vertices_local);
3750:   ISDestroy(&pcbddc->NeumannBoundaries);
3751:   ISDestroy(&pcbddc->NeumannBoundariesLocal);
3752:   ISDestroy(&pcbddc->DirichletBoundaries);
3753:   MatNullSpaceDestroy(&pcbddc->onearnullspace);
3754:   PetscFree(pcbddc->onearnullvecs_state);
3755:   ISDestroy(&pcbddc->DirichletBoundariesLocal);
3756:   PCBDDCSetDofsSplitting(pc,0,NULL);
3757:   PCBDDCSetDofsSplittingLocal(pc,0,NULL);
3758:   return(0);
3759: }

3761: PetscErrorCode PCBDDCResetTopography(PC pc)
3762: {
3763:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
3764:   PetscInt       i;

3768:   MatDestroy(&pcbddc->nedcG);
3769:   ISDestroy(&pcbddc->nedclocal);
3770:   MatDestroy(&pcbddc->discretegradient);
3771:   MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);
3772:   MatDestroy(&pcbddc->ChangeOfBasisMatrix);
3773:   MatDestroy(&pcbddc->switch_static_change);
3774:   VecDestroy(&pcbddc->work_change);
3775:   MatDestroy(&pcbddc->ConstraintMatrix);
3776:   MatDestroy(&pcbddc->divudotp);
3777:   ISDestroy(&pcbddc->divudotp_vl2l);
3778:   PCBDDCGraphDestroy(&pcbddc->mat_graph);
3779:   for (i=0;i<pcbddc->n_local_subs;i++) {
3780:     ISDestroy(&pcbddc->local_subs[i]);
3781:   }
3782:   pcbddc->n_local_subs = 0;
3783:   PetscFree(pcbddc->local_subs);
3784:   PCBDDCSubSchursDestroy(&pcbddc->sub_schurs);
3785:   pcbddc->graphanalyzed        = PETSC_FALSE;
3786:   pcbddc->recompute_topography = PETSC_TRUE;
3787:   pcbddc->corner_selected      = PETSC_FALSE;
3788:   return(0);
3789: }

3791: PetscErrorCode PCBDDCResetSolvers(PC pc)
3792: {
3793:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

3797:   VecDestroy(&pcbddc->coarse_vec);
3798:   if (pcbddc->coarse_phi_B) {
3799:     PetscScalar *array;
3800:     MatDenseGetArray(pcbddc->coarse_phi_B,&array);
3801:     PetscFree(array);
3802:   }
3803:   MatDestroy(&pcbddc->coarse_phi_B);
3804:   MatDestroy(&pcbddc->coarse_phi_D);
3805:   MatDestroy(&pcbddc->coarse_psi_B);
3806:   MatDestroy(&pcbddc->coarse_psi_D);
3807:   VecDestroy(&pcbddc->vec1_P);
3808:   VecDestroy(&pcbddc->vec1_C);
3809:   MatDestroy(&pcbddc->local_auxmat2);
3810:   MatDestroy(&pcbddc->local_auxmat1);
3811:   VecDestroy(&pcbddc->vec1_R);
3812:   VecDestroy(&pcbddc->vec2_R);
3813:   ISDestroy(&pcbddc->is_R_local);
3814:   VecScatterDestroy(&pcbddc->R_to_B);
3815:   VecScatterDestroy(&pcbddc->R_to_D);
3816:   VecScatterDestroy(&pcbddc->coarse_loc_to_glob);
3817:   KSPReset(pcbddc->ksp_D);
3818:   KSPReset(pcbddc->ksp_R);
3819:   KSPReset(pcbddc->coarse_ksp);
3820:   MatDestroy(&pcbddc->local_mat);
3821:   PetscFree(pcbddc->primal_indices_local_idxs);
3822:   PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);
3823:   PetscFree(pcbddc->global_primal_indices);
3824:   ISDestroy(&pcbddc->coarse_subassembling);
3825:   MatDestroy(&pcbddc->benign_change);
3826:   VecDestroy(&pcbddc->benign_vec);
3827:   PCBDDCBenignShellMat(pc,PETSC_TRUE);
3828:   MatDestroy(&pcbddc->benign_B0);
3829:   PetscSFDestroy(&pcbddc->benign_sf);
3830:   if (pcbddc->benign_zerodiag_subs) {
3831:     PetscInt i;
3832:     for (i=0;i<pcbddc->benign_n;i++) {
3833:       ISDestroy(&pcbddc->benign_zerodiag_subs[i]);
3834:     }
3835:     PetscFree(pcbddc->benign_zerodiag_subs);
3836:   }
3837:   PetscFree3(pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx,pcbddc->benign_p0);
3838:   return(0);
3839: }

3841: PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
3842: {
3843:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
3844:   PC_IS          *pcis = (PC_IS*)pc->data;
3845:   VecType        impVecType;
3846:   PetscInt       n_constraints,n_R,old_size;

3850:   n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - pcbddc->n_vertices;
3851:   n_R = pcis->n - pcbddc->n_vertices;
3852:   VecGetType(pcis->vec1_N,&impVecType);
3853:   /* local work vectors (try to avoid unneeded work)*/
3854:   /* R nodes */
3855:   old_size = -1;
3856:   if (pcbddc->vec1_R) {
3857:     VecGetSize(pcbddc->vec1_R,&old_size);
3858:   }
3859:   if (n_R != old_size) {
3860:     VecDestroy(&pcbddc->vec1_R);
3861:     VecDestroy(&pcbddc->vec2_R);
3862:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);
3863:     VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);
3864:     VecSetType(pcbddc->vec1_R,impVecType);
3865:     VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);
3866:   }
3867:   /* local primal dofs */
3868:   old_size = -1;
3869:   if (pcbddc->vec1_P) {
3870:     VecGetSize(pcbddc->vec1_P,&old_size);
3871:   }
3872:   if (pcbddc->local_primal_size != old_size) {
3873:     VecDestroy(&pcbddc->vec1_P);
3874:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);
3875:     VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,pcbddc->local_primal_size);
3876:     VecSetType(pcbddc->vec1_P,impVecType);
3877:   }
3878:   /* local explicit constraints */
3879:   old_size = -1;
3880:   if (pcbddc->vec1_C) {
3881:     VecGetSize(pcbddc->vec1_C,&old_size);
3882:   }
3883:   if (n_constraints && n_constraints != old_size) {
3884:     VecDestroy(&pcbddc->vec1_C);
3885:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);
3886:     VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);
3887:     VecSetType(pcbddc->vec1_C,impVecType);
3888:   }
3889:   return(0);
3890: }

3892: PetscErrorCode PCBDDCSetUpCorrection(PC pc, PetscScalar **coarse_submat_vals_n)
3893: {
3894:   PetscErrorCode  ierr;
3895:   /* pointers to pcis and pcbddc */
3896:   PC_IS*          pcis = (PC_IS*)pc->data;
3897:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
3898:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
3899:   /* submatrices of local problem */
3900:   Mat             A_RV,A_VR,A_VV,local_auxmat2_R;
3901:   /* submatrices of local coarse problem */
3902:   Mat             S_VV,S_CV,S_VC,S_CC;
3903:   /* working matrices */
3904:   Mat             C_CR;
3905:   /* additional working stuff */
3906:   PC              pc_R;
3907:   Mat             F,Brhs = NULL;
3908:   Vec             dummy_vec;
3909:   PetscBool       isLU,isCHOL,need_benign_correction,sparserhs;
3910:   PetscScalar     *coarse_submat_vals; /* TODO: use a PETSc matrix */
3911:   PetscScalar     *work;
3912:   PetscInt        *idx_V_B;
3913:   PetscInt        lda_rhs,n,n_vertices,n_constraints,*p0_lidx_I;
3914:   PetscInt        i,n_R,n_D,n_B;
3915:   PetscScalar     one=1.0,m_one=-1.0;

3918:   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");
3919:   PetscLogEventBegin(PC_BDDC_CorrectionSetUp[pcbddc->current_level],pc,0,0,0);

3921:   /* Set Non-overlapping dimensions */
3922:   n_vertices = pcbddc->n_vertices;
3923:   n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - n_vertices;
3924:   n_B = pcis->n_B;
3925:   n_D = pcis->n - n_B;
3926:   n_R = pcis->n - n_vertices;

3928:   /* vertices in boundary numbering */
3929:   PetscMalloc1(n_vertices,&idx_V_B);
3930:   ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,n_vertices,pcbddc->local_primal_ref_node,&i,idx_V_B);
3931:   if (i != n_vertices) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for BDDC vertices! %D != %D",n_vertices,i);

3933:   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
3934:   PetscCalloc1(pcbddc->local_primal_size*pcbddc->local_primal_size,&coarse_submat_vals);
3935:   MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_vertices,coarse_submat_vals,&S_VV);
3936:   MatSeqDenseSetLDA(S_VV,pcbddc->local_primal_size);
3937:   MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_vertices,coarse_submat_vals+n_vertices,&S_CV);
3938:   MatSeqDenseSetLDA(S_CV,pcbddc->local_primal_size);
3939:   MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_constraints,coarse_submat_vals+pcbddc->local_primal_size*n_vertices,&S_VC);
3940:   MatSeqDenseSetLDA(S_VC,pcbddc->local_primal_size);
3941:   MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_constraints,coarse_submat_vals+(pcbddc->local_primal_size+1)*n_vertices,&S_CC);
3942:   MatSeqDenseSetLDA(S_CC,pcbddc->local_primal_size);

3944:   /* determine if can use MatSolve routines instead of calling KSPSolve on ksp_R */
3945:   KSPGetPC(pcbddc->ksp_R,&pc_R);
3946:   PCSetUp(pc_R);
3947:   PetscObjectTypeCompare((PetscObject)pc_R,PCLU,&isLU);
3948:   PetscObjectTypeCompare((PetscObject)pc_R,PCCHOLESKY,&isCHOL);
3949:   lda_rhs = n_R;
3950:   need_benign_correction = PETSC_FALSE;
3951:   if (isLU || isCHOL) {
3952:     PCFactorGetMatrix(pc_R,&F);
3953:   } else if (sub_schurs && sub_schurs->reuse_solver) {
3954:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
3955:     MatFactorType      type;

3957:     F = reuse_solver->F;
3958:     MatGetFactorType(F,&type);
3959:     if (type == MAT_FACTOR_CHOLESKY) isCHOL = PETSC_TRUE;
3960:     if (type == MAT_FACTOR_LU) isLU = PETSC_TRUE;
3961:     MatGetSize(F,&lda_rhs,NULL);
3962:     need_benign_correction = (PetscBool)(!!reuse_solver->benign_n);
3963:   } else F = NULL;

3965:   /* determine if we can use a sparse right-hand side */
3966:   sparserhs = PETSC_FALSE;
3967:   if (F) {
3968:     MatSolverType solver;

3970:     MatFactorGetSolverType(F,&solver);
3971:     PetscStrcmp(solver,MATSOLVERMUMPS,&sparserhs);
3972:   }

3974:   /* allocate workspace */
3975:   n = 0;
3976:   if (n_constraints) {
3977:     n += lda_rhs*n_constraints;
3978:   }
3979:   if (n_vertices) {
3980:     n = PetscMax(2*lda_rhs*n_vertices,n);
3981:     n = PetscMax((lda_rhs+n_B)*n_vertices,n);
3982:   }
3983:   if (!pcbddc->symmetric_primal) {
3984:     n = PetscMax(2*lda_rhs*pcbddc->local_primal_size,n);
3985:   }
3986:   PetscMalloc1(n,&work);

3988:   /* create dummy vector to modify rhs and sol of MatMatSolve (work array will never be used) */
3989:   dummy_vec = NULL;
3990:   if (need_benign_correction && lda_rhs != n_R && F) {
3991:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&dummy_vec);
3992:     VecSetSizes(dummy_vec,lda_rhs,PETSC_DECIDE);
3993:     VecSetType(dummy_vec,((PetscObject)pcis->vec1_N)->type_name);
3994:   }

3996:   MatDestroy(&pcbddc->local_auxmat1);
3997:   MatDestroy(&pcbddc->local_auxmat2);

3999:   /* Precompute stuffs needed for preprocessing and application of BDDC*/
4000:   if (n_constraints) {
4001:     Mat         M3,C_B;
4002:     IS          is_aux;
4003:     PetscScalar *array,*array2;

4005:     /* Extract constraints on R nodes: C_{CR}  */
4006:     ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);
4007:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);
4008:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);

4010:     /* Assemble         local_auxmat2_R =        (- A_{RR}^{-1} C^T_{CR}) needed by BDDC setup */
4011:     /* Assemble pcbddc->local_auxmat2   = R_to_B (- A_{RR}^{-1} C^T_{CR}) needed by BDDC application */
4012:     if (!sparserhs) {
4013:       PetscArrayzero(work,lda_rhs*n_constraints);
4014:       for (i=0;i<n_constraints;i++) {
4015:         const PetscScalar *row_cmat_values;
4016:         const PetscInt    *row_cmat_indices;
4017:         PetscInt          size_of_constraint,j;

4019:         MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);
4020:         for (j=0;j<size_of_constraint;j++) {
4021:           work[row_cmat_indices[j]+i*lda_rhs] = -row_cmat_values[j];
4022:         }
4023:         MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);
4024:       }
4025:       MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,work,&Brhs);
4026:     } else {
4027:       Mat tC_CR;

4029:       MatScale(C_CR,-1.0);
4030:       if (lda_rhs != n_R) {
4031:         PetscScalar *aa;
4032:         PetscInt    r,*ii,*jj;
4033:         PetscBool   done;

4035:         MatGetRowIJ(C_CR,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
4036:         if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"GetRowIJ failed");
4037:         MatSeqAIJGetArray(C_CR,&aa);
4038:         MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,n_constraints,lda_rhs,ii,jj,aa,&tC_CR);
4039:         MatRestoreRowIJ(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,"RestoreRowIJ failed");
4041:       } else {
4042:         PetscObjectReference((PetscObject)C_CR);
4043:         tC_CR = C_CR;
4044:       }
4045:       MatCreateTranspose(tC_CR,&Brhs);
4046:       MatDestroy(&tC_CR);
4047:     }
4048:     MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,NULL,&local_auxmat2_R);
4049:     if (F) {
4050:       if (need_benign_correction) {
4051:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

4053:         /* rhs is already zero on interior dofs, no need to change the rhs */
4054:         PetscArrayzero(reuse_solver->benign_save_vals,pcbddc->benign_n);
4055:       }
4056:       MatMatSolve(F,Brhs,local_auxmat2_R);
4057:       if (need_benign_correction) {
4058:         PetscScalar        *marr;
4059:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

4061:         MatDenseGetArray(local_auxmat2_R,&marr);
4062:         if (lda_rhs != n_R) {
4063:           for (i=0;i<n_constraints;i++) {
4064:             VecPlaceArray(dummy_vec,marr+i*lda_rhs);
4065:             PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_TRUE,PETSC_TRUE);
4066:             VecResetArray(dummy_vec);
4067:           }
4068:         } else {
4069:           for (i=0;i<n_constraints;i++) {
4070:             VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
4071:             PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_TRUE,PETSC_TRUE);
4072:             VecResetArray(pcbddc->vec1_R);
4073:           }
4074:         }
4075:         MatDenseRestoreArray(local_auxmat2_R,&marr);
4076:       }
4077:     } else {
4078:       PetscScalar *marr;

4080:       MatDenseGetArray(local_auxmat2_R,&marr);
4081:       for (i=0;i<n_constraints;i++) {
4082:         VecPlaceArray(pcbddc->vec1_R,work+i*lda_rhs);
4083:         VecPlaceArray(pcbddc->vec2_R,marr+i*lda_rhs);
4084:         KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
4085:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
4086:         VecResetArray(pcbddc->vec1_R);
4087:         VecResetArray(pcbddc->vec2_R);
4088:       }
4089:       MatDenseRestoreArray(local_auxmat2_R,&marr);
4090:     }
4091:     if (sparserhs) {
4092:       MatScale(C_CR,-1.0);
4093:     }
4094:     MatDestroy(&Brhs);
4095:     if (!pcbddc->switch_static) {
4096:       MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_constraints,NULL,&pcbddc->local_auxmat2);
4097:       MatDenseGetArray(pcbddc->local_auxmat2,&array);
4098:       MatDenseGetArray(local_auxmat2_R,&array2);
4099:       for (i=0;i<n_constraints;i++) {
4100:         VecPlaceArray(pcbddc->vec1_R,array2+i*lda_rhs);
4101:         VecPlaceArray(pcis->vec1_B,array+i*n_B);
4102:         VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4103:         VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4104:         VecResetArray(pcis->vec1_B);
4105:         VecResetArray(pcbddc->vec1_R);
4106:       }
4107:       MatDenseRestoreArray(local_auxmat2_R,&array2);
4108:       MatDenseRestoreArray(pcbddc->local_auxmat2,&array);
4109:       MatMatMult(C_B,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);
4110:     } else {
4111:       if (lda_rhs != n_R) {
4112:         IS dummy;

4114:         ISCreateStride(PETSC_COMM_SELF,n_R,0,1,&dummy);
4115:         MatCreateSubMatrix(local_auxmat2_R,dummy,NULL,MAT_INITIAL_MATRIX,&pcbddc->local_auxmat2);
4116:         ISDestroy(&dummy);
4117:       } else {
4118:         PetscObjectReference((PetscObject)local_auxmat2_R);
4119:         pcbddc->local_auxmat2 = local_auxmat2_R;
4120:       }
4121:       MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);
4122:     }
4123:     ISDestroy(&is_aux);
4124:     /* Assemble explicitly S_CC = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1}  */
4125:     MatScale(M3,m_one);
4126:     if (isCHOL) {
4127:       MatCholeskyFactor(M3,NULL,NULL);
4128:     } else {
4129:       MatLUFactor(M3,NULL,NULL,NULL);
4130:     }
4131:     MatSeqDenseInvertFactors_Private(M3);
4132:     /* Assemble local_auxmat1 = S_CC*C_{CB} needed by BDDC application in KSP and in preproc */
4133:     MatMatMult(M3,C_B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);
4134:     MatDestroy(&C_B);
4135:     MatCopy(M3,S_CC,SAME_NONZERO_PATTERN); /* S_CC can have a different LDA, MatMatSolve doesn't support it */
4136:     MatDestroy(&M3);
4137:   }

4139:   /* Get submatrices from subdomain matrix */
4140:   if (n_vertices) {
4141: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4142:     PetscBool oldpin;
4143: #endif
4144:     PetscBool isaij;
4145:     IS        is_aux;

4147:     if (sub_schurs && sub_schurs->reuse_solver) { /* is_R_local is not sorted, ISComplement doesn't like it */
4148:       IS tis;

4150:       ISDuplicate(pcbddc->is_R_local,&tis);
4151:       ISSort(tis);
4152:       ISComplement(tis,0,pcis->n,&is_aux);
4153:       ISDestroy(&tis);
4154:     } else {
4155:       ISComplement(pcbddc->is_R_local,0,pcis->n,&is_aux);
4156:     }
4157: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4158:     oldpin = pcbddc->local_mat->pinnedtocpu;
4159: #endif
4160:     MatPinToCPU(pcbddc->local_mat,PETSC_TRUE);
4161:     MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);
4162:     MatCreateSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);
4163:     PetscObjectBaseTypeCompare((PetscObject)A_VR,MATSEQAIJ,&isaij);
4164:     if (!isaij) { /* TODO REMOVE: MatMatMult(A_VR,A_RRmA_RV) below may raise an error */
4165:       MatConvert(A_VR,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_VR);
4166:     }
4167:     MatCreateSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);
4168: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
4169:     MatPinToCPU(pcbddc->local_mat,oldpin);
4170: #endif
4171:     ISDestroy(&is_aux);
4172:   }

4174:   /* Matrix of coarse basis functions (local) */
4175:   if (pcbddc->coarse_phi_B) {
4176:     PetscInt on_B,on_primal,on_D=n_D;
4177:     if (pcbddc->coarse_phi_D) {
4178:       MatGetSize(pcbddc->coarse_phi_D,&on_D,NULL);
4179:     }
4180:     MatGetSize(pcbddc->coarse_phi_B,&on_B,&on_primal);
4181:     if (on_B != n_B || on_primal != pcbddc->local_primal_size || on_D != n_D) {
4182:       PetscScalar *marray;

4184:       MatDenseGetArray(pcbddc->coarse_phi_B,&marray);
4185:       PetscFree(marray);
4186:       MatDestroy(&pcbddc->coarse_phi_B);
4187:       MatDestroy(&pcbddc->coarse_psi_B);
4188:       MatDestroy(&pcbddc->coarse_phi_D);
4189:       MatDestroy(&pcbddc->coarse_psi_D);
4190:     }
4191:   }

4193:   if (!pcbddc->coarse_phi_B) {
4194:     PetscScalar *marr;

4196:     /* memory size */
4197:     n = n_B*pcbddc->local_primal_size;
4198:     if (pcbddc->switch_static || pcbddc->dbg_flag) n += n_D*pcbddc->local_primal_size;
4199:     if (!pcbddc->symmetric_primal) n *= 2;
4200:     PetscCalloc1(n,&marr);
4201:     MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marr,&pcbddc->coarse_phi_B);
4202:     marr += n_B*pcbddc->local_primal_size;
4203:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
4204:       MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marr,&pcbddc->coarse_phi_D);
4205:       marr += n_D*pcbddc->local_primal_size;
4206:     }
4207:     if (!pcbddc->symmetric_primal) {
4208:       MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marr,&pcbddc->coarse_psi_B);
4209:       marr += n_B*pcbddc->local_primal_size;
4210:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4211:         MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marr,&pcbddc->coarse_psi_D);
4212:       }
4213:     } else {
4214:       PetscObjectReference((PetscObject)pcbddc->coarse_phi_B);
4215:       pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
4216:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4217:         PetscObjectReference((PetscObject)pcbddc->coarse_phi_D);
4218:         pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
4219:       }
4220:     }
4221:   }

4223:   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
4224:   p0_lidx_I = NULL;
4225:   if (pcbddc->benign_n && (pcbddc->switch_static || pcbddc->dbg_flag)) {
4226:     const PetscInt *idxs;

4228:     ISGetIndices(pcis->is_I_local,&idxs);
4229:     PetscMalloc1(pcbddc->benign_n,&p0_lidx_I);
4230:     for (i=0;i<pcbddc->benign_n;i++) {
4231:       PetscFindInt(pcbddc->benign_p0_lidx[i],pcis->n-pcis->n_B,idxs,&p0_lidx_I[i]);
4232:     }
4233:     ISRestoreIndices(pcis->is_I_local,&idxs);
4234:   }

4236:   /* vertices */
4237:   if (n_vertices) {
4238:     PetscBool restoreavr = PETSC_FALSE;

4240:     MatConvert(A_VV,MATDENSE,MAT_INPLACE_MATRIX,&A_VV);

4242:     if (n_R) {
4243:       Mat               A_RRmA_RV,A_RV_bcorr=NULL,S_VVt; /* S_VVt with LDA=N */
4244:       PetscBLASInt      B_N,B_one = 1;
4245:       const PetscScalar *x;
4246:       PetscScalar       *y;

4248:       MatScale(A_RV,m_one);
4249:       if (need_benign_correction) {
4250:         ISLocalToGlobalMapping RtoN;
4251:         IS                     is_p0;
4252:         PetscInt               *idxs_p0,n;

4254:         PetscMalloc1(pcbddc->benign_n,&idxs_p0);
4255:         ISLocalToGlobalMappingCreateIS(pcbddc->is_R_local,&RtoN);
4256:         ISGlobalToLocalMappingApply(RtoN,IS_GTOLM_DROP,pcbddc->benign_n,pcbddc->benign_p0_lidx,&n,idxs_p0);
4257:         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);
4258:         ISLocalToGlobalMappingDestroy(&RtoN);
4259:         ISCreateGeneral(PETSC_COMM_SELF,n,idxs_p0,PETSC_OWN_POINTER,&is_p0);
4260:         MatCreateSubMatrix(A_RV,is_p0,NULL,MAT_INITIAL_MATRIX,&A_RV_bcorr);
4261:         ISDestroy(&is_p0);
4262:       }

4264:       MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,work,&A_RRmA_RV);
4265:       if (!sparserhs || need_benign_correction) {
4266:         if (lda_rhs == n_R) {
4267:           MatConvert(A_RV,MATDENSE,MAT_INPLACE_MATRIX,&A_RV);
4268:         } else {
4269:           PetscScalar    *av,*array;
4270:           const PetscInt *xadj,*adjncy;
4271:           PetscInt       n;
4272:           PetscBool      flg_row;

4274:           array = work+lda_rhs*n_vertices;
4275:           PetscArrayzero(array,lda_rhs*n_vertices);
4276:           MatConvert(A_RV,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_RV);
4277:           MatGetRowIJ(A_RV,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
4278:           MatSeqAIJGetArray(A_RV,&av);
4279:           for (i=0;i<n;i++) {
4280:             PetscInt j;
4281:             for (j=xadj[i];j<xadj[i+1];j++) array[lda_rhs*adjncy[j]+i] = av[j];
4282:           }
4283:           MatRestoreRowIJ(A_RV,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
4284:           MatDestroy(&A_RV);
4285:           MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,array,&A_RV);
4286:         }
4287:         if (need_benign_correction) {
4288:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4289:           PetscScalar        *marr;

4291:           MatDenseGetArray(A_RV,&marr);
4292:           /* need \Phi^T A_RV = (I+L)A_RV, L given by

4294:                  | 0 0  0 | (V)
4295:              L = | 0 0 -1 | (P-p0)
4296:                  | 0 0 -1 | (p0)

4298:           */
4299:           for (i=0;i<reuse_solver->benign_n;i++) {
4300:             const PetscScalar *vals;
4301:             const PetscInt    *idxs,*idxs_zero;
4302:             PetscInt          n,j,nz;

4304:             ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i],&nz);
4305:             ISGetIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
4306:             MatGetRow(A_RV_bcorr,i,&n,&idxs,&vals);
4307:             for (j=0;j<n;j++) {
4308:               PetscScalar val = vals[j];
4309:               PetscInt    k,col = idxs[j];
4310:               for (k=0;k<nz;k++) marr[idxs_zero[k]+lda_rhs*col] -= val;
4311:             }
4312:             MatRestoreRow(A_RV_bcorr,i,&n,&idxs,&vals);
4313:             ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
4314:           }
4315:           MatDenseRestoreArray(A_RV,&marr);
4316:         }
4317:         PetscObjectReference((PetscObject)A_RV);
4318:         Brhs = A_RV;
4319:       } else {
4320:         Mat tA_RVT,A_RVT;

4322:         if (!pcbddc->symmetric_primal) {
4323:           /* A_RV already scaled by -1 */
4324:           MatTranspose(A_RV,MAT_INITIAL_MATRIX,&A_RVT);
4325:         } else {
4326:           restoreavr = PETSC_TRUE;
4327:           MatScale(A_VR,-1.0);
4328:           PetscObjectReference((PetscObject)A_VR);
4329:           A_RVT = A_VR;
4330:         }
4331:         if (lda_rhs != n_R) {
4332:           PetscScalar *aa;
4333:           PetscInt    r,*ii,*jj;
4334:           PetscBool   done;

4336:           MatGetRowIJ(A_RVT,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
4337:           if (!done) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"GetRowIJ failed");
4338:           MatSeqAIJGetArray(A_RVT,&aa);
4339:           MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,n_vertices,lda_rhs,ii,jj,aa,&tA_RVT);
4340:           MatRestoreRowIJ(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,"RestoreRowIJ failed");
4342:         } else {
4343:           PetscObjectReference((PetscObject)A_RVT);
4344:           tA_RVT = A_RVT;
4345:         }
4346:         MatCreateTranspose(tA_RVT,&Brhs);
4347:         MatDestroy(&tA_RVT);
4348:         MatDestroy(&A_RVT);
4349:       }
4350:       if (F) {
4351:         /* need to correct the rhs */
4352:         if (need_benign_correction) {
4353:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4354:           PetscScalar        *marr;

4356:           MatDenseGetArray(Brhs,&marr);
4357:           if (lda_rhs != n_R) {
4358:             for (i=0;i<n_vertices;i++) {
4359:               VecPlaceArray(dummy_vec,marr+i*lda_rhs);
4360:               PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_FALSE,PETSC_TRUE);
4361:               VecResetArray(dummy_vec);
4362:             }
4363:           } else {
4364:             for (i=0;i<n_vertices;i++) {
4365:               VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
4366:               PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_FALSE,PETSC_TRUE);
4367:               VecResetArray(pcbddc->vec1_R);
4368:             }
4369:           }
4370:           MatDenseRestoreArray(Brhs,&marr);
4371:         }
4372:         MatMatSolve(F,Brhs,A_RRmA_RV);
4373:         if (restoreavr) {
4374:           MatScale(A_VR,-1.0);
4375:         }
4376:         /* need to correct the solution */
4377:         if (need_benign_correction) {
4378:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4379:           PetscScalar        *marr;

4381:           MatDenseGetArray(A_RRmA_RV,&marr);
4382:           if (lda_rhs != n_R) {
4383:             for (i=0;i<n_vertices;i++) {
4384:               VecPlaceArray(dummy_vec,marr+i*lda_rhs);
4385:               PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_TRUE,PETSC_TRUE);
4386:               VecResetArray(dummy_vec);
4387:             }
4388:           } else {
4389:             for (i=0;i<n_vertices;i++) {
4390:               VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
4391:               PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_TRUE,PETSC_TRUE);
4392:               VecResetArray(pcbddc->vec1_R);
4393:             }
4394:           }
4395:           MatDenseRestoreArray(A_RRmA_RV,&marr);
4396:         }
4397:       } else {
4398:         MatDenseGetArray(Brhs,&y);
4399:         for (i=0;i<n_vertices;i++) {
4400:           VecPlaceArray(pcbddc->vec1_R,y+i*lda_rhs);
4401:           VecPlaceArray(pcbddc->vec2_R,work+i*lda_rhs);
4402:           KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
4403:           KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
4404:           VecResetArray(pcbddc->vec1_R);
4405:           VecResetArray(pcbddc->vec2_R);
4406:         }
4407:         MatDenseRestoreArray(Brhs,&y);
4408:       }
4409:       MatDestroy(&A_RV);
4410:       MatDestroy(&Brhs);
4411:       /* S_VV and S_CV */
4412:       if (n_constraints) {
4413:         Mat B;

4415:         PetscArrayzero(work+lda_rhs*n_vertices,n_B*n_vertices);
4416:         for (i=0;i<n_vertices;i++) {
4417:           VecPlaceArray(pcbddc->vec1_R,work+i*lda_rhs);
4418:           VecPlaceArray(pcis->vec1_B,work+lda_rhs*n_vertices+i*n_B);
4419:           VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4420:           VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4421:           VecResetArray(pcis->vec1_B);
4422:           VecResetArray(pcbddc->vec1_R);
4423:         }
4424:         MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_vertices,work+lda_rhs*n_vertices,&B);
4425:         MatMatMult(pcbddc->local_auxmat1,B,MAT_REUSE_MATRIX,PETSC_DEFAULT,&S_CV);
4426:         MatDestroy(&B);
4427:         MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,work+lda_rhs*n_vertices,&B);
4428:         MatMatMult(local_auxmat2_R,S_CV,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B);
4429:         MatScale(S_CV,m_one);
4430:         PetscBLASIntCast(lda_rhs*n_vertices,&B_N);
4431:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,work+lda_rhs*n_vertices,&B_one,work,&B_one));
4432:         MatDestroy(&B);
4433:       }
4434:       if (lda_rhs != n_R) {
4435:         MatDestroy(&A_RRmA_RV);
4436:         MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&A_RRmA_RV);
4437:         MatSeqDenseSetLDA(A_RRmA_RV,lda_rhs);
4438:       }
4439:       MatMatMult(A_VR,A_RRmA_RV,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VVt);
4440:       /* need A_VR * \Phi * A_RRmA_RV = A_VR * (I+L)^T * A_RRmA_RV, L given as before */
4441:       if (need_benign_correction) {
4442:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
4443:         PetscScalar      *marr,*sums;

4445:         PetscMalloc1(n_vertices,&sums);
4446:         MatDenseGetArray(S_VVt,&marr);
4447:         for (i=0;i<reuse_solver->benign_n;i++) {
4448:           const PetscScalar *vals;
4449:           const PetscInt    *idxs,*idxs_zero;
4450:           PetscInt          n,j,nz;

4452:           ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i],&nz);
4453:           ISGetIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
4454:           for (j=0;j<n_vertices;j++) {
4455:             PetscInt k;
4456:             sums[j] = 0.;
4457:             for (k=0;k<nz;k++) sums[j] += work[idxs_zero[k]+j*lda_rhs];
4458:           }
4459:           MatGetRow(A_RV_bcorr,i,&n,&idxs,&vals);
4460:           for (j=0;j<n;j++) {
4461:             PetscScalar val = vals[j];
4462:             PetscInt k;
4463:             for (k=0;k<n_vertices;k++) {
4464:               marr[idxs[j]+k*n_vertices] += val*sums[k];
4465:             }
4466:           }
4467:           MatRestoreRow(A_RV_bcorr,i,&n,&idxs,&vals);
4468:           ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
4469:         }
4470:         PetscFree(sums);
4471:         MatDenseRestoreArray(S_VVt,&marr);
4472:         MatDestroy(&A_RV_bcorr);
4473:       }
4474:       MatDestroy(&A_RRmA_RV);
4475:       PetscBLASIntCast(n_vertices*n_vertices,&B_N);
4476:       MatDenseGetArrayRead(A_VV,&x);
4477:       MatDenseGetArray(S_VVt,&y);
4478:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,x,&B_one,y,&B_one));
4479:       MatDenseRestoreArrayRead(A_VV,&x);
4480:       MatDenseRestoreArray(S_VVt,&y);
4481:       MatCopy(S_VVt,S_VV,SAME_NONZERO_PATTERN);
4482:       MatDestroy(&S_VVt);
4483:     } else {
4484:       MatCopy(A_VV,S_VV,SAME_NONZERO_PATTERN);
4485:     }
4486:     MatDestroy(&A_VV);

4488:     /* coarse basis functions */
4489:     for (i=0;i<n_vertices;i++) {
4490:       PetscScalar *y;

4492:       VecPlaceArray(pcbddc->vec1_R,work+lda_rhs*i);
4493:       MatDenseGetArray(pcbddc->coarse_phi_B,&y);
4494:       VecPlaceArray(pcis->vec1_B,y+n_B*i);
4495:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4496:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4497:       y[n_B*i+idx_V_B[i]] = 1.0;
4498:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);
4499:       VecResetArray(pcis->vec1_B);

4501:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4502:         PetscInt j;

4504:         MatDenseGetArray(pcbddc->coarse_phi_D,&y);
4505:         VecPlaceArray(pcis->vec1_D,y+n_D*i);
4506:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4507:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4508:         VecResetArray(pcis->vec1_D);
4509:         for (j=0;j<pcbddc->benign_n;j++) y[n_D*i+p0_lidx_I[j]] = 0.0;
4510:         MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);
4511:       }
4512:       VecResetArray(pcbddc->vec1_R);
4513:     }
4514:     /* if n_R == 0 the object is not destroyed */
4515:     MatDestroy(&A_RV);
4516:   }
4517:   VecDestroy(&dummy_vec);

4519:   if (n_constraints) {
4520:     Mat B;

4522:     MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,work,&B);
4523:     MatScale(S_CC,m_one);
4524:     MatMatMult(local_auxmat2_R,S_CC,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B);
4525:     MatScale(S_CC,m_one);
4526:     if (n_vertices) {
4527:       if (isCHOL || need_benign_correction) { /* if we can solve the interior problem with cholesky, we should also be fine with transposing here */
4528:         MatTranspose(S_CV,MAT_REUSE_MATRIX,&S_VC);
4529:       } else {
4530:         Mat S_VCt;

4532:         if (lda_rhs != n_R) {
4533:           MatDestroy(&B);
4534:           MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work,&B);
4535:           MatSeqDenseSetLDA(B,lda_rhs);
4536:         }
4537:         MatMatMult(A_VR,B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VCt);
4538:         MatCopy(S_VCt,S_VC,SAME_NONZERO_PATTERN);
4539:         MatDestroy(&S_VCt);
4540:       }
4541:     }
4542:     MatDestroy(&B);
4543:     /* coarse basis functions */
4544:     for (i=0;i<n_constraints;i++) {
4545:       PetscScalar *y;

4547:       VecPlaceArray(pcbddc->vec1_R,work+lda_rhs*i);
4548:       MatDenseGetArray(pcbddc->coarse_phi_B,&y);
4549:       VecPlaceArray(pcis->vec1_B,y+n_B*(i+n_vertices));
4550:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4551:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4552:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);
4553:       VecResetArray(pcis->vec1_B);
4554:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4555:         PetscInt j;

4557:         MatDenseGetArray(pcbddc->coarse_phi_D,&y);
4558:         VecPlaceArray(pcis->vec1_D,y+n_D*(i+n_vertices));
4559:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4560:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4561:         VecResetArray(pcis->vec1_D);
4562:         for (j=0;j<pcbddc->benign_n;j++) y[n_D*i+p0_lidx_I[j]] = 0.0;
4563:         MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);
4564:       }
4565:       VecResetArray(pcbddc->vec1_R);
4566:     }
4567:   }
4568:   if (n_constraints) {
4569:     MatDestroy(&local_auxmat2_R);
4570:   }
4571:   PetscFree(p0_lidx_I);

4573:   /* coarse matrix entries relative to B_0 */
4574:   if (pcbddc->benign_n) {
4575:     Mat               B0_B,B0_BPHI;
4576:     IS                is_dummy;
4577:     const PetscScalar *data;
4578:     PetscInt          j;

4580:     ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy);
4581:     MatCreateSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
4582:     ISDestroy(&is_dummy);
4583:     MatMatMult(B0_B,pcbddc->coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&B0_BPHI);
4584:     MatConvert(B0_BPHI,MATSEQDENSE,MAT_INPLACE_MATRIX,&B0_BPHI);
4585:     MatDenseGetArrayRead(B0_BPHI,&data);
4586:     for (j=0;j<pcbddc->benign_n;j++) {
4587:       PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
4588:       for (i=0;i<pcbddc->local_primal_size;i++) {
4589:         coarse_submat_vals[primal_idx*pcbddc->local_primal_size+i] = data[i*pcbddc->benign_n+j];
4590:         coarse_submat_vals[i*pcbddc->local_primal_size+primal_idx] = data[i*pcbddc->benign_n+j];
4591:       }
4592:     }
4593:     MatDenseRestoreArrayRead(B0_BPHI,&data);
4594:     MatDestroy(&B0_B);
4595:     MatDestroy(&B0_BPHI);
4596:   }

4598:   /* compute other basis functions for non-symmetric problems */
4599:   if (!pcbddc->symmetric_primal) {
4600:     Mat         B_V=NULL,B_C=NULL;
4601:     PetscScalar *marray;

4603:     if (n_constraints) {
4604:       Mat S_CCT,C_CRT;

4606:       MatTranspose(C_CR,MAT_INITIAL_MATRIX,&C_CRT);
4607:       MatTranspose(S_CC,MAT_INITIAL_MATRIX,&S_CCT);
4608:       MatMatMult(C_CRT,S_CCT,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B_C);
4609:       MatDestroy(&S_CCT);
4610:       if (n_vertices) {
4611:         Mat S_VCT;

4613:         MatTranspose(S_VC,MAT_INITIAL_MATRIX,&S_VCT);
4614:         MatMatMult(C_CRT,S_VCT,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B_V);
4615:         MatDestroy(&S_VCT);
4616:       }
4617:       MatDestroy(&C_CRT);
4618:     } else {
4619:       MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,NULL,&B_V);
4620:     }
4621:     if (n_vertices && n_R) {
4622:       PetscScalar    *av,*marray;
4623:       const PetscInt *xadj,*adjncy;
4624:       PetscInt       n;
4625:       PetscBool      flg_row;

4627:       /* B_V = B_V - A_VR^T */
4628:       MatConvert(A_VR,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_VR);
4629:       MatGetRowIJ(A_VR,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
4630:       MatSeqAIJGetArray(A_VR,&av);
4631:       MatDenseGetArray(B_V,&marray);
4632:       for (i=0;i<n;i++) {
4633:         PetscInt j;
4634:         for (j=xadj[i];j<xadj[i+1];j++) marray[i*n_R + adjncy[j]] -= av[j];
4635:       }
4636:       MatDenseRestoreArray(B_V,&marray);
4637:       MatRestoreRowIJ(A_VR,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
4638:       MatDestroy(&A_VR);
4639:     }

4641:     /* currently there's no support for MatTransposeMatSolve(F,B,X) */
4642:     if (n_vertices) {
4643:       MatDenseGetArray(B_V,&marray);
4644:       for (i=0;i<n_vertices;i++) {
4645:         VecPlaceArray(pcbddc->vec1_R,marray+i*n_R);
4646:         VecPlaceArray(pcbddc->vec2_R,work+i*n_R);
4647:         KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
4648:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
4649:         VecResetArray(pcbddc->vec1_R);
4650:         VecResetArray(pcbddc->vec2_R);
4651:       }
4652:       MatDenseRestoreArray(B_V,&marray);
4653:     }
4654:     if (B_C) {
4655:       MatDenseGetArray(B_C,&marray);
4656:       for (i=n_vertices;i<n_constraints+n_vertices;i++) {
4657:         VecPlaceArray(pcbddc->vec1_R,marray+(i-n_vertices)*n_R);
4658:         VecPlaceArray(pcbddc->vec2_R,work+i*n_R);
4659:         KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
4660:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
4661:         VecResetArray(pcbddc->vec1_R);
4662:         VecResetArray(pcbddc->vec2_R);
4663:       }
4664:       MatDenseRestoreArray(B_C,&marray);
4665:     }
4666:     /* coarse basis functions */
4667:     for (i=0;i<pcbddc->local_primal_size;i++) {
4668:       PetscScalar *y;

4670:       VecPlaceArray(pcbddc->vec1_R,work+i*n_R);
4671:       MatDenseGetArray(pcbddc->coarse_psi_B,&y);
4672:       VecPlaceArray(pcis->vec1_B,y+n_B*i);
4673:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4674:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
4675:       if (i<n_vertices) {
4676:         y[n_B*i+idx_V_B[i]] = 1.0;
4677:       }
4678:       MatDenseRestoreArray(pcbddc->coarse_psi_B,&y);
4679:       VecResetArray(pcis->vec1_B);

4681:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
4682:         MatDenseGetArray(pcbddc->coarse_psi_D,&y);
4683:         VecPlaceArray(pcis->vec1_D,y+n_D*i);
4684:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4685:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
4686:         VecResetArray(pcis->vec1_D);
4687:         MatDenseRestoreArray(pcbddc->coarse_psi_D,&y);
4688:       }
4689:       VecResetArray(pcbddc->vec1_R);
4690:     }
4691:     MatDestroy(&B_V);
4692:     MatDestroy(&B_C);
4693:   }

4695:   /* free memory */
4696:   PetscFree(idx_V_B);
4697:   MatDestroy(&S_VV);
4698:   MatDestroy(&S_CV);
4699:   MatDestroy(&S_VC);
4700:   MatDestroy(&S_CC);
4701:   PetscFree(work);
4702:   if (n_vertices) {
4703:     MatDestroy(&A_VR);
4704:   }
4705:   if (n_constraints) {
4706:     MatDestroy(&C_CR);
4707:   }
4708:   PetscLogEventEnd(PC_BDDC_CorrectionSetUp[pcbddc->current_level],pc,0,0,0);

4710:   /* Checking coarse_sub_mat and coarse basis functios */
4711:   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
4712:   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
4713:   if (pcbddc->dbg_flag) {
4714:     Mat         coarse_sub_mat;
4715:     Mat         AUXMAT,TM1,TM2,TM3,TM4;
4716:     Mat         coarse_phi_D,coarse_phi_B;
4717:     Mat         coarse_psi_D,coarse_psi_B;
4718:     Mat         A_II,A_BB,A_IB,A_BI;
4719:     Mat         C_B,CPHI;
4720:     IS          is_dummy;
4721:     Vec         mones;
4722:     MatType     checkmattype=MATSEQAIJ;
4723:     PetscReal   real_value;

4725:     if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
4726:       Mat A;
4727:       PCBDDCBenignProject(pc,NULL,NULL,&A);
4728:       MatCreateSubMatrix(A,pcis->is_I_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&A_II);
4729:       MatCreateSubMatrix(A,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&A_IB);
4730:       MatCreateSubMatrix(A,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&A_BI);
4731:       MatCreateSubMatrix(A,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&A_BB);
4732:       MatDestroy(&A);
4733:     } else {
4734:       MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);
4735:       MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);
4736:       MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);
4737:       MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);
4738:     }
4739:     MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);
4740:     MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);
4741:     if (!pcbddc->symmetric_primal) {
4742:       MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);
4743:       MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);
4744:     }
4745:     MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);

4747:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
4748:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat computation (symmetric %d)\n",pcbddc->symmetric_primal);
4749:     PetscViewerFlush(pcbddc->dbg_viewer);
4750:     if (!pcbddc->symmetric_primal) {
4751:       MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4752:       MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);
4753:       MatDestroy(&AUXMAT);
4754:       MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4755:       MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);
4756:       MatDestroy(&AUXMAT);
4757:       MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4758:       MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);
4759:       MatDestroy(&AUXMAT);
4760:       MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4761:       MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);
4762:       MatDestroy(&AUXMAT);
4763:     } else {
4764:       MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);
4765:       MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);
4766:       MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4767:       MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);
4768:       MatDestroy(&AUXMAT);
4769:       MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
4770:       MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);
4771:       MatDestroy(&AUXMAT);
4772:     }
4773:     MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);
4774:     MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);
4775:     MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);
4776:     MatConvert(TM1,MATSEQDENSE,MAT_INPLACE_MATRIX,&TM1);
4777:     if (pcbddc->benign_n) {
4778:       Mat               B0_B,B0_BPHI;
4779:       const PetscScalar *data2;
4780:       PetscScalar       *data;
4781:       PetscInt          j;

4783:       ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy);
4784:       MatCreateSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
4785:       MatMatMult(B0_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&B0_BPHI);
4786:       MatConvert(B0_BPHI,MATSEQDENSE,MAT_INPLACE_MATRIX,&B0_BPHI);
4787:       MatDenseGetArray(TM1,&data);
4788:       MatDenseGetArrayRead(B0_BPHI,&data2);
4789:       for (j=0;j<pcbddc->benign_n;j++) {
4790:         PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
4791:         for (i=0;i<pcbddc->local_primal_size;i++) {
4792:           data[primal_idx*pcbddc->local_primal_size+i] += data2[i*pcbddc->benign_n+j];
4793:           data[i*pcbddc->local_primal_size+primal_idx] += data2[i*pcbddc->benign_n+j];
4794:         }
4795:       }
4796:       MatDenseRestoreArray(TM1,&data);
4797:       MatDenseRestoreArrayRead(B0_BPHI,&data2);
4798:       MatDestroy(&B0_B);
4799:       ISDestroy(&is_dummy);
4800:       MatDestroy(&B0_BPHI);
4801:     }
4802: #if 0
4803:   {
4804:     PetscViewer viewer;
4805:     char filename[256];
4806:     sprintf(filename,"details_local_coarse_mat%d_level%d.m",PetscGlobalRank,pcbddc->current_level);
4807:     PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);
4808:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
4809:     PetscObjectSetName((PetscObject)coarse_sub_mat,"computed");
4810:     MatView(coarse_sub_mat,viewer);
4811:     PetscObjectSetName((PetscObject)TM1,"projected");
4812:     MatView(TM1,viewer);
4813:     if (pcbddc->coarse_phi_B) {
4814:       PetscObjectSetName((PetscObject)pcbddc->coarse_phi_B,"phi_B");
4815:       MatView(pcbddc->coarse_phi_B,viewer);
4816:     }
4817:     if (pcbddc->coarse_phi_D) {
4818:       PetscObjectSetName((PetscObject)pcbddc->coarse_phi_D,"phi_D");
4819:       MatView(pcbddc->coarse_phi_D,viewer);
4820:     }
4821:     if (pcbddc->coarse_psi_B) {
4822:       PetscObjectSetName((PetscObject)pcbddc->coarse_psi_B,"psi_B");
4823:       MatView(pcbddc->coarse_psi_B,viewer);
4824:     }
4825:     if (pcbddc->coarse_psi_D) {
4826:       PetscObjectSetName((PetscObject)pcbddc->coarse_psi_D,"psi_D");
4827:       MatView(pcbddc->coarse_psi_D,viewer);
4828:     }
4829:     PetscObjectSetName((PetscObject)pcbddc->local_mat,"A");
4830:     MatView(pcbddc->local_mat,viewer);
4831:     PetscObjectSetName((PetscObject)pcbddc->ConstraintMatrix,"C");
4832:     MatView(pcbddc->ConstraintMatrix,viewer);
4833:     PetscObjectSetName((PetscObject)pcis->is_I_local,"I");
4834:     ISView(pcis->is_I_local,viewer);
4835:     PetscObjectSetName((PetscObject)pcis->is_B_local,"B");
4836:     ISView(pcis->is_B_local,viewer);
4837:     PetscObjectSetName((PetscObject)pcbddc->is_R_local,"R");
4838:     ISView(pcbddc->is_R_local,viewer);
4839:     PetscViewerDestroy(&viewer);
4840:   }
4841: #endif
4842:     MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);
4843:     MatNorm(TM1,NORM_FROBENIUS,&real_value);
4844:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
4845:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d          matrix error % 1.14e\n",PetscGlobalRank,real_value);

4847:     /* check constraints */
4848:     ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size-pcbddc->benign_n,0,1,&is_dummy);
4849:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);
4850:     if (!pcbddc->benign_n) { /* TODO: add benign case */
4851:       MatMatMult(C_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&CPHI);
4852:     } else {
4853:       PetscScalar *data;
4854:       Mat         tmat;
4855:       MatDenseGetArray(pcbddc->coarse_phi_B,&data);
4856:       MatCreateSeqDense(PETSC_COMM_SELF,pcis->n_B,pcbddc->local_primal_size-pcbddc->benign_n,data,&tmat);
4857:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&data);
4858:       MatMatMult(C_B,tmat,MAT_INITIAL_MATRIX,1.0,&CPHI);
4859:       MatDestroy(&tmat);
4860:     }
4861:     MatCreateVecs(CPHI,&mones,NULL);
4862:     VecSet(mones,-1.0);
4863:     MatDiagonalSet(CPHI,mones,ADD_VALUES);
4864:     MatNorm(CPHI,NORM_FROBENIUS,&real_value);
4865:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d phi constraints error % 1.14e\n",PetscGlobalRank,real_value);
4866:     if (!pcbddc->symmetric_primal) {
4867:       MatMatMult(C_B,coarse_psi_B,MAT_REUSE_MATRIX,1.0,&CPHI);
4868:       VecSet(mones,-1.0);
4869:       MatDiagonalSet(CPHI,mones,ADD_VALUES);
4870:       MatNorm(CPHI,NORM_FROBENIUS,&real_value);
4871:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d psi constraints error % 1.14e\n",PetscGlobalRank,real_value);
4872:     }
4873:     MatDestroy(&C_B);
4874:     MatDestroy(&CPHI);
4875:     ISDestroy(&is_dummy);
4876:     VecDestroy(&mones);
4877:     PetscViewerFlush(pcbddc->dbg_viewer);
4878:     MatDestroy(&A_II);
4879:     MatDestroy(&A_BB);
4880:     MatDestroy(&A_IB);
4881:     MatDestroy(&A_BI);
4882:     MatDestroy(&TM1);
4883:     MatDestroy(&TM2);
4884:     MatDestroy(&TM3);
4885:     MatDestroy(&TM4);
4886:     MatDestroy(&coarse_phi_D);
4887:     MatDestroy(&coarse_phi_B);
4888:     if (!pcbddc->symmetric_primal) {
4889:       MatDestroy(&coarse_psi_D);
4890:       MatDestroy(&coarse_psi_B);
4891:     }
4892:     MatDestroy(&coarse_sub_mat);
4893:   }
4894:   /* FINAL CUDA support (we cannot currently mix viennacl and cuda vectors */
4895:   {
4896:     PetscBool gpu;

4898:     PetscObjectTypeCompare((PetscObject)pcis->vec1_N,VECSEQCUDA,&gpu);
4899:     if (gpu) {
4900:       if (pcbddc->local_auxmat1) {
4901:         MatConvert(pcbddc->local_auxmat1,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->local_auxmat1);
4902:       }
4903:       if (pcbddc->local_auxmat2) {
4904:         MatConvert(pcbddc->local_auxmat2,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->local_auxmat2);
4905:       }
4906:       if (pcbddc->coarse_phi_B) {
4907:         MatConvert(pcbddc->coarse_phi_B,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_phi_B);
4908:       }
4909:       if (pcbddc->coarse_phi_D) {
4910:         MatConvert(pcbddc->coarse_phi_D,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_phi_D);
4911:       }
4912:       if (pcbddc->coarse_psi_B) {
4913:         MatConvert(pcbddc->coarse_psi_B,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_psi_B);
4914:       }
4915:       if (pcbddc->coarse_psi_D) {
4916:         MatConvert(pcbddc->coarse_psi_D,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_psi_D);
4917:       }
4918:     }
4919:   }
4920:   /* get back data */
4921:   *coarse_submat_vals_n = coarse_submat_vals;
4922:   return(0);
4923: }

4925: PetscErrorCode MatCreateSubMatrixUnsorted(Mat A, IS isrow, IS iscol, Mat* B)
4926: {
4927:   Mat            *work_mat;
4928:   IS             isrow_s,iscol_s;
4929:   PetscBool      rsorted,csorted;
4930:   PetscInt       rsize,*idxs_perm_r=NULL,csize,*idxs_perm_c=NULL;

4934:   ISSorted(isrow,&rsorted);
4935:   ISSorted(iscol,&csorted);
4936:   ISGetLocalSize(isrow,&rsize);
4937:   ISGetLocalSize(iscol,&csize);

4939:   if (!rsorted) {
4940:     const PetscInt *idxs;
4941:     PetscInt *idxs_sorted,i;

4943:     PetscMalloc1(rsize,&idxs_perm_r);
4944:     PetscMalloc1(rsize,&idxs_sorted);
4945:     for (i=0;i<rsize;i++) {
4946:       idxs_perm_r[i] = i;
4947:     }
4948:     ISGetIndices(isrow,&idxs);
4949:     PetscSortIntWithPermutation(rsize,idxs,idxs_perm_r);
4950:     for (i=0;i<rsize;i++) {
4951:       idxs_sorted[i] = idxs[idxs_perm_r[i]];
4952:     }
4953:     ISRestoreIndices(isrow,&idxs);
4954:     ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_sorted,PETSC_OWN_POINTER,&isrow_s);
4955:   } else {
4956:     PetscObjectReference((PetscObject)isrow);
4957:     isrow_s = isrow;
4958:   }

4960:   if (!csorted) {
4961:     if (isrow == iscol) {
4962:       PetscObjectReference((PetscObject)isrow_s);
4963:       iscol_s = isrow_s;
4964:     } else {
4965:       const PetscInt *idxs;
4966:       PetscInt       *idxs_sorted,i;

4968:       PetscMalloc1(csize,&idxs_perm_c);
4969:       PetscMalloc1(csize,&idxs_sorted);
4970:       for (i=0;i<csize;i++) {
4971:         idxs_perm_c[i] = i;
4972:       }
4973:       ISGetIndices(iscol,&idxs);
4974:       PetscSortIntWithPermutation(csize,idxs,idxs_perm_c);
4975:       for (i=0;i<csize;i++) {
4976:         idxs_sorted[i] = idxs[idxs_perm_c[i]];
4977:       }
4978:       ISRestoreIndices(iscol,&idxs);
4979:       ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_sorted,PETSC_OWN_POINTER,&iscol_s);
4980:     }
4981:   } else {
4982:     PetscObjectReference((PetscObject)iscol);
4983:     iscol_s = iscol;
4984:   }

4986:   MatCreateSubMatrices(A,1,&isrow_s,&iscol_s,MAT_INITIAL_MATRIX,&work_mat);

4988:   if (!rsorted || !csorted) {
4989:     Mat      new_mat;
4990:     IS       is_perm_r,is_perm_c;

4992:     if (!rsorted) {
4993:       PetscInt *idxs_r,i;
4994:       PetscMalloc1(rsize,&idxs_r);
4995:       for (i=0;i<rsize;i++) {
4996:         idxs_r[idxs_perm_r[i]] = i;
4997:       }
4998:       PetscFree(idxs_perm_r);
4999:       ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_r,PETSC_OWN_POINTER,&is_perm_r);
5000:     } else {
5001:       ISCreateStride(PETSC_COMM_SELF,rsize,0,1,&is_perm_r);
5002:     }
5003:     ISSetPermutation(is_perm_r);

5005:     if (!csorted) {
5006:       if (isrow_s == iscol_s) {
5007:         PetscObjectReference((PetscObject)is_perm_r);
5008:         is_perm_c = is_perm_r;
5009:       } else {
5010:         PetscInt *idxs_c,i;
5011:         if (!idxs_perm_c) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Permutation array not present");
5012:         PetscMalloc1(csize,&idxs_c);
5013:         for (i=0;i<csize;i++) {
5014:           idxs_c[idxs_perm_c[i]] = i;
5015:         }
5016:         PetscFree(idxs_perm_c);
5017:         ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_c,PETSC_OWN_POINTER,&is_perm_c);
5018:       }
5019:     } else {
5020:       ISCreateStride(PETSC_COMM_SELF,csize,0,1,&is_perm_c);
5021:     }
5022:     ISSetPermutation(is_perm_c);

5024:     MatPermute(work_mat[0],is_perm_r,is_perm_c,&new_mat);
5025:     MatDestroy(&work_mat[0]);
5026:     work_mat[0] = new_mat;
5027:     ISDestroy(&is_perm_r);
5028:     ISDestroy(&is_perm_c);
5029:   }

5031:   PetscObjectReference((PetscObject)work_mat[0]);
5032:   *B = work_mat[0];
5033:   MatDestroyMatrices(1,&work_mat);
5034:   ISDestroy(&isrow_s);
5035:   ISDestroy(&iscol_s);
5036:   return(0);
5037: }

5039: PetscErrorCode PCBDDCComputeLocalMatrix(PC pc, Mat ChangeOfBasisMatrix)
5040: {
5041:   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
5042:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
5043:   Mat            new_mat,lA;
5044:   IS             is_local,is_global;
5045:   PetscInt       local_size;
5046:   PetscBool      isseqaij;

5050:   MatDestroy(&pcbddc->local_mat);
5051:   MatGetSize(matis->A,&local_size,NULL);
5052:   ISCreateStride(PetscObjectComm((PetscObject)matis->A),local_size,0,1,&is_local);
5053:   ISLocalToGlobalMappingApplyIS(pc->pmat->rmap->mapping,is_local,&is_global);
5054:   ISDestroy(&is_local);
5055:   MatCreateSubMatrixUnsorted(ChangeOfBasisMatrix,is_global,is_global,&new_mat);
5056:   ISDestroy(&is_global);

5058:   if (pcbddc->dbg_flag) {
5059:     Vec       x,x_change;
5060:     PetscReal error;

5062:     MatCreateVecs(ChangeOfBasisMatrix,&x,&x_change);
5063:     VecSetRandom(x,NULL);
5064:     MatMult(ChangeOfBasisMatrix,x,x_change);
5065:     VecScatterBegin(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);
5066:     VecScatterEnd(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);
5067:     MatMult(new_mat,matis->x,matis->y);
5068:     if (!pcbddc->change_interior) {
5069:       const PetscScalar *x,*y,*v;
5070:       PetscReal         lerror = 0.;
5071:       PetscInt          i;

5073:       VecGetArrayRead(matis->x,&x);
5074:       VecGetArrayRead(matis->y,&y);
5075:       VecGetArrayRead(matis->counter,&v);
5076:       for (i=0;i<local_size;i++)
5077:         if (PetscRealPart(v[i]) < 1.5 && PetscAbsScalar(x[i]-y[i]) > lerror)
5078:           lerror = PetscAbsScalar(x[i]-y[i]);
5079:       VecRestoreArrayRead(matis->x,&x);
5080:       VecRestoreArrayRead(matis->y,&y);
5081:       VecRestoreArrayRead(matis->counter,&v);
5082:       MPIU_Allreduce(&lerror,&error,1,MPIU_REAL,MPI_MAX,PetscObjectComm((PetscObject)pc));
5083:       if (error > PETSC_SMALL) {
5084:         if (!pcbddc->user_ChangeOfBasisMatrix || pcbddc->current_level) {
5085:           SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on I: %1.6e",error);
5086:         } else {
5087:           SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_USER,"Error global vs local change on I: %1.6e",error);
5088:         }
5089:       }
5090:     }
5091:     VecScatterBegin(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);
5092:     VecScatterEnd(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);
5093:     VecAXPY(x,-1.0,x_change);
5094:     VecNorm(x,NORM_INFINITY,&error);
5095:     if (error > PETSC_SMALL) {
5096:       if (!pcbddc->user_ChangeOfBasisMatrix || pcbddc->current_level) {
5097:         SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on N: %1.6e",error);
5098:       } else {
5099:         SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_USER,"Error global vs local change on N: %1.6e",error);
5100:       }
5101:     }
5102:     VecDestroy(&x);
5103:     VecDestroy(&x_change);
5104:   }

5106:   /* lA is present if we are setting up an inner BDDC for a saddle point FETI-DP */
5107:   PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);

5109:   /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
5110:   PetscObjectBaseTypeCompare((PetscObject)matis->A,MATSEQAIJ,&isseqaij);
5111:   if (isseqaij) {
5112:     MatDestroy(&pcbddc->local_mat);
5113:     MatPtAP(matis->A,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);
5114:     if (lA) {
5115:       Mat work;
5116:       MatPtAP(lA,new_mat,MAT_INITIAL_MATRIX,2.0,&work);
5117:       PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject)work);
5118:       MatDestroy(&work);
5119:     }
5120:   } else {
5121:     Mat work_mat;

5123:     MatDestroy(&pcbddc->local_mat);
5124:     MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);
5125:     MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);
5126:     MatDestroy(&work_mat);
5127:     if (lA) {
5128:       Mat work;
5129:       MatConvert(lA,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);
5130:       MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&work);
5131:       PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject)work);
5132:       MatDestroy(&work);
5133:     }
5134:   }
5135:   if (matis->A->symmetric_set) {
5136:     MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);
5137: #if !defined(PETSC_USE_COMPLEX)
5138:     MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);
5139: #endif
5140:   }
5141:   MatDestroy(&new_mat);
5142:   return(0);
5143: }

5145: PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
5146: {
5147:   PC_IS*          pcis = (PC_IS*)(pc->data);
5148:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
5149:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5150:   PetscInt        *idx_R_local=NULL;
5151:   PetscInt        n_vertices,i,j,n_R,n_D,n_B;
5152:   PetscInt        vbs,bs;
5153:   PetscBT         bitmask=NULL;
5154:   PetscErrorCode  ierr;

5157:   /*
5158:     No need to setup local scatters if
5159:       - primal space is unchanged
5160:         AND
5161:       - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
5162:         AND
5163:       - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
5164:   */
5165:   if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) {
5166:     return(0);
5167:   }
5168:   /* destroy old objects */
5169:   ISDestroy(&pcbddc->is_R_local);
5170:   VecScatterDestroy(&pcbddc->R_to_B);
5171:   VecScatterDestroy(&pcbddc->R_to_D);
5172:   /* Set Non-overlapping dimensions */
5173:   n_B = pcis->n_B;
5174:   n_D = pcis->n - n_B;
5175:   n_vertices = pcbddc->n_vertices;

5177:   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */

5179:   /* create auxiliary bitmask and allocate workspace */
5180:   if (!sub_schurs || !sub_schurs->reuse_solver) {
5181:     PetscMalloc1(pcis->n-n_vertices,&idx_R_local);
5182:     PetscBTCreate(pcis->n,&bitmask);
5183:     for (i=0;i<n_vertices;i++) {
5184:       PetscBTSet(bitmask,pcbddc->local_primal_ref_node[i]);
5185:     }

5187:     for (i=0, n_R=0; i<pcis->n; i++) {
5188:       if (!PetscBTLookup(bitmask,i)) {
5189:         idx_R_local[n_R++] = i;
5190:       }
5191:     }
5192:   } else { /* A different ordering (already computed) is present if we are reusing the Schur solver */
5193:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5195:     ISGetIndices(reuse_solver->is_R,(const PetscInt**)&idx_R_local);
5196:     ISGetLocalSize(reuse_solver->is_R,&n_R);
5197:   }

5199:   /* Block code */
5200:   vbs = 1;
5201:   MatGetBlockSize(pcbddc->local_mat,&bs);
5202:   if (bs>1 && !(n_vertices%bs)) {
5203:     PetscBool is_blocked = PETSC_TRUE;
5204:     PetscInt  *vary;
5205:     if (!sub_schurs || !sub_schurs->reuse_solver) {
5206:       PetscMalloc1(pcis->n/bs,&vary);
5207:       PetscArrayzero(vary,pcis->n/bs);
5208:       /* Verify that the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
5209:       /* 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 */
5210:       for (i=0; i<n_vertices; i++) vary[pcbddc->local_primal_ref_node[i]/bs]++;
5211:       for (i=0; i<pcis->n/bs; i++) {
5212:         if (vary[i]!=0 && vary[i]!=bs) {
5213:           is_blocked = PETSC_FALSE;
5214:           break;
5215:         }
5216:       }
5217:       PetscFree(vary);
5218:     } else {
5219:       /* Verify directly the R set */
5220:       for (i=0; i<n_R/bs; i++) {
5221:         PetscInt j,node=idx_R_local[bs*i];
5222:         for (j=1; j<bs; j++) {
5223:           if (node != idx_R_local[bs*i+j]-j) {
5224:             is_blocked = PETSC_FALSE;
5225:             break;
5226:           }
5227:         }
5228:       }
5229:     }
5230:     if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
5231:       vbs = bs;
5232:       for (i=0;i<n_R/vbs;i++) {
5233:         idx_R_local[i] = idx_R_local[vbs*i]/vbs;
5234:       }
5235:     }
5236:   }
5237:   ISCreateBlock(PETSC_COMM_SELF,vbs,n_R/vbs,idx_R_local,PETSC_COPY_VALUES,&pcbddc->is_R_local);
5238:   if (sub_schurs && sub_schurs->reuse_solver) {
5239:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5241:     ISRestoreIndices(reuse_solver->is_R,(const PetscInt**)&idx_R_local);
5242:     ISDestroy(&reuse_solver->is_R);
5243:     PetscObjectReference((PetscObject)pcbddc->is_R_local);
5244:     reuse_solver->is_R = pcbddc->is_R_local;
5245:   } else {
5246:     PetscFree(idx_R_local);
5247:   }

5249:   /* print some info if requested */
5250:   if (pcbddc->dbg_flag) {
5251:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
5252:     PetscViewerFlush(pcbddc->dbg_viewer);
5253:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
5254:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);
5255:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %D, dirichlet_size = %D, boundary_size = %D\n",pcis->n,n_D,n_B);
5256:     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);
5257:     PetscViewerFlush(pcbddc->dbg_viewer);
5258:   }

5260:   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
5261:   if (!sub_schurs || !sub_schurs->reuse_solver) {
5262:     IS       is_aux1,is_aux2;
5263:     PetscInt *aux_array1,*aux_array2,*is_indices,*idx_R_local;

5265:     ISGetIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);
5266:     PetscMalloc1(pcis->n_B-n_vertices,&aux_array1);
5267:     PetscMalloc1(pcis->n_B-n_vertices,&aux_array2);
5268:     ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);
5269:     for (i=0; i<n_D; i++) {
5270:       PetscBTSet(bitmask,is_indices[i]);
5271:     }
5272:     ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);
5273:     for (i=0, j=0; i<n_R; i++) {
5274:       if (!PetscBTLookup(bitmask,idx_R_local[i])) {
5275:         aux_array1[j++] = i;
5276:       }
5277:     }
5278:     ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);
5279:     ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);
5280:     for (i=0, j=0; i<n_B; i++) {
5281:       if (!PetscBTLookup(bitmask,is_indices[i])) {
5282:         aux_array2[j++] = i;
5283:       }
5284:     }
5285:     ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);
5286:     ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);
5287:     VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);
5288:     ISDestroy(&is_aux1);
5289:     ISDestroy(&is_aux2);

5291:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
5292:       PetscMalloc1(n_D,&aux_array1);
5293:       for (i=0, j=0; i<n_R; i++) {
5294:         if (PetscBTLookup(bitmask,idx_R_local[i])) {
5295:           aux_array1[j++] = i;
5296:         }
5297:       }
5298:       ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);
5299:       VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);
5300:       ISDestroy(&is_aux1);
5301:     }
5302:     PetscBTDestroy(&bitmask);
5303:     ISRestoreIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);
5304:   } else {
5305:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
5306:     IS                 tis;
5307:     PetscInt           schur_size;

5309:     ISGetLocalSize(reuse_solver->is_B,&schur_size);
5310:     ISCreateStride(PETSC_COMM_SELF,schur_size,n_D,1,&tis);
5311:     VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_B,reuse_solver->is_B,&pcbddc->R_to_B);
5312:     ISDestroy(&tis);
5313:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
5314:       ISCreateStride(PETSC_COMM_SELF,n_D,0,1,&tis);
5315:       VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);
5316:       ISDestroy(&tis);
5317:     }
5318:   }
5319:   return(0);
5320: }

5322: static PetscErrorCode MatNullSpacePropagateAny_Private(Mat A, IS is, Mat B)
5323: {
5324:   MatNullSpace   NullSpace;
5325:   Mat            dmat;
5326:   const Vec      *nullvecs;
5327:   Vec            v,v2,*nullvecs2;
5328:   VecScatter     sct = NULL;
5329:   PetscInt       k,nnsp_size,bsiz,bsiz2,n,N,bs;
5330:   PetscBool      nnsp_has_cnst;

5334:   if (!is && !B) { /* MATIS */
5335:     Mat_IS* matis = (Mat_IS*)A->data;

5337:     if (!B) {
5338:       MatISGetLocalMat(A,&B);
5339:     }
5340:     sct  = matis->cctx;
5341:     PetscObjectReference((PetscObject)sct);
5342:   } else {
5343:     MatGetNullSpace(B,&NullSpace);
5344:     if (!NullSpace) {
5345:       MatGetNearNullSpace(B,&NullSpace);
5346:     }
5347:     if (NullSpace) return(0);
5348:   }
5349:   MatGetNullSpace(A,&NullSpace);
5350:   if (!NullSpace) {
5351:     MatGetNearNullSpace(A,&NullSpace);
5352:   }
5353:   if (!NullSpace) return(0);

5355:   MatCreateVecs(A,&v,NULL);
5356:   MatCreateVecs(B,&v2,NULL);
5357:   if (!sct) {
5358:     VecScatterCreate(v,is,v2,NULL,&sct);
5359:   }
5360:   MatNullSpaceGetVecs(NullSpace,&nnsp_has_cnst,&nnsp_size,(const Vec**)&nullvecs);
5361:   bsiz = bsiz2 = nnsp_size+!!nnsp_has_cnst;
5362:   PetscMalloc1(bsiz,&nullvecs2);
5363:   VecGetBlockSize(v2,&bs);
5364:   VecGetSize(v2,&N);
5365:   VecGetLocalSize(v2,&n);
5366:   MatCreateDense(PetscObjectComm((PetscObject)B),n,PETSC_DECIDE,N,bsiz,NULL,&dmat);
5367:   for (k=0;k<nnsp_size;k++) {
5368:     PetscScalar *arr;

5370:     MatDenseGetColumn(dmat,k,&arr);
5371:     VecCreateMPIWithArray(PetscObjectComm((PetscObject)B),bs,n,N,arr,&nullvecs2[k]);
5372:     VecScatterBegin(sct,nullvecs[k],nullvecs2[k],INSERT_VALUES,SCATTER_FORWARD);
5373:     VecScatterEnd(sct,nullvecs[k],nullvecs2[k],INSERT_VALUES,SCATTER_FORWARD);
5374:     MatDenseRestoreColumn(dmat,&arr);
5375:   }
5376:   if (nnsp_has_cnst) {
5377:     PetscScalar *arr;

5379:     MatDenseGetColumn(dmat,nnsp_size,&arr);
5380:     VecCreateMPIWithArray(PetscObjectComm((PetscObject)B),bs,n,N,arr,&nullvecs2[nnsp_size]);
5381:     VecSet(nullvecs2[nnsp_size],1.0);
5382:     MatDenseRestoreColumn(dmat,&arr);
5383:   }
5384:   PCBDDCOrthonormalizeVecs(&bsiz2,nullvecs2);
5385:   MatNullSpaceCreate(PetscObjectComm((PetscObject)B),PETSC_FALSE,bsiz2,nullvecs2,&NullSpace);
5386:   if (bsiz2 != bsiz) {
5387:     Mat      dmat2;
5388:     IS       r,c;
5389:     PetscInt rst,ren;

5391:     MatGetOwnershipRange(dmat,&rst,&ren);
5392:     ISCreateStride(PetscObjectComm((PetscObject)B),ren-rst,rst,1,&r);
5393:     ISCreateStride(PetscObjectComm((PetscObject)B),0,bsiz2,1,&c);
5394:     MatCreateSubMatrix(dmat,r,c,MAT_INITIAL_MATRIX,&dmat2);
5395:     MatDestroy(&dmat);
5396:     ISDestroy(&r);
5397:     ISDestroy(&c);
5398:     dmat = dmat2;
5399:   }
5400:   PetscObjectCompose((PetscObject)NullSpace,"_PBDDC_Null_dmat",(PetscObject)dmat);
5401:   MatDestroy(&dmat);
5402:   for (k=0;k<bsiz;k++) {
5403:     VecDestroy(&nullvecs2[k]);
5404:   }
5405:   PetscFree(nullvecs2);
5406:   MatSetNearNullSpace(B,NullSpace);
5407:   MatNullSpaceDestroy(&NullSpace);
5408:   VecDestroy(&v);
5409:   VecDestroy(&v2);
5410:   VecScatterDestroy(&sct);
5411:   return(0);
5412: }

5414: PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, PetscBool dirichlet, PetscBool neumann)
5415: {
5416:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
5417:   PC_IS          *pcis = (PC_IS*)pc->data;
5418:   PC             pc_temp;
5419:   Mat            A_RR;
5420:   MatNullSpace   nnsp;
5421:   MatReuse       reuse;
5422:   PetscScalar    m_one = -1.0;
5423:   PetscReal      value;
5424:   PetscInt       n_D,n_R;
5425:   PetscBool      issbaij,opts;
5427:   void           (*f)(void) = 0;
5428:   char           dir_prefix[256],neu_prefix[256],str_level[16];
5429:   size_t         len;

5432:   PetscLogEventBegin(PC_BDDC_LocalSolvers[pcbddc->current_level],pc,0,0,0);
5433:   /* approximate solver, propagate NearNullSpace if needed */
5434:   if (!pc->setupcalled && (pcbddc->NullSpace_corr[0] || pcbddc->NullSpace_corr[2])) {
5435:     MatNullSpace gnnsp1,gnnsp2;
5436:     PetscBool    lhas,ghas;

5438:     MatGetNearNullSpace(pcbddc->local_mat,&nnsp);
5439:     MatGetNearNullSpace(pc->pmat,&gnnsp1);
5440:     MatGetNullSpace(pc->pmat,&gnnsp2);
5441:     lhas = nnsp ? PETSC_TRUE : PETSC_FALSE;
5442:     MPIU_Allreduce(&lhas,&ghas,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
5443:     if (!ghas && (gnnsp1 || gnnsp2)) {
5444:       MatNullSpacePropagateAny_Private(pc->pmat,NULL,NULL);
5445:     }
5446:   }

5448:   /* compute prefixes */
5449:   PetscStrcpy(dir_prefix,"");
5450:   PetscStrcpy(neu_prefix,"");
5451:   if (!pcbddc->current_level) {
5452:     PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,sizeof(dir_prefix));
5453:     PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,sizeof(neu_prefix));
5454:     PetscStrlcat(dir_prefix,"pc_bddc_dirichlet_",sizeof(dir_prefix));
5455:     PetscStrlcat(neu_prefix,"pc_bddc_neumann_",sizeof(neu_prefix));
5456:   } else {
5457:     PetscSNPrintf(str_level,sizeof(str_level),"l%d_",(int)(pcbddc->current_level));
5458:     PetscStrlen(((PetscObject)pc)->prefix,&len);
5459:     len -= 15; /* remove "pc_bddc_coarse_" */
5460:     if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
5461:     if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
5462:     /* Nonstandard use of PetscStrncpy() to only copy a portion of the input string */
5463:     PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,len+1);
5464:     PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len+1);
5465:     PetscStrlcat(dir_prefix,"pc_bddc_dirichlet_",sizeof(dir_prefix));
5466:     PetscStrlcat(neu_prefix,"pc_bddc_neumann_",sizeof(neu_prefix));
5467:     PetscStrlcat(dir_prefix,str_level,sizeof(dir_prefix));
5468:     PetscStrlcat(neu_prefix,str_level,sizeof(neu_prefix));
5469:   }

5471:   /* DIRICHLET PROBLEM */
5472:   if (dirichlet) {
5473:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5474:     if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
5475:       if (!sub_schurs || !sub_schurs->reuse_solver) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented");
5476:       if (pcbddc->dbg_flag) {
5477:         Mat    A_IIn;

5479:         PCBDDCBenignProject(pc,pcis->is_I_local,pcis->is_I_local,&A_IIn);
5480:         MatDestroy(&pcis->A_II);
5481:         pcis->A_II = A_IIn;
5482:       }
5483:     }
5484:     if (pcbddc->local_mat->symmetric_set) {
5485:       MatSetOption(pcis->A_II,MAT_SYMMETRIC,pcbddc->local_mat->symmetric);
5486:     }
5487:     /* Matrix for Dirichlet problem is pcis->A_II */
5488:     n_D  = pcis->n - pcis->n_B;
5489:     opts = PETSC_FALSE;
5490:     if (!pcbddc->ksp_D) { /* create object if not yet build */
5491:       opts = PETSC_TRUE;
5492:       KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);
5493:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);
5494:       /* default */
5495:       KSPSetType(pcbddc->ksp_D,KSPPREONLY);
5496:       KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);
5497:       PetscObjectTypeCompare((PetscObject)pcis->pA_II,MATSEQSBAIJ,&issbaij);
5498:       KSPGetPC(pcbddc->ksp_D,&pc_temp);
5499:       if (issbaij) {
5500:         PCSetType(pc_temp,PCCHOLESKY);
5501:       } else {
5502:         PCSetType(pc_temp,PCLU);
5503:       }
5504:       KSPSetErrorIfNotConverged(pcbddc->ksp_D,pc->erroriffailure);
5505:     }
5506:     MatSetOptionsPrefix(pcis->pA_II,((PetscObject)pcbddc->ksp_D)->prefix);
5507:     KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->pA_II);
5508:     /* Allow user's customization */
5509:     if (opts) {
5510:       KSPSetFromOptions(pcbddc->ksp_D);
5511:     }
5512:     MatGetNearNullSpace(pcis->pA_II,&nnsp);
5513:     if (pcbddc->NullSpace_corr[0] && !nnsp) { /* approximate solver, propagate NearNullSpace */
5514:       MatNullSpacePropagateAny_Private(pcbddc->local_mat,pcis->is_I_local,pcis->pA_II);
5515:     }
5516:     MatGetNearNullSpace(pcis->pA_II,&nnsp);
5517:     KSPGetPC(pcbddc->ksp_D,&pc_temp);
5518:     PetscObjectQueryFunction((PetscObject)pc_temp,"PCSetCoordinates_C",&f);
5519:     if (f && pcbddc->mat_graph->cloc && !nnsp) {
5520:       PetscReal      *coords = pcbddc->mat_graph->coords,*scoords;
5521:       const PetscInt *idxs;
5522:       PetscInt       cdim = pcbddc->mat_graph->cdim,nl,i,d;

5524:       ISGetLocalSize(pcis->is_I_local,&nl);
5525:       ISGetIndices(pcis->is_I_local,&idxs);
5526:       PetscMalloc1(nl*cdim,&scoords);
5527:       for (i=0;i<nl;i++) {
5528:         for (d=0;d<cdim;d++) {
5529:           scoords[i*cdim+d] = coords[idxs[i]*cdim+d];
5530:         }
5531:       }
5532:       ISRestoreIndices(pcis->is_I_local,&idxs);
5533:       PCSetCoordinates(pc_temp,cdim,nl,scoords);
5534:       PetscFree(scoords);
5535:     }
5536:     if (sub_schurs && sub_schurs->reuse_solver) {
5537:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5539:       KSPSetPC(pcbddc->ksp_D,reuse_solver->interior_solver);
5540:     }

5542:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
5543:     if (!n_D) {
5544:       KSPGetPC(pcbddc->ksp_D,&pc_temp);
5545:       PCSetType(pc_temp,PCNONE);
5546:     }
5547:     KSPSetUp(pcbddc->ksp_D);
5548:     /* set ksp_D into pcis data */
5549:     PetscObjectReference((PetscObject)pcbddc->ksp_D);
5550:     KSPDestroy(&pcis->ksp_D);
5551:     pcis->ksp_D = pcbddc->ksp_D;
5552:   }

5554:   /* NEUMANN PROBLEM */
5555:   A_RR = 0;
5556:   if (neumann) {
5557:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5558:     PetscInt        ibs,mbs;
5559:     PetscBool       issbaij, reuse_neumann_solver;
5560:     Mat_IS*         matis = (Mat_IS*)pc->pmat->data;

5562:     reuse_neumann_solver = PETSC_FALSE;
5563:     if (sub_schurs && sub_schurs->reuse_solver) {
5564:       IS iP;

5566:       reuse_neumann_solver = PETSC_TRUE;
5567:       PetscObjectQuery((PetscObject)sub_schurs->A,"__KSPFETIDP_iP",(PetscObject*)&iP);
5568:       if (iP) reuse_neumann_solver = PETSC_FALSE;
5569:     }
5570:     /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
5571:     ISGetSize(pcbddc->is_R_local,&n_R);
5572:     if (pcbddc->ksp_R) { /* already created ksp */
5573:       PetscInt nn_R;
5574:       KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);
5575:       PetscObjectReference((PetscObject)A_RR);
5576:       MatGetSize(A_RR,&nn_R,NULL);
5577:       if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
5578:         KSPReset(pcbddc->ksp_R);
5579:         MatDestroy(&A_RR);
5580:         reuse = MAT_INITIAL_MATRIX;
5581:       } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
5582:         if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
5583:           MatDestroy(&A_RR);
5584:           reuse = MAT_INITIAL_MATRIX;
5585:         } else { /* safe to reuse the matrix */
5586:           reuse = MAT_REUSE_MATRIX;
5587:         }
5588:       }
5589:       /* last check */
5590:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
5591:         MatDestroy(&A_RR);
5592:         reuse = MAT_INITIAL_MATRIX;
5593:       }
5594:     } else { /* first time, so we need to create the matrix */
5595:       reuse = MAT_INITIAL_MATRIX;
5596:     }
5597:     /* convert pcbddc->local_mat if needed later in PCBDDCSetUpCorrection */
5598:     MatGetBlockSize(pcbddc->local_mat,&mbs);
5599:     ISGetBlockSize(pcbddc->is_R_local,&ibs);
5600:     PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);
5601:     if (ibs != mbs) { /* need to convert to SEQAIJ to extract any submatrix with is_R_local */
5602:       if (matis->A == pcbddc->local_mat) {
5603:         MatDestroy(&pcbddc->local_mat);
5604:         MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
5605:       } else {
5606:         MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
5607:       }
5608:     } else if (issbaij) { /* need to convert to BAIJ to get offdiagonal blocks */
5609:       if (matis->A == pcbddc->local_mat) {
5610:         MatDestroy(&pcbddc->local_mat);
5611:         MatConvert(matis->A,MATSEQBAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
5612:       } else {
5613:         MatConvert(pcbddc->local_mat,MATSEQBAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
5614:       }
5615:     }
5616:     /* extract A_RR */
5617:     if (reuse_neumann_solver) {
5618:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5620:       if (pcbddc->dbg_flag) { /* we need A_RR to test the solver later */
5621:         MatDestroy(&A_RR);
5622:         if (reuse_solver->benign_n) { /* we are not using the explicit change of basis on the pressures */
5623:           PCBDDCBenignProject(pc,pcbddc->is_R_local,pcbddc->is_R_local,&A_RR);
5624:         } else {
5625:           MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_RR);
5626:         }
5627:       } else {
5628:         MatDestroy(&A_RR);
5629:         PCGetOperators(reuse_solver->correction_solver,&A_RR,NULL);
5630:         PetscObjectReference((PetscObject)A_RR);
5631:       }
5632:     } else { /* we have to build the neumann solver, so we need to extract the relevant matrix */
5633:       MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);
5634:     }
5635:     if (pcbddc->local_mat->symmetric_set) {
5636:       MatSetOption(A_RR,MAT_SYMMETRIC,pcbddc->local_mat->symmetric);
5637:     }
5638:     opts = PETSC_FALSE;
5639:     if (!pcbddc->ksp_R) { /* create object if not present */
5640:       opts = PETSC_TRUE;
5641:       KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);
5642:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);
5643:       /* default */
5644:       KSPSetType(pcbddc->ksp_R,KSPPREONLY);
5645:       KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);
5646:       KSPGetPC(pcbddc->ksp_R,&pc_temp);
5647:       PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);
5648:       if (issbaij) {
5649:         PCSetType(pc_temp,PCCHOLESKY);
5650:       } else {
5651:         PCSetType(pc_temp,PCLU);
5652:       }
5653:       KSPSetErrorIfNotConverged(pcbddc->ksp_R,pc->erroriffailure);
5654:     }
5655:     KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);
5656:     MatSetOptionsPrefix(A_RR,((PetscObject)pcbddc->ksp_R)->prefix);
5657:     if (opts) { /* Allow user's customization once */
5658:       KSPSetFromOptions(pcbddc->ksp_R);
5659:     }
5660:     MatGetNearNullSpace(A_RR,&nnsp);
5661:     if (pcbddc->NullSpace_corr[2] && !nnsp) { /* approximate solver, propagate NearNullSpace */
5662:       MatNullSpacePropagateAny_Private(pcbddc->local_mat,pcbddc->is_R_local,A_RR);
5663:     }
5664:     MatGetNearNullSpace(A_RR,&nnsp);
5665:     KSPGetPC(pcbddc->ksp_R,&pc_temp);
5666:     PetscObjectQueryFunction((PetscObject)pc_temp,"PCSetCoordinates_C",&f);
5667:     if (f && pcbddc->mat_graph->cloc && !nnsp) {
5668:       PetscReal      *coords = pcbddc->mat_graph->coords,*scoords;
5669:       const PetscInt *idxs;
5670:       PetscInt       cdim = pcbddc->mat_graph->cdim,nl,i,d;

5672:       ISGetLocalSize(pcbddc->is_R_local,&nl);
5673:       ISGetIndices(pcbddc->is_R_local,&idxs);
5674:       PetscMalloc1(nl*cdim,&scoords);
5675:       for (i=0;i<nl;i++) {
5676:         for (d=0;d<cdim;d++) {
5677:           scoords[i*cdim+d] = coords[idxs[i]*cdim+d];
5678:         }
5679:       }
5680:       ISRestoreIndices(pcbddc->is_R_local,&idxs);
5681:       PCSetCoordinates(pc_temp,cdim,nl,scoords);
5682:       PetscFree(scoords);
5683:     }

5685:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
5686:     if (!n_R) {
5687:       KSPGetPC(pcbddc->ksp_R,&pc_temp);
5688:       PCSetType(pc_temp,PCNONE);
5689:     }
5690:     /* Reuse solver if it is present */
5691:     if (reuse_neumann_solver) {
5692:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5694:       KSPSetPC(pcbddc->ksp_R,reuse_solver->correction_solver);
5695:     }
5696:     KSPSetUp(pcbddc->ksp_R);
5697:   }

5699:   if (pcbddc->dbg_flag) {
5700:     PetscViewerFlush(pcbddc->dbg_viewer);
5701:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
5702:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
5703:   }
5704:   PetscLogEventEnd(PC_BDDC_LocalSolvers[pcbddc->current_level],pc,0,0,0);

5706:   /* adapt Dirichlet and Neumann solvers if a nullspace correction has been requested */
5707:   if (pcbddc->NullSpace_corr[0]) {
5708:     PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);
5709:   }
5710:   if (dirichlet && pcbddc->NullSpace_corr[0] && !pcbddc->switch_static) {
5711:     PCBDDCNullSpaceAssembleCorrection(pc,PETSC_TRUE,pcbddc->NullSpace_corr[1]);
5712:   }
5713:   if (neumann && pcbddc->NullSpace_corr[2]) {
5714:     PCBDDCNullSpaceAssembleCorrection(pc,PETSC_FALSE,pcbddc->NullSpace_corr[3]);
5715:   }
5716:   /* check Dirichlet and Neumann solvers */
5717:   if (pcbddc->dbg_flag) {
5718:     if (dirichlet) { /* Dirichlet */
5719:       VecSetRandom(pcis->vec1_D,NULL);
5720:       MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);
5721:       KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);
5722:       KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);
5723:       VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);
5724:       VecNorm(pcis->vec1_D,NORM_INFINITY,&value);
5725:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve (%s) = % 1.14e \n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_D))->prefix,value);
5726:       PetscViewerFlush(pcbddc->dbg_viewer);
5727:     }
5728:     if (neumann) { /* Neumann */
5729:       VecSetRandom(pcbddc->vec1_R,NULL);
5730:       MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);
5731:       KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);
5732:       KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
5733:       VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);
5734:       VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);
5735:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann solve (%s) = % 1.14e\n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_R))->prefix,value);
5736:       PetscViewerFlush(pcbddc->dbg_viewer);
5737:     }
5738:   }
5739:   /* free Neumann problem's matrix */
5740:   MatDestroy(&A_RR);
5741:   return(0);
5742: }

5744: static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec inout_B, Vec inout_D, PetscBool applytranspose)
5745: {
5746:   PetscErrorCode  ierr;
5747:   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
5748:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
5749:   PetscBool       reuse_solver = sub_schurs ? ( sub_schurs->reuse_solver ? PETSC_TRUE : PETSC_FALSE ) : PETSC_FALSE;

5752:   if (!reuse_solver) {
5753:     VecSet(pcbddc->vec1_R,0.);
5754:   }
5755:   if (!pcbddc->switch_static) {
5756:     if (applytranspose && pcbddc->local_auxmat1) {
5757:       MatMultTranspose(pcbddc->local_auxmat2,inout_B,pcbddc->vec1_C);
5758:       MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);
5759:     }
5760:     if (!reuse_solver) {
5761:       VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5762:       VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5763:     } else {
5764:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5766:       VecScatterBegin(reuse_solver->correction_scatter_B,inout_B,reuse_solver->rhs_B,INSERT_VALUES,SCATTER_FORWARD);
5767:       VecScatterEnd(reuse_solver->correction_scatter_B,inout_B,reuse_solver->rhs_B,INSERT_VALUES,SCATTER_FORWARD);
5768:     }
5769:   } else {
5770:     VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5771:     VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5772:     VecScatterBegin(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5773:     VecScatterEnd(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5774:     if (applytranspose && pcbddc->local_auxmat1) {
5775:       MatMultTranspose(pcbddc->local_auxmat2,pcbddc->vec1_R,pcbddc->vec1_C);
5776:       MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);
5777:       VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5778:       VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
5779:     }
5780:   }
5781:   if (!reuse_solver || pcbddc->switch_static) {
5782:     if (applytranspose) {
5783:       KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);
5784:     } else {
5785:       KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);
5786:     }
5787:     KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec1_R);
5788:   } else {
5789:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5791:     if (applytranspose) {
5792:       MatFactorSolveSchurComplementTranspose(reuse_solver->F,reuse_solver->rhs_B,reuse_solver->sol_B);
5793:     } else {
5794:       MatFactorSolveSchurComplement(reuse_solver->F,reuse_solver->rhs_B,reuse_solver->sol_B);
5795:     }
5796:   }
5797:   VecSet(inout_B,0.);
5798:   if (!pcbddc->switch_static) {
5799:     if (!reuse_solver) {
5800:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5801:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5802:     } else {
5803:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

5805:       VecScatterBegin(reuse_solver->correction_scatter_B,reuse_solver->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);
5806:       VecScatterEnd(reuse_solver->correction_scatter_B,reuse_solver->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);
5807:     }
5808:     if (!applytranspose && pcbddc->local_auxmat1) {
5809:       MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);
5810:       MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,inout_B,inout_B);
5811:     }
5812:   } else {
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:     VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
5816:     VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
5817:     if (!applytranspose && pcbddc->local_auxmat1) {
5818:       MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);
5819:       MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);
5820:     }
5821:     VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5822:     VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
5823:     VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
5824:     VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
5825:   }
5826:   return(0);
5827: }

5829: /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
5830: PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
5831: {
5833:   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
5834:   PC_IS*            pcis = (PC_IS*)  (pc->data);
5835:   const PetscScalar zero = 0.0;

5838:   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
5839:   if (!pcbddc->benign_apply_coarse_only) {
5840:     if (applytranspose) {
5841:       MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);
5842:       if (pcbddc->switch_static) { MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P); }
5843:     } else {
5844:       MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);
5845:       if (pcbddc->switch_static) { MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P); }
5846:     }
5847:   } else {
5848:     VecSet(pcbddc->vec1_P,zero);
5849:   }

5851:   /* add p0 to the last value of vec1_P holding the coarse dof relative to p0 */
5852:   if (pcbddc->benign_n) {
5853:     PetscScalar *array;
5854:     PetscInt    j;

5856:     VecGetArray(pcbddc->vec1_P,&array);
5857:     for (j=0;j<pcbddc->benign_n;j++) array[pcbddc->local_primal_size-pcbddc->benign_n+j] += pcbddc->benign_p0[j];
5858:     VecRestoreArray(pcbddc->vec1_P,&array);
5859:   }

5861:   /* start communications from local primal nodes to rhs of coarse solver */
5862:   VecSet(pcbddc->coarse_vec,zero);
5863:   PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);
5864:   PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);

5866:   /* Coarse solution -> rhs and sol updated inside PCBDDCScattarCoarseDataBegin/End */
5867:   if (pcbddc->coarse_ksp) {
5868:     Mat          coarse_mat;
5869:     Vec          rhs,sol;
5870:     MatNullSpace nullsp;
5871:     PetscBool    isbddc = PETSC_FALSE;

5873:     if (pcbddc->benign_have_null) {
5874:       PC        coarse_pc;

5876:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
5877:       PetscObjectTypeCompare((PetscObject)coarse_pc,PCBDDC,&isbddc);
5878:       /* we need to propagate to coarser levels the need for a possible benign correction */
5879:       if (isbddc && pcbddc->benign_apply_coarse_only && !pcbddc->benign_skip_correction) {
5880:         PC_BDDC* coarsepcbddc = (PC_BDDC*)(coarse_pc->data);
5881:         coarsepcbddc->benign_skip_correction = PETSC_FALSE;
5882:         coarsepcbddc->benign_apply_coarse_only = PETSC_TRUE;
5883:       }
5884:     }
5885:     KSPGetRhs(pcbddc->coarse_ksp,&rhs);
5886:     KSPGetSolution(pcbddc->coarse_ksp,&sol);
5887:     KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);
5888:     if (applytranspose) {
5889:       if (pcbddc->benign_apply_coarse_only) SETERRQ(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),PETSC_ERR_SUP,"Not yet implemented");
5890:       KSPSolveTranspose(pcbddc->coarse_ksp,rhs,sol);
5891:       KSPCheckSolve(pcbddc->coarse_ksp,pc,sol);
5892:       MatGetTransposeNullSpace(coarse_mat,&nullsp);
5893:       if (nullsp) {
5894:         MatNullSpaceRemove(nullsp,sol);
5895:       }
5896:     } else {
5897:       MatGetNullSpace(coarse_mat,&nullsp);
5898:       if (pcbddc->benign_apply_coarse_only && isbddc) { /* need just to apply the coarse preconditioner during presolve */
5899:         PC        coarse_pc;

5901:         if (nullsp) {
5902:           MatNullSpaceRemove(nullsp,rhs);
5903:         }
5904:         KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
5905:         PCPreSolve(coarse_pc,pcbddc->coarse_ksp);
5906:         PCBDDCBenignRemoveInterior(coarse_pc,rhs,sol);
5907:         PCPostSolve(coarse_pc,pcbddc->coarse_ksp);
5908:       } else {
5909:         KSPSolve(pcbddc->coarse_ksp,rhs,sol);
5910:         KSPCheckSolve(pcbddc->coarse_ksp,pc,sol);
5911:         if (nullsp) {
5912:           MatNullSpaceRemove(nullsp,sol);
5913:         }
5914:       }
5915:     }
5916:     /* we don't need the benign correction at coarser levels anymore */
5917:     if (pcbddc->benign_have_null && isbddc) {
5918:       PC        coarse_pc;
5919:       PC_BDDC*  coarsepcbddc;

5921:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
5922:       coarsepcbddc = (PC_BDDC*)(coarse_pc->data);
5923:       coarsepcbddc->benign_skip_correction = PETSC_TRUE;
5924:       coarsepcbddc->benign_apply_coarse_only = PETSC_FALSE;
5925:     }
5926:   }

5928:   /* Local solution on R nodes */
5929:   if (pcis->n && !pcbddc->benign_apply_coarse_only) {
5930:     PCBDDCSolveSubstructureCorrection(pc,pcis->vec1_B,pcis->vec1_D,applytranspose);
5931:   }
5932:   /* communications from coarse sol to local primal nodes */
5933:   PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);
5934:   PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);

5936:   /* Sum contributions from the two levels */
5937:   if (!pcbddc->benign_apply_coarse_only) {
5938:     if (applytranspose) {
5939:       MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);
5940:       if (pcbddc->switch_static) { MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D); }
5941:     } else {
5942:       MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);
5943:       if (pcbddc->switch_static) { MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D); }
5944:     }
5945:     /* store p0 */
5946:     if (pcbddc->benign_n) {
5947:       PetscScalar *array;
5948:       PetscInt    j;

5950:       VecGetArray(pcbddc->vec1_P,&array);
5951:       for (j=0;j<pcbddc->benign_n;j++) pcbddc->benign_p0[j] = array[pcbddc->local_primal_size-pcbddc->benign_n+j];
5952:       VecRestoreArray(pcbddc->vec1_P,&array);
5953:     }
5954:   } else { /* expand the coarse solution */
5955:     if (applytranspose) {
5956:       MatMult(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B);
5957:     } else {
5958:       MatMult(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B);
5959:     }
5960:   }
5961:   return(0);
5962: }

5964: PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
5965: {
5966:   PC_BDDC*          pcbddc = (PC_BDDC*)(pc->data);
5967:   Vec               from,to;
5968:   const PetscScalar *array;
5969:   PetscErrorCode    ierr;

5972:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
5973:     from = pcbddc->coarse_vec;
5974:     to = pcbddc->vec1_P;
5975:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
5976:       Vec tvec;

5978:       KSPGetRhs(pcbddc->coarse_ksp,&tvec);
5979:       VecResetArray(tvec);
5980:       KSPGetSolution(pcbddc->coarse_ksp,&tvec);
5981:       VecGetArrayRead(tvec,&array);
5982:       VecPlaceArray(from,array);
5983:       VecRestoreArrayRead(tvec,&array);
5984:     }
5985:   } else { /* from local to global -> put data in coarse right hand side */
5986:     from = pcbddc->vec1_P;
5987:     to = pcbddc->coarse_vec;
5988:   }
5989:   VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);
5990:   return(0);
5991: }

5993: PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
5994: {
5995:   PC_BDDC*          pcbddc = (PC_BDDC*)(pc->data);
5996:   Vec               from,to;
5997:   const PetscScalar *array;
5998:   PetscErrorCode    ierr;

6001:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
6002:     from = pcbddc->coarse_vec;
6003:     to = pcbddc->vec1_P;
6004:   } else { /* from local to global -> put data in coarse right hand side */
6005:     from = pcbddc->vec1_P;
6006:     to = pcbddc->coarse_vec;
6007:   }
6008:   VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);
6009:   if (smode == SCATTER_FORWARD) {
6010:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
6011:       Vec tvec;

6013:       KSPGetRhs(pcbddc->coarse_ksp,&tvec);
6014:       VecGetArrayRead(to,&array);
6015:       VecPlaceArray(tvec,array);
6016:       VecRestoreArrayRead(to,&array);
6017:     }
6018:   } else {
6019:     if (pcbddc->coarse_ksp) { /* restore array of pcbddc->coarse_vec */
6020:      VecResetArray(from);
6021:     }
6022:   }
6023:   return(0);
6024: }

6026: /* uncomment for testing purposes */
6027: /* #define PETSC_MISSING_LAPACK_GESVD 1 */
6028: PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
6029: {
6030:   PetscErrorCode    ierr;
6031:   PC_IS*            pcis = (PC_IS*)(pc->data);
6032:   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
6033:   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
6034:   /* one and zero */
6035:   PetscScalar       one=1.0,zero=0.0;
6036:   /* space to store constraints and their local indices */
6037:   PetscScalar       *constraints_data;
6038:   PetscInt          *constraints_idxs,*constraints_idxs_B;
6039:   PetscInt          *constraints_idxs_ptr,*constraints_data_ptr;
6040:   PetscInt          *constraints_n;
6041:   /* iterators */
6042:   PetscInt          i,j,k,total_counts,total_counts_cc,cum;
6043:   /* BLAS integers */
6044:   PetscBLASInt      lwork,lierr;
6045:   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
6046:   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
6047:   /* reuse */
6048:   PetscInt          olocal_primal_size,olocal_primal_size_cc;
6049:   PetscInt          *olocal_primal_ref_node,*olocal_primal_ref_mult;
6050:   /* change of basis */
6051:   PetscBool         qr_needed;
6052:   PetscBT           change_basis,qr_needed_idx;
6053:   /* auxiliary stuff */
6054:   PetscInt          *nnz,*is_indices;
6055:   PetscInt          ncc;
6056:   /* some quantities */
6057:   PetscInt          n_vertices,total_primal_vertices,valid_constraints;
6058:   PetscInt          size_of_constraint,max_size_of_constraint=0,max_constraints,temp_constraints;
6059:   PetscReal         tol; /* tolerance for retaining eigenmodes */

6062:   tol  = PetscSqrtReal(PETSC_SMALL);
6063:   /* Destroy Mat objects computed previously */
6064:   MatDestroy(&pcbddc->ChangeOfBasisMatrix);
6065:   MatDestroy(&pcbddc->ConstraintMatrix);
6066:   MatDestroy(&pcbddc->switch_static_change);
6067:   /* save info on constraints from previous setup (if any) */
6068:   olocal_primal_size = pcbddc->local_primal_size;
6069:   olocal_primal_size_cc = pcbddc->local_primal_size_cc;
6070:   PetscMalloc2(olocal_primal_size_cc,&olocal_primal_ref_node,olocal_primal_size_cc,&olocal_primal_ref_mult);
6071:   PetscArraycpy(olocal_primal_ref_node,pcbddc->local_primal_ref_node,olocal_primal_size_cc);
6072:   PetscArraycpy(olocal_primal_ref_mult,pcbddc->local_primal_ref_mult,olocal_primal_size_cc);
6073:   PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);
6074:   PetscFree(pcbddc->primal_indices_local_idxs);

6076:   if (!pcbddc->adaptive_selection) {
6077:     IS           ISForVertices,*ISForFaces,*ISForEdges;
6078:     MatNullSpace nearnullsp;
6079:     const Vec    *nearnullvecs;
6080:     Vec          *localnearnullsp;
6081:     PetscScalar  *array;
6082:     PetscInt     n_ISForFaces,n_ISForEdges,nnsp_size;
6083:     PetscBool    nnsp_has_cnst;
6084:     /* LAPACK working arrays for SVD or POD */
6085:     PetscBool    skip_lapack,boolforchange;
6086:     PetscScalar  *work;
6087:     PetscReal    *singular_vals;
6088: #if defined(PETSC_USE_COMPLEX)
6089:     PetscReal    *rwork;
6090: #endif
6091: #if defined(PETSC_MISSING_LAPACK_GESVD)
6092:     PetscScalar  *temp_basis,*correlation_mat;
6093: #else
6094:     PetscBLASInt dummy_int=1;
6095:     PetscScalar  dummy_scalar=1.;
6096: #endif

6098:     /* Get index sets for faces, edges and vertices from graph */
6099:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
6100:     /* print some info */
6101:     if (pcbddc->dbg_flag && (!pcbddc->sub_schurs || pcbddc->sub_schurs_rebuild)) {
6102:       PetscInt nv;

6104:       PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);
6105:       ISGetSize(ISForVertices,&nv);
6106:       PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
6107:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
6108:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%D)\n",PetscGlobalRank,nv,pcbddc->use_vertices);
6109:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%D)\n",PetscGlobalRank,n_ISForEdges,pcbddc->use_edges);
6110:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%D)\n",PetscGlobalRank,n_ISForFaces,pcbddc->use_faces);
6111:       PetscViewerFlush(pcbddc->dbg_viewer);
6112:       PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);
6113:     }

6115:     /* free unneeded index sets */
6116:     if (!pcbddc->use_vertices) {
6117:       ISDestroy(&ISForVertices);
6118:     }
6119:     if (!pcbddc->use_edges) {
6120:       for (i=0;i<n_ISForEdges;i++) {
6121:         ISDestroy(&ISForEdges[i]);
6122:       }
6123:       PetscFree(ISForEdges);
6124:       n_ISForEdges = 0;
6125:     }
6126:     if (!pcbddc->use_faces) {
6127:       for (i=0;i<n_ISForFaces;i++) {
6128:         ISDestroy(&ISForFaces[i]);
6129:       }
6130:       PetscFree(ISForFaces);
6131:       n_ISForFaces = 0;
6132:     }

6134:     /* check if near null space is attached to global mat */
6135:     if (pcbddc->use_nnsp) {
6136:       MatGetNearNullSpace(pc->pmat,&nearnullsp);
6137:     } else nearnullsp = NULL;

6139:     if (nearnullsp) {
6140:       MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);
6141:       /* remove any stored info */
6142:       MatNullSpaceDestroy(&pcbddc->onearnullspace);
6143:       PetscFree(pcbddc->onearnullvecs_state);
6144:       /* store information for BDDC solver reuse */
6145:       PetscObjectReference((PetscObject)nearnullsp);
6146:       pcbddc->onearnullspace = nearnullsp;
6147:       PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);
6148:       for (i=0;i<nnsp_size;i++) {
6149:         PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);
6150:       }
6151:     } else { /* if near null space is not provided BDDC uses constants by default */
6152:       nnsp_size = 0;
6153:       nnsp_has_cnst = PETSC_TRUE;
6154:     }
6155:     /* get max number of constraints on a single cc */
6156:     max_constraints = nnsp_size;
6157:     if (nnsp_has_cnst) max_constraints++;

6159:     /*
6160:          Evaluate maximum storage size needed by the procedure
6161:          - Indices for connected component i stored at "constraints_idxs + constraints_idxs_ptr[i]"
6162:          - Values for constraints on connected component i stored at "constraints_data + constraints_data_ptr[i]"
6163:          There can be multiple constraints per connected component
6164:                                                                                                                                                            */
6165:     n_vertices = 0;
6166:     if (ISForVertices) {
6167:       ISGetSize(ISForVertices,&n_vertices);
6168:     }
6169:     ncc = n_vertices+n_ISForFaces+n_ISForEdges;
6170:     PetscMalloc3(ncc+1,&constraints_idxs_ptr,ncc+1,&constraints_data_ptr,ncc,&constraints_n);

6172:     total_counts = n_ISForFaces+n_ISForEdges;
6173:     total_counts *= max_constraints;
6174:     total_counts += n_vertices;
6175:     PetscBTCreate(total_counts,&change_basis);

6177:     total_counts = 0;
6178:     max_size_of_constraint = 0;
6179:     for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
6180:       IS used_is;
6181:       if (i<n_ISForEdges) {
6182:         used_is = ISForEdges[i];
6183:       } else {
6184:         used_is = ISForFaces[i-n_ISForEdges];
6185:       }
6186:       ISGetSize(used_is,&j);
6187:       total_counts += j;
6188:       max_size_of_constraint = PetscMax(j,max_size_of_constraint);
6189:     }
6190:     PetscMalloc3(total_counts*max_constraints+n_vertices,&constraints_data,total_counts+n_vertices,&constraints_idxs,total_counts+n_vertices,&constraints_idxs_B);

6192:     /* get local part of global near null space vectors */
6193:     PetscMalloc1(nnsp_size,&localnearnullsp);
6194:     for (k=0;k<nnsp_size;k++) {
6195:       VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);
6196:       VecScatterBegin(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);
6197:       VecScatterEnd(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);
6198:     }

6200:     /* whether or not to skip lapack calls */
6201:     skip_lapack = PETSC_TRUE;
6202:     if (n_ISForFaces+n_ISForEdges && max_constraints > 1 && !pcbddc->use_nnsp_true) skip_lapack = PETSC_FALSE;

6204:     /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
6205:     if (!skip_lapack) {
6206:       PetscScalar temp_work;

6208: #if defined(PETSC_MISSING_LAPACK_GESVD)
6209:       /* Proper Orthogonal Decomposition (POD) using the snapshot method */
6210:       PetscMalloc1(max_constraints*max_constraints,&correlation_mat);
6211:       PetscMalloc1(max_constraints,&singular_vals);
6212:       PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);
6213: #if defined(PETSC_USE_COMPLEX)
6214:       PetscMalloc1(3*max_constraints,&rwork);
6215: #endif
6216:       /* now we evaluate the optimal workspace using query with lwork=-1 */
6217:       PetscBLASIntCast(max_constraints,&Blas_N);
6218:       PetscBLASIntCast(max_constraints,&Blas_LDA);
6219:       lwork = -1;
6220:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6221: #if !defined(PETSC_USE_COMPLEX)
6222:       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
6223: #else
6224:       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
6225: #endif
6226:       PetscFPTrapPop();
6227:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
6228: #else /* on missing GESVD */
6229:       /* SVD */
6230:       PetscInt max_n,min_n;
6231:       max_n = max_size_of_constraint;
6232:       min_n = max_constraints;
6233:       if (max_size_of_constraint < max_constraints) {
6234:         min_n = max_size_of_constraint;
6235:         max_n = max_constraints;
6236:       }
6237:       PetscMalloc1(min_n,&singular_vals);
6238: #if defined(PETSC_USE_COMPLEX)
6239:       PetscMalloc1(5*min_n,&rwork);
6240: #endif
6241:       /* now we evaluate the optimal workspace using query with lwork=-1 */
6242:       lwork = -1;
6243:       PetscBLASIntCast(max_n,&Blas_M);
6244:       PetscBLASIntCast(min_n,&Blas_N);
6245:       PetscBLASIntCast(max_n,&Blas_LDA);
6246:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6247: #if !defined(PETSC_USE_COMPLEX)
6248:       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));
6249: #else
6250:       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));
6251: #endif
6252:       PetscFPTrapPop();
6253:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
6254: #endif /* on missing GESVD */
6255:       /* Allocate optimal workspace */
6256:       PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);
6257:       PetscMalloc1(lwork,&work);
6258:     }
6259:     /* Now we can loop on constraining sets */
6260:     total_counts = 0;
6261:     constraints_idxs_ptr[0] = 0;
6262:     constraints_data_ptr[0] = 0;
6263:     /* vertices */
6264:     if (n_vertices) {
6265:       ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);
6266:       PetscArraycpy(constraints_idxs,is_indices,n_vertices);
6267:       for (i=0;i<n_vertices;i++) {
6268:         constraints_n[total_counts] = 1;
6269:         constraints_data[total_counts] = 1.0;
6270:         constraints_idxs_ptr[total_counts+1] = constraints_idxs_ptr[total_counts]+1;
6271:         constraints_data_ptr[total_counts+1] = constraints_data_ptr[total_counts]+1;
6272:         total_counts++;
6273:       }
6274:       ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);
6275:       n_vertices = total_counts;
6276:     }

6278:     /* edges and faces */
6279:     total_counts_cc = total_counts;
6280:     for (ncc=0;ncc<n_ISForEdges+n_ISForFaces;ncc++) {
6281:       IS        used_is;
6282:       PetscBool idxs_copied = PETSC_FALSE;

6284:       if (ncc<n_ISForEdges) {
6285:         used_is = ISForEdges[ncc];
6286:         boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
6287:       } else {
6288:         used_is = ISForFaces[ncc-n_ISForEdges];
6289:         boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
6290:       }
6291:       temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */

6293:       ISGetSize(used_is,&size_of_constraint);
6294:       ISGetIndices(used_is,(const PetscInt**)&is_indices);
6295:       /* change of basis should not be performed on local periodic nodes */
6296:       if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
6297:       if (nnsp_has_cnst) {
6298:         PetscScalar quad_value;

6300:         PetscArraycpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint);
6301:         idxs_copied = PETSC_TRUE;

6303:         if (!pcbddc->use_nnsp_true) {
6304:           quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
6305:         } else {
6306:           quad_value = 1.0;
6307:         }
6308:         for (j=0;j<size_of_constraint;j++) {
6309:           constraints_data[constraints_data_ptr[total_counts_cc]+j] = quad_value;
6310:         }
6311:         temp_constraints++;
6312:         total_counts++;
6313:       }
6314:       for (k=0;k<nnsp_size;k++) {
6315:         PetscReal real_value;
6316:         PetscScalar *ptr_to_data;

6318:         VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
6319:         ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]+temp_constraints*size_of_constraint];
6320:         for (j=0;j<size_of_constraint;j++) {
6321:           ptr_to_data[j] = array[is_indices[j]];
6322:         }
6323:         VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
6324:         /* check if array is null on the connected component */
6325:         PetscBLASIntCast(size_of_constraint,&Blas_N);
6326:         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,ptr_to_data,&Blas_one));
6327:         if (real_value > tol*size_of_constraint) { /* keep indices and values */
6328:           temp_constraints++;
6329:           total_counts++;
6330:           if (!idxs_copied) {
6331:             PetscArraycpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint);
6332:             idxs_copied = PETSC_TRUE;
6333:           }
6334:         }
6335:       }
6336:       ISRestoreIndices(used_is,(const PetscInt**)&is_indices);
6337:       valid_constraints = temp_constraints;
6338:       if (!pcbddc->use_nnsp_true && temp_constraints) {
6339:         if (temp_constraints == 1) { /* just normalize the constraint */
6340:           PetscScalar norm,*ptr_to_data;

6342:           ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];
6343:           PetscBLASIntCast(size_of_constraint,&Blas_N);
6344:           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,ptr_to_data,&Blas_one,ptr_to_data,&Blas_one));
6345:           norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
6346:           PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,ptr_to_data,&Blas_one));
6347:         } else { /* perform SVD */
6348:           PetscScalar *ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];

6350: #if defined(PETSC_MISSING_LAPACK_GESVD)
6351:           /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
6352:              POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
6353:              -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
6354:                 the constraints basis will differ (by a complex factor with absolute value equal to 1)
6355:                 from that computed using LAPACKgesvd
6356:              -> This is due to a different computation of eigenvectors in LAPACKheev
6357:              -> The quality of the POD-computed basis will be the same */
6358:           PetscArrayzero(correlation_mat,temp_constraints*temp_constraints);
6359:           /* Store upper triangular part of correlation matrix */
6360:           PetscBLASIntCast(size_of_constraint,&Blas_N);
6361:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6362:           for (j=0;j<temp_constraints;j++) {
6363:             for (k=0;k<j+1;k++) {
6364:               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));
6365:             }
6366:           }
6367:           /* compute eigenvalues and eigenvectors of correlation matrix */
6368:           PetscBLASIntCast(temp_constraints,&Blas_N);
6369:           PetscBLASIntCast(temp_constraints,&Blas_LDA);
6370: #if !defined(PETSC_USE_COMPLEX)
6371:           PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
6372: #else
6373:           PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
6374: #endif
6375:           PetscFPTrapPop();
6376:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
6377:           /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
6378:           j = 0;
6379:           while (j < temp_constraints && singular_vals[j]/singular_vals[temp_constraints-1] < tol) j++;
6380:           total_counts = total_counts-j;
6381:           valid_constraints = temp_constraints-j;
6382:           /* scale and copy POD basis into used quadrature memory */
6383:           PetscBLASIntCast(size_of_constraint,&Blas_M);
6384:           PetscBLASIntCast(temp_constraints,&Blas_N);
6385:           PetscBLASIntCast(temp_constraints,&Blas_K);
6386:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6387:           PetscBLASIntCast(temp_constraints,&Blas_LDB);
6388:           PetscBLASIntCast(size_of_constraint,&Blas_LDC);
6389:           if (j<temp_constraints) {
6390:             PetscInt ii;
6391:             for (k=j;k<temp_constraints;k++) singular_vals[k] = 1.0/PetscSqrtReal(singular_vals[k]);
6392:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6393:             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));
6394:             PetscFPTrapPop();
6395:             for (k=0;k<temp_constraints-j;k++) {
6396:               for (ii=0;ii<size_of_constraint;ii++) {
6397:                 ptr_to_data[k*size_of_constraint+ii] = singular_vals[temp_constraints-1-k]*temp_basis[(temp_constraints-1-k)*size_of_constraint+ii];
6398:               }
6399:             }
6400:           }
6401: #else  /* on missing GESVD */
6402:           PetscBLASIntCast(size_of_constraint,&Blas_M);
6403:           PetscBLASIntCast(temp_constraints,&Blas_N);
6404:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6405:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6406: #if !defined(PETSC_USE_COMPLEX)
6407:           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));
6408: #else
6409:           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));
6410: #endif
6411:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
6412:           PetscFPTrapPop();
6413:           /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
6414:           k = temp_constraints;
6415:           if (k > size_of_constraint) k = size_of_constraint;
6416:           j = 0;
6417:           while (j < k && singular_vals[k-j-1]/singular_vals[0] < tol) j++;
6418:           valid_constraints = k-j;
6419:           total_counts = total_counts-temp_constraints+valid_constraints;
6420: #endif /* on missing GESVD */
6421:         }
6422:       }
6423:       /* update pointers information */
6424:       if (valid_constraints) {
6425:         constraints_n[total_counts_cc] = valid_constraints;
6426:         constraints_idxs_ptr[total_counts_cc+1] = constraints_idxs_ptr[total_counts_cc]+size_of_constraint;
6427:         constraints_data_ptr[total_counts_cc+1] = constraints_data_ptr[total_counts_cc]+size_of_constraint*valid_constraints;
6428:         /* set change_of_basis flag */
6429:         if (boolforchange) {
6430:           PetscBTSet(change_basis,total_counts_cc);
6431:         }
6432:         total_counts_cc++;
6433:       }
6434:     }
6435:     /* free workspace */
6436:     if (!skip_lapack) {
6437:       PetscFree(work);
6438: #if defined(PETSC_USE_COMPLEX)
6439:       PetscFree(rwork);
6440: #endif
6441:       PetscFree(singular_vals);
6442: #if defined(PETSC_MISSING_LAPACK_GESVD)
6443:       PetscFree(correlation_mat);
6444:       PetscFree(temp_basis);
6445: #endif
6446:     }
6447:     for (k=0;k<nnsp_size;k++) {
6448:       VecDestroy(&localnearnullsp[k]);
6449:     }
6450:     PetscFree(localnearnullsp);
6451:     /* free index sets of faces, edges and vertices */
6452:     for (i=0;i<n_ISForFaces;i++) {
6453:       ISDestroy(&ISForFaces[i]);
6454:     }
6455:     if (n_ISForFaces) {
6456:       PetscFree(ISForFaces);
6457:     }
6458:     for (i=0;i<n_ISForEdges;i++) {
6459:       ISDestroy(&ISForEdges[i]);
6460:     }
6461:     if (n_ISForEdges) {
6462:       PetscFree(ISForEdges);
6463:     }
6464:     ISDestroy(&ISForVertices);
6465:   } else {
6466:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

6468:     total_counts = 0;
6469:     n_vertices = 0;
6470:     if (sub_schurs->is_vertices && pcbddc->use_vertices) {
6471:       ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);
6472:     }
6473:     max_constraints = 0;
6474:     total_counts_cc = 0;
6475:     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
6476:       total_counts += pcbddc->adaptive_constraints_n[i];
6477:       if (pcbddc->adaptive_constraints_n[i]) total_counts_cc++;
6478:       max_constraints = PetscMax(max_constraints,pcbddc->adaptive_constraints_n[i]);
6479:     }
6480:     constraints_idxs_ptr = pcbddc->adaptive_constraints_idxs_ptr;
6481:     constraints_data_ptr = pcbddc->adaptive_constraints_data_ptr;
6482:     constraints_idxs = pcbddc->adaptive_constraints_idxs;
6483:     constraints_data = pcbddc->adaptive_constraints_data;
6484:     /* constraints_n differs from pcbddc->adaptive_constraints_n */
6485:     PetscMalloc1(total_counts_cc,&constraints_n);
6486:     total_counts_cc = 0;
6487:     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
6488:       if (pcbddc->adaptive_constraints_n[i]) {
6489:         constraints_n[total_counts_cc++] = pcbddc->adaptive_constraints_n[i];
6490:       }
6491:     }

6493:     max_size_of_constraint = 0;
6494:     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]);
6495:     PetscMalloc1(constraints_idxs_ptr[total_counts_cc],&constraints_idxs_B);
6496:     /* Change of basis */
6497:     PetscBTCreate(total_counts_cc,&change_basis);
6498:     if (pcbddc->use_change_of_basis) {
6499:       for (i=0;i<sub_schurs->n_subs;i++) {
6500:         if (PetscBTLookup(sub_schurs->is_edge,i) || pcbddc->use_change_on_faces) {
6501:           PetscBTSet(change_basis,i+n_vertices);
6502:         }
6503:       }
6504:     }
6505:   }
6506:   pcbddc->local_primal_size = total_counts;
6507:   PetscMalloc1(pcbddc->local_primal_size+pcbddc->benign_n,&pcbddc->primal_indices_local_idxs);

6509:   /* map constraints_idxs in boundary numbering */
6510:   ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,constraints_idxs_ptr[total_counts_cc],constraints_idxs,&i,constraints_idxs_B);
6511:   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);

6513:   /* Create constraint matrix */
6514:   MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);
6515:   MatSetType(pcbddc->ConstraintMatrix,MATAIJ);
6516:   MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);

6518:   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
6519:   /* determine if a QR strategy is needed for change of basis */
6520:   qr_needed = pcbddc->use_qr_single;
6521:   PetscBTCreate(total_counts_cc,&qr_needed_idx);
6522:   total_primal_vertices=0;
6523:   pcbddc->local_primal_size_cc = 0;
6524:   for (i=0;i<total_counts_cc;i++) {
6525:     size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
6526:     if (size_of_constraint == 1 && pcbddc->mat_graph->custom_minimal_size) {
6527:       pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]];
6528:       pcbddc->local_primal_size_cc += 1;
6529:     } else if (PetscBTLookup(change_basis,i)) {
6530:       for (k=0;k<constraints_n[i];k++) {
6531:         pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]+k];
6532:       }
6533:       pcbddc->local_primal_size_cc += constraints_n[i];
6534:       if (constraints_n[i] > 1 || pcbddc->use_qr_single) {
6535:         PetscBTSet(qr_needed_idx,i);
6536:         qr_needed = PETSC_TRUE;
6537:       }
6538:     } else {
6539:       pcbddc->local_primal_size_cc += 1;
6540:     }
6541:   }
6542:   /* note that the local variable n_vertices used below stores the number of pointwise constraints */
6543:   pcbddc->n_vertices = total_primal_vertices;
6544:   /* permute indices in order to have a sorted set of vertices */
6545:   PetscSortInt(total_primal_vertices,pcbddc->primal_indices_local_idxs);
6546:   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);
6547:   PetscArraycpy(pcbddc->local_primal_ref_node,pcbddc->primal_indices_local_idxs,total_primal_vertices);
6548:   for (i=0;i<total_primal_vertices;i++) pcbddc->local_primal_ref_mult[i] = 1;

6550:   /* nonzero structure of constraint matrix */
6551:   /* and get reference dof for local constraints */
6552:   PetscMalloc1(pcbddc->local_primal_size,&nnz);
6553:   for (i=0;i<total_primal_vertices;i++) nnz[i] = 1;

6555:   j = total_primal_vertices;
6556:   total_counts = total_primal_vertices;
6557:   cum = total_primal_vertices;
6558:   for (i=n_vertices;i<total_counts_cc;i++) {
6559:     if (!PetscBTLookup(change_basis,i)) {
6560:       pcbddc->local_primal_ref_node[cum] = constraints_idxs[constraints_idxs_ptr[i]];
6561:       pcbddc->local_primal_ref_mult[cum] = constraints_n[i];
6562:       cum++;
6563:       size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
6564:       for (k=0;k<constraints_n[i];k++) {
6565:         pcbddc->primal_indices_local_idxs[total_counts++] = constraints_idxs[constraints_idxs_ptr[i]+k];
6566:         nnz[j+k] = size_of_constraint;
6567:       }
6568:       j += constraints_n[i];
6569:     }
6570:   }
6571:   MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);
6572:   MatSetOption(pcbddc->ConstraintMatrix,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
6573:   PetscFree(nnz);

6575:   /* set values in constraint matrix */
6576:   for (i=0;i<total_primal_vertices;i++) {
6577:     MatSetValue(pcbddc->ConstraintMatrix,i,pcbddc->local_primal_ref_node[i],1.0,INSERT_VALUES);
6578:   }
6579:   total_counts = total_primal_vertices;
6580:   for (i=n_vertices;i<total_counts_cc;i++) {
6581:     if (!PetscBTLookup(change_basis,i)) {
6582:       PetscInt *cols;

6584:       size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
6585:       cols = constraints_idxs+constraints_idxs_ptr[i];
6586:       for (k=0;k<constraints_n[i];k++) {
6587:         PetscInt    row = total_counts+k;
6588:         PetscScalar *vals;

6590:         vals = constraints_data+constraints_data_ptr[i]+k*size_of_constraint;
6591:         MatSetValues(pcbddc->ConstraintMatrix,1,&row,size_of_constraint,cols,vals,INSERT_VALUES);
6592:       }
6593:       total_counts += constraints_n[i];
6594:     }
6595:   }
6596:   /* assembling */
6597:   MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);
6598:   MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);
6599:   MatViewFromOptions(pcbddc->ConstraintMatrix,(PetscObject)pc,"-pc_bddc_constraint_mat_view");

6601:   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
6602:   if (pcbddc->use_change_of_basis) {
6603:     /* dual and primal dofs on a single cc */
6604:     PetscInt     dual_dofs,primal_dofs;
6605:     /* working stuff for GEQRF */
6606:     PetscScalar  *qr_basis = NULL,*qr_tau = NULL,*qr_work = NULL,lqr_work_t;
6607:     PetscBLASInt lqr_work;
6608:     /* working stuff for UNGQR */
6609:     PetscScalar  *gqr_work = NULL,lgqr_work_t;
6610:     PetscBLASInt lgqr_work;
6611:     /* working stuff for TRTRS */
6612:     PetscScalar  *trs_rhs = NULL;
6613:     PetscBLASInt Blas_NRHS;
6614:     /* pointers for values insertion into change of basis matrix */
6615:     PetscInt     *start_rows,*start_cols;
6616:     PetscScalar  *start_vals;
6617:     /* working stuff for values insertion */
6618:     PetscBT      is_primal;
6619:     PetscInt     *aux_primal_numbering_B;
6620:     /* matrix sizes */
6621:     PetscInt     global_size,local_size;
6622:     /* temporary change of basis */
6623:     Mat          localChangeOfBasisMatrix;
6624:     /* extra space for debugging */
6625:     PetscScalar  *dbg_work = NULL;

6627:     /* local temporary change of basis acts on local interfaces -> dimension is n_B x n_B */
6628:     MatCreate(PETSC_COMM_SELF,&localChangeOfBasisMatrix);
6629:     MatSetType(localChangeOfBasisMatrix,MATAIJ);
6630:     MatSetSizes(localChangeOfBasisMatrix,pcis->n,pcis->n,pcis->n,pcis->n);
6631:     /* nonzeros for local mat */
6632:     PetscMalloc1(pcis->n,&nnz);
6633:     if (!pcbddc->benign_change || pcbddc->fake_change) {
6634:       for (i=0;i<pcis->n;i++) nnz[i]=1;
6635:     } else {
6636:       const PetscInt *ii;
6637:       PetscInt       n;
6638:       PetscBool      flg_row;
6639:       MatGetRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,NULL,&flg_row);
6640:       for (i=0;i<n;i++) nnz[i] = ii[i+1]-ii[i];
6641:       MatRestoreRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,NULL,&flg_row);
6642:     }
6643:     for (i=n_vertices;i<total_counts_cc;i++) {
6644:       if (PetscBTLookup(change_basis,i)) {
6645:         size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
6646:         if (PetscBTLookup(qr_needed_idx,i)) {
6647:           for (j=0;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = size_of_constraint;
6648:         } else {
6649:           nnz[constraints_idxs[constraints_idxs_ptr[i]]] = size_of_constraint;
6650:           for (j=1;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = 2;
6651:         }
6652:       }
6653:     }
6654:     MatSeqAIJSetPreallocation(localChangeOfBasisMatrix,0,nnz);
6655:     MatSetOption(localChangeOfBasisMatrix,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
6656:     PetscFree(nnz);
6657:     /* Set interior change in the matrix */
6658:     if (!pcbddc->benign_change || pcbddc->fake_change) {
6659:       for (i=0;i<pcis->n;i++) {
6660:         MatSetValue(localChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);
6661:       }
6662:     } else {
6663:       const PetscInt *ii,*jj;
6664:       PetscScalar    *aa;
6665:       PetscInt       n;
6666:       PetscBool      flg_row;
6667:       MatGetRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&jj,&flg_row);
6668:       MatSeqAIJGetArray(pcbddc->benign_change,&aa);
6669:       for (i=0;i<n;i++) {
6670:         MatSetValues(localChangeOfBasisMatrix,1,&i,ii[i+1]-ii[i],jj+ii[i],aa+ii[i],INSERT_VALUES);
6671:       }
6672:       MatSeqAIJRestoreArray(pcbddc->benign_change,&aa);
6673:       MatRestoreRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&jj,&flg_row);
6674:     }

6676:     if (pcbddc->dbg_flag) {
6677:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
6678:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);
6679:     }


6682:     /* Now we loop on the constraints which need a change of basis */
6683:     /*
6684:        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
6685:        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)

6687:        Basic blocks of change of basis matrix T computed by

6689:           - Using the following block transformation if there is only a primal dof on the cc (and -pc_bddc_use_qr_single is not specified)

6691:             | 1        0   ...        0         s_1/S |
6692:             | 0        1   ...        0         s_2/S |
6693:             |              ...                        |
6694:             | 0        ...            1     s_{n-1}/S |
6695:             | -s_1/s_n ...    -s_{n-1}/s_n      s_n/S |

6697:             with S = \sum_{i=1}^n s_i^2
6698:             NOTE: in the above example, the primal dof is the last one of the edge in LOCAL ordering
6699:                   in the current implementation, the primal dof is the first one of the edge in GLOBAL ordering

6701:           - QR decomposition of constraints otherwise
6702:     */
6703:     if (qr_needed && max_size_of_constraint) {
6704:       /* space to store Q */
6705:       PetscMalloc1(max_size_of_constraint*max_size_of_constraint,&qr_basis);
6706:       /* array to store scaling factors for reflectors */
6707:       PetscMalloc1(max_constraints,&qr_tau);
6708:       /* first we issue queries for optimal work */
6709:       PetscBLASIntCast(max_size_of_constraint,&Blas_M);
6710:       PetscBLASIntCast(max_constraints,&Blas_N);
6711:       PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);
6712:       lqr_work = -1;
6713:       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
6714:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
6715:       PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);
6716:       PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);
6717:       lgqr_work = -1;
6718:       PetscBLASIntCast(max_size_of_constraint,&Blas_M);
6719:       PetscBLASIntCast(max_size_of_constraint,&Blas_N);
6720:       PetscBLASIntCast(max_constraints,&Blas_K);
6721:       PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);
6722:       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
6723:       PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
6724:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to ORGQR/UNGQR Lapack routine %d",(int)lierr);
6725:       PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);
6726:       PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);
6727:       /* array to store rhs and solution of triangular solver */
6728:       PetscMalloc1(max_constraints*max_constraints,&trs_rhs);
6729:       /* allocating workspace for check */
6730:       if (pcbddc->dbg_flag) {
6731:         PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&dbg_work);
6732:       }
6733:     }
6734:     /* array to store whether a node is primal or not */
6735:     PetscBTCreate(pcis->n_B,&is_primal);
6736:     PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);
6737:     ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,pcbddc->local_primal_ref_node,&i,aux_primal_numbering_B);
6738:     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);
6739:     for (i=0;i<total_primal_vertices;i++) {
6740:       PetscBTSet(is_primal,aux_primal_numbering_B[i]);
6741:     }
6742:     PetscFree(aux_primal_numbering_B);

6744:     /* loop on constraints and see whether or not they need a change of basis and compute it */
6745:     for (total_counts=n_vertices;total_counts<total_counts_cc;total_counts++) {
6746:       size_of_constraint = constraints_idxs_ptr[total_counts+1]-constraints_idxs_ptr[total_counts];
6747:       if (PetscBTLookup(change_basis,total_counts)) {
6748:         /* get constraint info */
6749:         primal_dofs = constraints_n[total_counts];
6750:         dual_dofs = size_of_constraint-primal_dofs;

6752:         if (pcbddc->dbg_flag) {
6753:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraints %D: %D need a change of basis (size %D)\n",total_counts,primal_dofs,size_of_constraint);
6754:         }

6756:         if (PetscBTLookup(qr_needed_idx,total_counts)) { /* QR */

6758:           /* copy quadrature constraints for change of basis check */
6759:           if (pcbddc->dbg_flag) {
6760:             PetscArraycpy(dbg_work,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);
6761:           }
6762:           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
6763:           PetscArraycpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);

6765:           /* compute QR decomposition of constraints */
6766:           PetscBLASIntCast(size_of_constraint,&Blas_M);
6767:           PetscBLASIntCast(primal_dofs,&Blas_N);
6768:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6769:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6770:           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
6771:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
6772:           PetscFPTrapPop();

6774:           /* explictly compute R^-T */
6775:           PetscArrayzero(trs_rhs,primal_dofs*primal_dofs);
6776:           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
6777:           PetscBLASIntCast(primal_dofs,&Blas_N);
6778:           PetscBLASIntCast(primal_dofs,&Blas_NRHS);
6779:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6780:           PetscBLASIntCast(primal_dofs,&Blas_LDB);
6781:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6782:           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
6783:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
6784:           PetscFPTrapPop();

6786:           /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
6787:           PetscBLASIntCast(size_of_constraint,&Blas_M);
6788:           PetscBLASIntCast(size_of_constraint,&Blas_N);
6789:           PetscBLASIntCast(primal_dofs,&Blas_K);
6790:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6791:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6792:           PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
6793:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in ORGQR/UNGQR Lapack routine %d",(int)lierr);
6794:           PetscFPTrapPop();

6796:           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
6797:              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
6798:              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
6799:           PetscBLASIntCast(size_of_constraint,&Blas_M);
6800:           PetscBLASIntCast(primal_dofs,&Blas_N);
6801:           PetscBLASIntCast(primal_dofs,&Blas_K);
6802:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6803:           PetscBLASIntCast(primal_dofs,&Blas_LDB);
6804:           PetscBLASIntCast(size_of_constraint,&Blas_LDC);
6805:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6806:           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));
6807:           PetscFPTrapPop();
6808:           PetscArraycpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);

6810:           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
6811:           start_rows = &constraints_idxs[constraints_idxs_ptr[total_counts]];
6812:           /* insert cols for primal dofs */
6813:           for (j=0;j<primal_dofs;j++) {
6814:             start_vals = &qr_basis[j*size_of_constraint];
6815:             start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+j];
6816:             MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);
6817:           }
6818:           /* insert cols for dual dofs */
6819:           for (j=0,k=0;j<dual_dofs;k++) {
6820:             if (!PetscBTLookup(is_primal,constraints_idxs_B[constraints_idxs_ptr[total_counts]+k])) {
6821:               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
6822:               start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+k];
6823:               MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);
6824:               j++;
6825:             }
6826:           }

6828:           /* check change of basis */
6829:           if (pcbddc->dbg_flag) {
6830:             PetscInt   ii,jj;
6831:             PetscBool valid_qr=PETSC_TRUE;
6832:             PetscBLASIntCast(primal_dofs,&Blas_M);
6833:             PetscBLASIntCast(size_of_constraint,&Blas_N);
6834:             PetscBLASIntCast(size_of_constraint,&Blas_K);
6835:             PetscBLASIntCast(size_of_constraint,&Blas_LDA);
6836:             PetscBLASIntCast(size_of_constraint,&Blas_LDB);
6837:             PetscBLASIntCast(primal_dofs,&Blas_LDC);
6838:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
6839:             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));
6840:             PetscFPTrapPop();
6841:             for (jj=0;jj<size_of_constraint;jj++) {
6842:               for (ii=0;ii<primal_dofs;ii++) {
6843:                 if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
6844:                 if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-(PetscReal)1) > 1.e-12) valid_qr = PETSC_FALSE;
6845:               }
6846:             }
6847:             if (!valid_qr) {
6848:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");
6849:               for (jj=0;jj<size_of_constraint;jj++) {
6850:                 for (ii=0;ii<primal_dofs;ii++) {
6851:                   if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
6852:                     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]));
6853:                   }
6854:                   if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-(PetscReal)1) > 1.e-12) {
6855:                     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]));
6856:                   }
6857:                 }
6858:               }
6859:             } else {
6860:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");
6861:             }
6862:           }
6863:         } else { /* simple transformation block */
6864:           PetscInt    row,col;
6865:           PetscScalar val,norm;

6867:           PetscBLASIntCast(size_of_constraint,&Blas_N);
6868:           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,constraints_data+constraints_data_ptr[total_counts],&Blas_one,constraints_data+constraints_data_ptr[total_counts],&Blas_one));
6869:           for (j=0;j<size_of_constraint;j++) {
6870:             PetscInt row_B = constraints_idxs_B[constraints_idxs_ptr[total_counts]+j];
6871:             row = constraints_idxs[constraints_idxs_ptr[total_counts]+j];
6872:             if (!PetscBTLookup(is_primal,row_B)) {
6873:               col = constraints_idxs[constraints_idxs_ptr[total_counts]];
6874:               MatSetValue(localChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);
6875:               MatSetValue(localChangeOfBasisMatrix,row,col,constraints_data[constraints_data_ptr[total_counts]+j]/norm,INSERT_VALUES);
6876:             } else {
6877:               for (k=0;k<size_of_constraint;k++) {
6878:                 col = constraints_idxs[constraints_idxs_ptr[total_counts]+k];
6879:                 if (row != col) {
6880:                   val = -constraints_data[constraints_data_ptr[total_counts]+k]/constraints_data[constraints_data_ptr[total_counts]];
6881:                 } else {
6882:                   val = constraints_data[constraints_data_ptr[total_counts]]/norm;
6883:                 }
6884:                 MatSetValue(localChangeOfBasisMatrix,row,col,val,INSERT_VALUES);
6885:               }
6886:             }
6887:           }
6888:           if (pcbddc->dbg_flag) {
6889:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");
6890:           }
6891:         }
6892:       } else {
6893:         if (pcbddc->dbg_flag) {
6894:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %D does not need a change of basis (size %D)\n",total_counts,size_of_constraint);
6895:         }
6896:       }
6897:     }

6899:     /* free workspace */
6900:     if (qr_needed) {
6901:       if (pcbddc->dbg_flag) {
6902:         PetscFree(dbg_work);
6903:       }
6904:       PetscFree(trs_rhs);
6905:       PetscFree(qr_tau);
6906:       PetscFree(qr_work);
6907:       PetscFree(gqr_work);
6908:       PetscFree(qr_basis);
6909:     }
6910:     PetscBTDestroy(&is_primal);
6911:     MatAssemblyBegin(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);
6912:     MatAssemblyEnd(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);

6914:     /* assembling of global change of variable */
6915:     if (!pcbddc->fake_change) {
6916:       Mat      tmat;
6917:       PetscInt bs;

6919:       VecGetSize(pcis->vec1_global,&global_size);
6920:       VecGetLocalSize(pcis->vec1_global,&local_size);
6921:       MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&tmat);
6922:       MatISSetLocalMat(tmat,localChangeOfBasisMatrix);
6923:       MatAssemblyBegin(tmat,MAT_FINAL_ASSEMBLY);
6924:       MatAssemblyEnd(tmat,MAT_FINAL_ASSEMBLY);
6925:       MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->ChangeOfBasisMatrix);
6926:       MatSetType(pcbddc->ChangeOfBasisMatrix,MATAIJ);
6927:       MatGetBlockSize(pc->pmat,&bs);
6928:       MatSetBlockSize(pcbddc->ChangeOfBasisMatrix,bs);
6929:       MatSetSizes(pcbddc->ChangeOfBasisMatrix,local_size,local_size,global_size,global_size);
6930:       MatISSetMPIXAIJPreallocation_Private(tmat,pcbddc->ChangeOfBasisMatrix,PETSC_TRUE);
6931:       MatConvert(tmat,MATAIJ,MAT_REUSE_MATRIX,&pcbddc->ChangeOfBasisMatrix);
6932:       MatDestroy(&tmat);
6933:       VecSet(pcis->vec1_global,0.0);
6934:       VecSet(pcis->vec1_N,1.0);
6935:       VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
6936:       VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
6937:       VecReciprocal(pcis->vec1_global);
6938:       MatDiagonalScale(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,NULL);

6940:       /* check */
6941:       if (pcbddc->dbg_flag) {
6942:         PetscReal error;
6943:         Vec       x,x_change;

6945:         VecDuplicate(pcis->vec1_global,&x);
6946:         VecDuplicate(pcis->vec1_global,&x_change);
6947:         VecSetRandom(x,NULL);
6948:         VecCopy(x,pcis->vec1_global);
6949:         VecScatterBegin(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
6950:         VecScatterEnd(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
6951:         MatMult(localChangeOfBasisMatrix,pcis->vec1_N,pcis->vec2_N);
6952:         VecScatterBegin(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);
6953:         VecScatterEnd(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);
6954:         MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);
6955:         VecAXPY(x,-1.0,x_change);
6956:         VecNorm(x,NORM_INFINITY,&error);
6957:         if (error > PETSC_SMALL) {
6958:           SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on N: %1.6e",error);
6959:         }
6960:         VecDestroy(&x);
6961:         VecDestroy(&x_change);
6962:       }
6963:       /* adapt sub_schurs computed (if any) */
6964:       if (pcbddc->use_deluxe_scaling) {
6965:         PCBDDCSubSchurs sub_schurs=pcbddc->sub_schurs;

6967:         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");
6968:         if (sub_schurs && sub_schurs->S_Ej_all) {
6969:           Mat                    S_new,tmat;
6970:           IS                     is_all_N,is_V_Sall = NULL;

6972:           ISLocalToGlobalMappingApplyIS(pcis->BtoNmap,sub_schurs->is_Ej_all,&is_all_N);
6973:           MatCreateSubMatrix(localChangeOfBasisMatrix,is_all_N,is_all_N,MAT_INITIAL_MATRIX,&tmat);
6974:           if (pcbddc->deluxe_zerorows) {
6975:             ISLocalToGlobalMapping NtoSall;
6976:             IS                     is_V;
6977:             ISCreateGeneral(PETSC_COMM_SELF,pcbddc->n_vertices,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&is_V);
6978:             ISLocalToGlobalMappingCreateIS(is_all_N,&NtoSall);
6979:             ISGlobalToLocalMappingApplyIS(NtoSall,IS_GTOLM_DROP,is_V,&is_V_Sall);
6980:             ISLocalToGlobalMappingDestroy(&NtoSall);
6981:             ISDestroy(&is_V);
6982:           }
6983:           ISDestroy(&is_all_N);
6984:           MatPtAP(sub_schurs->S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);
6985:           MatDestroy(&sub_schurs->S_Ej_all);
6986:           PetscObjectReference((PetscObject)S_new);
6987:           if (pcbddc->deluxe_zerorows) {
6988:             const PetscScalar *array;
6989:             const PetscInt    *idxs_V,*idxs_all;
6990:             PetscInt          i,n_V;

6992:             MatZeroRowsColumnsIS(S_new,is_V_Sall,1.,NULL,NULL);
6993:             ISGetLocalSize(is_V_Sall,&n_V);
6994:             ISGetIndices(is_V_Sall,&idxs_V);
6995:             ISGetIndices(sub_schurs->is_Ej_all,&idxs_all);
6996:             VecGetArrayRead(pcis->D,&array);
6997:             for (i=0;i<n_V;i++) {
6998:               PetscScalar val;
6999:               PetscInt    idx;

7001:               idx = idxs_V[i];
7002:               val = array[idxs_all[idxs_V[i]]];
7003:               MatSetValue(S_new,idx,idx,val,INSERT_VALUES);
7004:             }
7005:             MatAssemblyBegin(S_new,MAT_FINAL_ASSEMBLY);
7006:             MatAssemblyEnd(S_new,MAT_FINAL_ASSEMBLY);
7007:             VecRestoreArrayRead(pcis->D,&array);
7008:             ISRestoreIndices(sub_schurs->is_Ej_all,&idxs_all);
7009:             ISRestoreIndices(is_V_Sall,&idxs_V);
7010:           }
7011:           sub_schurs->S_Ej_all = S_new;
7012:           MatDestroy(&S_new);
7013:           if (sub_schurs->sum_S_Ej_all) {
7014:             MatPtAP(sub_schurs->sum_S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);
7015:             MatDestroy(&sub_schurs->sum_S_Ej_all);
7016:             PetscObjectReference((PetscObject)S_new);
7017:             if (pcbddc->deluxe_zerorows) {
7018:               MatZeroRowsColumnsIS(S_new,is_V_Sall,1.,NULL,NULL);
7019:             }
7020:             sub_schurs->sum_S_Ej_all = S_new;
7021:             MatDestroy(&S_new);
7022:           }
7023:           ISDestroy(&is_V_Sall);
7024:           MatDestroy(&tmat);
7025:         }
7026:         /* destroy any change of basis context in sub_schurs */
7027:         if (sub_schurs && sub_schurs->change) {
7028:           PetscInt i;

7030:           for (i=0;i<sub_schurs->n_subs;i++) {
7031:             KSPDestroy(&sub_schurs->change[i]);
7032:           }
7033:           PetscFree(sub_schurs->change);
7034:         }
7035:       }
7036:       if (pcbddc->switch_static) { /* need to save the local change */
7037:         pcbddc->switch_static_change = localChangeOfBasisMatrix;
7038:       } else {
7039:         MatDestroy(&localChangeOfBasisMatrix);
7040:       }
7041:       /* determine if any process has changed the pressures locally */
7042:       pcbddc->change_interior = pcbddc->benign_have_null;
7043:     } else { /* fake change (get back change of basis into ConstraintMatrix and info on qr) */
7044:       MatDestroy(&pcbddc->ConstraintMatrix);
7045:       pcbddc->ConstraintMatrix = localChangeOfBasisMatrix;
7046:       pcbddc->use_qr_single = qr_needed;
7047:     }
7048:   } else if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->benign_saddle_point) {
7049:     if (!pcbddc->benign_have_null && pcbddc->user_ChangeOfBasisMatrix) {
7050:       PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);
7051:       pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
7052:     } else {
7053:       Mat benign_global = NULL;
7054:       if (pcbddc->benign_have_null) {
7055:         Mat M;

7057:         pcbddc->change_interior = PETSC_TRUE;
7058:         VecCopy(matis->counter,pcis->vec1_N);
7059:         VecReciprocal(pcis->vec1_N);
7060:         MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&benign_global);
7061:         if (pcbddc->benign_change) {
7062:           MatDuplicate(pcbddc->benign_change,MAT_COPY_VALUES,&M);
7063:           MatDiagonalScale(M,pcis->vec1_N,NULL);
7064:         } else {
7065:           MatCreateSeqAIJ(PETSC_COMM_SELF,pcis->n,pcis->n,1,NULL,&M);
7066:           MatDiagonalSet(M,pcis->vec1_N,INSERT_VALUES);
7067:         }
7068:         MatISSetLocalMat(benign_global,M);
7069:         MatDestroy(&M);
7070:         MatAssemblyBegin(benign_global,MAT_FINAL_ASSEMBLY);
7071:         MatAssemblyEnd(benign_global,MAT_FINAL_ASSEMBLY);
7072:       }
7073:       if (pcbddc->user_ChangeOfBasisMatrix) {
7074:         MatMatMult(pcbddc->user_ChangeOfBasisMatrix,benign_global,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->ChangeOfBasisMatrix);
7075:         MatDestroy(&benign_global);
7076:       } else if (pcbddc->benign_have_null) {
7077:         pcbddc->ChangeOfBasisMatrix = benign_global;
7078:       }
7079:     }
7080:     if (pcbddc->switch_static && pcbddc->ChangeOfBasisMatrix) { /* need to save the local change */
7081:       IS             is_global;
7082:       const PetscInt *gidxs;

7084:       ISLocalToGlobalMappingGetIndices(pc->pmat->rmap->mapping,&gidxs);
7085:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcis->n,gidxs,PETSC_COPY_VALUES,&is_global);
7086:       ISLocalToGlobalMappingRestoreIndices(pc->pmat->rmap->mapping,&gidxs);
7087:       MatCreateSubMatrixUnsorted(pcbddc->ChangeOfBasisMatrix,is_global,is_global,&pcbddc->switch_static_change);
7088:       ISDestroy(&is_global);
7089:     }
7090:   }
7091:   if (!pcbddc->fake_change && pcbddc->ChangeOfBasisMatrix && !pcbddc->work_change) {
7092:     VecDuplicate(pcis->vec1_global,&pcbddc->work_change);
7093:   }

7095:   if (!pcbddc->fake_change) {
7096:     /* add pressure dofs to set of primal nodes for numbering purposes */
7097:     for (i=0;i<pcbddc->benign_n;i++) {
7098:       pcbddc->local_primal_ref_node[pcbddc->local_primal_size_cc] = pcbddc->benign_p0_lidx[i];
7099:       pcbddc->primal_indices_local_idxs[pcbddc->local_primal_size] = pcbddc->benign_p0_lidx[i];
7100:       pcbddc->local_primal_ref_mult[pcbddc->local_primal_size_cc] = 1;
7101:       pcbddc->local_primal_size_cc++;
7102:       pcbddc->local_primal_size++;
7103:     }

7105:     /* check if a new primal space has been introduced (also take into account benign trick) */
7106:     pcbddc->new_primal_space_local = PETSC_TRUE;
7107:     if (olocal_primal_size == pcbddc->local_primal_size) {
7108:       PetscArraycmp(pcbddc->local_primal_ref_node,olocal_primal_ref_node,olocal_primal_size_cc,&pcbddc->new_primal_space_local);
7109:       pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
7110:       if (!pcbddc->new_primal_space_local) {
7111:         PetscArraycmp(pcbddc->local_primal_ref_mult,olocal_primal_ref_mult,olocal_primal_size_cc,&pcbddc->new_primal_space_local);
7112:         pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
7113:       }
7114:     }
7115:     /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
7116:     MPIU_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
7117:   }
7118:   PetscFree2(olocal_primal_ref_node,olocal_primal_ref_mult);

7120:   /* flush dbg viewer */
7121:   if (pcbddc->dbg_flag) {
7122:     PetscViewerFlush(pcbddc->dbg_viewer);
7123:   }

7125:   /* free workspace */
7126:   PetscBTDestroy(&qr_needed_idx);
7127:   PetscBTDestroy(&change_basis);
7128:   if (!pcbddc->adaptive_selection) {
7129:     PetscFree3(constraints_idxs_ptr,constraints_data_ptr,constraints_n);
7130:     PetscFree3(constraints_data,constraints_idxs,constraints_idxs_B);
7131:   } else {
7132:     PetscFree5(pcbddc->adaptive_constraints_n,
7133:                       pcbddc->adaptive_constraints_idxs_ptr,
7134:                       pcbddc->adaptive_constraints_data_ptr,
7135:                       pcbddc->adaptive_constraints_idxs,
7136:                       pcbddc->adaptive_constraints_data);
7137:     PetscFree(constraints_n);
7138:     PetscFree(constraints_idxs_B);
7139:   }
7140:   return(0);
7141: }
7142: /* #undef PETSC_MISSING_LAPACK_GESVD */

7144: PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
7145: {
7146:   ISLocalToGlobalMapping map;
7147:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
7148:   Mat_IS                 *matis  = (Mat_IS*)pc->pmat->data;
7149:   PetscInt               i,N;
7150:   PetscBool              rcsr = PETSC_FALSE;
7151:   PetscErrorCode         ierr;

7154:   if (pcbddc->recompute_topography) {
7155:     pcbddc->graphanalyzed = PETSC_FALSE;
7156:     /* Reset previously computed graph */
7157:     PCBDDCGraphReset(pcbddc->mat_graph);
7158:     /* Init local Graph struct */
7159:     MatGetSize(pc->pmat,&N,NULL);
7160:     MatGetLocalToGlobalMapping(pc->pmat,&map,NULL);
7161:     PCBDDCGraphInit(pcbddc->mat_graph,map,N,pcbddc->graphmaxcount);

7163:     if (pcbddc->user_primal_vertices_local && !pcbddc->user_primal_vertices) {
7164:       PCBDDCConsistencyCheckIS(pc,MPI_LOR,&pcbddc->user_primal_vertices_local);
7165:     }
7166:     /* Check validity of the csr graph passed in by the user */
7167:     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);

7169:     /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
7170:     if (!pcbddc->mat_graph->xadj && pcbddc->use_local_adj) {
7171:       PetscInt  *xadj,*adjncy;
7172:       PetscInt  nvtxs;
7173:       PetscBool flg_row=PETSC_FALSE;

7175:       MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
7176:       if (flg_row) {
7177:         PCBDDCSetLocalAdjacencyGraph(pc,nvtxs,xadj,adjncy,PETSC_COPY_VALUES);
7178:         pcbddc->computed_rowadj = PETSC_TRUE;
7179:       }
7180:       MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
7181:       rcsr = PETSC_TRUE;
7182:     }
7183:     if (pcbddc->dbg_flag) {
7184:       PetscViewerFlush(pcbddc->dbg_viewer);
7185:     }

7187:     if (pcbddc->mat_graph->cdim && !pcbddc->mat_graph->cloc) {
7188:       PetscReal    *lcoords;
7189:       PetscInt     n;
7190:       MPI_Datatype dimrealtype;

7192:       /* TODO: support for blocked */
7193:       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);
7194:       MatGetLocalSize(matis->A,&n,NULL);
7195:       PetscMalloc1(pcbddc->mat_graph->cdim*n,&lcoords);
7196:       MPI_Type_contiguous(pcbddc->mat_graph->cdim,MPIU_REAL,&dimrealtype);
7197:       MPI_Type_commit(&dimrealtype);
7198:       PetscSFBcastBegin(matis->sf,dimrealtype,pcbddc->mat_graph->coords,lcoords);
7199:       PetscSFBcastEnd(matis->sf,dimrealtype,pcbddc->mat_graph->coords,lcoords);
7200:       MPI_Type_free(&dimrealtype);
7201:       PetscFree(pcbddc->mat_graph->coords);

7203:       pcbddc->mat_graph->coords = lcoords;
7204:       pcbddc->mat_graph->cloc   = PETSC_TRUE;
7205:       pcbddc->mat_graph->cnloc  = n;
7206:     }
7207:     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);
7208:     pcbddc->mat_graph->active_coords = (PetscBool)(pcbddc->corner_selection && !pcbddc->corner_selected);

7210:     /* Setup of Graph */
7211:     pcbddc->mat_graph->commsizelimit = 0; /* don't use the COMM_SELF variant of the graph */
7212:     PCBDDCGraphSetUp(pcbddc->mat_graph,pcbddc->vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices_local);

7214:     /* attach info on disconnected subdomains if present */
7215:     if (pcbddc->n_local_subs) {
7216:       PetscInt *local_subs,n,totn;

7218:       MatGetLocalSize(matis->A,&n,NULL);
7219:       PetscMalloc1(n,&local_subs);
7220:       for (i=0;i<n;i++) local_subs[i] = pcbddc->n_local_subs;
7221:       for (i=0;i<pcbddc->n_local_subs;i++) {
7222:         const PetscInt *idxs;
7223:         PetscInt       nl,j;

7225:         ISGetLocalSize(pcbddc->local_subs[i],&nl);
7226:         ISGetIndices(pcbddc->local_subs[i],&idxs);
7227:         for (j=0;j<nl;j++) local_subs[idxs[j]] = i;
7228:         ISRestoreIndices(pcbddc->local_subs[i],&idxs);
7229:       }
7230:       for (i=0,totn=0;i<n;i++) totn = PetscMax(totn,local_subs[i]);
7231:       pcbddc->mat_graph->n_local_subs = totn + 1;
7232:       pcbddc->mat_graph->local_subs = local_subs;
7233:     }
7234:   }

7236:   if (!pcbddc->graphanalyzed) {
7237:     /* Graph's connected components analysis */
7238:     PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);
7239:     pcbddc->graphanalyzed = PETSC_TRUE;
7240:     pcbddc->corner_selected = pcbddc->corner_selection;
7241:   }
7242:   if (rcsr) pcbddc->mat_graph->nvtxs_csr = 0;
7243:   return(0);
7244: }

7246: PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt *nio, Vec vecs[])
7247: {
7248:   PetscInt       i,j,n;
7249:   PetscScalar    *alphas;
7250:   PetscReal      norm,*onorms;

7254:   n = *nio;
7255:   if (!n) return(0);
7256:   PetscMalloc2(n,&alphas,n,&onorms);
7257:   VecNormalize(vecs[0],&norm);
7258:   if (norm < PETSC_SMALL) {
7259:     onorms[0] = 0.0;
7260:     VecSet(vecs[0],0.0);
7261:   } else {
7262:     onorms[0] = norm;
7263:   }

7265:   for (i=1;i<n;i++) {
7266:     VecMDot(vecs[i],i,vecs,alphas);
7267:     for (j=0;j<i;j++) alphas[j] = PetscConj(-alphas[j]);
7268:     VecMAXPY(vecs[i],i,alphas,vecs);
7269:     VecNormalize(vecs[i],&norm);
7270:     if (norm < PETSC_SMALL) {
7271:       onorms[i] = 0.0;
7272:       VecSet(vecs[i],0.0);
7273:     } else {
7274:       onorms[i] = norm;
7275:     }
7276:   }
7277:   /* push nonzero vectors at the beginning */
7278:   for (i=0;i<n;i++) {
7279:     if (onorms[i] == 0.0) {
7280:       for (j=i+1;j<n;j++) {
7281:         if (onorms[j] != 0.0) {
7282:           VecCopy(vecs[j],vecs[i]);
7283:           onorms[j] = 0.0;
7284:         }
7285:       }
7286:     }
7287:   }
7288:   for (i=0,*nio=0;i<n;i++) *nio += onorms[i] != 0.0 ? 1 : 0;
7289:   PetscFree2(alphas,onorms);
7290:   return(0);
7291: }

7293: PetscErrorCode PCBDDCMatISGetSubassemblingPattern(Mat mat, PetscInt *n_subdomains, PetscInt redprocs, IS* is_sends, PetscBool *have_void)
7294: {
7295:   Mat            A;
7296:   PetscInt       n_neighs,*neighs,*n_shared,**shared;
7297:   PetscMPIInt    size,rank,color;
7298:   PetscInt       *xadj,*adjncy;
7299:   PetscInt       *adjncy_wgt,*v_wgt,*ranks_send_to_idx;
7300:   PetscInt       im_active,active_procs,N,n,i,j,threshold = 2;
7301:   PetscInt       void_procs,*procs_candidates = NULL;
7302:   PetscInt       xadj_count,*count;
7303:   PetscBool      ismatis,use_vwgt=PETSC_FALSE;
7304:   PetscSubcomm   psubcomm;
7305:   MPI_Comm       subcomm;

7310:   PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);
7311:   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);
7314:   if (*n_subdomains <=0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Invalid number of subdomains requested %D",*n_subdomains);

7316:   if (have_void) *have_void = PETSC_FALSE;
7317:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
7318:   MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);
7319:   MatISGetLocalMat(mat,&A);
7320:   MatGetLocalSize(A,&n,NULL);
7321:   im_active = !!n;
7322:   MPIU_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)mat));
7323:   void_procs = size - active_procs;
7324:   /* get ranks of of non-active processes in mat communicator */
7325:   if (void_procs) {
7326:     PetscInt ncand;

7328:     if (have_void) *have_void = PETSC_TRUE;
7329:     PetscMalloc1(size,&procs_candidates);
7330:     MPI_Allgather(&im_active,1,MPIU_INT,procs_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)mat));
7331:     for (i=0,ncand=0;i<size;i++) {
7332:       if (!procs_candidates[i]) {
7333:         procs_candidates[ncand++] = i;
7334:       }
7335:     }
7336:     /* force n_subdomains to be not greater that the number of non-active processes */
7337:     *n_subdomains = PetscMin(void_procs,*n_subdomains);
7338:   }

7340:   /* number of subdomains requested greater than active processes or matrix size -> just shift the matrix
7341:      number of subdomains requested 1 -> send to master or first candidate in voids  */
7342:   MatGetSize(mat,&N,NULL);
7343:   if (active_procs < *n_subdomains || *n_subdomains == 1 || N <= *n_subdomains) {
7344:     PetscInt issize,isidx,dest;
7345:     if (*n_subdomains == 1) dest = 0;
7346:     else dest = rank;
7347:     if (im_active) {
7348:       issize = 1;
7349:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7350:         isidx = procs_candidates[dest];
7351:       } else {
7352:         isidx = dest;
7353:       }
7354:     } else {
7355:       issize = 0;
7356:       isidx = -1;
7357:     }
7358:     if (*n_subdomains != 1) *n_subdomains = active_procs;
7359:     ISCreateGeneral(PetscObjectComm((PetscObject)mat),issize,&isidx,PETSC_COPY_VALUES,is_sends);
7360:     PetscFree(procs_candidates);
7361:     return(0);
7362:   }
7363:   PetscOptionsGetBool(NULL,NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);
7364:   PetscOptionsGetInt(NULL,NULL,"-matis_partitioning_threshold",&threshold,NULL);
7365:   threshold = PetscMax(threshold,2);

7367:   /* Get info on mapping */
7368:   ISLocalToGlobalMappingGetInfo(mat->rmap->mapping,&n_neighs,&neighs,&n_shared,&shared);

7370:   /* build local CSR graph of subdomains' connectivity */
7371:   PetscMalloc1(2,&xadj);
7372:   xadj[0] = 0;
7373:   xadj[1] = PetscMax(n_neighs-1,0);
7374:   PetscMalloc1(xadj[1],&adjncy);
7375:   PetscMalloc1(xadj[1],&adjncy_wgt);
7376:   PetscCalloc1(n,&count);
7377:   for (i=1;i<n_neighs;i++)
7378:     for (j=0;j<n_shared[i];j++)
7379:       count[shared[i][j]] += 1;

7381:   xadj_count = 0;
7382:   for (i=1;i<n_neighs;i++) {
7383:     for (j=0;j<n_shared[i];j++) {
7384:       if (count[shared[i][j]] < threshold) {
7385:         adjncy[xadj_count] = neighs[i];
7386:         adjncy_wgt[xadj_count] = n_shared[i];
7387:         xadj_count++;
7388:         break;
7389:       }
7390:     }
7391:   }
7392:   xadj[1] = xadj_count;
7393:   PetscFree(count);
7394:   ISLocalToGlobalMappingRestoreInfo(mat->rmap->mapping,&n_neighs,&neighs,&n_shared,&shared);
7395:   PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);

7397:   PetscMalloc1(1,&ranks_send_to_idx);

7399:   /* Restrict work on active processes only */
7400:   PetscMPIIntCast(im_active,&color);
7401:   if (void_procs) {
7402:     PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&psubcomm);
7403:     PetscSubcommSetNumber(psubcomm,2); /* 2 groups, active process and not active processes */
7404:     PetscSubcommSetTypeGeneral(psubcomm,color,rank);
7405:     subcomm = PetscSubcommChild(psubcomm);
7406:   } else {
7407:     psubcomm = NULL;
7408:     subcomm = PetscObjectComm((PetscObject)mat);
7409:   }

7411:   v_wgt = NULL;
7412:   if (!color) {
7413:     PetscFree(xadj);
7414:     PetscFree(adjncy);
7415:     PetscFree(adjncy_wgt);
7416:   } else {
7417:     Mat             subdomain_adj;
7418:     IS              new_ranks,new_ranks_contig;
7419:     MatPartitioning partitioner;
7420:     PetscInt        rstart=0,rend=0;
7421:     PetscInt        *is_indices,*oldranks;
7422:     PetscMPIInt     size;
7423:     PetscBool       aggregate;

7425:     MPI_Comm_size(subcomm,&size);
7426:     if (void_procs) {
7427:       PetscInt prank = rank;
7428:       PetscMalloc1(size,&oldranks);
7429:       MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm);
7430:       for (i=0;i<xadj[1];i++) {
7431:         PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);
7432:       }
7433:       PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);
7434:     } else {
7435:       oldranks = NULL;
7436:     }
7437:     aggregate = ((redprocs > 0 && redprocs < size) ? PETSC_TRUE : PETSC_FALSE);
7438:     if (aggregate) { /* TODO: all this part could be made more efficient */
7439:       PetscInt    lrows,row,ncols,*cols;
7440:       PetscMPIInt nrank;
7441:       PetscScalar *vals;

7443:       MPI_Comm_rank(subcomm,&nrank);
7444:       lrows = 0;
7445:       if (nrank<redprocs) {
7446:         lrows = size/redprocs;
7447:         if (nrank<size%redprocs) lrows++;
7448:       }
7449:       MatCreateAIJ(subcomm,lrows,lrows,size,size,50,NULL,50,NULL,&subdomain_adj);
7450:       MatGetOwnershipRange(subdomain_adj,&rstart,&rend);
7451:       MatSetOption(subdomain_adj,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
7452:       MatSetOption(subdomain_adj,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
7453:       row = nrank;
7454:       ncols = xadj[1]-xadj[0];
7455:       cols = adjncy;
7456:       PetscMalloc1(ncols,&vals);
7457:       for (i=0;i<ncols;i++) vals[i] = adjncy_wgt[i];
7458:       MatSetValues(subdomain_adj,1,&row,ncols,cols,vals,INSERT_VALUES);
7459:       MatAssemblyBegin(subdomain_adj,MAT_FINAL_ASSEMBLY);
7460:       MatAssemblyEnd(subdomain_adj,MAT_FINAL_ASSEMBLY);
7461:       PetscFree(xadj);
7462:       PetscFree(adjncy);
7463:       PetscFree(adjncy_wgt);
7464:       PetscFree(vals);
7465:       if (use_vwgt) {
7466:         Vec               v;
7467:         const PetscScalar *array;
7468:         PetscInt          nl;

7470:         MatCreateVecs(subdomain_adj,&v,NULL);
7471:         VecSetValue(v,row,(PetscScalar)n,INSERT_VALUES);
7472:         VecAssemblyBegin(v);
7473:         VecAssemblyEnd(v);
7474:         VecGetLocalSize(v,&nl);
7475:         VecGetArrayRead(v,&array);
7476:         PetscMalloc1(nl,&v_wgt);
7477:         for (i=0;i<nl;i++) v_wgt[i] = (PetscInt)PetscRealPart(array[i]);
7478:         VecRestoreArrayRead(v,&array);
7479:         VecDestroy(&v);
7480:       }
7481:     } else {
7482:       MatCreateMPIAdj(subcomm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);
7483:       if (use_vwgt) {
7484:         PetscMalloc1(1,&v_wgt);
7485:         v_wgt[0] = n;
7486:       }
7487:     }
7488:     /* MatView(subdomain_adj,0); */

7490:     /* Partition */
7491:     MatPartitioningCreate(subcomm,&partitioner);
7492: #if defined(PETSC_HAVE_PTSCOTCH)
7493:     MatPartitioningSetType(partitioner,MATPARTITIONINGPTSCOTCH);
7494: #elif defined(PETSC_HAVE_PARMETIS)
7495:     MatPartitioningSetType(partitioner,MATPARTITIONINGPARMETIS);
7496: #else
7497:     MatPartitioningSetType(partitioner,MATPARTITIONINGAVERAGE);
7498: #endif
7499:     MatPartitioningSetAdjacency(partitioner,subdomain_adj);
7500:     if (v_wgt) {
7501:       MatPartitioningSetVertexWeights(partitioner,v_wgt);
7502:     }
7503:     *n_subdomains = PetscMin((PetscInt)size,*n_subdomains);
7504:     MatPartitioningSetNParts(partitioner,*n_subdomains);
7505:     MatPartitioningSetFromOptions(partitioner);
7506:     MatPartitioningApply(partitioner,&new_ranks);
7507:     /* MatPartitioningView(partitioner,0); */

7509:     /* renumber new_ranks to avoid "holes" in new set of processors */
7510:     ISRenumber(new_ranks,NULL,NULL,&new_ranks_contig);
7511:     ISDestroy(&new_ranks);
7512:     ISGetIndices(new_ranks_contig,(const PetscInt**)&is_indices);
7513:     if (!aggregate) {
7514:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7515: #if defined(PETSC_USE_DEBUG)
7516:         if (!oldranks) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
7517: #endif
7518:         ranks_send_to_idx[0] = procs_candidates[oldranks[is_indices[0]]];
7519:       } else if (oldranks) {
7520:         ranks_send_to_idx[0] = oldranks[is_indices[0]];
7521:       } else {
7522:         ranks_send_to_idx[0] = is_indices[0];
7523:       }
7524:     } else {
7525:       PetscInt    idx = 0;
7526:       PetscMPIInt tag;
7527:       MPI_Request *reqs;

7529:       PetscObjectGetNewTag((PetscObject)subdomain_adj,&tag);
7530:       PetscMalloc1(rend-rstart,&reqs);
7531:       for (i=rstart;i<rend;i++) {
7532:         MPI_Isend(is_indices+i-rstart,1,MPIU_INT,i,tag,subcomm,&reqs[i-rstart]);
7533:       }
7534:       MPI_Recv(&idx,1,MPIU_INT,MPI_ANY_SOURCE,tag,subcomm,MPI_STATUS_IGNORE);
7535:       MPI_Waitall(rend-rstart,reqs,MPI_STATUSES_IGNORE);
7536:       PetscFree(reqs);
7537:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
7538: #if defined(PETSC_USE_DEBUG)
7539:         if (!oldranks) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
7540: #endif
7541:         ranks_send_to_idx[0] = procs_candidates[oldranks[idx]];
7542:       } else if (oldranks) {
7543:         ranks_send_to_idx[0] = oldranks[idx];
7544:       } else {
7545:         ranks_send_to_idx[0] = idx;
7546:       }
7547:     }
7548:     ISRestoreIndices(new_ranks_contig,(const PetscInt**)&is_indices);
7549:     /* clean up */
7550:     PetscFree(oldranks);
7551:     ISDestroy(&new_ranks_contig);
7552:     MatDestroy(&subdomain_adj);
7553:     MatPartitioningDestroy(&partitioner);
7554:   }
7555:   PetscSubcommDestroy(&psubcomm);
7556:   PetscFree(procs_candidates);

7558:   /* assemble parallel IS for sends */
7559:   i = 1;
7560:   if (!color) i=0;
7561:   ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,is_sends);
7562:   return(0);
7563: }

7565: typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;

7567: 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[])
7568: {
7569:   Mat                    local_mat;
7570:   IS                     is_sends_internal;
7571:   PetscInt               rows,cols,new_local_rows;
7572:   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals,buf_size_vecs;
7573:   PetscBool              ismatis,isdense,newisdense,destroy_mat;
7574:   ISLocalToGlobalMapping l2gmap;
7575:   PetscInt*              l2gmap_indices;
7576:   const PetscInt*        is_indices;
7577:   MatType                new_local_type;
7578:   /* buffers */
7579:   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
7580:   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
7581:   PetscInt               *recv_buffer_idxs_local;
7582:   PetscScalar            *ptr_vals,*recv_buffer_vals;
7583:   const PetscScalar      *send_buffer_vals;
7584:   PetscScalar            *ptr_vecs,*send_buffer_vecs,*recv_buffer_vecs;
7585:   /* MPI */
7586:   MPI_Comm               comm,comm_n;
7587:   PetscSubcomm           subcomm;
7588:   PetscMPIInt            n_sends,n_recvs,size;
7589:   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
7590:   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
7591:   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,tag_vecs,source_dest;
7592:   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals,*send_req_vecs;
7593:   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals,*recv_req_vecs;
7594:   PetscErrorCode         ierr;

7598:   PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);
7599:   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);
7606:   if (nvecs) {
7607:     if (nvecs > 1) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Just 1 vector supported");
7609:   }
7610:   /* further checks */
7611:   MatISGetLocalMat(mat,&local_mat);
7612:   PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);
7613:   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
7614:   MatGetSize(local_mat,&rows,&cols);
7615:   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
7616:   if (reuse && *mat_n) {
7617:     PetscInt mrows,mcols,mnrows,mncols;
7619:     PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);
7620:     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
7621:     MatGetSize(mat,&mrows,&mcols);
7622:     MatGetSize(*mat_n,&mnrows,&mncols);
7623:     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
7624:     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
7625:   }
7626:   MatGetBlockSize(local_mat,&bs);

7629:   /* prepare IS for sending if not provided */
7630:   if (!is_sends) {
7631:     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
7632:     PCBDDCMatISGetSubassemblingPattern(mat,&n_subdomains,0,&is_sends_internal,NULL);
7633:   } else {
7634:     PetscObjectReference((PetscObject)is_sends);
7635:     is_sends_internal = is_sends;
7636:   }

7638:   /* get comm */
7639:   PetscObjectGetComm((PetscObject)mat,&comm);

7641:   /* compute number of sends */
7642:   ISGetLocalSize(is_sends_internal,&i);
7643:   PetscMPIIntCast(i,&n_sends);

7645:   /* compute number of receives */
7646:   MPI_Comm_size(comm,&size);
7647:   PetscMalloc1(size,&iflags);
7648:   PetscArrayzero(iflags,size);
7649:   ISGetIndices(is_sends_internal,&is_indices);
7650:   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
7651:   PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);
7652:   PetscFree(iflags);

7654:   /* restrict comm if requested */
7655:   subcomm = 0;
7656:   destroy_mat = PETSC_FALSE;
7657:   if (restrict_comm) {
7658:     PetscMPIInt color,subcommsize;

7660:     color = 0;
7661:     if (restrict_full) {
7662:       if (!n_recvs) color = 1; /* processes not receiving anything will not partecipate in new comm (full restriction) */
7663:     } else {
7664:       if (!n_recvs && n_sends) color = 1; /* just those processes that are sending but not receiving anything will not partecipate in new comm */
7665:     }
7666:     MPIU_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);
7667:     subcommsize = size - subcommsize;
7668:     /* check if reuse has been requested */
7669:     if (reuse) {
7670:       if (*mat_n) {
7671:         PetscMPIInt subcommsize2;
7672:         MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);
7673:         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
7674:         comm_n = PetscObjectComm((PetscObject)*mat_n);
7675:       } else {
7676:         comm_n = PETSC_COMM_SELF;
7677:       }
7678:     } else { /* MAT_INITIAL_MATRIX */
7679:       PetscMPIInt rank;

7681:       MPI_Comm_rank(comm,&rank);
7682:       PetscSubcommCreate(comm,&subcomm);
7683:       PetscSubcommSetNumber(subcomm,2);
7684:       PetscSubcommSetTypeGeneral(subcomm,color,rank);
7685:       comm_n = PetscSubcommChild(subcomm);
7686:     }
7687:     /* flag to destroy *mat_n if not significative */
7688:     if (color) destroy_mat = PETSC_TRUE;
7689:   } else {
7690:     comm_n = comm;
7691:   }

7693:   /* prepare send/receive buffers */
7694:   PetscMalloc1(size,&ilengths_idxs);
7695:   PetscArrayzero(ilengths_idxs,size);
7696:   PetscMalloc1(size,&ilengths_vals);
7697:   PetscArrayzero(ilengths_vals,size);
7698:   if (nis) {
7699:     PetscCalloc1(size,&ilengths_idxs_is);
7700:   }

7702:   /* Get data from local matrices */
7703:   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Subassembling of AIJ local matrices not yet implemented");
7704:     /* TODO: See below some guidelines on how to prepare the local buffers */
7705:     /*
7706:        send_buffer_vals should contain the raw values of the local matrix
7707:        send_buffer_idxs should contain:
7708:        - MatType_PRIVATE type
7709:        - PetscInt        size_of_l2gmap
7710:        - PetscInt        global_row_indices[size_of_l2gmap]
7711:        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
7712:     */
7713:   else {
7714:     MatDenseGetArrayRead(local_mat,&send_buffer_vals);
7715:     ISLocalToGlobalMappingGetSize(mat->rmap->mapping,&i);
7716:     PetscMalloc1(i+2,&send_buffer_idxs);
7717:     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
7718:     send_buffer_idxs[1] = i;
7719:     ISLocalToGlobalMappingGetIndices(mat->rmap->mapping,(const PetscInt**)&ptr_idxs);
7720:     PetscArraycpy(&send_buffer_idxs[2],ptr_idxs,i);
7721:     ISLocalToGlobalMappingRestoreIndices(mat->rmap->mapping,(const PetscInt**)&ptr_idxs);
7722:     PetscMPIIntCast(i,&len);
7723:     for (i=0;i<n_sends;i++) {
7724:       ilengths_vals[is_indices[i]] = len*len;
7725:       ilengths_idxs[is_indices[i]] = len+2;
7726:     }
7727:   }
7728:   PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);
7729:   /* additional is (if any) */
7730:   if (nis) {
7731:     PetscMPIInt psum;
7732:     PetscInt j;
7733:     for (j=0,psum=0;j<nis;j++) {
7734:       PetscInt plen;
7735:       ISGetLocalSize(isarray[j],&plen);
7736:       PetscMPIIntCast(plen,&len);
7737:       psum += len+1; /* indices + lenght */
7738:     }
7739:     PetscMalloc1(psum,&send_buffer_idxs_is);
7740:     for (j=0,psum=0;j<nis;j++) {
7741:       PetscInt plen;
7742:       const PetscInt *is_array_idxs;
7743:       ISGetLocalSize(isarray[j],&plen);
7744:       send_buffer_idxs_is[psum] = plen;
7745:       ISGetIndices(isarray[j],&is_array_idxs);
7746:       PetscArraycpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen);
7747:       ISRestoreIndices(isarray[j],&is_array_idxs);
7748:       psum += plen+1; /* indices + lenght */
7749:     }
7750:     for (i=0;i<n_sends;i++) {
7751:       ilengths_idxs_is[is_indices[i]] = psum;
7752:     }
7753:     PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);
7754:   }
7755:   MatISRestoreLocalMat(mat,&local_mat);

7757:   buf_size_idxs = 0;
7758:   buf_size_vals = 0;
7759:   buf_size_idxs_is = 0;
7760:   buf_size_vecs = 0;
7761:   for (i=0;i<n_recvs;i++) {
7762:     buf_size_idxs += (PetscInt)olengths_idxs[i];
7763:     buf_size_vals += (PetscInt)olengths_vals[i];
7764:     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
7765:     if (nvecs) buf_size_vecs += (PetscInt)olengths_idxs[i];
7766:   }
7767:   PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);
7768:   PetscMalloc1(buf_size_vals,&recv_buffer_vals);
7769:   PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);
7770:   PetscMalloc1(buf_size_vecs,&recv_buffer_vecs);

7772:   /* get new tags for clean communications */
7773:   PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);
7774:   PetscObjectGetNewTag((PetscObject)mat,&tag_vals);
7775:   PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);
7776:   PetscObjectGetNewTag((PetscObject)mat,&tag_vecs);

7778:   /* allocate for requests */
7779:   PetscMalloc1(n_sends,&send_req_idxs);
7780:   PetscMalloc1(n_sends,&send_req_vals);
7781:   PetscMalloc1(n_sends,&send_req_idxs_is);
7782:   PetscMalloc1(n_sends,&send_req_vecs);
7783:   PetscMalloc1(n_recvs,&recv_req_idxs);
7784:   PetscMalloc1(n_recvs,&recv_req_vals);
7785:   PetscMalloc1(n_recvs,&recv_req_idxs_is);
7786:   PetscMalloc1(n_recvs,&recv_req_vecs);

7788:   /* communications */
7789:   ptr_idxs = recv_buffer_idxs;
7790:   ptr_vals = recv_buffer_vals;
7791:   ptr_idxs_is = recv_buffer_idxs_is;
7792:   ptr_vecs = recv_buffer_vecs;
7793:   for (i=0;i<n_recvs;i++) {
7794:     source_dest = onodes[i];
7795:     MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);
7796:     MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);
7797:     ptr_idxs += olengths_idxs[i];
7798:     ptr_vals += olengths_vals[i];
7799:     if (nis) {
7800:       source_dest = onodes_is[i];
7801:       MPI_Irecv(ptr_idxs_is,olengths_idxs_is[i],MPIU_INT,source_dest,tag_idxs_is,comm,&recv_req_idxs_is[i]);
7802:       ptr_idxs_is += olengths_idxs_is[i];
7803:     }
7804:     if (nvecs) {
7805:       source_dest = onodes[i];
7806:       MPI_Irecv(ptr_vecs,olengths_idxs[i]-2,MPIU_SCALAR,source_dest,tag_vecs,comm,&recv_req_vecs[i]);
7807:       ptr_vecs += olengths_idxs[i]-2;
7808:     }
7809:   }
7810:   for (i=0;i<n_sends;i++) {
7811:     PetscMPIIntCast(is_indices[i],&source_dest);
7812:     MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);
7813:     MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);
7814:     if (nis) {
7815:       MPI_Isend(send_buffer_idxs_is,ilengths_idxs_is[source_dest],MPIU_INT,source_dest,tag_idxs_is,comm,&send_req_idxs_is[i]);
7816:     }
7817:     if (nvecs) {
7818:       VecGetArray(nnsp_vec[0],&send_buffer_vecs);
7819:       MPI_Isend(send_buffer_vecs,ilengths_idxs[source_dest]-2,MPIU_SCALAR,source_dest,tag_vecs,comm,&send_req_vecs[i]);
7820:     }
7821:   }
7822:   ISRestoreIndices(is_sends_internal,&is_indices);
7823:   ISDestroy(&is_sends_internal);

7825:   /* assemble new l2g map */
7826:   MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);
7827:   ptr_idxs = recv_buffer_idxs;
7828:   new_local_rows = 0;
7829:   for (i=0;i<n_recvs;i++) {
7830:     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
7831:     ptr_idxs += olengths_idxs[i];
7832:   }
7833:   PetscMalloc1(new_local_rows,&l2gmap_indices);
7834:   ptr_idxs = recv_buffer_idxs;
7835:   new_local_rows = 0;
7836:   for (i=0;i<n_recvs;i++) {
7837:     PetscArraycpy(&l2gmap_indices[new_local_rows],ptr_idxs+2,*(ptr_idxs+1));
7838:     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
7839:     ptr_idxs += olengths_idxs[i];
7840:   }
7841:   PetscSortRemoveDupsInt(&new_local_rows,l2gmap_indices);
7842:   ISLocalToGlobalMappingCreate(comm_n,1,new_local_rows,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);
7843:   PetscFree(l2gmap_indices);

7845:   /* infer new local matrix type from received local matrices type */
7846:   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
7847:   /* 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) */
7848:   if (n_recvs) {
7849:     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
7850:     ptr_idxs = recv_buffer_idxs;
7851:     for (i=0;i<n_recvs;i++) {
7852:       if ((PetscInt)new_local_type_private != *ptr_idxs) {
7853:         new_local_type_private = MATAIJ_PRIVATE;
7854:         break;
7855:       }
7856:       ptr_idxs += olengths_idxs[i];
7857:     }
7858:     switch (new_local_type_private) {
7859:       case MATDENSE_PRIVATE:
7860:         new_local_type = MATSEQAIJ;
7861:         bs = 1;
7862:         break;
7863:       case MATAIJ_PRIVATE:
7864:         new_local_type = MATSEQAIJ;
7865:         bs = 1;
7866:         break;
7867:       case MATBAIJ_PRIVATE:
7868:         new_local_type = MATSEQBAIJ;
7869:         break;
7870:       case MATSBAIJ_PRIVATE:
7871:         new_local_type = MATSEQSBAIJ;
7872:         break;
7873:       default:
7874:         SETERRQ2(comm,PETSC_ERR_SUP,"Unsupported private type %d in %s",new_local_type_private,PETSC_FUNCTION_NAME);
7875:         break;
7876:     }
7877:   } else { /* by default, new_local_type is seqaij */
7878:     new_local_type = MATSEQAIJ;
7879:     bs = 1;
7880:   }

7882:   /* create MATIS object if needed */
7883:   if (!reuse) {
7884:     MatGetSize(mat,&rows,&cols);
7885:     MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,NULL,mat_n);
7886:   } else {
7887:     /* it also destroys the local matrices */
7888:     if (*mat_n) {
7889:       MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);
7890:     } else { /* this is a fake object */
7891:       MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,NULL,mat_n);
7892:     }
7893:   }
7894:   MatISGetLocalMat(*mat_n,&local_mat);
7895:   MatSetType(local_mat,new_local_type);

7897:   MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);

7899:   /* Global to local map of received indices */
7900:   PetscMalloc1(buf_size_idxs,&recv_buffer_idxs_local); /* needed for values insertion */
7901:   ISGlobalToLocalMappingApply(l2gmap,IS_GTOLM_MASK,buf_size_idxs,recv_buffer_idxs,&i,recv_buffer_idxs_local);
7902:   ISLocalToGlobalMappingDestroy(&l2gmap);

7904:   /* restore attributes -> type of incoming data and its size */
7905:   buf_size_idxs = 0;
7906:   for (i=0;i<n_recvs;i++) {
7907:     recv_buffer_idxs_local[buf_size_idxs] = recv_buffer_idxs[buf_size_idxs];
7908:     recv_buffer_idxs_local[buf_size_idxs+1] = recv_buffer_idxs[buf_size_idxs+1];
7909:     buf_size_idxs += (PetscInt)olengths_idxs[i];
7910:   }
7911:   PetscFree(recv_buffer_idxs);

7913:   /* set preallocation */
7914:   PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&newisdense);
7915:   if (!newisdense) {
7916:     PetscInt *new_local_nnz=0;

7918:     ptr_idxs = recv_buffer_idxs_local;
7919:     if (n_recvs) {
7920:       PetscCalloc1(new_local_rows,&new_local_nnz);
7921:     }
7922:     for (i=0;i<n_recvs;i++) {
7923:       PetscInt j;
7924:       if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
7925:         for (j=0;j<*(ptr_idxs+1);j++) {
7926:           new_local_nnz[*(ptr_idxs+2+j)] += *(ptr_idxs+1);
7927:         }
7928:       } else {
7929:         /* TODO */
7930:       }
7931:       ptr_idxs += olengths_idxs[i];
7932:     }
7933:     if (new_local_nnz) {
7934:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMin(new_local_nnz[i],new_local_rows);
7935:       MatSeqAIJSetPreallocation(local_mat,0,new_local_nnz);
7936:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] /= bs;
7937:       MatSeqBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);
7938:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMax(new_local_nnz[i]-i,0);
7939:       MatSeqSBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);
7940:     } else {
7941:       MatSetUp(local_mat);
7942:     }
7943:     PetscFree(new_local_nnz);
7944:   } else {
7945:     MatSetUp(local_mat);
7946:   }

7948:   /* set values */
7949:   ptr_vals = recv_buffer_vals;
7950:   ptr_idxs = recv_buffer_idxs_local;
7951:   for (i=0;i<n_recvs;i++) {
7952:     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
7953:       MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);
7954:       MatSetValues(local_mat,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);
7955:       MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);
7956:       MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);
7957:       MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);
7958:     } else {
7959:       /* TODO */
7960:     }
7961:     ptr_idxs += olengths_idxs[i];
7962:     ptr_vals += olengths_vals[i];
7963:   }
7964:   MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);
7965:   MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);
7966:   MatISRestoreLocalMat(*mat_n,&local_mat);
7967:   MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);
7968:   MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);
7969:   PetscFree(recv_buffer_vals);

7971: #if 0
7972:   if (!restrict_comm) { /* check */
7973:     Vec       lvec,rvec;
7974:     PetscReal infty_error;

7976:     MatCreateVecs(mat,&rvec,&lvec);
7977:     VecSetRandom(rvec,NULL);
7978:     MatMult(mat,rvec,lvec);
7979:     VecScale(lvec,-1.0);
7980:     MatMultAdd(*mat_n,rvec,lvec,lvec);
7981:     VecNorm(lvec,NORM_INFINITY,&infty_error);
7982:     PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
7983:     VecDestroy(&rvec);
7984:     VecDestroy(&lvec);
7985:   }
7986: #endif

7988:   /* assemble new additional is (if any) */
7989:   if (nis) {
7990:     PetscInt **temp_idxs,*count_is,j,psum;

7992:     MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);
7993:     PetscCalloc1(nis,&count_is);
7994:     ptr_idxs = recv_buffer_idxs_is;
7995:     psum = 0;
7996:     for (i=0;i<n_recvs;i++) {
7997:       for (j=0;j<nis;j++) {
7998:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
7999:         count_is[j] += plen; /* increment counting of buffer for j-th IS */
8000:         psum += plen;
8001:         ptr_idxs += plen+1; /* shift pointer to received data */
8002:       }
8003:     }
8004:     PetscMalloc1(nis,&temp_idxs);
8005:     PetscMalloc1(psum,&temp_idxs[0]);
8006:     for (i=1;i<nis;i++) {
8007:       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
8008:     }
8009:     PetscArrayzero(count_is,nis);
8010:     ptr_idxs = recv_buffer_idxs_is;
8011:     for (i=0;i<n_recvs;i++) {
8012:       for (j=0;j<nis;j++) {
8013:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
8014:         PetscArraycpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen);
8015:         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
8016:         ptr_idxs += plen+1; /* shift pointer to received data */
8017:       }
8018:     }
8019:     for (i=0;i<nis;i++) {
8020:       ISDestroy(&isarray[i]);
8021:       PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);
8022:       ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);
8023:     }
8024:     PetscFree(count_is);
8025:     PetscFree(temp_idxs[0]);
8026:     PetscFree(temp_idxs);
8027:   }
8028:   /* free workspace */
8029:   PetscFree(recv_buffer_idxs_is);
8030:   MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);
8031:   PetscFree(send_buffer_idxs);
8032:   MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);
8033:   if (isdense) {
8034:     MatISGetLocalMat(mat,&local_mat);
8035:     MatDenseRestoreArrayRead(local_mat,&send_buffer_vals);
8036:     MatISRestoreLocalMat(mat,&local_mat);
8037:   } else {
8038:     /* PetscFree(send_buffer_vals); */
8039:   }
8040:   if (nis) {
8041:     MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);
8042:     PetscFree(send_buffer_idxs_is);
8043:   }

8045:   if (nvecs) {
8046:     MPI_Waitall(n_recvs,recv_req_vecs,MPI_STATUSES_IGNORE);
8047:     MPI_Waitall(n_sends,send_req_vecs,MPI_STATUSES_IGNORE);
8048:     VecRestoreArray(nnsp_vec[0],&send_buffer_vecs);
8049:     VecDestroy(&nnsp_vec[0]);
8050:     VecCreate(comm_n,&nnsp_vec[0]);
8051:     VecSetSizes(nnsp_vec[0],new_local_rows,PETSC_DECIDE);
8052:     VecSetType(nnsp_vec[0],VECSTANDARD);
8053:     /* set values */
8054:     ptr_vals = recv_buffer_vecs;
8055:     ptr_idxs = recv_buffer_idxs_local;
8056:     VecGetArray(nnsp_vec[0],&send_buffer_vecs);
8057:     for (i=0;i<n_recvs;i++) {
8058:       PetscInt j;
8059:       for (j=0;j<*(ptr_idxs+1);j++) {
8060:         send_buffer_vecs[*(ptr_idxs+2+j)] += *(ptr_vals + j);
8061:       }
8062:       ptr_idxs += olengths_idxs[i];
8063:       ptr_vals += olengths_idxs[i]-2;
8064:     }
8065:     VecRestoreArray(nnsp_vec[0],&send_buffer_vecs);
8066:     VecAssemblyBegin(nnsp_vec[0]);
8067:     VecAssemblyEnd(nnsp_vec[0]);
8068:   }

8070:   PetscFree(recv_buffer_vecs);
8071:   PetscFree(recv_buffer_idxs_local);
8072:   PetscFree(recv_req_idxs);
8073:   PetscFree(recv_req_vals);
8074:   PetscFree(recv_req_vecs);
8075:   PetscFree(recv_req_idxs_is);
8076:   PetscFree(send_req_idxs);
8077:   PetscFree(send_req_vals);
8078:   PetscFree(send_req_vecs);
8079:   PetscFree(send_req_idxs_is);
8080:   PetscFree(ilengths_vals);
8081:   PetscFree(ilengths_idxs);
8082:   PetscFree(olengths_vals);
8083:   PetscFree(olengths_idxs);
8084:   PetscFree(onodes);
8085:   if (nis) {
8086:     PetscFree(ilengths_idxs_is);
8087:     PetscFree(olengths_idxs_is);
8088:     PetscFree(onodes_is);
8089:   }
8090:   PetscSubcommDestroy(&subcomm);
8091:   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
8092:     MatDestroy(mat_n);
8093:     for (i=0;i<nis;i++) {
8094:       ISDestroy(&isarray[i]);
8095:     }
8096:     if (nvecs) { /* need to match VecDestroy nnsp_vec called in the other code path */
8097:       VecDestroy(&nnsp_vec[0]);
8098:     }
8099:     *mat_n = NULL;
8100:   }
8101:   return(0);
8102: }

8104: /* temporary hack into ksp private data structure */
8105:  #include <petsc/private/kspimpl.h>

8107: PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
8108: {
8109:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
8110:   PC_IS                  *pcis = (PC_IS*)pc->data;
8111:   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
8112:   Mat                    coarsedivudotp = NULL;
8113:   Mat                    coarseG,t_coarse_mat_is;
8114:   MatNullSpace           CoarseNullSpace = NULL;
8115:   ISLocalToGlobalMapping coarse_islg;
8116:   IS                     coarse_is,*isarray,corners;
8117:   PetscInt               i,im_active=-1,active_procs=-1;
8118:   PetscInt               nis,nisdofs,nisneu,nisvert;
8119:   PetscInt               coarse_eqs_per_proc;
8120:   PC                     pc_temp;
8121:   PCType                 coarse_pc_type;
8122:   KSPType                coarse_ksp_type;
8123:   PetscBool              multilevel_requested,multilevel_allowed;
8124:   PetscBool              coarse_reuse;
8125:   PetscInt               ncoarse,nedcfield;
8126:   PetscBool              compute_vecs = PETSC_FALSE;
8127:   PetscScalar            *array;
8128:   MatReuse               coarse_mat_reuse;
8129:   PetscBool              restr, full_restr, have_void;
8130:   PetscMPIInt            size;
8131:   PetscErrorCode         ierr;

8134:   PetscLogEventBegin(PC_BDDC_CoarseSetUp[pcbddc->current_level],pc,0,0,0);
8135:   /* Assign global numbering to coarse dofs */
8136:   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 */
8137:     PetscInt ocoarse_size;
8138:     compute_vecs = PETSC_TRUE;

8140:     pcbddc->new_primal_space = PETSC_TRUE;
8141:     ocoarse_size = pcbddc->coarse_size;
8142:     PetscFree(pcbddc->global_primal_indices);
8143:     PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);
8144:     /* see if we can avoid some work */
8145:     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
8146:       /* if the coarse size is different or we are using adaptive selection, better to not reuse the coarse matrix */
8147:       if (ocoarse_size != pcbddc->coarse_size || pcbddc->adaptive_selection) {
8148:         KSPReset(pcbddc->coarse_ksp);
8149:         coarse_reuse = PETSC_FALSE;
8150:       } else { /* we can safely reuse already computed coarse matrix */
8151:         coarse_reuse = PETSC_TRUE;
8152:       }
8153:     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
8154:       coarse_reuse = PETSC_FALSE;
8155:     }
8156:     /* reset any subassembling information */
8157:     if (!coarse_reuse || pcbddc->recompute_topography) {
8158:       ISDestroy(&pcbddc->coarse_subassembling);
8159:     }
8160:   } else { /* primal space is unchanged, so we can reuse coarse matrix */
8161:     coarse_reuse = PETSC_TRUE;
8162:   }
8163:   if (coarse_reuse && pcbddc->coarse_ksp) {
8164:     KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);
8165:     PetscObjectReference((PetscObject)coarse_mat);
8166:     coarse_mat_reuse = MAT_REUSE_MATRIX;
8167:   } else {
8168:     coarse_mat = NULL;
8169:     coarse_mat_reuse = MAT_INITIAL_MATRIX;
8170:   }

8172:   /* creates temporary l2gmap and IS for coarse indexes */
8173:   ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);
8174:   ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);

8176:   /* creates temporary MATIS object for coarse matrix */
8177:   MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_submat_dense);
8178:   MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,NULL,&t_coarse_mat_is);
8179:   MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);
8180:   MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);
8181:   MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);
8182:   MatDestroy(&coarse_submat_dense);

8184:   /* count "active" (i.e. with positive local size) and "void" processes */
8185:   im_active = !!(pcis->n);
8186:   MPIU_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));

8188:   /* determine number of processes partecipating to coarse solver and compute subassembling pattern */
8189:   /* restr : whether we want to exclude senders (which are not receivers) from the subassembling pattern */
8190:   /* full_restr : just use the receivers from the subassembling pattern */
8191:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
8192:   coarse_mat_is        = NULL;
8193:   multilevel_allowed   = PETSC_FALSE;
8194:   multilevel_requested = PETSC_FALSE;
8195:   coarse_eqs_per_proc  = PetscMin(PetscMax(pcbddc->coarse_size,1),pcbddc->coarse_eqs_per_proc);
8196:   if (coarse_eqs_per_proc < 0) coarse_eqs_per_proc = pcbddc->coarse_size;
8197:   if (pcbddc->current_level < pcbddc->max_levels) multilevel_requested = PETSC_TRUE;
8198:   if (pcbddc->coarse_size <= pcbddc->coarse_eqs_limit) multilevel_requested = PETSC_FALSE;
8199:   if (multilevel_requested) {
8200:     ncoarse    = active_procs/pcbddc->coarsening_ratio;
8201:     restr      = PETSC_FALSE;
8202:     full_restr = PETSC_FALSE;
8203:   } else {
8204:     ncoarse    = pcbddc->coarse_size/coarse_eqs_per_proc + !!(pcbddc->coarse_size%coarse_eqs_per_proc);
8205:     restr      = PETSC_TRUE;
8206:     full_restr = PETSC_TRUE;
8207:   }
8208:   if (!pcbddc->coarse_size || size == 1) multilevel_allowed = multilevel_requested = restr = full_restr = PETSC_FALSE;
8209:   ncoarse = PetscMax(1,ncoarse);
8210:   if (!pcbddc->coarse_subassembling) {
8211:     if (pcbddc->coarsening_ratio > 1) {
8212:       if (multilevel_requested) {
8213:         PCBDDCMatISGetSubassemblingPattern(pc->pmat,&ncoarse,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling,&have_void);
8214:       } else {
8215:         PCBDDCMatISGetSubassemblingPattern(t_coarse_mat_is,&ncoarse,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling,&have_void);
8216:       }
8217:     } else {
8218:       PetscMPIInt rank;

8220:       MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
8221:       have_void = (active_procs == (PetscInt)size) ? PETSC_FALSE : PETSC_TRUE;
8222:       ISCreateStride(PetscObjectComm((PetscObject)pc),1,rank,1,&pcbddc->coarse_subassembling);
8223:     }
8224:   } else { /* if a subassembling pattern exists, then we can reuse the coarse ksp and compute the number of process involved */
8225:     PetscInt    psum;
8226:     if (pcbddc->coarse_ksp) psum = 1;
8227:     else psum = 0;
8228:     MPIU_Allreduce(&psum,&ncoarse,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
8229:     have_void = ncoarse < size ? PETSC_TRUE : PETSC_FALSE;
8230:   }
8231:   /* determine if we can go multilevel */
8232:   if (multilevel_requested) {
8233:     if (ncoarse > 1) multilevel_allowed = PETSC_TRUE; /* found enough processes */
8234:     else restr = full_restr = PETSC_TRUE; /* 1 subdomain, use a direct solver */
8235:   }
8236:   if (multilevel_allowed && have_void) restr = PETSC_TRUE;

8238:   /* dump subassembling pattern */
8239:   if (pcbddc->dbg_flag && multilevel_allowed) {
8240:     ISView(pcbddc->coarse_subassembling,pcbddc->dbg_viewer);
8241:   }
8242:   /* compute dofs splitting and neumann boundaries for coarse dofs */
8243:   nedcfield = -1;
8244:   corners = NULL;
8245:   if (multilevel_allowed && !coarse_reuse && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal || pcbddc->nedclocal || pcbddc->corner_selected)) { /* protects from unneeded computations */
8246:     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
8247:     const PetscInt         *idxs;
8248:     ISLocalToGlobalMapping tmap;

8250:     /* create map between primal indices (in local representative ordering) and local primal numbering */
8251:     ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);
8252:     /* allocate space for temporary storage */
8253:     PetscMalloc1(pcbddc->local_primal_size,&tidxs);
8254:     PetscMalloc1(pcbddc->local_primal_size,&tidxs2);
8255:     /* allocate for IS array */
8256:     nisdofs = pcbddc->n_ISForDofsLocal;
8257:     if (pcbddc->nedclocal) {
8258:       if (pcbddc->nedfield > -1) {
8259:         nedcfield = pcbddc->nedfield;
8260:       } else {
8261:         nedcfield = 0;
8262:         if (nisdofs) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen (%D)",nisdofs);
8263:         nisdofs = 1;
8264:       }
8265:     }
8266:     nisneu = !!pcbddc->NeumannBoundariesLocal;
8267:     nisvert = 0; /* nisvert is not used */
8268:     nis = nisdofs + nisneu + nisvert;
8269:     PetscMalloc1(nis,&isarray);
8270:     /* dofs splitting */
8271:     for (i=0;i<nisdofs;i++) {
8272:       /* ISView(pcbddc->ISForDofsLocal[i],0); */
8273:       if (nedcfield != i) {
8274:         ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);
8275:         ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);
8276:         ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
8277:         ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);
8278:       } else {
8279:         ISGetLocalSize(pcbddc->nedclocal,&tsize);
8280:         ISGetIndices(pcbddc->nedclocal,&idxs);
8281:         ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
8282:         if (tsize != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Failed when mapping coarse nedelec field! %D != %D",tsize,nout);
8283:         ISRestoreIndices(pcbddc->nedclocal,&idxs);
8284:       }
8285:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
8286:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);
8287:       /* ISView(isarray[i],0); */
8288:     }
8289:     /* neumann boundaries */
8290:     if (pcbddc->NeumannBoundariesLocal) {
8291:       /* ISView(pcbddc->NeumannBoundariesLocal,0); */
8292:       ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);
8293:       ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);
8294:       ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
8295:       ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);
8296:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
8297:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);
8298:       /* ISView(isarray[nisdofs],0); */
8299:     }
8300:     /* coordinates */
8301:     if (pcbddc->corner_selected) {
8302:       PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&corners);
8303:       ISGetLocalSize(corners,&tsize);
8304:       ISGetIndices(corners,&idxs);
8305:       ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
8306:       if (tsize != nout) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Failed when mapping corners! %D != %D",tsize,nout);
8307:       ISRestoreIndices(corners,&idxs);
8308:       PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&corners);
8309:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
8310:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&corners);
8311:     }
8312:     PetscFree(tidxs);
8313:     PetscFree(tidxs2);
8314:     ISLocalToGlobalMappingDestroy(&tmap);
8315:   } else {
8316:     nis = 0;
8317:     nisdofs = 0;
8318:     nisneu = 0;
8319:     nisvert = 0;
8320:     isarray = NULL;
8321:   }
8322:   /* destroy no longer needed map */
8323:   ISLocalToGlobalMappingDestroy(&coarse_islg);

8325:   /* subassemble */
8326:   if (multilevel_allowed) {
8327:     Vec       vp[1];
8328:     PetscInt  nvecs = 0;
8329:     PetscBool reuse,reuser;

8331:     if (coarse_mat) reuse = PETSC_TRUE;
8332:     else reuse = PETSC_FALSE;
8333:     MPIU_Allreduce(&reuse,&reuser,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
8334:     vp[0] = NULL;
8335:     if (pcbddc->benign_have_null) { /* propagate no-net-flux quadrature to coarser level */
8336:       VecCreate(PetscObjectComm((PetscObject)pc),&vp[0]);
8337:       VecSetSizes(vp[0],pcbddc->local_primal_size,PETSC_DECIDE);
8338:       VecSetType(vp[0],VECSTANDARD);
8339:       nvecs = 1;

8341:       if (pcbddc->divudotp) {
8342:         Mat      B,loc_divudotp;
8343:         Vec      v,p;
8344:         IS       dummy;
8345:         PetscInt np;

8347:         MatISGetLocalMat(pcbddc->divudotp,&loc_divudotp);
8348:         MatGetSize(loc_divudotp,&np,NULL);
8349:         ISCreateStride(PETSC_COMM_SELF,np,0,1,&dummy);
8350:         MatCreateSubMatrix(loc_divudotp,dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B);
8351:         MatCreateVecs(B,&v,&p);
8352:         VecSet(p,1.);
8353:         MatMultTranspose(B,p,v);
8354:         VecDestroy(&p);
8355:         MatDestroy(&B);
8356:         VecGetArray(vp[0],&array);
8357:         VecPlaceArray(pcbddc->vec1_P,array);
8358:         VecRestoreArray(vp[0],&array);
8359:         MatMultTranspose(pcbddc->coarse_phi_B,v,pcbddc->vec1_P);
8360:         VecResetArray(pcbddc->vec1_P);
8361:         ISDestroy(&dummy);
8362:         VecDestroy(&v);
8363:       }
8364:     }
8365:     if (reuser) {
8366:       PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_TRUE,&coarse_mat,nis,isarray,nvecs,vp);
8367:     } else {
8368:       PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_FALSE,&coarse_mat_is,nis,isarray,nvecs,vp);
8369:     }
8370:     if (vp[0]) { /* vp[0] could have been placed on a different set of processes */
8371:       PetscScalar       *arraym;
8372:       const PetscScalar *arrayv;
8373:       PetscInt          nl;
8374:       VecGetLocalSize(vp[0],&nl);
8375:       MatCreateSeqDense(PETSC_COMM_SELF,1,nl,NULL,&coarsedivudotp);
8376:       MatDenseGetArray(coarsedivudotp,&arraym);
8377:       VecGetArrayRead(vp[0],&arrayv);
8378:       PetscArraycpy(arraym,arrayv,nl);
8379:       VecRestoreArrayRead(vp[0],&arrayv);
8380:       MatDenseRestoreArray(coarsedivudotp,&arraym);
8381:       VecDestroy(&vp[0]);
8382:     } else {
8383:       MatCreateSeqAIJ(PETSC_COMM_SELF,0,0,1,NULL,&coarsedivudotp);
8384:     }
8385:   } else {
8386:     PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_FALSE,&coarse_mat_is,0,NULL,0,NULL);
8387:   }
8388:   if (coarse_mat_is || coarse_mat) {
8389:     if (!multilevel_allowed) {
8390:       MatConvert(coarse_mat_is,MATAIJ,coarse_mat_reuse,&coarse_mat);
8391:     } else {
8392:       /* if this matrix is present, it means we are not reusing the coarse matrix */
8393:       if (coarse_mat_is) {
8394:         if (coarse_mat) SETERRQ(PetscObjectComm((PetscObject)coarse_mat_is),PETSC_ERR_PLIB,"This should not happen");
8395:         PetscObjectReference((PetscObject)coarse_mat_is);
8396:         coarse_mat = coarse_mat_is;
8397:       }
8398:     }
8399:   }
8400:   MatDestroy(&t_coarse_mat_is);
8401:   MatDestroy(&coarse_mat_is);

8403:   /* create local to global scatters for coarse problem */
8404:   if (compute_vecs) {
8405:     PetscInt lrows;
8406:     VecDestroy(&pcbddc->coarse_vec);
8407:     if (coarse_mat) {
8408:       MatGetLocalSize(coarse_mat,&lrows,NULL);
8409:     } else {
8410:       lrows = 0;
8411:     }
8412:     VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);
8413:     VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);
8414:     VecSetType(pcbddc->coarse_vec,coarse_mat ? coarse_mat->defaultvectype : VECSTANDARD);
8415:     VecScatterDestroy(&pcbddc->coarse_loc_to_glob);
8416:     VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);
8417:   }
8418:   ISDestroy(&coarse_is);

8420:   /* set defaults for coarse KSP and PC */
8421:   if (multilevel_allowed) {
8422:     coarse_ksp_type = KSPRICHARDSON;
8423:     coarse_pc_type  = PCBDDC;
8424:   } else {
8425:     coarse_ksp_type = KSPPREONLY;
8426:     coarse_pc_type  = PCREDUNDANT;
8427:   }

8429:   /* print some info if requested */
8430:   if (pcbddc->dbg_flag) {
8431:     if (!multilevel_allowed) {
8432:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
8433:       if (multilevel_requested) {
8434:         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);
8435:       } else if (pcbddc->max_levels) {
8436:         PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%D)\n",pcbddc->max_levels);
8437:       }
8438:       PetscViewerFlush(pcbddc->dbg_viewer);
8439:     }
8440:   }

8442:   /* communicate coarse discrete gradient */
8443:   coarseG = NULL;
8444:   if (pcbddc->nedcG && multilevel_allowed) {
8445:     MPI_Comm ccomm;
8446:     if (coarse_mat) {
8447:       ccomm = PetscObjectComm((PetscObject)coarse_mat);
8448:     } else {
8449:       ccomm = MPI_COMM_NULL;
8450:     }
8451:     MatMPIAIJRestrict(pcbddc->nedcG,ccomm,&coarseG);
8452:   }

8454:   /* create the coarse KSP object only once with defaults */
8455:   if (coarse_mat) {
8456:     PetscBool   isredundant,isbddc,force,valid;
8457:     PetscViewer dbg_viewer = NULL;

8459:     if (pcbddc->dbg_flag) {
8460:       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat));
8461:       PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);
8462:     }
8463:     if (!pcbddc->coarse_ksp) {
8464:       char   prefix[256],str_level[16];
8465:       size_t len;

8467:       KSPCreate(PetscObjectComm((PetscObject)coarse_mat),&pcbddc->coarse_ksp);
8468:       KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,pc->erroriffailure);
8469:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);
8470:       KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);
8471:       KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);
8472:       KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);
8473:       KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);
8474:       KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
8475:       /* TODO is this logic correct? should check for coarse_mat type */
8476:       PCSetType(pc_temp,coarse_pc_type);
8477:       /* prefix */
8478:       PetscStrcpy(prefix,"");
8479:       PetscStrcpy(str_level,"");
8480:       if (!pcbddc->current_level) {
8481:         PetscStrncpy(prefix,((PetscObject)pc)->prefix,sizeof(prefix));
8482:         PetscStrlcat(prefix,"pc_bddc_coarse_",sizeof(prefix));
8483:       } else {
8484:         PetscStrlen(((PetscObject)pc)->prefix,&len);
8485:         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
8486:         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
8487:         /* Nonstandard use of PetscStrncpy() to copy only a portion of the string */
8488:         PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);
8489:         PetscSNPrintf(str_level,sizeof(str_level),"l%d_",(int)(pcbddc->current_level));
8490:         PetscStrlcat(prefix,str_level,sizeof(prefix));
8491:       }
8492:       KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);
8493:       /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
8494:       PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);
8495:       PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);
8496:       PCBDDCSetLevels(pc_temp,pcbddc->max_levels);
8497:       /* allow user customization */
8498:       KSPSetFromOptions(pcbddc->coarse_ksp);
8499:       /* get some info after set from options */
8500:       KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
8501:       /* multilevel cannot be done with coarse PC different from BDDC, NN, HPDDM, unless forced to */
8502:       force = PETSC_FALSE;
8503:       PetscOptionsGetBool(NULL,((PetscObject)pc_temp)->prefix,"-pc_type_forced",&force,NULL);
8504:       PetscObjectTypeCompareAny((PetscObject)pc_temp,&valid,PCBDDC,PCNN,PCHPDDM,"");
8505:       PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);
8506:       if (multilevel_allowed && !force && !valid) {
8507:         isbddc = PETSC_TRUE;
8508:         PCSetType(pc_temp,PCBDDC);
8509:         PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);
8510:         PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);
8511:         PCBDDCSetLevels(pc_temp,pcbddc->max_levels);
8512:         if (pc_temp->ops->setfromoptions) { /* need to setfromoptions again, skipping the pc_type */
8513:           PetscObjectOptionsBegin((PetscObject)pc_temp);
8514:           (*pc_temp->ops->setfromoptions)(PetscOptionsObject,pc_temp);
8515:           PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)pc_temp);
8516:           PetscOptionsEnd();
8517:           pc_temp->setfromoptionscalled++;
8518:         }
8519:       }
8520:     }
8521:     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
8522:     KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
8523:     if (nisdofs) {
8524:       PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);
8525:       for (i=0;i<nisdofs;i++) {
8526:         ISDestroy(&isarray[i]);
8527:       }
8528:     }
8529:     if (nisneu) {
8530:       PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);
8531:       ISDestroy(&isarray[nisdofs]);
8532:     }
8533:     if (nisvert) {
8534:       PCBDDCSetPrimalVerticesIS(pc_temp,isarray[nis-1]);
8535:       ISDestroy(&isarray[nis-1]);
8536:     }
8537:     if (coarseG) {
8538:       PCBDDCSetDiscreteGradient(pc_temp,coarseG,1,nedcfield,PETSC_FALSE,PETSC_TRUE);
8539:     }

8541:     /* get some info after set from options */
8542:     PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);

8544:     /* multilevel can only be requested via -pc_bddc_levels or PCBDDCSetLevels */
8545:     if (isbddc && !multilevel_allowed) {
8546:       PCSetType(pc_temp,coarse_pc_type);
8547:     }
8548:     /* multilevel cannot be done with coarse PC different from BDDC, NN, HPDDM, unless forced to */
8549:     force = PETSC_FALSE;
8550:     PetscOptionsGetBool(NULL,((PetscObject)pc_temp)->prefix,"-pc_type_forced",&force,NULL);
8551:     PetscObjectTypeCompareAny((PetscObject)pc_temp,&valid,PCBDDC,PCNN,PCHPDDM,"");
8552:     if (multilevel_requested && multilevel_allowed && !valid && !force) {
8553:       PCSetType(pc_temp,PCBDDC);
8554:     }
8555:     PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);
8556:     if (isredundant) {
8557:       KSP inner_ksp;
8558:       PC  inner_pc;

8560:       PCRedundantGetKSP(pc_temp,&inner_ksp);
8561:       KSPGetPC(inner_ksp,&inner_pc);
8562:     }

8564:     /* parameters which miss an API */
8565:     PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);
8566:     if (isbddc) {
8567:       PC_BDDC* pcbddc_coarse = (PC_BDDC*)pc_temp->data;

8569:       pcbddc_coarse->detect_disconnected = PETSC_TRUE;
8570:       pcbddc_coarse->coarse_eqs_per_proc = pcbddc->coarse_eqs_per_proc;
8571:       pcbddc_coarse->coarse_eqs_limit    = pcbddc->coarse_eqs_limit;
8572:       pcbddc_coarse->benign_saddle_point = pcbddc->benign_have_null;
8573:       if (pcbddc_coarse->benign_saddle_point) {
8574:         Mat                    coarsedivudotp_is;
8575:         ISLocalToGlobalMapping l2gmap,rl2g,cl2g;
8576:         IS                     row,col;
8577:         const PetscInt         *gidxs;
8578:         PetscInt               n,st,M,N;

8580:         MatGetSize(coarsedivudotp,&n,NULL);
8581:         MPI_Scan(&n,&st,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)coarse_mat));
8582:         st   = st-n;
8583:         ISCreateStride(PetscObjectComm((PetscObject)coarse_mat),1,st,1,&row);
8584:         MatGetLocalToGlobalMapping(coarse_mat,&l2gmap,NULL);
8585:         ISLocalToGlobalMappingGetSize(l2gmap,&n);
8586:         ISLocalToGlobalMappingGetIndices(l2gmap,&gidxs);
8587:         ISCreateGeneral(PetscObjectComm((PetscObject)coarse_mat),n,gidxs,PETSC_COPY_VALUES,&col);
8588:         ISLocalToGlobalMappingRestoreIndices(l2gmap,&gidxs);
8589:         ISLocalToGlobalMappingCreateIS(row,&rl2g);
8590:         ISLocalToGlobalMappingCreateIS(col,&cl2g);
8591:         ISGetSize(row,&M);
8592:         MatGetSize(coarse_mat,&N,NULL);
8593:         ISDestroy(&row);
8594:         ISDestroy(&col);
8595:         MatCreate(PetscObjectComm((PetscObject)coarse_mat),&coarsedivudotp_is);
8596:         MatSetType(coarsedivudotp_is,MATIS);
8597:         MatSetSizes(coarsedivudotp_is,PETSC_DECIDE,PETSC_DECIDE,M,N);
8598:         MatSetLocalToGlobalMapping(coarsedivudotp_is,rl2g,cl2g);
8599:         ISLocalToGlobalMappingDestroy(&rl2g);
8600:         ISLocalToGlobalMappingDestroy(&cl2g);
8601:         MatISSetLocalMat(coarsedivudotp_is,coarsedivudotp);
8602:         MatDestroy(&coarsedivudotp);
8603:         PCBDDCSetDivergenceMat(pc_temp,coarsedivudotp_is,PETSC_FALSE,NULL);
8604:         MatDestroy(&coarsedivudotp_is);
8605:         pcbddc_coarse->adaptive_userdefined = PETSC_TRUE;
8606:         if (pcbddc->adaptive_threshold[0] == 0.0) pcbddc_coarse->deluxe_zerorows = PETSC_TRUE;
8607:       }
8608:     }

8610:     /* propagate symmetry info of coarse matrix */
8611:     MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);
8612:     if (pc->pmat->symmetric_set) {
8613:       MatSetOption(coarse_mat,MAT_SYMMETRIC,pc->pmat->symmetric);
8614:     }
8615:     if (pc->pmat->hermitian_set) {
8616:       MatSetOption(coarse_mat,MAT_HERMITIAN,pc->pmat->hermitian);
8617:     }
8618:     if (pc->pmat->spd_set) {
8619:       MatSetOption(coarse_mat,MAT_SPD,pc->pmat->spd);
8620:     }
8621:     if (pcbddc->benign_saddle_point && !pcbddc->benign_have_null) {
8622:       MatSetOption(coarse_mat,MAT_SPD,PETSC_TRUE);
8623:     }
8624:     /* set operators */
8625:     MatViewFromOptions(coarse_mat,(PetscObject)pc,"-pc_bddc_coarse_mat_view");
8626:     MatSetOptionsPrefix(coarse_mat,((PetscObject)pcbddc->coarse_ksp)->prefix);
8627:     KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);
8628:     if (pcbddc->dbg_flag) {
8629:       PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);
8630:     }
8631:   }
8632:   MatDestroy(&coarseG);
8633:   PetscFree(isarray);
8634: #if 0
8635:   {
8636:     PetscViewer viewer;
8637:     char filename[256];
8638:     sprintf(filename,"coarse_mat_level%d.m",pcbddc->current_level);
8639:     PetscViewerASCIIOpen(PetscObjectComm((PetscObject)coarse_mat),filename,&viewer);
8640:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
8641:     MatView(coarse_mat,viewer);
8642:     PetscViewerPopFormat(viewer);
8643:     PetscViewerDestroy(&viewer);
8644:   }
8645: #endif

8647:   if (corners) {
8648:     Vec            gv;
8649:     IS             is;
8650:     const PetscInt *idxs;
8651:     PetscInt       i,d,N,n,cdim = pcbddc->mat_graph->cdim;
8652:     PetscScalar    *coords;

8654:     if (!pcbddc->mat_graph->cloc) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing local coordinates");
8655:     VecGetSize(pcbddc->coarse_vec,&N);
8656:     VecGetLocalSize(pcbddc->coarse_vec,&n);
8657:     VecCreate(PetscObjectComm((PetscObject)pcbddc->coarse_vec),&gv);
8658:     VecSetBlockSize(gv,cdim);
8659:     VecSetSizes(gv,n*cdim,N*cdim);
8660:     VecSetType(gv,VECSTANDARD);
8661:     VecSetFromOptions(gv);
8662:     VecSet(gv,PETSC_MAX_REAL); /* we only propagate coordinates from vertices constraints */

8664:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&is);
8665:     ISGetLocalSize(is,&n);
8666:     ISGetIndices(is,&idxs);
8667:     PetscMalloc1(n*cdim,&coords);
8668:     for (i=0;i<n;i++) {
8669:       for (d=0;d<cdim;d++) {
8670:         coords[cdim*i+d] = pcbddc->mat_graph->coords[cdim*idxs[i]+d];
8671:       }
8672:     }
8673:     ISRestoreIndices(is,&idxs);
8674:     PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&is);

8676:     ISGetLocalSize(corners,&n);
8677:     ISGetIndices(corners,&idxs);
8678:     VecSetValuesBlocked(gv,n,idxs,coords,INSERT_VALUES);
8679:     ISRestoreIndices(corners,&idxs);
8680:     PetscFree(coords);
8681:     VecAssemblyBegin(gv);
8682:     VecAssemblyEnd(gv);
8683:     VecGetArray(gv,&coords);
8684:     if (pcbddc->coarse_ksp) {
8685:       PC        coarse_pc;
8686:       PetscBool isbddc;

8688:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
8689:       PetscObjectTypeCompare((PetscObject)coarse_pc,PCBDDC,&isbddc);
8690:       if (isbddc) { /* coarse coordinates have PETSC_MAX_REAL, specific for BDDC */
8691:         PetscReal *realcoords;

8693:         VecGetLocalSize(gv,&n);
8694: #if defined(PETSC_USE_COMPLEX)
8695:         PetscMalloc1(n,&realcoords);
8696:         for (i=0;i<n;i++) realcoords[i] = PetscRealPart(coords[i]);
8697: #else
8698:         realcoords = coords;
8699: #endif
8700:         PCSetCoordinates(coarse_pc,cdim,n/cdim,realcoords);
8701: #if defined(PETSC_USE_COMPLEX)
8702:         PetscFree(realcoords);
8703: #endif
8704:       }
8705:     }
8706:     VecRestoreArray(gv,&coords);
8707:     VecDestroy(&gv);
8708:   }
8709:   ISDestroy(&corners);

8711:   if (pcbddc->coarse_ksp) {
8712:     Vec crhs,csol;

8714:     KSPGetSolution(pcbddc->coarse_ksp,&csol);
8715:     KSPGetRhs(pcbddc->coarse_ksp,&crhs);
8716:     if (!csol) {
8717:       MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);
8718:     }
8719:     if (!crhs) {
8720:       MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));
8721:     }
8722:   }
8723:   MatDestroy(&coarsedivudotp);

8725:   /* compute null space for coarse solver if the benign trick has been requested */
8726:   if (pcbddc->benign_null) {

8728:     VecSet(pcbddc->vec1_P,0.);
8729:     for (i=0;i<pcbddc->benign_n;i++) {
8730:       VecSetValue(pcbddc->vec1_P,pcbddc->local_primal_size-pcbddc->benign_n+i,1.0,INSERT_VALUES);
8731:     }
8732:     VecAssemblyBegin(pcbddc->vec1_P);
8733:     VecAssemblyEnd(pcbddc->vec1_P);
8734:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,INSERT_VALUES,SCATTER_FORWARD);
8735:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,INSERT_VALUES,SCATTER_FORWARD);
8736:     if (coarse_mat) {
8737:       Vec         nullv;
8738:       PetscScalar *array,*array2;
8739:       PetscInt    nl;

8741:       MatCreateVecs(coarse_mat,&nullv,NULL);
8742:       VecGetLocalSize(nullv,&nl);
8743:       VecGetArrayRead(pcbddc->coarse_vec,(const PetscScalar**)&array);
8744:       VecGetArray(nullv,&array2);
8745:       PetscArraycpy(array2,array,nl);
8746:       VecRestoreArray(nullv,&array2);
8747:       VecRestoreArrayRead(pcbddc->coarse_vec,(const PetscScalar**)&array);
8748:       VecNormalize(nullv,NULL);
8749:       MatNullSpaceCreate(PetscObjectComm((PetscObject)coarse_mat),PETSC_FALSE,1,&nullv,&CoarseNullSpace);
8750:       VecDestroy(&nullv);
8751:     }
8752:   }
8753:   PetscLogEventEnd(PC_BDDC_CoarseSetUp[pcbddc->current_level],pc,0,0,0);

8755:   PetscLogEventBegin(PC_BDDC_CoarseSolver[pcbddc->current_level],pc,0,0,0);
8756:   if (pcbddc->coarse_ksp) {
8757:     PetscBool ispreonly;

8759:     if (CoarseNullSpace) {
8760:       PetscBool isnull;
8761:       MatNullSpaceTest(CoarseNullSpace,coarse_mat,&isnull);
8762:       if (isnull) {
8763:         MatSetNullSpace(coarse_mat,CoarseNullSpace);
8764:       }
8765:       /* TODO: add local nullspaces (if any) */
8766:     }
8767:     /* setup coarse ksp */
8768:     KSPSetUp(pcbddc->coarse_ksp);
8769:     /* Check coarse problem if in debug mode or if solving with an iterative method */
8770:     PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);
8771:     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
8772:       KSP       check_ksp;
8773:       KSPType   check_ksp_type;
8774:       PC        check_pc;
8775:       Vec       check_vec,coarse_vec;
8776:       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
8777:       PetscInt  its;
8778:       PetscBool compute_eigs;
8779:       PetscReal *eigs_r,*eigs_c;
8780:       PetscInt  neigs;
8781:       const char *prefix;

8783:       /* Create ksp object suitable for estimation of extreme eigenvalues */
8784:       KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);
8785:       PetscObjectIncrementTabLevel((PetscObject)check_ksp,(PetscObject)pcbddc->coarse_ksp,0);
8786:       KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,PETSC_FALSE);
8787:       KSPSetOperators(check_ksp,coarse_mat,coarse_mat);
8788:       KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);
8789:       /* prevent from setup unneeded object */
8790:       KSPGetPC(check_ksp,&check_pc);
8791:       PCSetType(check_pc,PCNONE);
8792:       if (ispreonly) {
8793:         check_ksp_type = KSPPREONLY;
8794:         compute_eigs = PETSC_FALSE;
8795:       } else {
8796:         check_ksp_type = KSPGMRES;
8797:         compute_eigs = PETSC_TRUE;
8798:       }
8799:       KSPSetType(check_ksp,check_ksp_type);
8800:       KSPSetComputeSingularValues(check_ksp,compute_eigs);
8801:       KSPSetComputeEigenvalues(check_ksp,compute_eigs);
8802:       KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);
8803:       KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);
8804:       KSPSetOptionsPrefix(check_ksp,prefix);
8805:       KSPAppendOptionsPrefix(check_ksp,"check_");
8806:       KSPSetFromOptions(check_ksp);
8807:       KSPSetUp(check_ksp);
8808:       KSPGetPC(pcbddc->coarse_ksp,&check_pc);
8809:       KSPSetPC(check_ksp,check_pc);
8810:       /* create random vec */
8811:       MatCreateVecs(coarse_mat,&coarse_vec,&check_vec);
8812:       VecSetRandom(check_vec,NULL);
8813:       MatMult(coarse_mat,check_vec,coarse_vec);
8814:       /* solve coarse problem */
8815:       KSPSolve(check_ksp,coarse_vec,coarse_vec);
8816:       KSPCheckSolve(check_ksp,pc,coarse_vec);
8817:       /* set eigenvalue estimation if preonly has not been requested */
8818:       if (compute_eigs) {
8819:         PetscMalloc1(pcbddc->coarse_size+1,&eigs_r);
8820:         PetscMalloc1(pcbddc->coarse_size+1,&eigs_c);
8821:         KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);
8822:         if (neigs) {
8823:           lambda_max = eigs_r[neigs-1];
8824:           lambda_min = eigs_r[0];
8825:           if (pcbddc->use_coarse_estimates) {
8826:             if (lambda_max>=lambda_min) { /* using PETSC_SMALL since lambda_max == lambda_min is not allowed by KSPChebyshevSetEigenvalues */
8827:               KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max+PETSC_SMALL,lambda_min);
8828:               KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));
8829:             }
8830:           }
8831:         }
8832:       }

8834:       /* check coarse problem residual error */
8835:       if (pcbddc->dbg_flag) {
8836:         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
8837:         PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));
8838:         VecAXPY(check_vec,-1.0,coarse_vec);
8839:         VecNorm(check_vec,NORM_INFINITY,&infty_error);
8840:         MatMult(coarse_mat,check_vec,coarse_vec);
8841:         VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);
8842:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (use estimates %d)\n",pcbddc->use_coarse_estimates);
8843:         PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);
8844:         PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);
8845:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);
8846:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);
8847:         if (CoarseNullSpace) {
8848:           PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem is singular\n");
8849:         }
8850:         if (compute_eigs) {
8851:           PetscReal          lambda_max_s,lambda_min_s;
8852:           KSPConvergedReason reason;
8853:           KSPGetType(check_ksp,&check_ksp_type);
8854:           KSPGetIterationNumber(check_ksp,&its);
8855:           KSPGetConvergedReason(check_ksp,&reason);
8856:           KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);
8857:           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);
8858:           for (i=0;i<neigs;i++) {
8859:             PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);
8860:           }
8861:         }
8862:         PetscViewerFlush(dbg_viewer);
8863:         PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));
8864:       }
8865:       VecDestroy(&check_vec);
8866:       VecDestroy(&coarse_vec);
8867:       KSPDestroy(&check_ksp);
8868:       if (compute_eigs) {
8869:         PetscFree(eigs_r);
8870:         PetscFree(eigs_c);
8871:       }
8872:     }
8873:   }
8874:   MatNullSpaceDestroy(&CoarseNullSpace);
8875:   /* print additional info */
8876:   if (pcbddc->dbg_flag) {
8877:     /* waits until all processes reaches this point */
8878:     PetscBarrier((PetscObject)pc);
8879:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %D\n",pcbddc->current_level);
8880:     PetscViewerFlush(pcbddc->dbg_viewer);
8881:   }

8883:   /* free memory */
8884:   MatDestroy(&coarse_mat);
8885:   PetscLogEventEnd(PC_BDDC_CoarseSolver[pcbddc->current_level],pc,0,0,0);
8886:   return(0);
8887: }

8889: PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
8890: {
8891:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
8892:   PC_IS*         pcis = (PC_IS*)pc->data;
8893:   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
8894:   IS             subset,subset_mult,subset_n;
8895:   PetscInt       local_size,coarse_size=0;
8896:   PetscInt       *local_primal_indices=NULL;
8897:   const PetscInt *t_local_primal_indices;

8901:   /* Compute global number of coarse dofs */
8902:   if (pcbddc->local_primal_size && !pcbddc->local_primal_ref_node) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"BDDC ConstraintsSetUp should be called first");
8903:   ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&subset_n);
8904:   ISLocalToGlobalMappingApplyIS(pcis->mapping,subset_n,&subset);
8905:   ISDestroy(&subset_n);
8906:   ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_mult,PETSC_COPY_VALUES,&subset_mult);
8907:   ISRenumber(subset,subset_mult,&coarse_size,&subset_n);
8908:   ISDestroy(&subset);
8909:   ISDestroy(&subset_mult);
8910:   ISGetLocalSize(subset_n,&local_size);
8911:   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);
8912:   PetscMalloc1(local_size,&local_primal_indices);
8913:   ISGetIndices(subset_n,&t_local_primal_indices);
8914:   PetscArraycpy(local_primal_indices,t_local_primal_indices,local_size);
8915:   ISRestoreIndices(subset_n,&t_local_primal_indices);
8916:   ISDestroy(&subset_n);

8918:   /* check numbering */
8919:   if (pcbddc->dbg_flag) {
8920:     PetscScalar coarsesum,*array,*array2;
8921:     PetscInt    i;
8922:     PetscBool   set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;

8924:     PetscViewerFlush(pcbddc->dbg_viewer);
8925:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
8926:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");
8927:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
8928:     /* counter */
8929:     VecSet(pcis->vec1_global,0.0);
8930:     VecSet(pcis->vec1_N,1.0);
8931:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8932:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8933:     VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);
8934:     VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);
8935:     VecSet(pcis->vec1_N,0.0);
8936:     for (i=0;i<pcbddc->local_primal_size;i++) {
8937:       VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);
8938:     }
8939:     VecAssemblyBegin(pcis->vec1_N);
8940:     VecAssemblyEnd(pcis->vec1_N);
8941:     VecSet(pcis->vec1_global,0.0);
8942:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8943:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8944:     VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
8945:     VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
8946:     VecGetArray(pcis->vec1_N,&array);
8947:     VecGetArray(pcis->vec2_N,&array2);
8948:     for (i=0;i<pcis->n;i++) {
8949:       if (array[i] != 0.0 && array[i] != array2[i]) {
8950:         PetscInt owned = (PetscInt)PetscRealPart(array[i]),gi;
8951:         PetscInt neigh = (PetscInt)PetscRealPart(array2[i]);
8952:         set_error = PETSC_TRUE;
8953:         ISLocalToGlobalMappingApply(pcis->mapping,1,&i,&gi);
8954:         PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %D (gid %D) owned by %D processes instead of %D!\n",PetscGlobalRank,i,gi,owned,neigh);
8955:       }
8956:     }
8957:     VecRestoreArray(pcis->vec2_N,&array2);
8958:     MPIU_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
8959:     PetscViewerFlush(pcbddc->dbg_viewer);
8960:     for (i=0;i<pcis->n;i++) {
8961:       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
8962:     }
8963:     VecRestoreArray(pcis->vec1_N,&array);
8964:     VecSet(pcis->vec1_global,0.0);
8965:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8966:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
8967:     VecSum(pcis->vec1_global,&coarsesum);
8968:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %D (%lf)\n",coarse_size,PetscRealPart(coarsesum));
8969:     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
8970:       PetscInt *gidxs;

8972:       PetscMalloc1(pcbddc->local_primal_size,&gidxs);
8973:       ISLocalToGlobalMappingApply(pcis->mapping,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,gidxs);
8974:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");
8975:       PetscViewerFlush(pcbddc->dbg_viewer);
8976:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);
8977:       for (i=0;i<pcbddc->local_primal_size;i++) {
8978:         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]);
8979:       }
8980:       PetscViewerFlush(pcbddc->dbg_viewer);
8981:       PetscFree(gidxs);
8982:     }
8983:     PetscViewerFlush(pcbddc->dbg_viewer);
8984:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
8985:     if (set_error_reduced) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
8986:   }

8988:   /* get back data */
8989:   *coarse_size_n = coarse_size;
8990:   *local_primal_indices_n = local_primal_indices;
8991:   return(0);
8992: }

8994: PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
8995: {
8996:   IS             localis_t;
8997:   PetscInt       i,lsize,*idxs,n;
8998:   PetscScalar    *vals;

9002:   /* get indices in local ordering exploiting local to global map */
9003:   ISGetLocalSize(globalis,&lsize);
9004:   PetscMalloc1(lsize,&vals);
9005:   for (i=0;i<lsize;i++) vals[i] = 1.0;
9006:   ISGetIndices(globalis,(const PetscInt**)&idxs);
9007:   VecSet(gwork,0.0);
9008:   VecSet(lwork,0.0);
9009:   if (idxs) { /* multilevel guard */
9010:     VecSetOption(gwork,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);
9011:     VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);
9012:   }
9013:   VecAssemblyBegin(gwork);
9014:   ISRestoreIndices(globalis,(const PetscInt**)&idxs);
9015:   PetscFree(vals);
9016:   VecAssemblyEnd(gwork);
9017:   /* now compute set in local ordering */
9018:   VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);
9019:   VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);
9020:   VecGetArrayRead(lwork,(const PetscScalar**)&vals);
9021:   VecGetSize(lwork,&n);
9022:   for (i=0,lsize=0;i<n;i++) {
9023:     if (PetscRealPart(vals[i]) > 0.5) {
9024:       lsize++;
9025:     }
9026:   }
9027:   PetscMalloc1(lsize,&idxs);
9028:   for (i=0,lsize=0;i<n;i++) {
9029:     if (PetscRealPart(vals[i]) > 0.5) {
9030:       idxs[lsize++] = i;
9031:     }
9032:   }
9033:   VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);
9034:   ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);
9035:   *localis = localis_t;
9036:   return(0);
9037: }

9039: PetscErrorCode PCBDDCSetUpSubSchurs(PC pc)
9040: {
9041:   PC_IS               *pcis=(PC_IS*)pc->data;
9042:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
9043:   PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
9044:   Mat                 S_j;
9045:   PetscInt            *used_xadj,*used_adjncy;
9046:   PetscBool           free_used_adj;
9047:   PetscErrorCode      ierr;

9050:   PetscLogEventBegin(PC_BDDC_Schurs[pcbddc->current_level],pc,0,0,0);
9051:   /* decide the adjacency to be used for determining internal problems for local schur on subsets */
9052:   free_used_adj = PETSC_FALSE;
9053:   if (pcbddc->sub_schurs_layers == -1) {
9054:     used_xadj = NULL;
9055:     used_adjncy = NULL;
9056:   } else {
9057:     if (pcbddc->sub_schurs_use_useradj && pcbddc->mat_graph->xadj) {
9058:       used_xadj = pcbddc->mat_graph->xadj;
9059:       used_adjncy = pcbddc->mat_graph->adjncy;
9060:     } else if (pcbddc->computed_rowadj) {
9061:       used_xadj = pcbddc->mat_graph->xadj;
9062:       used_adjncy = pcbddc->mat_graph->adjncy;
9063:     } else {
9064:       PetscBool      flg_row=PETSC_FALSE;
9065:       const PetscInt *xadj,*adjncy;
9066:       PetscInt       nvtxs;

9068:       MatGetRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);
9069:       if (flg_row) {
9070:         PetscMalloc2(nvtxs+1,&used_xadj,xadj[nvtxs],&used_adjncy);
9071:         PetscArraycpy(used_xadj,xadj,nvtxs+1);
9072:         PetscArraycpy(used_adjncy,adjncy,xadj[nvtxs]);
9073:         free_used_adj = PETSC_TRUE;
9074:       } else {
9075:         pcbddc->sub_schurs_layers = -1;
9076:         used_xadj = NULL;
9077:         used_adjncy = NULL;
9078:       }
9079:       MatRestoreRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);
9080:     }
9081:   }

9083:   /* setup sub_schurs data */
9084:   MatCreateSchurComplement(pcis->A_II,pcis->pA_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);
9085:   if (!sub_schurs->schur_explicit) {
9086:     /* pcbddc->ksp_D up to date only if not using MatFactor with Schur complement support */
9087:     MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);
9088:     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);
9089:   } else {
9090:     Mat       change = NULL;
9091:     Vec       scaling = NULL;
9092:     IS        change_primal = NULL, iP;
9093:     PetscInt  benign_n;
9094:     PetscBool reuse_solvers = (PetscBool)!pcbddc->use_change_of_basis;
9095:     PetscBool need_change = PETSC_FALSE;
9096:     PetscBool discrete_harmonic = PETSC_FALSE;

9098:     if (!pcbddc->use_vertices && reuse_solvers) {
9099:       PetscInt n_vertices;

9101:       ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);
9102:       reuse_solvers = (PetscBool)!n_vertices;
9103:     }
9104:     if (!pcbddc->benign_change_explicit) {
9105:       benign_n = pcbddc->benign_n;
9106:     } else {
9107:       benign_n = 0;
9108:     }
9109:     /* sub_schurs->change is a local object; instead, PCBDDCConstraintsSetUp and the quantities used in the test below are logically collective on pc.
9110:        We need a global reduction to avoid possible deadlocks.
9111:        We assume that sub_schurs->change is created once, and then reused for different solves, unless the topography has been recomputed */
9112:     if (pcbddc->adaptive_userdefined || (pcbddc->deluxe_zerorows && !pcbddc->use_change_of_basis)) {
9113:       PetscBool have_loc_change = (PetscBool)(!!sub_schurs->change);
9114:       MPIU_Allreduce(&have_loc_change,&need_change,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
9115:       need_change = (PetscBool)(!need_change);
9116:     }
9117:     /* If the user defines additional constraints, we import them here.
9118:        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 */
9119:     if (need_change) {
9120:       PC_IS   *pcisf;
9121:       PC_BDDC *pcbddcf;
9122:       PC      pcf;

9124:       if (pcbddc->sub_schurs_rebuild) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot compute change of basis with a different graph");
9125:       PCCreate(PetscObjectComm((PetscObject)pc),&pcf);
9126:       PCSetOperators(pcf,pc->mat,pc->pmat);
9127:       PCSetType(pcf,PCBDDC);

9129:       /* hacks */
9130:       pcisf                        = (PC_IS*)pcf->data;
9131:       pcisf->is_B_local            = pcis->is_B_local;
9132:       pcisf->vec1_N                = pcis->vec1_N;
9133:       pcisf->BtoNmap               = pcis->BtoNmap;
9134:       pcisf->n                     = pcis->n;
9135:       pcisf->n_B                   = pcis->n_B;
9136:       pcbddcf                      = (PC_BDDC*)pcf->data;
9137:       PetscFree(pcbddcf->mat_graph);
9138:       pcbddcf->mat_graph           = pcbddc->mat_graph;
9139:       pcbddcf->use_faces           = PETSC_TRUE;
9140:       pcbddcf->use_change_of_basis = PETSC_TRUE;
9141:       pcbddcf->use_change_on_faces = PETSC_TRUE;
9142:       pcbddcf->use_qr_single       = PETSC_TRUE;
9143:       pcbddcf->fake_change         = PETSC_TRUE;

9145:       /* setup constraints so that we can get information on primal vertices and change of basis (in local numbering) */
9146:       PCBDDCConstraintsSetUp(pcf);
9147:       sub_schurs->change_with_qr = pcbddcf->use_qr_single;
9148:       ISCreateGeneral(PETSC_COMM_SELF,pcbddcf->n_vertices,pcbddcf->local_primal_ref_node,PETSC_COPY_VALUES,&change_primal);
9149:       change = pcbddcf->ConstraintMatrix;
9150:       pcbddcf->ConstraintMatrix = NULL;

9152:       /* free unneeded memory allocated in PCBDDCConstraintsSetUp */
9153:       PetscFree(pcbddcf->sub_schurs);
9154:       MatNullSpaceDestroy(&pcbddcf->onearnullspace);
9155:       PetscFree2(pcbddcf->local_primal_ref_node,pcbddcf->local_primal_ref_mult);
9156:       PetscFree(pcbddcf->primal_indices_local_idxs);
9157:       PetscFree(pcbddcf->onearnullvecs_state);
9158:       PetscFree(pcf->data);
9159:       pcf->ops->destroy = NULL;
9160:       pcf->ops->reset   = NULL;
9161:       PCDestroy(&pcf);
9162:     }
9163:     if (!pcbddc->use_deluxe_scaling) scaling = pcis->D;

9165:     PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_iP",(PetscObject*)&iP);
9166:     if (iP) {
9167:       PetscOptionsBegin(PetscObjectComm((PetscObject)iP),sub_schurs->prefix,"BDDC sub_schurs options","PC");
9168:       PetscOptionsBool("-sub_schurs_discrete_harmonic",NULL,NULL,discrete_harmonic,&discrete_harmonic,NULL);
9169:       PetscOptionsEnd();
9170:     }
9171:     if (discrete_harmonic) {
9172:       Mat A;
9173:       MatDuplicate(pcbddc->local_mat,MAT_COPY_VALUES,&A);
9174:       MatZeroRowsColumnsIS(A,iP,1.0,NULL,NULL);
9175:       PetscObjectCompose((PetscObject)A,"__KSPFETIDP_iP",(PetscObject)iP);
9176:       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);
9177:       MatDestroy(&A);
9178:     } else {
9179:       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);
9180:     }
9181:     MatDestroy(&change);
9182:     ISDestroy(&change_primal);
9183:   }
9184:   MatDestroy(&S_j);

9186:   /* free adjacency */
9187:   if (free_used_adj) {
9188:     PetscFree2(used_xadj,used_adjncy);
9189:   }
9190:   PetscLogEventEnd(PC_BDDC_Schurs[pcbddc->current_level],pc,0,0,0);
9191:   return(0);
9192: }

9194: PetscErrorCode PCBDDCInitSubSchurs(PC pc)
9195: {
9196:   PC_IS               *pcis=(PC_IS*)pc->data;
9197:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
9198:   PCBDDCGraph         graph;
9199:   PetscErrorCode      ierr;

9202:   /* attach interface graph for determining subsets */
9203:   if (pcbddc->sub_schurs_rebuild) { /* in case rebuild has been requested, it uses a graph generated only by the neighbouring information */
9204:     IS       verticesIS,verticescomm;
9205:     PetscInt vsize,*idxs;

9207:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);
9208:     ISGetSize(verticesIS,&vsize);
9209:     ISGetIndices(verticesIS,(const PetscInt**)&idxs);
9210:     ISCreateGeneral(PetscObjectComm((PetscObject)pc),vsize,idxs,PETSC_COPY_VALUES,&verticescomm);
9211:     ISRestoreIndices(verticesIS,(const PetscInt**)&idxs);
9212:     PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);
9213:     PCBDDCGraphCreate(&graph);
9214:     PCBDDCGraphInit(graph,pcbddc->mat_graph->l2gmap,pcbddc->mat_graph->nvtxs_global,pcbddc->graphmaxcount);
9215:     PCBDDCGraphSetUp(graph,pcbddc->mat_graph->custom_minimal_size,NULL,pcbddc->DirichletBoundariesLocal,0,NULL,verticescomm);
9216:     ISDestroy(&verticescomm);
9217:     PCBDDCGraphComputeConnectedComponents(graph);
9218:   } else {
9219:     graph = pcbddc->mat_graph;
9220:   }
9221:   /* print some info */
9222:   if (pcbddc->dbg_flag && !pcbddc->sub_schurs_rebuild) {
9223:     IS       vertices;
9224:     PetscInt nv,nedges,nfaces;
9225:     PCBDDCGraphASCIIView(graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);
9226:     PCBDDCGraphGetCandidatesIS(graph,&nfaces,NULL,&nedges,NULL,&vertices);
9227:     ISGetSize(vertices,&nv);
9228:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
9229:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
9230:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%D)\n",PetscGlobalRank,(int)nv,pcbddc->use_vertices);
9231:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%D)\n",PetscGlobalRank,(int)nedges,pcbddc->use_edges);
9232:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%D)\n",PetscGlobalRank,(int)nfaces,pcbddc->use_faces);
9233:     PetscViewerFlush(pcbddc->dbg_viewer);
9234:     PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);
9235:     PCBDDCGraphRestoreCandidatesIS(graph,&nfaces,NULL,&nedges,NULL,&vertices);
9236:   }

9238:   /* sub_schurs init */
9239:   if (!pcbddc->sub_schurs) {
9240:     PCBDDCSubSchursCreate(&pcbddc->sub_schurs);
9241:   }
9242:   PCBDDCSubSchursInit(pcbddc->sub_schurs,((PetscObject)pc)->prefix,pcis->is_I_local,pcis->is_B_local,graph,pcis->BtoNmap,pcbddc->sub_schurs_rebuild);

9244:   /* free graph struct */
9245:   if (pcbddc->sub_schurs_rebuild) {
9246:     PCBDDCGraphDestroy(&graph);
9247:   }
9248:   return(0);
9249: }

9251: PetscErrorCode PCBDDCCheckOperator(PC pc)
9252: {
9253:   PC_IS               *pcis=(PC_IS*)pc->data;
9254:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
9255:   PetscErrorCode      ierr;

9258:   if (pcbddc->n_vertices == pcbddc->local_primal_size) {
9259:     IS             zerodiag = NULL;
9260:     Mat            S_j,B0_B=NULL;
9261:     Vec            dummy_vec=NULL,vec_check_B,vec_scale_P;
9262:     PetscScalar    *p0_check,*array,*array2;
9263:     PetscReal      norm;
9264:     PetscInt       i;

9266:     /* B0 and B0_B */
9267:     if (zerodiag) {
9268:       IS       dummy;

9270:       ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&dummy);
9271:       MatCreateSubMatrix(pcbddc->benign_B0,dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
9272:       MatCreateVecs(B0_B,NULL,&dummy_vec);
9273:       ISDestroy(&dummy);
9274:     }
9275:     /* I need a primal vector to scale primal nodes since BDDC sums contibutions */
9276:     VecDuplicate(pcbddc->vec1_P,&vec_scale_P);
9277:     VecSet(pcbddc->vec1_P,1.0);
9278:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
9279:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
9280:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);
9281:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);
9282:     VecReciprocal(vec_scale_P);
9283:     /* S_j */
9284:     MatCreateSchurComplement(pcis->A_II,pcis->pA_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);
9285:     MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);

9287:     /* mimic vector in \widetilde{W}_\Gamma */
9288:     VecSetRandom(pcis->vec1_N,NULL);
9289:     /* continuous in primal space */
9290:     VecSetRandom(pcbddc->coarse_vec,NULL);
9291:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
9292:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
9293:     VecGetArray(pcbddc->vec1_P,&array);
9294:     PetscCalloc1(pcbddc->benign_n,&p0_check);
9295:     for (i=0;i<pcbddc->benign_n;i++) p0_check[i] = array[pcbddc->local_primal_size-pcbddc->benign_n+i];
9296:     VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);
9297:     VecRestoreArray(pcbddc->vec1_P,&array);
9298:     VecAssemblyBegin(pcis->vec1_N);
9299:     VecAssemblyEnd(pcis->vec1_N);
9300:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
9301:     VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
9302:     VecDuplicate(pcis->vec2_B,&vec_check_B);
9303:     VecCopy(pcis->vec2_B,vec_check_B);

9305:     /* assemble rhs for coarse problem */
9306:     /* widetilde{S}_\Gamma w_\Gamma + \widetilde{B0}^T_B p0 */
9307:     /* local with Schur */
9308:     MatMult(S_j,pcis->vec2_B,pcis->vec1_B);
9309:     if (zerodiag) {
9310:       VecGetArray(dummy_vec,&array);
9311:       for (i=0;i<pcbddc->benign_n;i++) array[i] = p0_check[i];
9312:       VecRestoreArray(dummy_vec,&array);
9313:       MatMultTransposeAdd(B0_B,dummy_vec,pcis->vec1_B,pcis->vec1_B);
9314:     }
9315:     /* sum on primal nodes the local contributions */
9316:     VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);
9317:     VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);
9318:     VecGetArray(pcis->vec1_N,&array);
9319:     VecGetArray(pcbddc->vec1_P,&array2);
9320:     for (i=0;i<pcbddc->local_primal_size;i++) array2[i] = array[pcbddc->local_primal_ref_node[i]];
9321:     VecRestoreArray(pcbddc->vec1_P,&array2);
9322:     VecRestoreArray(pcis->vec1_N,&array);
9323:     VecSet(pcbddc->coarse_vec,0.);
9324:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
9325:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
9326:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
9327:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
9328:     VecGetArray(pcbddc->vec1_P,&array);
9329:     /* scale primal nodes (BDDC sums contibutions) */
9330:     VecPointwiseMult(pcbddc->vec1_P,vec_scale_P,pcbddc->vec1_P);
9331:     VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);
9332:     VecRestoreArray(pcbddc->vec1_P,&array);
9333:     VecAssemblyBegin(pcis->vec1_N);
9334:     VecAssemblyEnd(pcis->vec1_N);
9335:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
9336:     VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
9337:     /* global: \widetilde{B0}_B w_\Gamma */
9338:     if (zerodiag) {
9339:       MatMult(B0_B,pcis->vec2_B,dummy_vec);
9340:       VecGetArray(dummy_vec,&array);
9341:       for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = array[i];
9342:       VecRestoreArray(dummy_vec,&array);
9343:     }
9344:     /* BDDC */
9345:     VecSet(pcis->vec1_D,0.);
9346:     PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);

9348:     VecCopy(pcis->vec1_B,pcis->vec2_B);
9349:     VecAXPY(pcis->vec1_B,-1.0,vec_check_B);
9350:     VecNorm(pcis->vec1_B,NORM_INFINITY,&norm);
9351:     PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC local error is %1.4e\n",PetscGlobalRank,norm);
9352:     for (i=0;i<pcbddc->benign_n;i++) {
9353:       PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC p0[%D] error is %1.4e\n",PetscGlobalRank,i,PetscAbsScalar(pcbddc->benign_p0[i]-p0_check[i]));
9354:     }
9355:     PetscFree(p0_check);
9356:     VecDestroy(&vec_scale_P);
9357:     VecDestroy(&vec_check_B);
9358:     VecDestroy(&dummy_vec);
9359:     MatDestroy(&S_j);
9360:     MatDestroy(&B0_B);
9361:   }
9362:   return(0);
9363: }

9365:  #include <../src/mat/impls/aij/mpi/mpiaij.h>
9366: PetscErrorCode MatMPIAIJRestrict(Mat A, MPI_Comm ccomm, Mat *B)
9367: {
9368:   Mat            At;
9369:   IS             rows;
9370:   PetscInt       rst,ren;
9372:   PetscLayout    rmap;

9375:   rst = ren = 0;
9376:   if (ccomm != MPI_COMM_NULL) {
9377:     PetscLayoutCreate(ccomm,&rmap);
9378:     PetscLayoutSetSize(rmap,A->rmap->N);
9379:     PetscLayoutSetBlockSize(rmap,1);
9380:     PetscLayoutSetUp(rmap);
9381:     PetscLayoutGetRange(rmap,&rst,&ren);
9382:   }
9383:   ISCreateStride(PetscObjectComm((PetscObject)A),ren-rst,rst,1,&rows);
9384:   MatCreateSubMatrix(A,rows,NULL,MAT_INITIAL_MATRIX,&At);
9385:   ISDestroy(&rows);

9387:   if (ccomm != MPI_COMM_NULL) {
9388:     Mat_MPIAIJ *a,*b;
9389:     IS         from,to;
9390:     Vec        gvec;
9391:     PetscInt   lsize;

9393:     MatCreate(ccomm,B);
9394:     MatSetSizes(*B,ren-rst,PETSC_DECIDE,PETSC_DECIDE,At->cmap->N);
9395:     MatSetType(*B,MATAIJ);
9396:     PetscLayoutDestroy(&((*B)->rmap));
9397:     PetscLayoutSetUp((*B)->cmap);
9398:     a    = (Mat_MPIAIJ*)At->data;
9399:     b    = (Mat_MPIAIJ*)(*B)->data;
9400:     MPI_Comm_size(ccomm,&b->size);
9401:     MPI_Comm_rank(ccomm,&b->rank);
9402:     PetscObjectReference((PetscObject)a->A);
9403:     PetscObjectReference((PetscObject)a->B);
9404:     b->A = a->A;
9405:     b->B = a->B;

9407:     b->donotstash      = a->donotstash;
9408:     b->roworiented     = a->roworiented;
9409:     b->rowindices      = 0;
9410:     b->rowvalues       = 0;
9411:     b->getrowactive    = PETSC_FALSE;

9413:     (*B)->rmap         = rmap;
9414:     (*B)->factortype   = A->factortype;
9415:     (*B)->assembled    = PETSC_TRUE;
9416:     (*B)->insertmode   = NOT_SET_VALUES;
9417:     (*B)->preallocated = PETSC_TRUE;

9419:     if (a->colmap) {
9420: #if defined(PETSC_USE_CTABLE)
9421:       PetscTableCreateCopy(a->colmap,&b->colmap);
9422: #else
9423:       PetscMalloc1(At->cmap->N,&b->colmap);
9424:       PetscLogObjectMemory((PetscObject)*B,At->cmap->N*sizeof(PetscInt));
9425:       PetscArraycpy(b->colmap,a->colmap,At->cmap->N);
9426: #endif
9427:     } else b->colmap = 0;
9428:     if (a->garray) {
9429:       PetscInt len;
9430:       len  = a->B->cmap->n;
9431:       PetscMalloc1(len+1,&b->garray);
9432:       PetscLogObjectMemory((PetscObject)(*B),len*sizeof(PetscInt));
9433:       if (len) { PetscArraycpy(b->garray,a->garray,len); }
9434:     } else b->garray = 0;

9436:     PetscObjectReference((PetscObject)a->lvec);
9437:     b->lvec = a->lvec;
9438:     PetscLogObjectParent((PetscObject)*B,(PetscObject)b->lvec);

9440:     /* cannot use VecScatterCopy */
9441:     VecGetLocalSize(b->lvec,&lsize);
9442:     ISCreateGeneral(ccomm,lsize,b->garray,PETSC_USE_POINTER,&from);
9443:     ISCreateStride(PETSC_COMM_SELF,lsize,0,1,&to);
9444:     MatCreateVecs(*B,&gvec,NULL);
9445:     VecScatterCreate(gvec,from,b->lvec,to,&b->Mvctx);
9446:     PetscLogObjectParent((PetscObject)*B,(PetscObject)b->Mvctx);
9447:     ISDestroy(&from);
9448:     ISDestroy(&to);
9449:     VecDestroy(&gvec);
9450:   }
9451:   MatDestroy(&At);
9452:   return(0);
9453: }