Actual source code: bddcprivate.c

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

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

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

     25:   MatGetSize(A,&nr,&nc);
     26:   if (!nr || !nc) return 0;

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

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

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

     88: PetscErrorCode PCBDDCComputeNedelecChangeEdge(Mat lG, IS edge, IS extrow, IS extcol, IS corners, Mat* Gins, Mat* GKins, PetscScalar cvals[2], PetscScalar *work, PetscReal *rwork)
     89: {
     90:   Mat            GE,GEd;
     91:   PetscInt       rsize,csize,esize;
     92:   PetscScalar    *ptr;

     94:   ISGetSize(edge,&esize);
     95:   if (!esize) return 0;
     96:   ISGetSize(extrow,&rsize);
     97:   ISGetSize(extcol,&csize);

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

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

    115:   if (corners) {
    116:     Mat               GEc;
    117:     const PetscScalar *vals;
    118:     PetscScalar       v;

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

    149:   return 0;
    150: }

    152: PetscErrorCode PCBDDCNedelecSupport(PC pc)
    153: {
    154:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
    155:   Mat_IS                 *matis = (Mat_IS*)pc->pmat->data;
    156:   Mat                    G,T,conn,lG,lGt,lGis,lGall,lGe,lGinit;
    157:   Vec                    tvec;
    158:   PetscSF                sfv;
    159:   ISLocalToGlobalMapping el2g,vl2g,fl2g,al2g;
    160:   MPI_Comm               comm;
    161:   IS                     lned,primals,allprimals,nedfieldlocal;
    162:   IS                     *eedges,*extrows,*extcols,*alleedges;
    163:   PetscBT                btv,bte,btvc,btb,btbd,btvcand,btvi,btee,bter;
    164:   PetscScalar            *vals,*work;
    165:   PetscReal              *rwork;
    166:   const PetscInt         *idxs,*ii,*jj,*iit,*jjt;
    167:   PetscInt               ne,nv,Lv,order,n,field;
    168:   PetscInt               n_neigh,*neigh,*n_shared,**shared;
    169:   PetscInt               i,j,extmem,cum,maxsize,nee;
    170:   PetscInt               *extrow,*extrowcum,*marks,*vmarks,*gidxs;
    171:   PetscInt               *sfvleaves,*sfvroots;
    172:   PetscInt               *corners,*cedges;
    173:   PetscInt               *ecount,**eneighs,*vcount,**vneighs;
    174:   PetscInt               *emarks;
    175:   PetscBool              print,eerr,done,lrc[2],conforming,global,singular,setprimal;
    176:   PetscErrorCode         ierr;

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

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

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

    216:   /* Get Nedelec field */
    218:   if (pcbddc->n_ISForDofsLocal && field >= 0) {
    219:     PetscObjectReference((PetscObject)pcbddc->ISForDofsLocal[field]);
    220:     nedfieldlocal = pcbddc->ISForDofsLocal[field];
    221:     ISGetLocalSize(nedfieldlocal,&ne);
    222:   } else if (!pcbddc->n_ISForDofsLocal && field != PETSC_DECIDE) {
    223:     ne            = n;
    224:     nedfieldlocal = NULL;
    225:     global        = PETSC_TRUE;
    226:   } else if (field == PETSC_DECIDE) {
    227:     PetscInt rst,ren,*idx;

    229:     PetscArrayzero(matis->sf_leafdata,n);
    230:     PetscArrayzero(matis->sf_rootdata,pc->pmat->rmap->n);
    231:     MatGetOwnershipRange(pcbddc->discretegradient,&rst,&ren);
    232:     for (i=rst;i<ren;i++) {
    233:       PetscInt nc;

    235:       MatGetRow(pcbddc->discretegradient,i,&nc,NULL,NULL);
    236:       if (nc > 1) matis->sf_rootdata[i-rst] = 1;
    237:       MatRestoreRow(pcbddc->discretegradient,i,&nc,NULL,NULL);
    238:     }
    239:     PetscSFBcastBegin(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
    240:     PetscSFBcastEnd(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
    241:     PetscMalloc1(n,&idx);
    242:     for (i=0,ne=0;i<n;i++) if (matis->sf_leafdata[i]) idx[ne++] = i;
    243:     ISCreateGeneral(comm,ne,idx,PETSC_OWN_POINTER,&nedfieldlocal);
    244:   } else {
    245:     SETERRQ(comm,PETSC_ERR_USER,"When multiple fields are present, the Nedelec field has to be specified");
    246:   }

    248:   /* Sanity checks */

    253:   /* Just set primal dofs and return */
    254:   if (setprimal) {
    255:     IS       enedfieldlocal;
    256:     PetscInt *eidxs;

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

    284:   /* Compute some l2g maps */
    285:   if (nedfieldlocal) {
    286:     IS is;

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

    300:       ISRenumber(is,NULL,NULL,&gis);
    301:       ISLocalToGlobalMappingCreateIS(gis,&el2g);
    302:       ISDestroy(&gis);
    303:     }
    304:     ISDestroy(&is);
    305:   } else {
    306:     /* restore default */
    307:     pcbddc->nedfield = -1;
    308:     /* one ref for the destruction of al2g, one for el2g */
    309:     PetscObjectReference((PetscObject)al2g);
    310:     PetscObjectReference((PetscObject)al2g);
    311:     el2g = al2g;
    312:     fl2g = NULL;
    313:   }

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

    328:   if (!singular) { /* drop connections with interior edges to avoid unneeded communications and memory movements */
    329:     MatDuplicate(pcbddc->discretegradient,MAT_COPY_VALUES,&G);
    330:     MatSetOption(G,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);
    331:     if (global) {
    332:       PetscInt rst;

    334:       MatGetOwnershipRange(G,&rst,NULL);
    335:       for (i=0,cum=0;i<pc->pmat->rmap->n;i++) {
    336:         if (matis->sf_rootdata[i] < 2) {
    337:           matis->sf_rootdata[cum++] = i + rst;
    338:         }
    339:       }
    340:       MatSetOption(G,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE);
    341:       MatZeroRows(G,cum,matis->sf_rootdata,0.,NULL,NULL);
    342:     } else {
    343:       PetscInt *tbz;

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

    362:   /* Extract subdomain relevant rows of G */
    363:   ISLocalToGlobalMappingGetIndices(el2g,&idxs);
    364:   ISCreateGeneral(comm,ne,idxs,PETSC_USE_POINTER,&lned);
    365:   MatCreateSubMatrix(G,lned,NULL,MAT_INITIAL_MATRIX,&lGall);
    366:   ISLocalToGlobalMappingRestoreIndices(el2g,&idxs);
    367:   ISDestroy(&lned);
    368:   MatConvert(lGall,MATIS,MAT_INITIAL_MATRIX,&lGis);
    369:   MatDestroy(&lGall);
    370:   MatISGetLocalMat(lGis,&lG);

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

    384:   /* Destroy temporary G created in MATIS format and modified G */
    385:   PetscObjectReference((PetscObject)lG);
    386:   MatDestroy(&lGis);
    387:   MatDestroy(&G);

    389:   if (print) {
    390:     PetscObjectSetName((PetscObject)lG,"initial_lG");
    391:     MatView(lG,NULL);
    392:   }

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

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

    410:     if (fl2g) {
    411:       ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_MASK,pcbddc->DirichletBoundariesLocal,&is);
    412:     } else {
    413:       is = pcbddc->DirichletBoundariesLocal;
    414:     }
    415:     ISGetLocalSize(is,&cum);
    416:     ISGetIndices(is,&idxs);
    417:     for (i=0;i<cum;i++) {
    418:       if (idxs[i] >= 0) {
    419:         PetscBTSet(btb,idxs[i]);
    420:         PetscBTSet(btbd,idxs[i]);
    421:       }
    422:     }
    423:     ISRestoreIndices(is,&idxs);
    424:     if (fl2g) {
    425:       ISDestroy(&is);
    426:     }
    427:   }
    428:   if (pcbddc->NeumannBoundariesLocal) {
    429:     IS is;

    431:     if (fl2g) {
    432:       ISGlobalToLocalMappingApplyIS(fl2g,IS_GTOLM_MASK,pcbddc->NeumannBoundariesLocal,&is);
    433:     } else {
    434:       is = pcbddc->NeumannBoundariesLocal;
    435:     }
    436:     ISGetLocalSize(is,&cum);
    437:     ISGetIndices(is,&idxs);
    438:     for (i=0;i<cum;i++) {
    439:       if (idxs[i] >= 0) {
    440:         PetscBTSet(btb,idxs[i]);
    441:       }
    442:     }
    443:     ISRestoreIndices(is,&idxs);
    444:     if (fl2g) {
    445:       ISDestroy(&is);
    446:     }
    447:   }

    449:   /* Count neighs per dof */
    450:   ISLocalToGlobalMappingGetNodeInfo(el2g,NULL,&ecount,&eneighs);
    451:   ISLocalToGlobalMappingGetNodeInfo(vl2g,NULL,&vcount,&vneighs);

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

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

    539:       for (j=ii[i];j<ii[i+1];j++) vorder += PetscRealPart(vals[j]);
    540:       test = PetscFloorReal(vorder+10.*PETSC_SQRT_MACHINE_EPSILON);
    542:       ord  = 1;
    543:     }
    544:     PetscAssert(test%ord == 0,PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected number of edge dofs %" PetscInt_FMT " connected with nodal dof %" PetscInt_FMT " with order %" PetscInt_FMT,test,i,ord);
    545:     for (j=ii[i];j<ii[i+1] && sneighs;j++) {
    546:       if (PetscBTLookup(btbd,jj[j])) {
    547:         bdir = PETSC_TRUE;
    548:         break;
    549:       }
    550:       if (vc != ecount[jj[j]]) {
    551:         sneighs = PETSC_FALSE;
    552:       } else {
    553:         PetscInt k,*vn = vneighs[i], *en = eneighs[jj[j]];
    554:         for (k=0;k<vc;k++) {
    555:           if (vn[k] != en[k]) {
    556:             sneighs = PETSC_FALSE;
    557:             break;
    558:           }
    559:         }
    560:       }
    561:     }
    562:     if (!sneighs || test >= 3*ord || bdir) { /* splitpoints */
    563:       if (print) PetscPrintf(PETSC_COMM_SELF,"SPLITPOINT %D (%D %D %D)\n",i,!sneighs,test >= 3*ord,bdir);
    564:       PetscBTSet(btv,i);
    565:     } else if (test == ord) {
    566:       if (order == 1 || (!order && ii[i+1]-ii[i] == 1)) {
    567:         if (print) PetscPrintf(PETSC_COMM_SELF,"ENDPOINT %D\n",i);
    568:         PetscBTSet(btv,i);
    569:       } else {
    570:         if (print) PetscPrintf(PETSC_COMM_SELF,"CORNER CANDIDATE %D\n",i);
    571:         PetscBTSet(btvcand,i);
    572:       }
    573:     }
    574:   }
    575:   ISLocalToGlobalMappingRestoreNodeInfo(el2g,NULL,&ecount,&eneighs);
    576:   ISLocalToGlobalMappingRestoreNodeInfo(vl2g,NULL,&vcount,&vneighs);
    577:   PetscBTDestroy(&btbd);

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

    611:   /* Get the local G^T explicitly */
    612:   MatDestroy(&lGt);
    613:   MatTranspose(lG,MAT_INITIAL_MATRIX,&lGt);
    614:   MatSetOption(lGt,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);

    616:   /* Mark interior nodal dofs */
    617:   ISLocalToGlobalMappingGetInfo(vl2g,&n_neigh,&neigh,&n_shared,&shared);
    618:   PetscBTCreate(nv,&btvi);
    619:   for (i=1;i<n_neigh;i++) {
    620:     for (j=0;j<n_shared[i];j++) {
    621:       PetscBTSet(btvi,shared[i][j]);
    622:     }
    623:   }
    624:   ISLocalToGlobalMappingRestoreInfo(vl2g,&n_neigh,&neigh,&n_shared,&shared);

    626:   /* communicate corners and splitpoints */
    627:   PetscMalloc1(nv,&vmarks);
    628:   PetscArrayzero(sfvleaves,nv);
    629:   PetscArrayzero(sfvroots,Lv);
    630:   for (i=0;i<nv;i++) if (PetscUnlikely(PetscBTLookup(btv,i))) sfvleaves[i] = 1;

    632:   if (print) {
    633:     IS tbz;

    635:     cum = 0;
    636:     for (i=0;i<nv;i++)
    637:       if (sfvleaves[i])
    638:         vmarks[cum++] = i;

    640:     ISCreateGeneral(PETSC_COMM_SELF,cum,vmarks,PETSC_COPY_VALUES,&tbz);
    641:     PetscObjectSetName((PetscObject)tbz,"corners_to_be_zeroed_local");
    642:     ISView(tbz,NULL);
    643:     ISDestroy(&tbz);
    644:   }

    646:   PetscSFReduceBegin(sfv,MPIU_INT,sfvleaves,sfvroots,MPI_SUM);
    647:   PetscSFReduceEnd(sfv,MPIU_INT,sfvleaves,sfvroots,MPI_SUM);
    648:   PetscSFBcastBegin(sfv,MPIU_INT,sfvroots,sfvleaves,MPI_REPLACE);
    649:   PetscSFBcastEnd(sfv,MPIU_INT,sfvroots,sfvleaves,MPI_REPLACE);

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

    665:     ISCreateGeneral(PETSC_COMM_SELF,cum,vmarks,PETSC_COPY_VALUES,&tbz);
    666:     PetscObjectSetName((PetscObject)tbz,"corners_to_be_zeroed_with_interior");
    667:     ISView(tbz,NULL);
    668:     ISDestroy(&tbz);
    669:   }
    670:   MatZeroRows(lGt,cum,vmarks,0.,NULL,NULL);
    671:   PetscFree(vmarks);
    672:   PetscSFDestroy(&sfv);
    673:   PetscFree2(sfvleaves,sfvroots);

    675:   /* Recompute G */
    676:   MatDestroy(&lG);
    677:   MatTranspose(lGt,MAT_INITIAL_MATRIX,&lG);
    678:   if (print) {
    679:     PetscObjectSetName((PetscObject)lG,"used_lG");
    680:     MatView(lG,NULL);
    681:     PetscObjectSetName((PetscObject)lGt,"used_lGt");
    682:     MatView(lGt,NULL);
    683:   }

    685:   /* Get primal dofs (if any) */
    686:   cum = 0;
    687:   for (i=0;i<ne;i++) {
    688:     if (PetscUnlikely(PetscBTLookup(bte,i))) marks[cum++] = i;
    689:   }
    690:   if (fl2g) {
    691:     ISLocalToGlobalMappingApply(fl2g,cum,marks,marks);
    692:   }
    693:   ISCreateGeneral(comm,cum,marks,PETSC_COPY_VALUES,&primals);
    694:   if (print) {
    695:     PetscObjectSetName((PetscObject)primals,"prescribed_primal_dofs");
    696:     ISView(primals,NULL);
    697:   }
    698:   PetscBTDestroy(&bte);
    699:   /* TODO: what if the user passed in some of them ?  */
    700:   PCBDDCSetPrimalVerticesLocalIS(pc,primals);
    701:   ISDestroy(&primals);

    703:   /* Compute edge connectivity */
    704:   PetscObjectSetOptionsPrefix((PetscObject)lG,"econn_");

    706:   /* Symbolic conn = lG*lGt */
    707:   MatProductCreate(lG,lGt,NULL,&conn);
    708:   MatProductSetType(conn,MATPRODUCT_AB);
    709:   MatProductSetAlgorithm(conn,"default");
    710:   MatProductSetFill(conn,PETSC_DEFAULT);
    711:   PetscObjectSetOptionsPrefix((PetscObject)conn,"econn_");
    712:   MatProductSetFromOptions(conn);
    713:   MatProductSymbolic(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 */
    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;
    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;
    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:   }
    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;
    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 */

    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;
    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)) {
    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:       SETERRQ(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 (PetscDefined(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:           SETERRQ(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:   }

    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];
    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);
    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: {
    1412:   PetscInt       i;

    1414:   for (i=0;i<nvecs;i++) {
    1415:     PetscInt first,last;

    1417:     VecGetOwnershipRange(quad_vecs[i],&first,&last);
    1419:     if (i>=first && i < last) {
    1420:       PetscScalar *data;
    1421:       VecGetArray(quad_vecs[i],&data);
    1422:       if (!has_const) {
    1423:         data[i-first] = 1.;
    1424:       } else {
    1425:         data[2*i-first] = 1./PetscSqrtReal(2.);
    1426:         data[2*i-first+1] = -1./PetscSqrtReal(2.);
    1427:       }
    1428:       VecRestoreArray(quad_vecs[i],&data);
    1429:     }
    1430:     PetscObjectStateIncrease((PetscObject)quad_vecs[i]);
    1431:   }
    1432:   MatNullSpaceCreate(comm,has_const,nvecs,quad_vecs,nnsp);
    1433:   for (i=0;i<nvecs;i++) { /* reset vectors */
    1434:     PetscInt first,last;
    1435:     VecLockReadPop(quad_vecs[i]);
    1436:     VecGetOwnershipRange(quad_vecs[i],&first,&last);
    1437:     if (i>=first && i < last) {
    1438:       PetscScalar *data;
    1439:       VecGetArray(quad_vecs[i],&data);
    1440:       if (!has_const) {
    1441:         data[i-first] = 0.;
    1442:       } else {
    1443:         data[2*i-first] = 0.;
    1444:         data[2*i-first+1] = 0.;
    1445:       }
    1446:       VecRestoreArray(quad_vecs[i],&data);
    1447:     }
    1448:     PetscObjectStateIncrease((PetscObject)quad_vecs[i]);
    1449:     VecLockReadPush(quad_vecs[i]);
    1450:   }
    1451:   return 0;
    1452: }

    1454: PetscErrorCode PCBDDCComputeNoNetFlux(Mat A, Mat divudotp, PetscBool transpose, IS vl2l, PCBDDCGraph graph, MatNullSpace *nnsp)
    1455: {
    1456:   Mat                    loc_divudotp;
    1457:   Vec                    p,v,vins,quad_vec,*quad_vecs;
    1458:   ISLocalToGlobalMapping map;
    1459:   PetscScalar            *vals;
    1460:   const PetscScalar      *array;
    1461:   PetscInt               i,maxneighs = 0,maxsize,*gidxs;
    1462:   PetscInt               n_neigh,*neigh,*n_shared,**shared;
    1463:   PetscMPIInt            rank;

    1465:   ISLocalToGlobalMappingGetInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
    1466:   for (i=0;i<n_neigh;i++) maxneighs = PetscMax(graph->count[shared[i][0]]+1,maxneighs);
    1467:   MPIU_Allreduce(MPI_IN_PLACE,&maxneighs,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)A));
    1468:   if (!maxneighs) {
    1469:     ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
    1470:     *nnsp = NULL;
    1471:     return 0;
    1472:   }
    1473:   maxsize = 0;
    1474:   for (i=0;i<n_neigh;i++) maxsize = PetscMax(n_shared[i],maxsize);
    1475:   PetscMalloc2(maxsize,&gidxs,maxsize,&vals);
    1476:   /* create vectors to hold quadrature weights */
    1477:   MatCreateVecs(A,&quad_vec,NULL);
    1478:   if (!transpose) {
    1479:     MatISGetLocalToGlobalMapping(A,&map,NULL);
    1480:   } else {
    1481:     MatISGetLocalToGlobalMapping(A,NULL,&map);
    1482:   }
    1483:   VecDuplicateVecs(quad_vec,maxneighs,&quad_vecs);
    1484:   VecDestroy(&quad_vec);
    1485:   PCBDDCNullSpaceCreate(PetscObjectComm((PetscObject)A),PETSC_FALSE,maxneighs,quad_vecs,nnsp);
    1486:   for (i=0;i<maxneighs;i++) {
    1487:     VecLockReadPop(quad_vecs[i]);
    1488:   }

    1490:   /* compute local quad vec */
    1491:   MatISGetLocalMat(divudotp,&loc_divudotp);
    1492:   if (!transpose) {
    1493:     MatCreateVecs(loc_divudotp,&v,&p);
    1494:   } else {
    1495:     MatCreateVecs(loc_divudotp,&p,&v);
    1496:   }
    1497:   VecSet(p,1.);
    1498:   if (!transpose) {
    1499:     MatMultTranspose(loc_divudotp,p,v);
    1500:   } else {
    1501:     MatMult(loc_divudotp,p,v);
    1502:   }
    1503:   if (vl2l) {
    1504:     Mat        lA;
    1505:     VecScatter sc;

    1507:     MatISGetLocalMat(A,&lA);
    1508:     MatCreateVecs(lA,&vins,NULL);
    1509:     VecScatterCreate(v,NULL,vins,vl2l,&sc);
    1510:     VecScatterBegin(sc,v,vins,INSERT_VALUES,SCATTER_FORWARD);
    1511:     VecScatterEnd(sc,v,vins,INSERT_VALUES,SCATTER_FORWARD);
    1512:     VecScatterDestroy(&sc);
    1513:   } else {
    1514:     vins = v;
    1515:   }
    1516:   VecGetArrayRead(vins,&array);
    1517:   VecDestroy(&p);

    1519:   /* insert in global quadrature vecs */
    1520:   MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);
    1521:   for (i=1;i<n_neigh;i++) {
    1522:     const PetscInt    *idxs;
    1523:     PetscInt          idx,nn,j;

    1525:     idxs = shared[i];
    1526:     nn   = n_shared[i];
    1527:     for (j=0;j<nn;j++) vals[j] = array[idxs[j]];
    1528:     PetscFindInt(rank,graph->count[idxs[0]],graph->neighbours_set[idxs[0]],&idx);
    1529:     idx  = -(idx+1);
    1531:     ISLocalToGlobalMappingApply(map,nn,idxs,gidxs);
    1532:     VecSetValues(quad_vecs[idx],nn,gidxs,vals,INSERT_VALUES);
    1533:   }
    1534:   ISLocalToGlobalMappingRestoreInfo(graph->l2gmap,&n_neigh,&neigh,&n_shared,&shared);
    1535:   VecRestoreArrayRead(vins,&array);
    1536:   if (vl2l) {
    1537:     VecDestroy(&vins);
    1538:   }
    1539:   VecDestroy(&v);
    1540:   PetscFree2(gidxs,vals);

    1542:   /* assemble near null space */
    1543:   for (i=0;i<maxneighs;i++) {
    1544:     VecAssemblyBegin(quad_vecs[i]);
    1545:   }
    1546:   for (i=0;i<maxneighs;i++) {
    1547:     VecAssemblyEnd(quad_vecs[i]);
    1548:     VecViewFromOptions(quad_vecs[i],NULL,"-pc_bddc_quad_vecs_view");
    1549:     VecLockReadPush(quad_vecs[i]);
    1550:   }
    1551:   VecDestroyVecs(maxneighs,&quad_vecs);
    1552:   return 0;
    1553: }

    1555: PetscErrorCode PCBDDCAddPrimalVerticesLocalIS(PC pc, IS primalv)
    1556: {
    1557:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

    1559:   if (primalv) {
    1560:     if (pcbddc->user_primal_vertices_local) {
    1561:       IS list[2], newp;

    1563:       list[0] = primalv;
    1564:       list[1] = pcbddc->user_primal_vertices_local;
    1565:       ISConcatenate(PetscObjectComm((PetscObject)pc),2,list,&newp);
    1566:       ISSortRemoveDups(newp);
    1567:       ISDestroy(&list[1]);
    1568:       pcbddc->user_primal_vertices_local = newp;
    1569:     } else {
    1570:       PCBDDCSetPrimalVerticesLocalIS(pc,primalv);
    1571:     }
    1572:   }
    1573:   return 0;
    1574: }

    1576: static PetscErrorCode func_coords_private(PetscInt dim, PetscReal t, const PetscReal X[], PetscInt Nf, PetscScalar *out, void *ctx)
    1577: {
    1578:   PetscInt f, *comp  = (PetscInt *)ctx;

    1580:   for (f=0;f<Nf;f++) out[f] = X[*comp];
    1581:   return 0;
    1582: }

    1584: PetscErrorCode PCBDDCComputeLocalTopologyInfo(PC pc)
    1585: {
    1587:   Vec            local,global;
    1588:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
    1589:   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
    1590:   PetscBool      monolithic = PETSC_FALSE;

    1592:   PetscOptionsBegin(PetscObjectComm((PetscObject)pc),((PetscObject)pc)->prefix,"BDDC topology options","PC");
    1593:   PetscOptionsBool("-pc_bddc_monolithic","Discard any information on dofs splitting",NULL,monolithic,&monolithic,NULL);
    1594:   PetscOptionsEnd();
    1595:   /* need to convert from global to local topology information and remove references to information in global ordering */
    1596:   MatCreateVecs(pc->pmat,&global,NULL);
    1597:   MatCreateVecs(matis->A,&local,NULL);
    1598:   VecBindToCPU(global,PETSC_TRUE);
    1599:   VecBindToCPU(local,PETSC_TRUE);
    1600:   if (monolithic) { /* just get block size to properly compute vertices */
    1601:     if (pcbddc->vertex_size == 1) {
    1602:       MatGetBlockSize(pc->pmat,&pcbddc->vertex_size);
    1603:     }
    1604:     goto boundary;
    1605:   }

    1607:   if (pcbddc->user_provided_isfordofs) {
    1608:     if (pcbddc->n_ISForDofs) {
    1609:       PetscInt i;

    1611:       PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);
    1612:       for (i=0;i<pcbddc->n_ISForDofs;i++) {
    1613:         PetscInt bs;

    1615:         PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);
    1616:         ISGetBlockSize(pcbddc->ISForDofs[i],&bs);
    1617:         ISSetBlockSize(pcbddc->ISForDofsLocal[i],bs);
    1618:         ISDestroy(&pcbddc->ISForDofs[i]);
    1619:       }
    1620:       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
    1621:       pcbddc->n_ISForDofs = 0;
    1622:       PetscFree(pcbddc->ISForDofs);
    1623:     }
    1624:   } else {
    1625:     if (!pcbddc->n_ISForDofsLocal) { /* field split not present */
    1626:       DM dm;

    1628:       MatGetDM(pc->pmat, &dm);
    1629:       if (!dm) {
    1630:         PCGetDM(pc, &dm);
    1631:       }
    1632:       if (dm) {
    1633:         IS      *fields;
    1634:         PetscInt nf,i;

    1636:         DMCreateFieldDecomposition(dm,&nf,NULL,&fields,NULL);
    1637:         PetscMalloc1(nf,&pcbddc->ISForDofsLocal);
    1638:         for (i=0;i<nf;i++) {
    1639:           PetscInt bs;

    1641:           PCBDDCGlobalToLocal(matis->rctx,global,local,fields[i],&pcbddc->ISForDofsLocal[i]);
    1642:           ISGetBlockSize(fields[i],&bs);
    1643:           ISSetBlockSize(pcbddc->ISForDofsLocal[i],bs);
    1644:           ISDestroy(&fields[i]);
    1645:         }
    1646:         PetscFree(fields);
    1647:         pcbddc->n_ISForDofsLocal = nf;
    1648:       } else { /* See if MATIS has fields attached by the conversion from MatNest */
    1649:         PetscContainer   c;

    1651:         PetscObjectQuery((PetscObject)pc->pmat,"_convert_nest_lfields",(PetscObject*)&c);
    1652:         if (c) {
    1653:           MatISLocalFields lf;
    1654:           PetscContainerGetPointer(c,(void**)&lf);
    1655:           PCBDDCSetDofsSplittingLocal(pc,lf->nr,lf->rf);
    1656:         } else { /* fallback, create the default fields if bs > 1 */
    1657:           PetscInt i, n = matis->A->rmap->n;
    1658:           MatGetBlockSize(pc->pmat,&i);
    1659:           if (i > 1) {
    1660:             pcbddc->n_ISForDofsLocal = i;
    1661:             PetscMalloc1(pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal);
    1662:             for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
    1663:               ISCreateStride(PetscObjectComm((PetscObject)pc),n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);
    1664:             }
    1665:           }
    1666:         }
    1667:       }
    1668:     } else {
    1669:       PetscInt i;
    1670:       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
    1671:         PCBDDCConsistencyCheckIS(pc,MPI_LAND,&pcbddc->ISForDofsLocal[i]);
    1672:       }
    1673:     }
    1674:   }

    1676: boundary:
    1677:   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) {
    1678:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);
    1679:   } else if (pcbddc->DirichletBoundariesLocal) {
    1680:     PCBDDCConsistencyCheckIS(pc,MPI_LAND,&pcbddc->DirichletBoundariesLocal);
    1681:   }
    1682:   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) {
    1683:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);
    1684:   } else if (pcbddc->NeumannBoundariesLocal) {
    1685:     PCBDDCConsistencyCheckIS(pc,MPI_LOR,&pcbddc->NeumannBoundariesLocal);
    1686:   }
    1687:   if (!pcbddc->user_primal_vertices_local && pcbddc->user_primal_vertices) {
    1688:     PCBDDCGlobalToLocal(matis->rctx,global,local,pcbddc->user_primal_vertices,&pcbddc->user_primal_vertices_local);
    1689:   }
    1690:   VecDestroy(&global);
    1691:   VecDestroy(&local);
    1692:   /* detect local disconnected subdomains if requested (use matis->A) */
    1693:   if (pcbddc->detect_disconnected) {
    1694:     IS        primalv = NULL;
    1695:     PetscInt  i;
    1696:     PetscBool filter = pcbddc->detect_disconnected_filter;

    1698:     for (i=0;i<pcbddc->n_local_subs;i++) {
    1699:       ISDestroy(&pcbddc->local_subs[i]);
    1700:     }
    1701:     PetscFree(pcbddc->local_subs);
    1702:     PCBDDCDetectDisconnectedComponents(pc,filter,&pcbddc->n_local_subs,&pcbddc->local_subs,&primalv);
    1703:     PCBDDCAddPrimalVerticesLocalIS(pc,primalv);
    1704:     ISDestroy(&primalv);
    1705:   }
    1706:   /* early stage corner detection */
    1707:   {
    1708:     DM dm;

    1710:     MatGetDM(pc->pmat,&dm);
    1711:     if (!dm) {
    1712:       PCGetDM(pc,&dm);
    1713:     }
    1714:     if (dm) {
    1715:       PetscBool isda;

    1717:       PetscObjectTypeCompare((PetscObject)dm,DMDA,&isda);
    1718:       if (isda) {
    1719:         ISLocalToGlobalMapping l2l;
    1720:         IS                     corners;
    1721:         Mat                    lA;
    1722:         PetscBool              gl,lo;

    1724:         {
    1725:           Vec               cvec;
    1726:           const PetscScalar *coords;
    1727:           PetscInt          dof,n,cdim;
    1728:           PetscBool         memc = PETSC_TRUE;

    1730:           DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    1731:           DMGetCoordinates(dm,&cvec);
    1732:           VecGetLocalSize(cvec,&n);
    1733:           VecGetBlockSize(cvec,&cdim);
    1734:           n   /= cdim;
    1735:           PetscFree(pcbddc->mat_graph->coords);
    1736:           PetscMalloc1(dof*n*cdim,&pcbddc->mat_graph->coords);
    1737:           VecGetArrayRead(cvec,&coords);
    1738: #if defined(PETSC_USE_COMPLEX)
    1739:           memc = PETSC_FALSE;
    1740: #endif
    1741:           if (dof != 1) memc = PETSC_FALSE;
    1742:           if (memc) {
    1743:             PetscArraycpy(pcbddc->mat_graph->coords,coords,cdim*n*dof);
    1744:           } else { /* BDDC graph does not use any blocked information, we need to replicate the data */
    1745:             PetscReal *bcoords = pcbddc->mat_graph->coords;
    1746:             PetscInt  i, b, d;

    1748:             for (i=0;i<n;i++) {
    1749:               for (b=0;b<dof;b++) {
    1750:                 for (d=0;d<cdim;d++) {
    1751:                   bcoords[i*dof*cdim + b*cdim + d] = PetscRealPart(coords[i*cdim+d]);
    1752:                 }
    1753:               }
    1754:             }
    1755:           }
    1756:           VecRestoreArrayRead(cvec,&coords);
    1757:           pcbddc->mat_graph->cdim  = cdim;
    1758:           pcbddc->mat_graph->cnloc = dof*n;
    1759:           pcbddc->mat_graph->cloc  = PETSC_FALSE;
    1760:         }
    1761:         DMDAGetSubdomainCornersIS(dm,&corners);
    1762:         MatISGetLocalMat(pc->pmat,&lA);
    1763:         MatGetLocalToGlobalMapping(lA,&l2l,NULL);
    1764:         MatISRestoreLocalMat(pc->pmat,&lA);
    1765:         lo   = (PetscBool)(l2l && corners);
    1766:         MPIU_Allreduce(&lo,&gl,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));
    1767:         if (gl) { /* From PETSc's DMDA */
    1768:           const PetscInt    *idx;
    1769:           PetscInt          dof,bs,*idxout,n;

    1771:           DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);
    1772:           ISLocalToGlobalMappingGetBlockSize(l2l,&bs);
    1773:           ISGetLocalSize(corners,&n);
    1774:           ISGetIndices(corners,&idx);
    1775:           if (bs == dof) {
    1776:             PetscMalloc1(n,&idxout);
    1777:             ISLocalToGlobalMappingApplyBlock(l2l,n,idx,idxout);
    1778:           } else { /* the original DMDA local-to-local map have been modified */
    1779:             PetscInt i,d;

    1781:             PetscMalloc1(dof*n,&idxout);
    1782:             for (i=0;i<n;i++) for (d=0;d<dof;d++) idxout[dof*i+d] = dof*idx[i]+d;
    1783:             ISLocalToGlobalMappingApply(l2l,dof*n,idxout,idxout);

    1785:             bs = 1;
    1786:             n *= dof;
    1787:           }
    1788:           ISRestoreIndices(corners,&idx);
    1789:           DMDARestoreSubdomainCornersIS(dm,&corners);
    1790:           ISCreateBlock(PetscObjectComm((PetscObject)pc),bs,n,idxout,PETSC_OWN_POINTER,&corners);
    1791:           PCBDDCAddPrimalVerticesLocalIS(pc,corners);
    1792:           ISDestroy(&corners);
    1793:           pcbddc->corner_selected  = PETSC_TRUE;
    1794:           pcbddc->corner_selection = PETSC_TRUE;
    1795:         }
    1796:         if (corners) {
    1797:           DMDARestoreSubdomainCornersIS(dm,&corners);
    1798:         }
    1799:       }
    1800:     }
    1801:   }
    1802:   if (pcbddc->corner_selection && !pcbddc->mat_graph->cdim) {
    1803:     DM dm;

    1805:     MatGetDM(pc->pmat,&dm);
    1806:     if (!dm) {
    1807:       PCGetDM(pc,&dm);
    1808:     }
    1809:     if (dm) { /* this can get very expensive, I need to find a faster alternative */
    1810:       Vec            vcoords;
    1811:       PetscSection   section;
    1812:       PetscReal      *coords;
    1813:       PetscInt       d,cdim,nl,nf,**ctxs;
    1814:       PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *);
    1815:       /* debug coordinates */
    1816:       PetscViewer       viewer;
    1817:       PetscBool         flg;
    1818:       PetscViewerFormat format;
    1819:       const char        *prefix;

    1821:       DMGetCoordinateDim(dm,&cdim);
    1822:       DMGetLocalSection(dm,&section);
    1823:       PetscSectionGetNumFields(section,&nf);
    1824:       DMCreateGlobalVector(dm,&vcoords);
    1825:       VecGetLocalSize(vcoords,&nl);
    1826:       PetscMalloc1(nl*cdim,&coords);
    1827:       PetscMalloc2(nf,&funcs,nf,&ctxs);
    1828:       PetscMalloc1(nf,&ctxs[0]);
    1829:       for (d=0;d<nf;d++) funcs[d] = func_coords_private;
    1830:       for (d=1;d<nf;d++) ctxs[d] = ctxs[d-1] + 1;

    1832:       /* debug coordinates */
    1833:       PCGetOptionsPrefix(pc,&prefix);
    1834:       PetscOptionsGetViewer(PetscObjectComm((PetscObject)vcoords),((PetscObject)vcoords)->options,prefix,"-pc_bddc_coords_vec_view",&viewer,&format,&flg);
    1835:       if (flg) PetscViewerPushFormat(viewer,format);
    1836:       for (d=0;d<cdim;d++) {
    1837:         PetscInt          i;
    1838:         const PetscScalar *v;
    1839:         char              name[16];

    1841:         for (i=0;i<nf;i++) ctxs[i][0] = d;
    1842:         PetscSNPrintf(name,sizeof(name),"bddc_coords_%d",(int)d);
    1843:         PetscObjectSetName((PetscObject)vcoords,name);
    1844:         DMProjectFunction(dm,0.0,funcs,(void**)ctxs,INSERT_VALUES,vcoords);
    1845:         if (flg) VecView(vcoords,viewer);
    1846:         VecGetArrayRead(vcoords,&v);
    1847:         for (i=0;i<nl;i++) coords[i*cdim+d] = PetscRealPart(v[i]);
    1848:         VecRestoreArrayRead(vcoords,&v);
    1849:       }
    1850:       VecDestroy(&vcoords);
    1851:       PCSetCoordinates(pc,cdim,nl,coords);
    1852:       PetscFree(coords);
    1853:       PetscFree(ctxs[0]);
    1854:       PetscFree2(funcs,ctxs);
    1855:       if (flg) {
    1856:         PetscViewerPopFormat(viewer);
    1857:         PetscViewerDestroy(&viewer);
    1858:       }
    1859:     }
    1860:   }
    1861:   return 0;
    1862: }

    1864: PetscErrorCode PCBDDCConsistencyCheckIS(PC pc, MPI_Op mop, IS *is)
    1865: {
    1866:   Mat_IS          *matis = (Mat_IS*)(pc->pmat->data);
    1867:   IS              nis;
    1868:   const PetscInt  *idxs;
    1869:   PetscInt        i,nd,n = matis->A->rmap->n,*nidxs,nnd;

    1872:   if (mop == MPI_LAND) {
    1873:     /* init rootdata with true */
    1874:     for (i=0;i<pc->pmat->rmap->n;i++) matis->sf_rootdata[i] = 1;
    1875:   } else {
    1876:     PetscArrayzero(matis->sf_rootdata,pc->pmat->rmap->n);
    1877:   }
    1878:   PetscArrayzero(matis->sf_leafdata,n);
    1879:   ISGetLocalSize(*is,&nd);
    1880:   ISGetIndices(*is,&idxs);
    1881:   for (i=0;i<nd;i++)
    1882:     if (-1 < idxs[i] && idxs[i] < n)
    1883:       matis->sf_leafdata[idxs[i]] = 1;
    1884:   ISRestoreIndices(*is,&idxs);
    1885:   PetscSFReduceBegin(matis->sf,MPIU_INT,matis->sf_leafdata,matis->sf_rootdata,mop);
    1886:   PetscSFReduceEnd(matis->sf,MPIU_INT,matis->sf_leafdata,matis->sf_rootdata,mop);
    1887:   PetscSFBcastBegin(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
    1888:   PetscSFBcastEnd(matis->sf,MPIU_INT,matis->sf_rootdata,matis->sf_leafdata,MPI_REPLACE);
    1889:   if (mop == MPI_LAND) {
    1890:     PetscMalloc1(nd,&nidxs);
    1891:   } else {
    1892:     PetscMalloc1(n,&nidxs);
    1893:   }
    1894:   for (i=0,nnd=0;i<n;i++)
    1895:     if (matis->sf_leafdata[i])
    1896:       nidxs[nnd++] = i;
    1897:   ISCreateGeneral(PetscObjectComm((PetscObject)(*is)),nnd,nidxs,PETSC_OWN_POINTER,&nis);
    1898:   ISDestroy(is);
    1899:   *is  = nis;
    1900:   return 0;
    1901: }

    1903: PetscErrorCode PCBDDCBenignRemoveInterior(PC pc,Vec r,Vec z)
    1904: {
    1905:   PC_IS             *pcis = (PC_IS*)(pc->data);
    1906:   PC_BDDC           *pcbddc = (PC_BDDC*)(pc->data);

    1908:   if (!pcbddc->benign_have_null) {
    1909:     return 0;
    1910:   }
    1911:   if (pcbddc->ChangeOfBasisMatrix) {
    1912:     Vec swap;

    1914:     MatMultTranspose(pcbddc->ChangeOfBasisMatrix,r,pcbddc->work_change);
    1915:     swap = pcbddc->work_change;
    1916:     pcbddc->work_change = r;
    1917:     r = swap;
    1918:   }
    1919:   VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
    1920:   VecScatterEnd(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
    1921:   PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][0],pc,0,0,0);
    1922:   KSPSolve(pcbddc->ksp_D,pcis->vec1_D,pcis->vec2_D);
    1923:   PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][0],pc,0,0,0);
    1924:   KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);
    1925:   VecSet(z,0.);
    1926:   VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
    1927:   VecScatterEnd(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
    1928:   if (pcbddc->ChangeOfBasisMatrix) {
    1929:     pcbddc->work_change = r;
    1930:     VecCopy(z,pcbddc->work_change);
    1931:     MatMult(pcbddc->ChangeOfBasisMatrix,pcbddc->work_change,z);
    1932:   }
    1933:   return 0;
    1934: }

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

    1941:   MatShellGetContext(A,&ctx);
    1942:   if (transpose) {
    1943:     apply_right = ctx->apply_left;
    1944:     apply_left = ctx->apply_right;
    1945:   } else {
    1946:     apply_right = ctx->apply_right;
    1947:     apply_left = ctx->apply_left;
    1948:   }
    1949:   reset_x = PETSC_FALSE;
    1950:   if (apply_right) {
    1951:     const PetscScalar *ax;
    1952:     PetscInt          nl,i;

    1954:     VecGetLocalSize(x,&nl);
    1955:     VecGetArrayRead(x,&ax);
    1956:     PetscArraycpy(ctx->work,ax,nl);
    1957:     VecRestoreArrayRead(x,&ax);
    1958:     for (i=0;i<ctx->benign_n;i++) {
    1959:       PetscScalar    sum,val;
    1960:       const PetscInt *idxs;
    1961:       PetscInt       nz,j;
    1962:       ISGetLocalSize(ctx->benign_zerodiag_subs[i],&nz);
    1963:       ISGetIndices(ctx->benign_zerodiag_subs[i],&idxs);
    1964:       sum = 0.;
    1965:       if (ctx->apply_p0) {
    1966:         val = ctx->work[idxs[nz-1]];
    1967:         for (j=0;j<nz-1;j++) {
    1968:           sum += ctx->work[idxs[j]];
    1969:           ctx->work[idxs[j]] += val;
    1970:         }
    1971:       } else {
    1972:         for (j=0;j<nz-1;j++) {
    1973:           sum += ctx->work[idxs[j]];
    1974:         }
    1975:       }
    1976:       ctx->work[idxs[nz-1]] -= sum;
    1977:       ISRestoreIndices(ctx->benign_zerodiag_subs[i],&idxs);
    1978:     }
    1979:     VecPlaceArray(x,ctx->work);
    1980:     reset_x = PETSC_TRUE;
    1981:   }
    1982:   if (transpose) {
    1983:     MatMultTranspose(ctx->A,x,y);
    1984:   } else {
    1985:     MatMult(ctx->A,x,y);
    1986:   }
    1987:   if (reset_x) {
    1988:     VecResetArray(x);
    1989:   }
    1990:   if (apply_left) {
    1991:     PetscScalar *ay;
    1992:     PetscInt    i;

    1994:     VecGetArray(y,&ay);
    1995:     for (i=0;i<ctx->benign_n;i++) {
    1996:       PetscScalar    sum,val;
    1997:       const PetscInt *idxs;
    1998:       PetscInt       nz,j;
    1999:       ISGetLocalSize(ctx->benign_zerodiag_subs[i],&nz);
    2000:       ISGetIndices(ctx->benign_zerodiag_subs[i],&idxs);
    2001:       val = -ay[idxs[nz-1]];
    2002:       if (ctx->apply_p0) {
    2003:         sum = 0.;
    2004:         for (j=0;j<nz-1;j++) {
    2005:           sum += ay[idxs[j]];
    2006:           ay[idxs[j]] += val;
    2007:         }
    2008:         ay[idxs[nz-1]] += sum;
    2009:       } else {
    2010:         for (j=0;j<nz-1;j++) {
    2011:           ay[idxs[j]] += val;
    2012:         }
    2013:         ay[idxs[nz-1]] = 0.;
    2014:       }
    2015:       ISRestoreIndices(ctx->benign_zerodiag_subs[i],&idxs);
    2016:     }
    2017:     VecRestoreArray(y,&ay);
    2018:   }
    2019:   return 0;
    2020: }

    2022: PetscErrorCode PCBDDCBenignMatMultTranspose_Private(Mat A, Vec x, Vec y)
    2023: {
    2024:   PCBDDCBenignMatMult_Private_Private(A,x,y,PETSC_TRUE);
    2025:   return 0;
    2026: }

    2028: PetscErrorCode PCBDDCBenignMatMult_Private(Mat A, Vec x, Vec y)
    2029: {
    2030:   PCBDDCBenignMatMult_Private_Private(A,x,y,PETSC_FALSE);
    2031:   return 0;
    2032: }

    2034: PetscErrorCode PCBDDCBenignShellMat(PC pc, PetscBool restore)
    2035: {
    2036:   PC_IS                   *pcis = (PC_IS*)pc->data;
    2037:   PC_BDDC                 *pcbddc = (PC_BDDC*)pc->data;
    2038:   PCBDDCBenignMatMult_ctx ctx;

    2040:   if (!restore) {
    2041:     Mat                A_IB,A_BI;
    2042:     PetscScalar        *work;
    2043:     PCBDDCReuseSolvers reuse = pcbddc->sub_schurs ? pcbddc->sub_schurs->reuse_solver : NULL;

    2046:     if (!pcbddc->benign_change || !pcbddc->benign_n || pcbddc->benign_change_explicit) return 0;
    2047:     PetscMalloc1(pcis->n,&work);
    2048:     MatCreate(PETSC_COMM_SELF,&A_IB);
    2049:     MatSetSizes(A_IB,pcis->n-pcis->n_B,pcis->n_B,PETSC_DECIDE,PETSC_DECIDE);
    2050:     MatSetType(A_IB,MATSHELL);
    2051:     MatShellSetOperation(A_IB,MATOP_MULT,(void (*)(void))PCBDDCBenignMatMult_Private);
    2052:     MatShellSetOperation(A_IB,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCBenignMatMultTranspose_Private);
    2053:     PetscNew(&ctx);
    2054:     MatShellSetContext(A_IB,ctx);
    2055:     ctx->apply_left = PETSC_TRUE;
    2056:     ctx->apply_right = PETSC_FALSE;
    2057:     ctx->apply_p0 = PETSC_FALSE;
    2058:     ctx->benign_n = pcbddc->benign_n;
    2059:     if (reuse) {
    2060:       ctx->benign_zerodiag_subs = reuse->benign_zerodiag_subs;
    2061:       ctx->free = PETSC_FALSE;
    2062:     } else { /* TODO: could be optimized for successive solves */
    2063:       ISLocalToGlobalMapping N_to_D;
    2064:       PetscInt               i;

    2066:       ISLocalToGlobalMappingCreateIS(pcis->is_I_local,&N_to_D);
    2067:       PetscMalloc1(pcbddc->benign_n,&ctx->benign_zerodiag_subs);
    2068:       for (i=0;i<pcbddc->benign_n;i++) {
    2069:         ISGlobalToLocalMappingApplyIS(N_to_D,IS_GTOLM_DROP,pcbddc->benign_zerodiag_subs[i],&ctx->benign_zerodiag_subs[i]);
    2070:       }
    2071:       ISLocalToGlobalMappingDestroy(&N_to_D);
    2072:       ctx->free = PETSC_TRUE;
    2073:     }
    2074:     ctx->A = pcis->A_IB;
    2075:     ctx->work = work;
    2076:     MatSetUp(A_IB);
    2077:     MatAssemblyBegin(A_IB,MAT_FINAL_ASSEMBLY);
    2078:     MatAssemblyEnd(A_IB,MAT_FINAL_ASSEMBLY);
    2079:     pcis->A_IB = A_IB;

    2081:     /* A_BI as A_IB^T */
    2082:     MatCreateTranspose(A_IB,&A_BI);
    2083:     pcbddc->benign_original_mat = pcis->A_BI;
    2084:     pcis->A_BI = A_BI;
    2085:   } else {
    2086:     if (!pcbddc->benign_original_mat) {
    2087:       return 0;
    2088:     }
    2089:     MatShellGetContext(pcis->A_IB,&ctx);
    2090:     MatDestroy(&pcis->A_IB);
    2091:     pcis->A_IB = ctx->A;
    2092:     ctx->A = NULL;
    2093:     MatDestroy(&pcis->A_BI);
    2094:     pcis->A_BI = pcbddc->benign_original_mat;
    2095:     pcbddc->benign_original_mat = NULL;
    2096:     if (ctx->free) {
    2097:       PetscInt i;
    2098:       for (i=0;i<ctx->benign_n;i++) {
    2099:         ISDestroy(&ctx->benign_zerodiag_subs[i]);
    2100:       }
    2101:       PetscFree(ctx->benign_zerodiag_subs);
    2102:     }
    2103:     PetscFree(ctx->work);
    2104:     PetscFree(ctx);
    2105:   }
    2106:   return 0;
    2107: }

    2109: /* used just in bddc debug mode */
    2110: PetscErrorCode PCBDDCBenignProject(PC pc, IS is1, IS is2, Mat *B)
    2111: {
    2112:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
    2113:   Mat_IS         *matis = (Mat_IS*)pc->pmat->data;
    2114:   Mat            An;

    2116:   MatPtAP(matis->A,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&An);
    2117:   MatZeroRowsColumns(An,pcbddc->benign_n,pcbddc->benign_p0_lidx,1.0,NULL,NULL);
    2118:   if (is1) {
    2119:     MatCreateSubMatrix(An,is1,is2,MAT_INITIAL_MATRIX,B);
    2120:     MatDestroy(&An);
    2121:   } else {
    2122:     *B = An;
    2123:   }
    2124:   return 0;
    2125: }

    2127: /* TODO: add reuse flag */
    2128: PetscErrorCode MatSeqAIJCompress(Mat A, Mat *B)
    2129: {
    2130:   Mat            Bt;
    2131:   PetscScalar    *a,*bdata;
    2132:   const PetscInt *ii,*ij;
    2133:   PetscInt       m,n,i,nnz,*bii,*bij;
    2134:   PetscBool      flg_row;

    2136:   MatGetSize(A,&n,&m);
    2137:   MatGetRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&ij,&flg_row);
    2138:   MatSeqAIJGetArray(A,&a);
    2139:   nnz = n;
    2140:   for (i=0;i<ii[n];i++) {
    2141:     if (PetscLikely(PetscAbsScalar(a[i]) > PETSC_SMALL)) nnz++;
    2142:   }
    2143:   PetscMalloc1(n+1,&bii);
    2144:   PetscMalloc1(nnz,&bij);
    2145:   PetscMalloc1(nnz,&bdata);
    2146:   nnz = 0;
    2147:   bii[0] = 0;
    2148:   for (i=0;i<n;i++) {
    2149:     PetscInt j;
    2150:     for (j=ii[i];j<ii[i+1];j++) {
    2151:       PetscScalar entry = a[j];
    2152:       if (PetscLikely(PetscAbsScalar(entry) > PETSC_SMALL) || (n == m && ij[j] == i)) {
    2153:         bij[nnz] = ij[j];
    2154:         bdata[nnz] = entry;
    2155:         nnz++;
    2156:       }
    2157:     }
    2158:     bii[i+1] = nnz;
    2159:   }
    2160:   MatSeqAIJRestoreArray(A,&a);
    2161:   MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),n,m,bii,bij,bdata,&Bt);
    2162:   MatRestoreRowIJ(A,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&ij,&flg_row);
    2163:   {
    2164:     Mat_SeqAIJ *b = (Mat_SeqAIJ*)(Bt->data);
    2165:     b->free_a = PETSC_TRUE;
    2166:     b->free_ij = PETSC_TRUE;
    2167:   }
    2168:   if (*B == A) {
    2169:     MatDestroy(&A);
    2170:   }
    2171:   *B = Bt;
    2172:   return 0;
    2173: }

    2175: PetscErrorCode PCBDDCDetectDisconnectedComponents(PC pc, PetscBool filter, PetscInt *ncc, IS* cc[], IS* primalv)
    2176: {
    2177:   Mat                    B = NULL;
    2178:   DM                     dm;
    2179:   IS                     is_dummy,*cc_n;
    2180:   ISLocalToGlobalMapping l2gmap_dummy;
    2181:   PCBDDCGraph            graph;
    2182:   PetscInt               *xadj_filtered = NULL,*adjncy_filtered = NULL;
    2183:   PetscInt               i,n;
    2184:   PetscInt               *xadj,*adjncy;
    2185:   PetscBool              isplex = PETSC_FALSE;

    2187:   if (ncc) *ncc = 0;
    2188:   if (cc) *cc = NULL;
    2189:   if (primalv) *primalv = NULL;
    2190:   PCBDDCGraphCreate(&graph);
    2191:   MatGetDM(pc->pmat,&dm);
    2192:   if (!dm) {
    2193:     PCGetDM(pc,&dm);
    2194:   }
    2195:   if (dm) {
    2196:     PetscObjectTypeCompare((PetscObject)dm,DMPLEX,&isplex);
    2197:   }
    2198:   if (filter) isplex = PETSC_FALSE;

    2200:   if (isplex) { /* this code has been modified from plexpartition.c */
    2201:     PetscInt       p, pStart, pEnd, a, adjSize, idx, size, nroots;
    2202:     PetscInt      *adj = NULL;
    2203:     IS             cellNumbering;
    2204:     const PetscInt *cellNum;
    2205:     PetscBool      useCone, useClosure;
    2206:     PetscSection   section;
    2207:     PetscSegBuffer adjBuffer;
    2208:     PetscSF        sfPoint;

    2210:     DMPlexGetHeightStratum(dm, 0, &pStart, &pEnd);
    2211:     DMGetPointSF(dm, &sfPoint);
    2212:     PetscSFGetGraph(sfPoint, &nroots, NULL, NULL, NULL);
    2213:     /* Build adjacency graph via a section/segbuffer */
    2214:     PetscSectionCreate(PetscObjectComm((PetscObject) dm), &section);
    2215:     PetscSectionSetChart(section, pStart, pEnd);
    2216:     PetscSegBufferCreate(sizeof(PetscInt),1000,&adjBuffer);
    2217:     /* Always use FVM adjacency to create partitioner graph */
    2218:     DMGetBasicAdjacency(dm, &useCone, &useClosure);
    2219:     DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE);
    2220:     DMPlexGetCellNumbering(dm, &cellNumbering);
    2221:     ISGetIndices(cellNumbering, &cellNum);
    2222:     for (n = 0, p = pStart; p < pEnd; p++) {
    2223:       /* Skip non-owned cells in parallel (ParMetis expects no overlap) */
    2224:       if (nroots > 0) {if (cellNum[p] < 0) continue;}
    2225:       adjSize = PETSC_DETERMINE;
    2226:       DMPlexGetAdjacency(dm, p, &adjSize, &adj);
    2227:       for (a = 0; a < adjSize; ++a) {
    2228:         const PetscInt point = adj[a];
    2229:         if (pStart <= point && point < pEnd) {
    2230:           PetscInt *PETSC_RESTRICT pBuf;
    2231:           PetscSectionAddDof(section, p, 1);
    2232:           PetscSegBufferGetInts(adjBuffer, 1, &pBuf);
    2233:           *pBuf = point;
    2234:         }
    2235:       }
    2236:       n++;
    2237:     }
    2238:     DMSetBasicAdjacency(dm, useCone, useClosure);
    2239:     /* Derive CSR graph from section/segbuffer */
    2240:     PetscSectionSetUp(section);
    2241:     PetscSectionGetStorageSize(section, &size);
    2242:     PetscMalloc1(n+1, &xadj);
    2243:     for (idx = 0, p = pStart; p < pEnd; p++) {
    2244:       if (nroots > 0) {if (cellNum[p] < 0) continue;}
    2245:       PetscSectionGetOffset(section, p, &(xadj[idx++]));
    2246:     }
    2247:     xadj[n] = size;
    2248:     PetscSegBufferExtractAlloc(adjBuffer, &adjncy);
    2249:     /* Clean up */
    2250:     PetscSegBufferDestroy(&adjBuffer);
    2251:     PetscSectionDestroy(&section);
    2252:     PetscFree(adj);
    2253:     graph->xadj = xadj;
    2254:     graph->adjncy = adjncy;
    2255:   } else {
    2256:     Mat       A;
    2257:     PetscBool isseqaij, flg_row;

    2259:     MatISGetLocalMat(pc->pmat,&A);
    2260:     if (!A->rmap->N || !A->cmap->N) {
    2261:       PCBDDCGraphDestroy(&graph);
    2262:       return 0;
    2263:     }
    2264:     PetscObjectBaseTypeCompare((PetscObject)A,MATSEQAIJ,&isseqaij);
    2265:     if (!isseqaij && filter) {
    2266:       PetscBool isseqdense;

    2268:       PetscObjectTypeCompare((PetscObject)A,MATSEQDENSE,&isseqdense);
    2269:       if (!isseqdense) {
    2270:         MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&B);
    2271:       } else { /* TODO: rectangular case and LDA */
    2272:         PetscScalar *array;
    2273:         PetscReal   chop=1.e-6;

    2275:         MatDuplicate(A,MAT_COPY_VALUES,&B);
    2276:         MatDenseGetArray(B,&array);
    2277:         MatGetSize(B,&n,NULL);
    2278:         for (i=0;i<n;i++) {
    2279:           PetscInt j;
    2280:           for (j=i+1;j<n;j++) {
    2281:             PetscReal thresh = chop*(PetscAbsScalar(array[i*(n+1)])+PetscAbsScalar(array[j*(n+1)]));
    2282:             if (PetscAbsScalar(array[i*n+j]) < thresh) array[i*n+j] = 0.;
    2283:             if (PetscAbsScalar(array[j*n+i]) < thresh) array[j*n+i] = 0.;
    2284:           }
    2285:         }
    2286:         MatDenseRestoreArray(B,&array);
    2287:         MatConvert(B,MATSEQAIJ,MAT_INPLACE_MATRIX,&B);
    2288:       }
    2289:     } else {
    2290:       PetscObjectReference((PetscObject)A);
    2291:       B = A;
    2292:     }
    2293:     MatGetRowIJ(B,0,PETSC_TRUE,PETSC_FALSE,&n,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);

    2295:     /* if filter is true, then removes entries lower than PETSC_SMALL in magnitude */
    2296:     if (filter) {
    2297:       PetscScalar *data;
    2298:       PetscInt    j,cum;

    2300:       PetscCalloc2(n+1,&xadj_filtered,xadj[n],&adjncy_filtered);
    2301:       MatSeqAIJGetArray(B,&data);
    2302:       cum = 0;
    2303:       for (i=0;i<n;i++) {
    2304:         PetscInt t;

    2306:         for (j=xadj[i];j<xadj[i+1];j++) {
    2307:           if (PetscUnlikely(PetscAbsScalar(data[j]) < PETSC_SMALL)) {
    2308:             continue;
    2309:           }
    2310:           adjncy_filtered[cum+xadj_filtered[i]++] = adjncy[j];
    2311:         }
    2312:         t = xadj_filtered[i];
    2313:         xadj_filtered[i] = cum;
    2314:         cum += t;
    2315:       }
    2316:       MatSeqAIJRestoreArray(B,&data);
    2317:       graph->xadj = xadj_filtered;
    2318:       graph->adjncy = adjncy_filtered;
    2319:     } else {
    2320:       graph->xadj = xadj;
    2321:       graph->adjncy = adjncy;
    2322:     }
    2323:   }
    2324:   /* compute local connected components using PCBDDCGraph */
    2325:   ISCreateStride(PETSC_COMM_SELF,n,0,1,&is_dummy);
    2326:   ISLocalToGlobalMappingCreateIS(is_dummy,&l2gmap_dummy);
    2327:   ISDestroy(&is_dummy);
    2328:   PCBDDCGraphInit(graph,l2gmap_dummy,n,PETSC_MAX_INT);
    2329:   ISLocalToGlobalMappingDestroy(&l2gmap_dummy);
    2330:   PCBDDCGraphSetUp(graph,1,NULL,NULL,0,NULL,NULL);
    2331:   PCBDDCGraphComputeConnectedComponents(graph);

    2333:   /* partial clean up */
    2334:   PetscFree2(xadj_filtered,adjncy_filtered);
    2335:   if (B) {
    2336:     PetscBool flg_row;
    2337:     MatRestoreRowIJ(B,0,PETSC_TRUE,PETSC_FALSE,&n,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
    2338:     MatDestroy(&B);
    2339:   }
    2340:   if (isplex) {
    2341:     PetscFree(xadj);
    2342:     PetscFree(adjncy);
    2343:   }

    2345:   /* get back data */
    2346:   if (isplex) {
    2347:     if (ncc) *ncc = graph->ncc;
    2348:     if (cc || primalv) {
    2349:       Mat          A;
    2350:       PetscBT      btv,btvt;
    2351:       PetscSection subSection;
    2352:       PetscInt     *ids,cum,cump,*cids,*pids;

    2354:       DMPlexGetSubdomainSection(dm,&subSection);
    2355:       MatISGetLocalMat(pc->pmat,&A);
    2356:       PetscMalloc3(A->rmap->n,&ids,graph->ncc+1,&cids,A->rmap->n,&pids);
    2357:       PetscBTCreate(A->rmap->n,&btv);
    2358:       PetscBTCreate(A->rmap->n,&btvt);

    2360:       cids[0] = 0;
    2361:       for (i = 0, cump = 0, cum = 0; i < graph->ncc; i++) {
    2362:         PetscInt j;

    2364:         PetscBTMemzero(A->rmap->n,btvt);
    2365:         for (j = graph->cptr[i]; j < graph->cptr[i+1]; j++) {
    2366:           PetscInt k, size, *closure = NULL, cell = graph->queue[j];

    2368:           DMPlexGetTransitiveClosure(dm,cell,PETSC_TRUE,&size,&closure);
    2369:           for (k = 0; k < 2*size; k += 2) {
    2370:             PetscInt s, pp, p = closure[k], off, dof, cdof;

    2372:             PetscSectionGetConstraintDof(subSection,p,&cdof);
    2373:             PetscSectionGetOffset(subSection,p,&off);
    2374:             PetscSectionGetDof(subSection,p,&dof);
    2375:             for (s = 0; s < dof-cdof; s++) {
    2376:               if (PetscBTLookupSet(btvt,off+s)) continue;
    2377:               if (!PetscBTLookup(btv,off+s)) ids[cum++] = off+s;
    2378:               else pids[cump++] = off+s; /* cross-vertex */
    2379:             }
    2380:             DMPlexGetTreeParent(dm,p,&pp,NULL);
    2381:             if (pp != p) {
    2382:               PetscSectionGetConstraintDof(subSection,pp,&cdof);
    2383:               PetscSectionGetOffset(subSection,pp,&off);
    2384:               PetscSectionGetDof(subSection,pp,&dof);
    2385:               for (s = 0; s < dof-cdof; s++) {
    2386:                 if (PetscBTLookupSet(btvt,off+s)) continue;
    2387:                 if (!PetscBTLookup(btv,off+s)) ids[cum++] = off+s;
    2388:                 else pids[cump++] = off+s; /* cross-vertex */
    2389:               }
    2390:             }
    2391:           }
    2392:           DMPlexRestoreTransitiveClosure(dm,cell,PETSC_TRUE,&size,&closure);
    2393:         }
    2394:         cids[i+1] = cum;
    2395:         /* mark dofs as already assigned */
    2396:         for (j = cids[i]; j < cids[i+1]; j++) {
    2397:           PetscBTSet(btv,ids[j]);
    2398:         }
    2399:       }
    2400:       if (cc) {
    2401:         PetscMalloc1(graph->ncc,&cc_n);
    2402:         for (i = 0; i < graph->ncc; i++) {
    2403:           ISCreateGeneral(PETSC_COMM_SELF,cids[i+1]-cids[i],ids+cids[i],PETSC_COPY_VALUES,&cc_n[i]);
    2404:         }
    2405:         *cc = cc_n;
    2406:       }
    2407:       if (primalv) {
    2408:         ISCreateGeneral(PetscObjectComm((PetscObject)pc),cump,pids,PETSC_COPY_VALUES,primalv);
    2409:       }
    2410:       PetscFree3(ids,cids,pids);
    2411:       PetscBTDestroy(&btv);
    2412:       PetscBTDestroy(&btvt);
    2413:     }
    2414:   } else {
    2415:     if (ncc) *ncc = graph->ncc;
    2416:     if (cc) {
    2417:       PetscMalloc1(graph->ncc,&cc_n);
    2418:       for (i=0;i<graph->ncc;i++) {
    2419:         ISCreateGeneral(PETSC_COMM_SELF,graph->cptr[i+1]-graph->cptr[i],graph->queue+graph->cptr[i],PETSC_COPY_VALUES,&cc_n[i]);
    2420:       }
    2421:       *cc = cc_n;
    2422:     }
    2423:   }
    2424:   /* clean up graph */
    2425:   graph->xadj = NULL;
    2426:   graph->adjncy = NULL;
    2427:   PCBDDCGraphDestroy(&graph);
    2428:   return 0;
    2429: }

    2431: PetscErrorCode PCBDDCBenignCheck(PC pc, IS zerodiag)
    2432: {
    2433:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
    2434:   PC_IS*         pcis = (PC_IS*)(pc->data);
    2435:   IS             dirIS = NULL;
    2436:   PetscInt       i;

    2438:   PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph,&dirIS);
    2439:   if (zerodiag) {
    2440:     Mat            A;
    2441:     Vec            vec3_N;
    2442:     PetscScalar    *vals;
    2443:     const PetscInt *idxs;
    2444:     PetscInt       nz,*count;

    2446:     /* p0 */
    2447:     VecSet(pcis->vec1_N,0.);
    2448:     PetscMalloc1(pcis->n,&vals);
    2449:     ISGetLocalSize(zerodiag,&nz);
    2450:     ISGetIndices(zerodiag,&idxs);
    2451:     for (i=0;i<nz;i++) vals[i] = 1.;
    2452:     VecSetValues(pcis->vec1_N,nz,idxs,vals,INSERT_VALUES);
    2453:     VecAssemblyBegin(pcis->vec1_N);
    2454:     VecAssemblyEnd(pcis->vec1_N);
    2455:     /* v_I */
    2456:     VecSetRandom(pcis->vec2_N,NULL);
    2457:     for (i=0;i<nz;i++) vals[i] = 0.;
    2458:     VecSetValues(pcis->vec2_N,nz,idxs,vals,INSERT_VALUES);
    2459:     ISRestoreIndices(zerodiag,&idxs);
    2460:     ISGetIndices(pcis->is_B_local,&idxs);
    2461:     for (i=0;i<pcis->n_B;i++) vals[i] = 0.;
    2462:     VecSetValues(pcis->vec2_N,pcis->n_B,idxs,vals,INSERT_VALUES);
    2463:     ISRestoreIndices(pcis->is_B_local,&idxs);
    2464:     if (dirIS) {
    2465:       PetscInt n;

    2467:       ISGetLocalSize(dirIS,&n);
    2468:       ISGetIndices(dirIS,&idxs);
    2469:       for (i=0;i<n;i++) vals[i] = 0.;
    2470:       VecSetValues(pcis->vec2_N,n,idxs,vals,INSERT_VALUES);
    2471:       ISRestoreIndices(dirIS,&idxs);
    2472:     }
    2473:     VecAssemblyBegin(pcis->vec2_N);
    2474:     VecAssemblyEnd(pcis->vec2_N);
    2475:     VecDuplicate(pcis->vec1_N,&vec3_N);
    2476:     VecSet(vec3_N,0.);
    2477:     MatISGetLocalMat(pc->pmat,&A);
    2478:     MatMult(A,pcis->vec1_N,vec3_N);
    2479:     VecDot(vec3_N,pcis->vec2_N,&vals[0]);
    2481:     PetscFree(vals);
    2482:     VecDestroy(&vec3_N);

    2484:     /* there should not be any pressure dofs lying on the interface */
    2485:     PetscCalloc1(pcis->n,&count);
    2486:     ISGetIndices(pcis->is_B_local,&idxs);
    2487:     for (i=0;i<pcis->n_B;i++) count[idxs[i]]++;
    2488:     ISRestoreIndices(pcis->is_B_local,&idxs);
    2489:     ISGetIndices(zerodiag,&idxs);
    2491:     ISRestoreIndices(zerodiag,&idxs);
    2492:     PetscFree(count);
    2493:   }
    2494:   ISDestroy(&dirIS);

    2496:   /* check PCBDDCBenignGetOrSetP0 */
    2497:   VecSetRandom(pcis->vec1_global,NULL);
    2498:   for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = -PetscGlobalRank-i;
    2499:   PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_FALSE);
    2500:   for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = 1;
    2501:   PCBDDCBenignGetOrSetP0(pc,pcis->vec1_global,PETSC_TRUE);
    2502:   for (i=0;i<pcbddc->benign_n;i++) {
    2503:     PetscInt val = PetscRealPart(pcbddc->benign_p0[i]);
    2505:   }
    2506:   return 0;
    2507: }

    2509: PetscErrorCode PCBDDCBenignDetectSaddlePoint(PC pc, PetscBool reuse, IS *zerodiaglocal)
    2510: {
    2511:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
    2512:   Mat_IS*        matis = (Mat_IS*)(pc->pmat->data);
    2513:   IS             pressures = NULL,zerodiag = NULL,*bzerodiag = NULL,zerodiag_save,*zerodiag_subs;
    2514:   PetscInt       nz,n,benign_n,bsp = 1;
    2515:   PetscInt       *interior_dofs,n_interior_dofs,nneu;
    2516:   PetscBool      sorted,have_null,has_null_pressures,recompute_zerodiag,checkb;

    2519:   if (reuse) goto project_b0;
    2520:   PetscSFDestroy(&pcbddc->benign_sf);
    2521:   MatDestroy(&pcbddc->benign_B0);
    2522:   for (n=0;n<pcbddc->benign_n;n++) {
    2523:     ISDestroy(&pcbddc->benign_zerodiag_subs[n]);
    2524:   }
    2525:   PetscFree(pcbddc->benign_zerodiag_subs);
    2526:   has_null_pressures = PETSC_TRUE;
    2527:   have_null = PETSC_TRUE;
    2528:   /* if a local information on dofs is present, gets pressure dofs from command line (uses the last field is not provided)
    2529:      Without local information, it uses only the zerodiagonal dofs (ok if the pressure block is all zero and it is a scalar field)
    2530:      Checks if all the pressure dofs in each subdomain have a zero diagonal
    2531:      If not, a change of basis on pressures is not needed
    2532:      since the local Schur complements are already SPD
    2533:   */
    2534:   if (pcbddc->n_ISForDofsLocal) {
    2535:     IS        iP = NULL;
    2536:     PetscInt  p,*pp;
    2537:     PetscBool flg;

    2539:     PetscMalloc1(pcbddc->n_ISForDofsLocal,&pp);
    2540:     n    = pcbddc->n_ISForDofsLocal;
    2541:     PetscOptionsBegin(PetscObjectComm((PetscObject)pc),((PetscObject)pc)->prefix,"BDDC benign options","PC");
    2542:     PetscOptionsIntArray("-pc_bddc_pressure_field","Field id for pressures",NULL,pp,&n,&flg);
    2543:     PetscOptionsEnd();
    2544:     if (!flg) {
    2545:       n = 1;
    2546:       pp[0] = pcbddc->n_ISForDofsLocal-1;
    2547:     }

    2549:     bsp = 0;
    2550:     for (p=0;p<n;p++) {
    2551:       PetscInt bs;

    2554:       ISGetBlockSize(pcbddc->ISForDofsLocal[pp[p]],&bs);
    2555:       bsp += bs;
    2556:     }
    2557:     PetscMalloc1(bsp,&bzerodiag);
    2558:     bsp  = 0;
    2559:     for (p=0;p<n;p++) {
    2560:       const PetscInt *idxs;
    2561:       PetscInt       b,bs,npl,*bidxs;

    2563:       ISGetBlockSize(pcbddc->ISForDofsLocal[pp[p]],&bs);
    2564:       ISGetLocalSize(pcbddc->ISForDofsLocal[pp[p]],&npl);
    2565:       ISGetIndices(pcbddc->ISForDofsLocal[pp[p]],&idxs);
    2566:       PetscMalloc1(npl/bs,&bidxs);
    2567:       for (b=0;b<bs;b++) {
    2568:         PetscInt i;

    2570:         for (i=0;i<npl/bs;i++) bidxs[i] = idxs[bs*i+b];
    2571:         ISCreateGeneral(PETSC_COMM_SELF,npl/bs,bidxs,PETSC_COPY_VALUES,&bzerodiag[bsp]);
    2572:         bsp++;
    2573:       }
    2574:       PetscFree(bidxs);
    2575:       ISRestoreIndices(pcbddc->ISForDofsLocal[pp[p]],&idxs);
    2576:     }
    2577:     ISConcatenate(PETSC_COMM_SELF,bsp,bzerodiag,&pressures);

    2579:     /* remove zeroed out pressures if we are setting up a BDDC solver for a saddle-point FETI-DP */
    2580:     PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lP",(PetscObject*)&iP);
    2581:     if (iP) {
    2582:       IS newpressures;

    2584:       ISDifference(pressures,iP,&newpressures);
    2585:       ISDestroy(&pressures);
    2586:       pressures = newpressures;
    2587:     }
    2588:     ISSorted(pressures,&sorted);
    2589:     if (!sorted) {
    2590:       ISSort(pressures);
    2591:     }
    2592:     PetscFree(pp);
    2593:   }

    2595:   /* pcis has not been setup yet, so get the local size from the subdomain matrix */
    2596:   MatGetLocalSize(pcbddc->local_mat,&n,NULL);
    2597:   if (!n) pcbddc->benign_change_explicit = PETSC_TRUE;
    2598:   MatFindZeroDiagonals(pcbddc->local_mat,&zerodiag);
    2599:   ISSorted(zerodiag,&sorted);
    2600:   if (!sorted) {
    2601:     ISSort(zerodiag);
    2602:   }
    2603:   PetscObjectReference((PetscObject)zerodiag);
    2604:   zerodiag_save = zerodiag;
    2605:   ISGetLocalSize(zerodiag,&nz);
    2606:   if (!nz) {
    2607:     if (n) have_null = PETSC_FALSE;
    2608:     has_null_pressures = PETSC_FALSE;
    2609:     ISDestroy(&zerodiag);
    2610:   }
    2611:   recompute_zerodiag = PETSC_FALSE;

    2613:   /* in case disconnected subdomains info is present, split the pressures accordingly (otherwise the benign trick could fail) */
    2614:   zerodiag_subs    = NULL;
    2615:   benign_n         = 0;
    2616:   n_interior_dofs  = 0;
    2617:   interior_dofs    = NULL;
    2618:   nneu             = 0;
    2619:   if (pcbddc->NeumannBoundariesLocal) {
    2620:     ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&nneu);
    2621:   }
    2622:   checkb = (PetscBool)(!pcbddc->NeumannBoundariesLocal || pcbddc->current_level);
    2623:   if (checkb) { /* need to compute interior nodes */
    2624:     PetscInt n,i,j;
    2625:     PetscInt n_neigh,*neigh,*n_shared,**shared;
    2626:     PetscInt *iwork;

    2628:     ISLocalToGlobalMappingGetSize(matis->rmapping,&n);
    2629:     ISLocalToGlobalMappingGetInfo(matis->rmapping,&n_neigh,&neigh,&n_shared,&shared);
    2630:     PetscCalloc1(n,&iwork);
    2631:     PetscMalloc1(n,&interior_dofs);
    2632:     for (i=1;i<n_neigh;i++)
    2633:       for (j=0;j<n_shared[i];j++)
    2634:           iwork[shared[i][j]] += 1;
    2635:     for (i=0;i<n;i++)
    2636:       if (!iwork[i])
    2637:         interior_dofs[n_interior_dofs++] = i;
    2638:     PetscFree(iwork);
    2639:     ISLocalToGlobalMappingRestoreInfo(matis->rmapping,&n_neigh,&neigh,&n_shared,&shared);
    2640:   }
    2641:   if (has_null_pressures) {
    2642:     IS             *subs;
    2643:     PetscInt       nsubs,i,j,nl;
    2644:     const PetscInt *idxs;
    2645:     PetscScalar    *array;
    2646:     Vec            *work;

    2648:     subs  = pcbddc->local_subs;
    2649:     nsubs = pcbddc->n_local_subs;
    2650:     /* 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) */
    2651:     if (checkb) {
    2652:       VecDuplicateVecs(matis->y,2,&work);
    2653:       ISGetLocalSize(zerodiag,&nl);
    2654:       ISGetIndices(zerodiag,&idxs);
    2655:       /* work[0] = 1_p */
    2656:       VecSet(work[0],0.);
    2657:       VecGetArray(work[0],&array);
    2658:       for (j=0;j<nl;j++) array[idxs[j]] = 1.;
    2659:       VecRestoreArray(work[0],&array);
    2660:       /* work[0] = 1_v */
    2661:       VecSet(work[1],1.);
    2662:       VecGetArray(work[1],&array);
    2663:       for (j=0;j<nl;j++) array[idxs[j]] = 0.;
    2664:       VecRestoreArray(work[1],&array);
    2665:       ISRestoreIndices(zerodiag,&idxs);
    2666:     }

    2668:     if (nsubs > 1 || bsp > 1) {
    2669:       IS       *is;
    2670:       PetscInt b,totb;

    2672:       totb  = bsp;
    2673:       is    = bsp > 1 ? bzerodiag : &zerodiag;
    2674:       nsubs = PetscMax(nsubs,1);
    2675:       PetscCalloc1(nsubs*totb,&zerodiag_subs);
    2676:       for (b=0;b<totb;b++) {
    2677:         for (i=0;i<nsubs;i++) {
    2678:           ISLocalToGlobalMapping l2g;
    2679:           IS                     t_zerodiag_subs;
    2680:           PetscInt               nl;

    2682:           if (subs) {
    2683:             ISLocalToGlobalMappingCreateIS(subs[i],&l2g);
    2684:           } else {
    2685:             IS tis;

    2687:             MatGetLocalSize(pcbddc->local_mat,&nl,NULL);
    2688:             ISCreateStride(PETSC_COMM_SELF,nl,0,1,&tis);
    2689:             ISLocalToGlobalMappingCreateIS(tis,&l2g);
    2690:             ISDestroy(&tis);
    2691:           }
    2692:           ISGlobalToLocalMappingApplyIS(l2g,IS_GTOLM_DROP,is[b],&t_zerodiag_subs);
    2693:           ISGetLocalSize(t_zerodiag_subs,&nl);
    2694:           if (nl) {
    2695:             PetscBool valid = PETSC_TRUE;

    2697:             if (checkb) {
    2698:               VecSet(matis->x,0);
    2699:               ISGetLocalSize(subs[i],&nl);
    2700:               ISGetIndices(subs[i],&idxs);
    2701:               VecGetArray(matis->x,&array);
    2702:               for (j=0;j<nl;j++) array[idxs[j]] = 1.;
    2703:               VecRestoreArray(matis->x,&array);
    2704:               ISRestoreIndices(subs[i],&idxs);
    2705:               VecPointwiseMult(matis->x,work[0],matis->x);
    2706:               MatMult(matis->A,matis->x,matis->y);
    2707:               VecPointwiseMult(matis->y,work[1],matis->y);
    2708:               VecGetArray(matis->y,&array);
    2709:               for (j=0;j<n_interior_dofs;j++) {
    2710:                 if (PetscAbsScalar(array[interior_dofs[j]]) > PETSC_SMALL) {
    2711:                   valid = PETSC_FALSE;
    2712:                   break;
    2713:                 }
    2714:               }
    2715:               VecRestoreArray(matis->y,&array);
    2716:             }
    2717:             if (valid && nneu) {
    2718:               const PetscInt *idxs;
    2719:               PetscInt       nzb;

    2721:               ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);
    2722:               ISGlobalToLocalMappingApply(l2g,IS_GTOLM_DROP,nneu,idxs,&nzb,NULL);
    2723:               ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);
    2724:               if (nzb) valid = PETSC_FALSE;
    2725:             }
    2726:             if (valid && pressures) {
    2727:               IS       t_pressure_subs,tmp;
    2728:               PetscInt i1,i2;

    2730:               ISGlobalToLocalMappingApplyIS(l2g,IS_GTOLM_DROP,pressures,&t_pressure_subs);
    2731:               ISEmbed(t_zerodiag_subs,t_pressure_subs,PETSC_TRUE,&tmp);
    2732:               ISGetLocalSize(tmp,&i1);
    2733:               ISGetLocalSize(t_zerodiag_subs,&i2);
    2734:               if (i2 != i1) valid = PETSC_FALSE;
    2735:               ISDestroy(&t_pressure_subs);
    2736:               ISDestroy(&tmp);
    2737:             }
    2738:             if (valid) {
    2739:               ISLocalToGlobalMappingApplyIS(l2g,t_zerodiag_subs,&zerodiag_subs[benign_n]);
    2740:               benign_n++;
    2741:             } else recompute_zerodiag = PETSC_TRUE;
    2742:           }
    2743:           ISDestroy(&t_zerodiag_subs);
    2744:           ISLocalToGlobalMappingDestroy(&l2g);
    2745:         }
    2746:       }
    2747:     } else { /* there's just one subdomain (or zero if they have not been detected */
    2748:       PetscBool valid = PETSC_TRUE;

    2750:       if (nneu) valid = PETSC_FALSE;
    2751:       if (valid && pressures) {
    2752:         ISEqual(pressures,zerodiag,&valid);
    2753:       }
    2754:       if (valid && checkb) {
    2755:         MatMult(matis->A,work[0],matis->x);
    2756:         VecPointwiseMult(matis->x,work[1],matis->x);
    2757:         VecGetArray(matis->x,&array);
    2758:         for (j=0;j<n_interior_dofs;j++) {
    2759:           if (PetscAbsScalar(array[interior_dofs[j]]) > PETSC_SMALL) {
    2760:             valid = PETSC_FALSE;
    2761:             break;
    2762:           }
    2763:         }
    2764:         VecRestoreArray(matis->x,&array);
    2765:       }
    2766:       if (valid) {
    2767:         benign_n = 1;
    2768:         PetscMalloc1(benign_n,&zerodiag_subs);
    2769:         PetscObjectReference((PetscObject)zerodiag);
    2770:         zerodiag_subs[0] = zerodiag;
    2771:       }
    2772:     }
    2773:     if (checkb) {
    2774:       VecDestroyVecs(2,&work);
    2775:     }
    2776:   }
    2777:   PetscFree(interior_dofs);

    2779:   if (!benign_n) {
    2780:     PetscInt n;

    2782:     ISDestroy(&zerodiag);
    2783:     recompute_zerodiag = PETSC_FALSE;
    2784:     MatGetLocalSize(pcbddc->local_mat,&n,NULL);
    2785:     if (n) have_null = PETSC_FALSE;
    2786:   }

    2788:   /* final check for null pressures */
    2789:   if (zerodiag && pressures) {
    2790:     ISEqual(pressures,zerodiag,&have_null);
    2791:   }

    2793:   if (recompute_zerodiag) {
    2794:     ISDestroy(&zerodiag);
    2795:     if (benign_n == 1) {
    2796:       PetscObjectReference((PetscObject)zerodiag_subs[0]);
    2797:       zerodiag = zerodiag_subs[0];
    2798:     } else {
    2799:       PetscInt i,nzn,*new_idxs;

    2801:       nzn = 0;
    2802:       for (i=0;i<benign_n;i++) {
    2803:         PetscInt ns;
    2804:         ISGetLocalSize(zerodiag_subs[i],&ns);
    2805:         nzn += ns;
    2806:       }
    2807:       PetscMalloc1(nzn,&new_idxs);
    2808:       nzn = 0;
    2809:       for (i=0;i<benign_n;i++) {
    2810:         PetscInt ns,*idxs;
    2811:         ISGetLocalSize(zerodiag_subs[i],&ns);
    2812:         ISGetIndices(zerodiag_subs[i],(const PetscInt**)&idxs);
    2813:         PetscArraycpy(new_idxs+nzn,idxs,ns);
    2814:         ISRestoreIndices(zerodiag_subs[i],(const PetscInt**)&idxs);
    2815:         nzn += ns;
    2816:       }
    2817:       PetscSortInt(nzn,new_idxs);
    2818:       ISCreateGeneral(PETSC_COMM_SELF,nzn,new_idxs,PETSC_OWN_POINTER,&zerodiag);
    2819:     }
    2820:     have_null = PETSC_FALSE;
    2821:   }

    2823:   /* determines if the coarse solver will be singular or not */
    2824:   MPIU_Allreduce(&have_null,&pcbddc->benign_null,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));

    2826:   /* Prepare matrix to compute no-net-flux */
    2827:   if (pcbddc->compute_nonetflux && !pcbddc->divudotp) {
    2828:     Mat                    A,loc_divudotp;
    2829:     ISLocalToGlobalMapping rl2g,cl2g,l2gmap;
    2830:     IS                     row,col,isused = NULL;
    2831:     PetscInt               M,N,n,st,n_isused;

    2833:     if (pressures) {
    2834:       isused = pressures;
    2835:     } else {
    2836:       isused = zerodiag_save;
    2837:     }
    2838:     MatISGetLocalToGlobalMapping(pc->pmat,&l2gmap,NULL);
    2839:     MatISGetLocalMat(pc->pmat,&A);
    2840:     MatGetLocalSize(A,&n,NULL);
    2842:     n_isused = 0;
    2843:     if (isused) {
    2844:       ISGetLocalSize(isused,&n_isused);
    2845:     }
    2846:     MPI_Scan(&n_isused,&st,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
    2847:     st = st-n_isused;
    2848:     if (n) {
    2849:       const PetscInt *gidxs;

    2851:       MatCreateSubMatrix(A,isused,NULL,MAT_INITIAL_MATRIX,&loc_divudotp);
    2852:       ISLocalToGlobalMappingGetIndices(l2gmap,&gidxs);
    2853:       /* TODO: extend ISCreateStride with st = PETSC_DECIDE */
    2854:       ISCreateStride(PetscObjectComm((PetscObject)pc),n_isused,st,1,&row);
    2855:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),n,gidxs,PETSC_COPY_VALUES,&col);
    2856:       ISLocalToGlobalMappingRestoreIndices(l2gmap,&gidxs);
    2857:     } else {
    2858:       MatCreateSeqAIJ(PETSC_COMM_SELF,0,0,1,NULL,&loc_divudotp);
    2859:       ISCreateStride(PetscObjectComm((PetscObject)pc),n_isused,st,1,&row);
    2860:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),0,NULL,PETSC_COPY_VALUES,&col);
    2861:     }
    2862:     MatGetSize(pc->pmat,NULL,&N);
    2863:     ISGetSize(row,&M);
    2864:     ISLocalToGlobalMappingCreateIS(row,&rl2g);
    2865:     ISLocalToGlobalMappingCreateIS(col,&cl2g);
    2866:     ISDestroy(&row);
    2867:     ISDestroy(&col);
    2868:     MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->divudotp);
    2869:     MatSetType(pcbddc->divudotp,MATIS);
    2870:     MatSetSizes(pcbddc->divudotp,PETSC_DECIDE,PETSC_DECIDE,M,N);
    2871:     MatSetLocalToGlobalMapping(pcbddc->divudotp,rl2g,cl2g);
    2872:     ISLocalToGlobalMappingDestroy(&rl2g);
    2873:     ISLocalToGlobalMappingDestroy(&cl2g);
    2874:     MatISSetLocalMat(pcbddc->divudotp,loc_divudotp);
    2875:     MatDestroy(&loc_divudotp);
    2876:     MatAssemblyBegin(pcbddc->divudotp,MAT_FINAL_ASSEMBLY);
    2877:     MatAssemblyEnd(pcbddc->divudotp,MAT_FINAL_ASSEMBLY);
    2878:   }
    2879:   ISDestroy(&zerodiag_save);
    2880:   ISDestroy(&pressures);
    2881:   if (bzerodiag) {
    2882:     PetscInt i;

    2884:     for (i=0;i<bsp;i++) {
    2885:       ISDestroy(&bzerodiag[i]);
    2886:     }
    2887:     PetscFree(bzerodiag);
    2888:   }
    2889:   pcbddc->benign_n = benign_n;
    2890:   pcbddc->benign_zerodiag_subs = zerodiag_subs;

    2892:   /* determines if the problem has subdomains with 0 pressure block */
    2893:   have_null = (PetscBool)(!!pcbddc->benign_n);
    2894:   MPIU_Allreduce(&have_null,&pcbddc->benign_have_null,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));

    2896: project_b0:
    2897:   MatGetLocalSize(pcbddc->local_mat,&n,NULL);
    2898:   /* change of basis and p0 dofs */
    2899:   if (pcbddc->benign_n) {
    2900:     PetscInt i,s,*nnz;

    2902:     /* local change of basis for pressures */
    2903:     MatDestroy(&pcbddc->benign_change);
    2904:     MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat),&pcbddc->benign_change);
    2905:     MatSetType(pcbddc->benign_change,MATAIJ);
    2906:     MatSetSizes(pcbddc->benign_change,n,n,PETSC_DECIDE,PETSC_DECIDE);
    2907:     PetscMalloc1(n,&nnz);
    2908:     for (i=0;i<n;i++) nnz[i] = 1; /* defaults to identity */
    2909:     for (i=0;i<pcbddc->benign_n;i++) {
    2910:       const PetscInt *idxs;
    2911:       PetscInt       nzs,j;

    2913:       ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nzs);
    2914:       ISGetIndices(pcbddc->benign_zerodiag_subs[i],&idxs);
    2915:       for (j=0;j<nzs-1;j++) nnz[idxs[j]] = 2; /* change on pressures */
    2916:       nnz[idxs[nzs-1]] = nzs; /* last local pressure dof in subdomain */
    2917:       ISRestoreIndices(pcbddc->benign_zerodiag_subs[i],&idxs);
    2918:     }
    2919:     MatSeqAIJSetPreallocation(pcbddc->benign_change,0,nnz);
    2920:     MatSetOption(pcbddc->benign_change,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
    2921:     PetscFree(nnz);
    2922:     /* set identity by default */
    2923:     for (i=0;i<n;i++) {
    2924:       MatSetValue(pcbddc->benign_change,i,i,1.,INSERT_VALUES);
    2925:     }
    2926:     PetscFree3(pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx,pcbddc->benign_p0);
    2927:     PetscMalloc3(pcbddc->benign_n,&pcbddc->benign_p0_lidx,pcbddc->benign_n,&pcbddc->benign_p0_gidx,pcbddc->benign_n,&pcbddc->benign_p0);
    2928:     /* set change on pressures */
    2929:     for (s=0;s<pcbddc->benign_n;s++) {
    2930:       PetscScalar    *array;
    2931:       const PetscInt *idxs;
    2932:       PetscInt       nzs;

    2934:       ISGetLocalSize(pcbddc->benign_zerodiag_subs[s],&nzs);
    2935:       ISGetIndices(pcbddc->benign_zerodiag_subs[s],&idxs);
    2936:       for (i=0;i<nzs-1;i++) {
    2937:         PetscScalar vals[2];
    2938:         PetscInt    cols[2];

    2940:         cols[0] = idxs[i];
    2941:         cols[1] = idxs[nzs-1];
    2942:         vals[0] = 1.;
    2943:         vals[1] = 1.;
    2944:         MatSetValues(pcbddc->benign_change,1,cols,2,cols,vals,INSERT_VALUES);
    2945:       }
    2946:       PetscMalloc1(nzs,&array);
    2947:       for (i=0;i<nzs-1;i++) array[i] = -1.;
    2948:       array[nzs-1] = 1.;
    2949:       MatSetValues(pcbddc->benign_change,1,idxs+nzs-1,nzs,idxs,array,INSERT_VALUES);
    2950:       /* store local idxs for p0 */
    2951:       pcbddc->benign_p0_lidx[s] = idxs[nzs-1];
    2952:       ISRestoreIndices(pcbddc->benign_zerodiag_subs[s],&idxs);
    2953:       PetscFree(array);
    2954:     }
    2955:     MatAssemblyBegin(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);
    2956:     MatAssemblyEnd(pcbddc->benign_change,MAT_FINAL_ASSEMBLY);

    2958:     /* project if needed */
    2959:     if (pcbddc->benign_change_explicit) {
    2960:       Mat M;

    2962:       MatPtAP(pcbddc->local_mat,pcbddc->benign_change,MAT_INITIAL_MATRIX,2.0,&M);
    2963:       MatDestroy(&pcbddc->local_mat);
    2964:       MatSeqAIJCompress(M,&pcbddc->local_mat);
    2965:       MatDestroy(&M);
    2966:     }
    2967:     /* store global idxs for p0 */
    2968:     ISLocalToGlobalMappingApply(matis->rmapping,pcbddc->benign_n,pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx);
    2969:   }
    2970:   *zerodiaglocal = zerodiag;
    2971:   return 0;
    2972: }

    2974: PetscErrorCode PCBDDCBenignGetOrSetP0(PC pc, Vec v, PetscBool get)
    2975: {
    2976:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
    2977:   PetscScalar    *array;

    2979:   if (!pcbddc->benign_sf) {
    2980:     PetscSFCreate(PetscObjectComm((PetscObject)pc),&pcbddc->benign_sf);
    2981:     PetscSFSetGraphLayout(pcbddc->benign_sf,pc->pmat->rmap,pcbddc->benign_n,NULL,PETSC_OWN_POINTER,pcbddc->benign_p0_gidx);
    2982:   }
    2983:   if (get) {
    2984:     VecGetArrayRead(v,(const PetscScalar**)&array);
    2985:     PetscSFBcastBegin(pcbddc->benign_sf,MPIU_SCALAR,array,pcbddc->benign_p0,MPI_REPLACE);
    2986:     PetscSFBcastEnd(pcbddc->benign_sf,MPIU_SCALAR,array,pcbddc->benign_p0,MPI_REPLACE);
    2987:     VecRestoreArrayRead(v,(const PetscScalar**)&array);
    2988:   } else {
    2989:     VecGetArray(v,&array);
    2990:     PetscSFReduceBegin(pcbddc->benign_sf,MPIU_SCALAR,pcbddc->benign_p0,array,MPI_REPLACE);
    2991:     PetscSFReduceEnd(pcbddc->benign_sf,MPIU_SCALAR,pcbddc->benign_p0,array,MPI_REPLACE);
    2992:     VecRestoreArray(v,&array);
    2993:   }
    2994:   return 0;
    2995: }

    2997: PetscErrorCode PCBDDCBenignPopOrPushB0(PC pc, PetscBool pop)
    2998: {
    2999:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;

    3001:   /* TODO: add error checking
    3002:     - avoid nested pop (or push) calls.
    3003:     - cannot push before pop.
    3004:     - cannot call this if pcbddc->local_mat is NULL
    3005:   */
    3006:   if (!pcbddc->benign_n) {
    3007:     return 0;
    3008:   }
    3009:   if (pop) {
    3010:     if (pcbddc->benign_change_explicit) {
    3011:       IS       is_p0;
    3012:       MatReuse reuse;

    3014:       /* extract B_0 */
    3015:       reuse = MAT_INITIAL_MATRIX;
    3016:       if (pcbddc->benign_B0) {
    3017:         reuse = MAT_REUSE_MATRIX;
    3018:       }
    3019:       ISCreateGeneral(PETSC_COMM_SELF,pcbddc->benign_n,pcbddc->benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);
    3020:       MatCreateSubMatrix(pcbddc->local_mat,is_p0,NULL,reuse,&pcbddc->benign_B0);
    3021:       /* remove rows and cols from local problem */
    3022:       MatSetOption(pcbddc->local_mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
    3023:       MatSetOption(pcbddc->local_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
    3024:       MatZeroRowsColumnsIS(pcbddc->local_mat,is_p0,1.0,NULL,NULL);
    3025:       ISDestroy(&is_p0);
    3026:     } else {
    3027:       Mat_IS      *matis = (Mat_IS*)pc->pmat->data;
    3028:       PetscScalar *vals;
    3029:       PetscInt    i,n,*idxs_ins;

    3031:       VecGetLocalSize(matis->y,&n);
    3032:       PetscMalloc2(n,&idxs_ins,n,&vals);
    3033:       if (!pcbddc->benign_B0) {
    3034:         PetscInt *nnz;
    3035:         MatCreate(PetscObjectComm((PetscObject)pcbddc->local_mat),&pcbddc->benign_B0);
    3036:         MatSetType(pcbddc->benign_B0,MATAIJ);
    3037:         MatSetSizes(pcbddc->benign_B0,pcbddc->benign_n,n,PETSC_DECIDE,PETSC_DECIDE);
    3038:         PetscMalloc1(pcbddc->benign_n,&nnz);
    3039:         for (i=0;i<pcbddc->benign_n;i++) {
    3040:           ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nnz[i]);
    3041:           nnz[i] = n - nnz[i];
    3042:         }
    3043:         MatSeqAIJSetPreallocation(pcbddc->benign_B0,0,nnz);
    3044:         MatSetOption(pcbddc->benign_B0,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
    3045:         PetscFree(nnz);
    3046:       }

    3048:       for (i=0;i<pcbddc->benign_n;i++) {
    3049:         PetscScalar *array;
    3050:         PetscInt    *idxs,j,nz,cum;

    3052:         VecSet(matis->x,0.);
    3053:         ISGetLocalSize(pcbddc->benign_zerodiag_subs[i],&nz);
    3054:         ISGetIndices(pcbddc->benign_zerodiag_subs[i],(const PetscInt**)&idxs);
    3055:         for (j=0;j<nz;j++) vals[j] = 1.;
    3056:         VecSetValues(matis->x,nz,idxs,vals,INSERT_VALUES);
    3057:         VecAssemblyBegin(matis->x);
    3058:         VecAssemblyEnd(matis->x);
    3059:         VecSet(matis->y,0.);
    3060:         MatMult(matis->A,matis->x,matis->y);
    3061:         VecGetArray(matis->y,&array);
    3062:         cum = 0;
    3063:         for (j=0;j<n;j++) {
    3064:           if (PetscUnlikely(PetscAbsScalar(array[j]) > PETSC_SMALL)) {
    3065:             vals[cum] = array[j];
    3066:             idxs_ins[cum] = j;
    3067:             cum++;
    3068:           }
    3069:         }
    3070:         MatSetValues(pcbddc->benign_B0,1,&i,cum,idxs_ins,vals,INSERT_VALUES);
    3071:         VecRestoreArray(matis->y,&array);
    3072:         ISRestoreIndices(pcbddc->benign_zerodiag_subs[i],(const PetscInt**)&idxs);
    3073:       }
    3074:       MatAssemblyBegin(pcbddc->benign_B0,MAT_FINAL_ASSEMBLY);
    3075:       MatAssemblyEnd(pcbddc->benign_B0,MAT_FINAL_ASSEMBLY);
    3076:       PetscFree2(idxs_ins,vals);
    3077:     }
    3078:   } else { /* push */
    3079:     if (pcbddc->benign_change_explicit) {
    3080:       PetscInt i;

    3082:       for (i=0;i<pcbddc->benign_n;i++) {
    3083:         PetscScalar *B0_vals;
    3084:         PetscInt    *B0_cols,B0_ncol;

    3086:         MatGetRow(pcbddc->benign_B0,i,&B0_ncol,(const PetscInt**)&B0_cols,(const PetscScalar**)&B0_vals);
    3087:         MatSetValues(pcbddc->local_mat,1,pcbddc->benign_p0_lidx+i,B0_ncol,B0_cols,B0_vals,INSERT_VALUES);
    3088:         MatSetValues(pcbddc->local_mat,B0_ncol,B0_cols,1,pcbddc->benign_p0_lidx+i,B0_vals,INSERT_VALUES);
    3089:         MatSetValue(pcbddc->local_mat,pcbddc->benign_p0_lidx[i],pcbddc->benign_p0_lidx[i],0.0,INSERT_VALUES);
    3090:         MatRestoreRow(pcbddc->benign_B0,i,&B0_ncol,(const PetscInt**)&B0_cols,(const PetscScalar**)&B0_vals);
    3091:       }
    3092:       MatAssemblyBegin(pcbddc->local_mat,MAT_FINAL_ASSEMBLY);
    3093:       MatAssemblyEnd(pcbddc->local_mat,MAT_FINAL_ASSEMBLY);
    3094:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cannot push B0!");
    3095:   }
    3096:   return 0;
    3097: }

    3099: PetscErrorCode PCBDDCAdaptiveSelection(PC pc)
    3100: {
    3101:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
    3102:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    3103:   PetscBLASInt    B_dummyint,B_neigs,B_ierr,B_lwork;
    3104:   PetscBLASInt    *B_iwork,*B_ifail;
    3105:   PetscScalar     *work,lwork;
    3106:   PetscScalar     *St,*S,*eigv;
    3107:   PetscScalar     *Sarray,*Starray;
    3108:   PetscReal       *eigs,thresh,lthresh,uthresh;
    3109:   PetscInt        i,nmax,nmin,nv,cum,mss,cum2,cumarray,maxneigs;
    3110:   PetscBool       allocated_S_St;
    3111: #if defined(PETSC_USE_COMPLEX)
    3112:   PetscReal       *rwork;
    3113: #endif
    3114:   PetscErrorCode  ierr;

    3119:   PetscLogEventBegin(PC_BDDC_AdaptiveSetUp[pcbddc->current_level],pc,0,0,0);

    3121:   if (pcbddc->dbg_flag) {
    3122:     PetscViewerFlush(pcbddc->dbg_viewer);
    3123:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    3124:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check adaptive selection of constraints\n");
    3125:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    3126:   }

    3128:   if (pcbddc->dbg_flag) {
    3129:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d cc %D (%d,%d).\n",PetscGlobalRank,sub_schurs->n_subs,sub_schurs->is_hermitian,sub_schurs->is_posdef);
    3130:   }

    3132:   /* max size of subsets */
    3133:   mss = 0;
    3134:   for (i=0;i<sub_schurs->n_subs;i++) {
    3135:     PetscInt subset_size;

    3137:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    3138:     mss = PetscMax(mss,subset_size);
    3139:   }

    3141:   /* min/max and threshold */
    3142:   nmax = pcbddc->adaptive_nmax > 0 ? pcbddc->adaptive_nmax : mss;
    3143:   nmin = pcbddc->adaptive_nmin > 0 ? pcbddc->adaptive_nmin : 0;
    3144:   nmax = PetscMax(nmin,nmax);
    3145:   allocated_S_St = PETSC_FALSE;
    3146:   if (nmin || !sub_schurs->is_posdef) { /* XXX */
    3147:     allocated_S_St = PETSC_TRUE;
    3148:   }

    3150:   /* allocate lapack workspace */
    3151:   cum = cum2 = 0;
    3152:   maxneigs = 0;
    3153:   for (i=0;i<sub_schurs->n_subs;i++) {
    3154:     PetscInt n,subset_size;

    3156:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    3157:     n = PetscMin(subset_size,nmax);
    3158:     cum += subset_size;
    3159:     cum2 += subset_size*n;
    3160:     maxneigs = PetscMax(maxneigs,n);
    3161:   }
    3162:   lwork = 0;
    3163:   if (mss) {
    3164:     if (sub_schurs->is_symmetric) {
    3165:       PetscScalar  sdummy = 0.;
    3166:       PetscBLASInt B_itype = 1;
    3167:       PetscBLASInt B_N = mss, idummy = 0;
    3168:       PetscReal    rdummy = 0.,zero = 0.0;
    3169:       PetscReal    eps = 0.0; /* dlamch? */

    3171:       B_lwork = -1;
    3172:       /* some implementations may complain about NULL pointers, even if we are querying */
    3173:       S = &sdummy;
    3174:       St = &sdummy;
    3175:       eigs = &rdummy;
    3176:       eigv = &sdummy;
    3177:       B_iwork = &idummy;
    3178:       B_ifail = &idummy;
    3179: #if defined(PETSC_USE_COMPLEX)
    3180:       rwork = &rdummy;
    3181: #endif
    3182:       thresh = 1.0;
    3183:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    3184: #if defined(PETSC_USE_COMPLEX)
    3185:       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));
    3186: #else
    3187:       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));
    3188: #endif
    3190:       PetscFPTrapPop();
    3191:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented");
    3192:   }

    3194:   nv = 0;
    3195:   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) */
    3196:     ISGetLocalSize(sub_schurs->is_vertices,&nv);
    3197:   }
    3198:   PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);
    3199:   if (allocated_S_St) {
    3200:     PetscMalloc2(mss*mss,&S,mss*mss,&St);
    3201:   }
    3202:   PetscMalloc5(mss*mss,&eigv,mss,&eigs,B_lwork,&work,5*mss,&B_iwork,mss,&B_ifail);
    3203: #if defined(PETSC_USE_COMPLEX)
    3204:   PetscMalloc1(7*mss,&rwork);
    3205: #endif
    3206:   PetscMalloc5(nv+sub_schurs->n_subs,&pcbddc->adaptive_constraints_n,
    3207:                       nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_idxs_ptr,
    3208:                       nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_data_ptr,
    3209:                       nv+cum,&pcbddc->adaptive_constraints_idxs,
    3210:                       nv+cum2,&pcbddc->adaptive_constraints_data);
    3211:   PetscArrayzero(pcbddc->adaptive_constraints_n,nv+sub_schurs->n_subs);

    3213:   maxneigs = 0;
    3214:   cum = cumarray = 0;
    3215:   pcbddc->adaptive_constraints_idxs_ptr[0] = 0;
    3216:   pcbddc->adaptive_constraints_data_ptr[0] = 0;
    3217:   if (sub_schurs->is_vertices && pcbddc->use_vertices) {
    3218:     const PetscInt *idxs;

    3220:     ISGetIndices(sub_schurs->is_vertices,&idxs);
    3221:     for (cum=0;cum<nv;cum++) {
    3222:       pcbddc->adaptive_constraints_n[cum] = 1;
    3223:       pcbddc->adaptive_constraints_idxs[cum] = idxs[cum];
    3224:       pcbddc->adaptive_constraints_data[cum] = 1.0;
    3225:       pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum]+1;
    3226:       pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum]+1;
    3227:     }
    3228:     ISRestoreIndices(sub_schurs->is_vertices,&idxs);
    3229:   }

    3231:   if (mss) { /* multilevel */
    3232:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);
    3233:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);
    3234:   }

    3236:   lthresh = pcbddc->adaptive_threshold[0];
    3237:   uthresh = pcbddc->adaptive_threshold[1];
    3238:   for (i=0;i<sub_schurs->n_subs;i++) {
    3239:     const PetscInt *idxs;
    3240:     PetscReal      upper,lower;
    3241:     PetscInt       j,subset_size,eigs_start = 0;
    3242:     PetscBLASInt   B_N;
    3243:     PetscBool      same_data = PETSC_FALSE;
    3244:     PetscBool      scal = PETSC_FALSE;

    3246:     if (pcbddc->use_deluxe_scaling) {
    3247:       upper = PETSC_MAX_REAL;
    3248:       lower = uthresh;
    3249:     } else {
    3251:       upper = 1./uthresh;
    3252:       lower = 0.;
    3253:     }
    3254:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    3255:     ISGetIndices(sub_schurs->is_subs[i],&idxs);
    3256:     PetscBLASIntCast(subset_size,&B_N);
    3257:     /* this is experimental: we assume the dofs have been properly grouped to have
    3258:        the diagonal blocks Schur complements either positive or negative definite (true for Stokes) */
    3259:     if (!sub_schurs->is_posdef) {
    3260:       Mat T;

    3262:       for (j=0;j<subset_size;j++) {
    3263:         if (PetscRealPart(*(Sarray+cumarray+j*(subset_size+1))) < 0.0) {
    3264:           MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,Sarray+cumarray,&T);
    3265:           MatScale(T,-1.0);
    3266:           MatDestroy(&T);
    3267:           MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,Starray+cumarray,&T);
    3268:           MatScale(T,-1.0);
    3269:           MatDestroy(&T);
    3270:           if (sub_schurs->change_primal_sub) {
    3271:             PetscInt       nz,k;
    3272:             const PetscInt *idxs;

    3274:             ISGetLocalSize(sub_schurs->change_primal_sub[i],&nz);
    3275:             ISGetIndices(sub_schurs->change_primal_sub[i],&idxs);
    3276:             for (k=0;k<nz;k++) {
    3277:               *( Sarray + cumarray + idxs[k]*(subset_size+1)) *= -1.0;
    3278:               *(Starray + cumarray + idxs[k]*(subset_size+1))  = 0.0;
    3279:             }
    3280:             ISRestoreIndices(sub_schurs->change_primal_sub[i],&idxs);
    3281:           }
    3282:           scal = PETSC_TRUE;
    3283:           break;
    3284:         }
    3285:       }
    3286:     }

    3288:     if (allocated_S_St) { /* S and S_t should be copied since we could need them later */
    3289:       if (sub_schurs->is_symmetric) {
    3290:         PetscInt j,k;
    3291:         if (sub_schurs->n_subs == 1) { /* zeroing memory to use PetscArraycmp() later */
    3292:           PetscArrayzero(S,subset_size*subset_size);
    3293:           PetscArrayzero(St,subset_size*subset_size);
    3294:         }
    3295:         for (j=0;j<subset_size;j++) {
    3296:           for (k=j;k<subset_size;k++) {
    3297:             S [j*subset_size+k] = Sarray [cumarray+j*subset_size+k];
    3298:             St[j*subset_size+k] = Starray[cumarray+j*subset_size+k];
    3299:           }
    3300:         }
    3301:       } else {
    3302:         PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
    3303:         PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
    3304:       }
    3305:     } else {
    3306:       S = Sarray + cumarray;
    3307:       St = Starray + cumarray;
    3308:     }
    3309:     /* see if we can save some work */
    3310:     if (sub_schurs->n_subs == 1 && pcbddc->use_deluxe_scaling) {
    3311:       PetscArraycmp(S,St,subset_size*subset_size,&same_data);
    3312:     }

    3314:     if (same_data && !sub_schurs->change) { /* there's no need of constraints here */
    3315:       B_neigs = 0;
    3316:     } else {
    3317:       if (sub_schurs->is_symmetric) {
    3318:         PetscBLASInt B_itype = 1;
    3319:         PetscBLASInt B_IL, B_IU;
    3320:         PetscReal    eps = -1.0; /* dlamch? */
    3321:         PetscInt     nmin_s;
    3322:         PetscBool    compute_range;

    3324:         B_neigs = 0;
    3325:         compute_range = (PetscBool)!same_data;
    3326:         if (nmin >= subset_size) compute_range = PETSC_FALSE;

    3328:         if (pcbddc->dbg_flag) {
    3329:           PetscInt nc = 0;

    3331:           if (sub_schurs->change_primal_sub) {
    3332:             ISGetLocalSize(sub_schurs->change_primal_sub[i],&nc);
    3333:           }
    3334:           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);
    3335:         }

    3337:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    3338:         if (compute_range) {

    3340:           /* ask for eigenvalues larger than thresh */
    3341:           if (sub_schurs->is_posdef) {
    3342: #if defined(PETSC_USE_COMPLEX)
    3343:             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));
    3344: #else
    3345:             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));
    3346: #endif
    3347:             PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3348:           } else { /* no theory so far, but it works nicely */
    3349:             PetscInt  recipe = 0,recipe_m = 1;
    3350:             PetscReal bb[2];

    3352:             PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe",&recipe,NULL);
    3353:             switch (recipe) {
    3354:             case 0:
    3355:               if (scal) { bb[0] = PETSC_MIN_REAL; bb[1] = lthresh; }
    3356:               else { bb[0] = uthresh; bb[1] = PETSC_MAX_REAL; }
    3357: #if defined(PETSC_USE_COMPLEX)
    3358:               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));
    3359: #else
    3360:               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));
    3361: #endif
    3362:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3363:               break;
    3364:             case 1:
    3365:               bb[0] = PETSC_MIN_REAL; bb[1] = lthresh*lthresh;
    3366: #if defined(PETSC_USE_COMPLEX)
    3367:               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));
    3368: #else
    3369:               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));
    3370: #endif
    3371:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3372:               if (!scal) {
    3373:                 PetscBLASInt B_neigs2 = 0;

    3375:                 bb[0] = PetscMax(lthresh*lthresh,uthresh); bb[1] = PETSC_MAX_REAL;
    3376:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
    3377:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
    3378: #if defined(PETSC_USE_COMPLEX)
    3379:                 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));
    3380: #else
    3381:                 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));
    3382: #endif
    3383:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3384:                 B_neigs += B_neigs2;
    3385:               }
    3386:               break;
    3387:             case 2:
    3388:               if (scal) {
    3389:                 bb[0] = PETSC_MIN_REAL;
    3390:                 bb[1] = 0;
    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:               } else {
    3398:                 PetscBLASInt B_neigs2 = 0;
    3399:                 PetscBool    import = PETSC_FALSE;

    3401:                 lthresh = PetscMax(lthresh,0.0);
    3402:                 if (lthresh > 0.0) {
    3403:                   bb[0] = PETSC_MIN_REAL;
    3404:                   bb[1] = lthresh*lthresh;

    3406:                   import = PETSC_TRUE;
    3407: #if defined(PETSC_USE_COMPLEX)
    3408:                   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));
    3409: #else
    3410:                   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));
    3411: #endif
    3412:                   PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3413:                 }
    3414:                 bb[0] = PetscMax(lthresh*lthresh,uthresh);
    3415:                 bb[1] = PETSC_MAX_REAL;
    3416:                 if (import) {
    3417:                   PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
    3418:                   PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
    3419:                 }
    3420: #if defined(PETSC_USE_COMPLEX)
    3421:                 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));
    3422: #else
    3423:                 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));
    3424: #endif
    3425:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3426:                 B_neigs += B_neigs2;
    3427:               }
    3428:               break;
    3429:             case 3:
    3430:               if (scal) {
    3431:                 PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe3_min_scal",&recipe_m,NULL);
    3432:               } else {
    3433:                 PetscOptionsGetInt(NULL,((PetscObject)pc)->prefix,"-pc_bddc_adaptive_recipe3_min",&recipe_m,NULL);
    3434:               }
    3435:               if (!scal) {
    3436:                 bb[0] = uthresh;
    3437:                 bb[1] = PETSC_MAX_REAL;
    3438: #if defined(PETSC_USE_COMPLEX)
    3439:                 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));
    3440: #else
    3441:                 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));
    3442: #endif
    3443:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3444:               }
    3445:               if (recipe_m > 0 && B_N - B_neigs > 0) {
    3446:                 PetscBLASInt B_neigs2 = 0;

    3448:                 B_IL = 1;
    3449:                 PetscBLASIntCast(PetscMin(recipe_m,B_N - B_neigs),&B_IU);
    3450:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
    3451:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
    3452: #if defined(PETSC_USE_COMPLEX)
    3453:                 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));
    3454: #else
    3455:                 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));
    3456: #endif
    3457:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3458:                 B_neigs += B_neigs2;
    3459:               }
    3460:               break;
    3461:             case 4:
    3462:               bb[0] = PETSC_MIN_REAL; bb[1] = lthresh;
    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:                 PetscBLASInt B_neigs2 = 0;

    3472:                 bb[0] = PetscMax(lthresh+PETSC_SMALL,uthresh); bb[1] = PETSC_MAX_REAL;
    3473:                 PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
    3474:                 PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
    3475: #if defined(PETSC_USE_COMPLEX)
    3476:                 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));
    3477: #else
    3478:                 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));
    3479: #endif
    3480:                 PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3481:                 B_neigs += B_neigs2;
    3482:               }
    3483:               break;
    3484:             case 5: /* same as before: first compute all eigenvalues, then filter */
    3485: #if defined(PETSC_USE_COMPLEX)
    3486:               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));
    3487: #else
    3488:               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));
    3489: #endif
    3490:               PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3491:               {
    3492:                 PetscInt e,k,ne;
    3493:                 for (e=0,ne=0;e<B_neigs;e++) {
    3494:                   if (eigs[e] < lthresh || eigs[e] > uthresh) {
    3495:                     for (k=0;k<B_N;k++) S[ne*B_N+k] = eigv[e*B_N+k];
    3496:                     eigs[ne] = eigs[e];
    3497:                     ne++;
    3498:                   }
    3499:                 }
    3500:                 PetscArraycpy(eigv,S,B_N*ne);
    3501:                 B_neigs = ne;
    3502:               }
    3503:               break;
    3504:             default:
    3505:               SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Unknown recipe %D",recipe);
    3506:             }
    3507:           }
    3508:         } else if (!same_data) { /* this is just to see all the eigenvalues */
    3509:           B_IU = PetscMax(1,PetscMin(B_N,nmax));
    3510:           B_IL = 1;
    3511: #if defined(PETSC_USE_COMPLEX)
    3512:           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));
    3513: #else
    3514:           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));
    3515: #endif
    3516:           PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3517:         } else { /* same_data is true, so just get the adaptive functional requested by the user */
    3518:           PetscInt k;
    3520:           ISGetLocalSize(sub_schurs->change_primal_sub[i],&nmax);
    3521:           PetscBLASIntCast(nmax,&B_neigs);
    3522:           nmin = nmax;
    3523:           PetscArrayzero(eigv,subset_size*nmax);
    3524:           for (k=0;k<nmax;k++) {
    3525:             eigs[k] = 1./PETSC_SMALL;
    3526:             eigv[k*(subset_size+1)] = 1.0;
    3527:           }
    3528:         }
    3529:         PetscFPTrapPop();
    3530:         if (B_ierr) {
    3533:           else SETERRQ(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);
    3534:         }

    3536:         if (B_neigs > nmax) {
    3537:           if (pcbddc->dbg_flag) {
    3538:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, more than maximum required %D.\n",B_neigs,nmax);
    3539:           }
    3540:           if (pcbddc->use_deluxe_scaling) eigs_start = scal ? 0 : B_neigs-nmax;
    3541:           B_neigs = nmax;
    3542:         }

    3544:         nmin_s = PetscMin(nmin,B_N);
    3545:         if (B_neigs < nmin_s) {
    3546:           PetscBLASInt B_neigs2 = 0;

    3548:           if (pcbddc->use_deluxe_scaling) {
    3549:             if (scal) {
    3550:               B_IU = nmin_s;
    3551:               B_IL = B_neigs + 1;
    3552:             } else {
    3553:               B_IL = B_N - nmin_s + 1;
    3554:               B_IU = B_N - B_neigs;
    3555:             }
    3556:           } else {
    3557:             B_IL = B_neigs + 1;
    3558:             B_IU = nmin_s;
    3559:           }
    3560:           if (pcbddc->dbg_flag) {
    3561:             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);
    3562:           }
    3563:           if (sub_schurs->is_symmetric) {
    3564:             PetscInt j,k;
    3565:             for (j=0;j<subset_size;j++) {
    3566:               for (k=j;k<subset_size;k++) {
    3567:                 S [j*subset_size+k] = Sarray [cumarray+j*subset_size+k];
    3568:                 St[j*subset_size+k] = Starray[cumarray+j*subset_size+k];
    3569:               }
    3570:             }
    3571:           } else {
    3572:             PetscArraycpy(S,Sarray+cumarray,subset_size*subset_size);
    3573:             PetscArraycpy(St,Starray+cumarray,subset_size*subset_size);
    3574:           }
    3575:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    3576: #if defined(PETSC_USE_COMPLEX)
    3577:           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));
    3578: #else
    3579:           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));
    3580: #endif
    3581:           PetscLogFlops((4.0*subset_size*subset_size*subset_size)/3.0);
    3582:           PetscFPTrapPop();
    3583:           B_neigs += B_neigs2;
    3584:         }
    3585:         if (B_ierr) {
    3588:           else SETERRQ(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);
    3589:         }
    3590:         if (pcbddc->dbg_flag) {
    3591:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Got %d eigs\n",B_neigs);
    3592:           for (j=0;j<B_neigs;j++) {
    3593:             if (eigs[j] == 0.0) {
    3594:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     Inf\n");
    3595:             } else {
    3596:               if (pcbddc->use_deluxe_scaling) {
    3597:                 PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",eigs[j+eigs_start]);
    3598:               } else {
    3599:                 PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",1./eigs[j+eigs_start]);
    3600:               }
    3601:             }
    3602:           }
    3603:         }
    3604:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented");
    3605:     }
    3606:     /* change the basis back to the original one */
    3607:     if (sub_schurs->change) {
    3608:       Mat change,phi,phit;

    3610:       if (pcbddc->dbg_flag > 2) {
    3611:         PetscInt ii;
    3612:         for (ii=0;ii<B_neigs;ii++) {
    3613:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector (old basis) %d/%d (%d)\n",ii,B_neigs,B_N);
    3614:           for (j=0;j<B_N;j++) {
    3615: #if defined(PETSC_USE_COMPLEX)
    3616:             PetscReal r = PetscRealPart(eigv[(ii+eigs_start)*subset_size+j]);
    3617:             PetscReal c = PetscImaginaryPart(eigv[(ii+eigs_start)*subset_size+j]);
    3618:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e + %1.4e i\n",r,c);
    3619: #else
    3620:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",eigv[(ii+eigs_start)*subset_size+j]);
    3621: #endif
    3622:           }
    3623:         }
    3624:       }
    3625:       KSPGetOperators(sub_schurs->change[i],&change,NULL);
    3626:       MatCreateSeqDense(PETSC_COMM_SELF,subset_size,B_neigs,eigv+eigs_start*subset_size,&phit);
    3627:       MatMatMult(change,phit,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&phi);
    3628:       MatCopy(phi,phit,SAME_NONZERO_PATTERN);
    3629:       MatDestroy(&phit);
    3630:       MatDestroy(&phi);
    3631:     }
    3632:     maxneigs = PetscMax(B_neigs,maxneigs);
    3633:     pcbddc->adaptive_constraints_n[i+nv] = B_neigs;
    3634:     if (B_neigs) {
    3635:       PetscArraycpy(pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum],eigv+eigs_start*subset_size,B_neigs*subset_size);

    3637:       if (pcbddc->dbg_flag > 1) {
    3638:         PetscInt ii;
    3639:         for (ii=0;ii<B_neigs;ii++) {
    3640:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector %d/%d (%d)\n",ii,B_neigs,B_N);
    3641:           for (j=0;j<B_N;j++) {
    3642: #if defined(PETSC_USE_COMPLEX)
    3643:             PetscReal r = PetscRealPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
    3644:             PetscReal c = PetscImaginaryPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
    3645:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e + %1.4e i\n",r,c);
    3646: #else
    3647:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
    3648: #endif
    3649:           }
    3650:         }
    3651:       }
    3652:       PetscArraycpy(pcbddc->adaptive_constraints_idxs+pcbddc->adaptive_constraints_idxs_ptr[cum],idxs,subset_size);
    3653:       pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum] + subset_size;
    3654:       pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum] + subset_size*B_neigs;
    3655:       cum++;
    3656:     }
    3657:     ISRestoreIndices(sub_schurs->is_subs[i],&idxs);
    3658:     /* shift for next computation */
    3659:     cumarray += subset_size*subset_size;
    3660:   }
    3661:   if (pcbddc->dbg_flag) {
    3662:     PetscViewerFlush(pcbddc->dbg_viewer);
    3663:   }

    3665:   if (mss) {
    3666:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);
    3667:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);
    3668:     /* destroy matrices (junk) */
    3669:     MatDestroy(&sub_schurs->sum_S_Ej_inv_all);
    3670:     MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);
    3671:   }
    3672:   if (allocated_S_St) {
    3673:     PetscFree2(S,St);
    3674:   }
    3675:   PetscFree5(eigv,eigs,work,B_iwork,B_ifail);
    3676: #if defined(PETSC_USE_COMPLEX)
    3677:   PetscFree(rwork);
    3678: #endif
    3679:   if (pcbddc->dbg_flag) {
    3680:     PetscInt maxneigs_r;
    3681:     MPIU_Allreduce(&maxneigs,&maxneigs_r,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));
    3682:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of constraints per cc %D\n",maxneigs_r);
    3683:   }
    3684:   PetscLogEventEnd(PC_BDDC_AdaptiveSetUp[pcbddc->current_level],pc,0,0,0);
    3685:   return 0;
    3686: }

    3688: PetscErrorCode PCBDDCSetUpSolvers(PC pc)
    3689: {
    3690:   PetscScalar    *coarse_submat_vals;

    3692:   /* Setup local scatters R_to_B and (optionally) R_to_D */
    3693:   /* PCBDDCSetUpLocalWorkVectors should be called first! */
    3694:   PCBDDCSetUpLocalScatters(pc);

    3696:   /* Setup local neumann solver ksp_R */
    3697:   /* PCBDDCSetUpLocalScatters should be called first! */
    3698:   PCBDDCSetUpLocalSolvers(pc,PETSC_FALSE,PETSC_TRUE);

    3700:   /*
    3701:      Setup local correction and local part of coarse basis.
    3702:      Gives back the dense local part of the coarse matrix in column major ordering
    3703:   */
    3704:   PCBDDCSetUpCorrection(pc,&coarse_submat_vals);

    3706:   /* Compute total number of coarse nodes and setup coarse solver */
    3707:   PCBDDCSetUpCoarseSolver(pc,coarse_submat_vals);

    3709:   /* free */
    3710:   PetscFree(coarse_submat_vals);
    3711:   return 0;
    3712: }

    3714: PetscErrorCode PCBDDCResetCustomization(PC pc)
    3715: {
    3716:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

    3718:   ISDestroy(&pcbddc->user_primal_vertices);
    3719:   ISDestroy(&pcbddc->user_primal_vertices_local);
    3720:   ISDestroy(&pcbddc->NeumannBoundaries);
    3721:   ISDestroy(&pcbddc->NeumannBoundariesLocal);
    3722:   ISDestroy(&pcbddc->DirichletBoundaries);
    3723:   MatNullSpaceDestroy(&pcbddc->onearnullspace);
    3724:   PetscFree(pcbddc->onearnullvecs_state);
    3725:   ISDestroy(&pcbddc->DirichletBoundariesLocal);
    3726:   PCBDDCSetDofsSplitting(pc,0,NULL);
    3727:   PCBDDCSetDofsSplittingLocal(pc,0,NULL);
    3728:   return 0;
    3729: }

    3731: PetscErrorCode PCBDDCResetTopography(PC pc)
    3732: {
    3733:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
    3734:   PetscInt       i;

    3736:   MatDestroy(&pcbddc->nedcG);
    3737:   ISDestroy(&pcbddc->nedclocal);
    3738:   MatDestroy(&pcbddc->discretegradient);
    3739:   MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);
    3740:   MatDestroy(&pcbddc->ChangeOfBasisMatrix);
    3741:   MatDestroy(&pcbddc->switch_static_change);
    3742:   VecDestroy(&pcbddc->work_change);
    3743:   MatDestroy(&pcbddc->ConstraintMatrix);
    3744:   MatDestroy(&pcbddc->divudotp);
    3745:   ISDestroy(&pcbddc->divudotp_vl2l);
    3746:   PCBDDCGraphDestroy(&pcbddc->mat_graph);
    3747:   for (i=0;i<pcbddc->n_local_subs;i++) {
    3748:     ISDestroy(&pcbddc->local_subs[i]);
    3749:   }
    3750:   pcbddc->n_local_subs = 0;
    3751:   PetscFree(pcbddc->local_subs);
    3752:   PCBDDCSubSchursDestroy(&pcbddc->sub_schurs);
    3753:   pcbddc->graphanalyzed        = PETSC_FALSE;
    3754:   pcbddc->recompute_topography = PETSC_TRUE;
    3755:   pcbddc->corner_selected      = PETSC_FALSE;
    3756:   return 0;
    3757: }

    3759: PetscErrorCode PCBDDCResetSolvers(PC pc)
    3760: {
    3761:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

    3763:   VecDestroy(&pcbddc->coarse_vec);
    3764:   if (pcbddc->coarse_phi_B) {
    3765:     PetscScalar *array;
    3766:     MatDenseGetArray(pcbddc->coarse_phi_B,&array);
    3767:     PetscFree(array);
    3768:   }
    3769:   MatDestroy(&pcbddc->coarse_phi_B);
    3770:   MatDestroy(&pcbddc->coarse_phi_D);
    3771:   MatDestroy(&pcbddc->coarse_psi_B);
    3772:   MatDestroy(&pcbddc->coarse_psi_D);
    3773:   VecDestroy(&pcbddc->vec1_P);
    3774:   VecDestroy(&pcbddc->vec1_C);
    3775:   MatDestroy(&pcbddc->local_auxmat2);
    3776:   MatDestroy(&pcbddc->local_auxmat1);
    3777:   VecDestroy(&pcbddc->vec1_R);
    3778:   VecDestroy(&pcbddc->vec2_R);
    3779:   ISDestroy(&pcbddc->is_R_local);
    3780:   VecScatterDestroy(&pcbddc->R_to_B);
    3781:   VecScatterDestroy(&pcbddc->R_to_D);
    3782:   VecScatterDestroy(&pcbddc->coarse_loc_to_glob);
    3783:   KSPReset(pcbddc->ksp_D);
    3784:   KSPReset(pcbddc->ksp_R);
    3785:   KSPReset(pcbddc->coarse_ksp);
    3786:   MatDestroy(&pcbddc->local_mat);
    3787:   PetscFree(pcbddc->primal_indices_local_idxs);
    3788:   PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);
    3789:   PetscFree(pcbddc->global_primal_indices);
    3790:   ISDestroy(&pcbddc->coarse_subassembling);
    3791:   MatDestroy(&pcbddc->benign_change);
    3792:   VecDestroy(&pcbddc->benign_vec);
    3793:   PCBDDCBenignShellMat(pc,PETSC_TRUE);
    3794:   MatDestroy(&pcbddc->benign_B0);
    3795:   PetscSFDestroy(&pcbddc->benign_sf);
    3796:   if (pcbddc->benign_zerodiag_subs) {
    3797:     PetscInt i;
    3798:     for (i=0;i<pcbddc->benign_n;i++) {
    3799:       ISDestroy(&pcbddc->benign_zerodiag_subs[i]);
    3800:     }
    3801:     PetscFree(pcbddc->benign_zerodiag_subs);
    3802:   }
    3803:   PetscFree3(pcbddc->benign_p0_lidx,pcbddc->benign_p0_gidx,pcbddc->benign_p0);
    3804:   return 0;
    3805: }

    3807: PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
    3808: {
    3809:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
    3810:   PC_IS          *pcis = (PC_IS*)pc->data;
    3811:   VecType        impVecType;
    3812:   PetscInt       n_constraints,n_R,old_size;

    3814:   n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - pcbddc->n_vertices;
    3815:   n_R = pcis->n - pcbddc->n_vertices;
    3816:   VecGetType(pcis->vec1_N,&impVecType);
    3817:   /* local work vectors (try to avoid unneeded work)*/
    3818:   /* R nodes */
    3819:   old_size = -1;
    3820:   if (pcbddc->vec1_R) {
    3821:     VecGetSize(pcbddc->vec1_R,&old_size);
    3822:   }
    3823:   if (n_R != old_size) {
    3824:     VecDestroy(&pcbddc->vec1_R);
    3825:     VecDestroy(&pcbddc->vec2_R);
    3826:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);
    3827:     VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);
    3828:     VecSetType(pcbddc->vec1_R,impVecType);
    3829:     VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);
    3830:   }
    3831:   /* local primal dofs */
    3832:   old_size = -1;
    3833:   if (pcbddc->vec1_P) {
    3834:     VecGetSize(pcbddc->vec1_P,&old_size);
    3835:   }
    3836:   if (pcbddc->local_primal_size != old_size) {
    3837:     VecDestroy(&pcbddc->vec1_P);
    3838:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);
    3839:     VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,pcbddc->local_primal_size);
    3840:     VecSetType(pcbddc->vec1_P,impVecType);
    3841:   }
    3842:   /* local explicit constraints */
    3843:   old_size = -1;
    3844:   if (pcbddc->vec1_C) {
    3845:     VecGetSize(pcbddc->vec1_C,&old_size);
    3846:   }
    3847:   if (n_constraints && n_constraints != old_size) {
    3848:     VecDestroy(&pcbddc->vec1_C);
    3849:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);
    3850:     VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);
    3851:     VecSetType(pcbddc->vec1_C,impVecType);
    3852:   }
    3853:   return 0;
    3854: }

    3856: PetscErrorCode PCBDDCSetUpCorrection(PC pc, PetscScalar **coarse_submat_vals_n)
    3857: {
    3858:   /* pointers to pcis and pcbddc */
    3859:   PC_IS*          pcis = (PC_IS*)pc->data;
    3860:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
    3861:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    3862:   /* submatrices of local problem */
    3863:   Mat             A_RV,A_VR,A_VV,local_auxmat2_R;
    3864:   /* submatrices of local coarse problem */
    3865:   Mat             S_VV,S_CV,S_VC,S_CC;
    3866:   /* working matrices */
    3867:   Mat             C_CR;
    3868:   /* additional working stuff */
    3869:   PC              pc_R;
    3870:   Mat             F,Brhs = NULL;
    3871:   Vec             dummy_vec;
    3872:   PetscBool       isLU,isCHOL,need_benign_correction,sparserhs;
    3873:   PetscScalar     *coarse_submat_vals; /* TODO: use a PETSc matrix */
    3874:   PetscScalar     *work;
    3875:   PetscInt        *idx_V_B;
    3876:   PetscInt        lda_rhs,n,n_vertices,n_constraints,*p0_lidx_I;
    3877:   PetscInt        i,n_R,n_D,n_B;
    3878:   PetscScalar     one=1.0,m_one=-1.0;

    3881:   PetscLogEventBegin(PC_BDDC_CorrectionSetUp[pcbddc->current_level],pc,0,0,0);

    3883:   /* Set Non-overlapping dimensions */
    3884:   n_vertices = pcbddc->n_vertices;
    3885:   n_constraints = pcbddc->local_primal_size - pcbddc->benign_n - n_vertices;
    3886:   n_B = pcis->n_B;
    3887:   n_D = pcis->n - n_B;
    3888:   n_R = pcis->n - n_vertices;

    3890:   /* vertices in boundary numbering */
    3891:   PetscMalloc1(n_vertices,&idx_V_B);
    3892:   ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,n_vertices,pcbddc->local_primal_ref_node,&i,idx_V_B);

    3895:   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
    3896:   PetscCalloc1(pcbddc->local_primal_size*pcbddc->local_primal_size,&coarse_submat_vals);
    3897:   MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_vertices,coarse_submat_vals,&S_VV);
    3898:   MatDenseSetLDA(S_VV,pcbddc->local_primal_size);
    3899:   MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_vertices,coarse_submat_vals+n_vertices,&S_CV);
    3900:   MatDenseSetLDA(S_CV,pcbddc->local_primal_size);
    3901:   MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_constraints,coarse_submat_vals+pcbddc->local_primal_size*n_vertices,&S_VC);
    3902:   MatDenseSetLDA(S_VC,pcbddc->local_primal_size);
    3903:   MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_constraints,coarse_submat_vals+(pcbddc->local_primal_size+1)*n_vertices,&S_CC);
    3904:   MatDenseSetLDA(S_CC,pcbddc->local_primal_size);

    3906:   /* determine if can use MatSolve routines instead of calling KSPSolve on ksp_R */
    3907:   KSPGetPC(pcbddc->ksp_R,&pc_R);
    3908:   PCSetUp(pc_R);
    3909:   PetscObjectTypeCompare((PetscObject)pc_R,PCLU,&isLU);
    3910:   PetscObjectTypeCompare((PetscObject)pc_R,PCCHOLESKY,&isCHOL);
    3911:   lda_rhs = n_R;
    3912:   need_benign_correction = PETSC_FALSE;
    3913:   if (isLU || isCHOL) {
    3914:     PCFactorGetMatrix(pc_R,&F);
    3915:   } else if (sub_schurs && sub_schurs->reuse_solver) {
    3916:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
    3917:     MatFactorType      type;

    3919:     F = reuse_solver->F;
    3920:     MatGetFactorType(F,&type);
    3921:     if (type == MAT_FACTOR_CHOLESKY) isCHOL = PETSC_TRUE;
    3922:     if (type == MAT_FACTOR_LU) isLU = PETSC_TRUE;
    3923:     MatGetSize(F,&lda_rhs,NULL);
    3924:     need_benign_correction = (PetscBool)(!!reuse_solver->benign_n);
    3925:   } else F = NULL;

    3927:   /* determine if we can use a sparse right-hand side */
    3928:   sparserhs = PETSC_FALSE;
    3929:   if (F) {
    3930:     MatSolverType solver;

    3932:     MatFactorGetSolverType(F,&solver);
    3933:     PetscStrcmp(solver,MATSOLVERMUMPS,&sparserhs);
    3934:   }

    3936:   /* allocate workspace */
    3937:   n = 0;
    3938:   if (n_constraints) {
    3939:     n += lda_rhs*n_constraints;
    3940:   }
    3941:   if (n_vertices) {
    3942:     n = PetscMax(2*lda_rhs*n_vertices,n);
    3943:     n = PetscMax((lda_rhs+n_B)*n_vertices,n);
    3944:   }
    3945:   if (!pcbddc->symmetric_primal) {
    3946:     n = PetscMax(2*lda_rhs*pcbddc->local_primal_size,n);
    3947:   }
    3948:   PetscMalloc1(n,&work);

    3950:   /* create dummy vector to modify rhs and sol of MatMatSolve (work array will never be used) */
    3951:   dummy_vec = NULL;
    3952:   if (need_benign_correction && lda_rhs != n_R && F) {
    3953:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&dummy_vec);
    3954:     VecSetSizes(dummy_vec,lda_rhs,PETSC_DECIDE);
    3955:     VecSetType(dummy_vec,((PetscObject)pcis->vec1_N)->type_name);
    3956:   }

    3958:   MatDestroy(&pcbddc->local_auxmat1);
    3959:   MatDestroy(&pcbddc->local_auxmat2);

    3961:   /* Precompute stuffs needed for preprocessing and application of BDDC*/
    3962:   if (n_constraints) {
    3963:     Mat         M3,C_B;
    3964:     IS          is_aux;

    3966:     /* Extract constraints on R nodes: C_{CR}  */
    3967:     ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);
    3968:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);
    3969:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);

    3971:     /* Assemble         local_auxmat2_R =        (- A_{RR}^{-1} C^T_{CR}) needed by BDDC setup */
    3972:     /* Assemble pcbddc->local_auxmat2   = R_to_B (- A_{RR}^{-1} C^T_{CR}) needed by BDDC application */
    3973:     if (!sparserhs) {
    3974:       PetscArrayzero(work,lda_rhs*n_constraints);
    3975:       for (i=0;i<n_constraints;i++) {
    3976:         const PetscScalar *row_cmat_values;
    3977:         const PetscInt    *row_cmat_indices;
    3978:         PetscInt          size_of_constraint,j;

    3980:         MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);
    3981:         for (j=0;j<size_of_constraint;j++) {
    3982:           work[row_cmat_indices[j]+i*lda_rhs] = -row_cmat_values[j];
    3983:         }
    3984:         MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);
    3985:       }
    3986:       MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,work,&Brhs);
    3987:     } else {
    3988:       Mat tC_CR;

    3990:       MatScale(C_CR,-1.0);
    3991:       if (lda_rhs != n_R) {
    3992:         PetscScalar *aa;
    3993:         PetscInt    r,*ii,*jj;
    3994:         PetscBool   done;

    3996:         MatGetRowIJ(C_CR,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
    3998:         MatSeqAIJGetArray(C_CR,&aa);
    3999:         MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,n_constraints,lda_rhs,ii,jj,aa,&tC_CR);
    4000:         MatRestoreRowIJ(C_CR,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
    4002:       } else {
    4003:         PetscObjectReference((PetscObject)C_CR);
    4004:         tC_CR = C_CR;
    4005:       }
    4006:       MatCreateTranspose(tC_CR,&Brhs);
    4007:       MatDestroy(&tC_CR);
    4008:     }
    4009:     MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,NULL,&local_auxmat2_R);
    4010:     if (F) {
    4011:       if (need_benign_correction) {
    4012:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    4014:         /* rhs is already zero on interior dofs, no need to change the rhs */
    4015:         PetscArrayzero(reuse_solver->benign_save_vals,pcbddc->benign_n);
    4016:       }
    4017:       MatMatSolve(F,Brhs,local_auxmat2_R);
    4018:       if (need_benign_correction) {
    4019:         PetscScalar        *marr;
    4020:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    4022:         MatDenseGetArray(local_auxmat2_R,&marr);
    4023:         if (lda_rhs != n_R) {
    4024:           for (i=0;i<n_constraints;i++) {
    4025:             VecPlaceArray(dummy_vec,marr+i*lda_rhs);
    4026:             PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_TRUE,PETSC_TRUE);
    4027:             VecResetArray(dummy_vec);
    4028:           }
    4029:         } else {
    4030:           for (i=0;i<n_constraints;i++) {
    4031:             VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
    4032:             PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_TRUE,PETSC_TRUE);
    4033:             VecResetArray(pcbddc->vec1_R);
    4034:           }
    4035:         }
    4036:         MatDenseRestoreArray(local_auxmat2_R,&marr);
    4037:       }
    4038:     } else {
    4039:       PetscScalar *marr;

    4041:       MatDenseGetArray(local_auxmat2_R,&marr);
    4042:       for (i=0;i<n_constraints;i++) {
    4043:         VecPlaceArray(pcbddc->vec1_R,work+i*lda_rhs);
    4044:         VecPlaceArray(pcbddc->vec2_R,marr+i*lda_rhs);
    4045:         KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
    4046:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
    4047:         VecResetArray(pcbddc->vec1_R);
    4048:         VecResetArray(pcbddc->vec2_R);
    4049:       }
    4050:       MatDenseRestoreArray(local_auxmat2_R,&marr);
    4051:     }
    4052:     if (sparserhs) {
    4053:       MatScale(C_CR,-1.0);
    4054:     }
    4055:     MatDestroy(&Brhs);
    4056:     if (!pcbddc->switch_static) {
    4057:       MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_constraints,NULL,&pcbddc->local_auxmat2);
    4058:       for (i=0;i<n_constraints;i++) {
    4059:         Vec r, b;
    4060:         MatDenseGetColumnVecRead(local_auxmat2_R,i,&r);
    4061:         MatDenseGetColumnVec(pcbddc->local_auxmat2,i,&b);
    4062:         VecScatterBegin(pcbddc->R_to_B,r,b,INSERT_VALUES,SCATTER_FORWARD);
    4063:         VecScatterEnd(pcbddc->R_to_B,r,b,INSERT_VALUES,SCATTER_FORWARD);
    4064:         MatDenseRestoreColumnVec(pcbddc->local_auxmat2,i,&b);
    4065:         MatDenseRestoreColumnVecRead(local_auxmat2_R,i,&r);
    4066:       }
    4067:       MatMatMult(C_B,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);
    4068:     } else {
    4069:       if (lda_rhs != n_R) {
    4070:         IS dummy;

    4072:         ISCreateStride(PETSC_COMM_SELF,n_R,0,1,&dummy);
    4073:         MatCreateSubMatrix(local_auxmat2_R,dummy,NULL,MAT_INITIAL_MATRIX,&pcbddc->local_auxmat2);
    4074:         ISDestroy(&dummy);
    4075:       } else {
    4076:         PetscObjectReference((PetscObject)local_auxmat2_R);
    4077:         pcbddc->local_auxmat2 = local_auxmat2_R;
    4078:       }
    4079:       MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);
    4080:     }
    4081:     ISDestroy(&is_aux);
    4082:     /* Assemble explicitly S_CC = ( C_{CR} A_{RR}^{-1} C^T_{CR})^{-1}  */
    4083:     MatScale(M3,m_one);
    4084:     if (isCHOL) {
    4085:       MatCholeskyFactor(M3,NULL,NULL);
    4086:     } else {
    4087:       MatLUFactor(M3,NULL,NULL,NULL);
    4088:     }
    4089:     MatSeqDenseInvertFactors_Private(M3);
    4090:     /* Assemble local_auxmat1 = S_CC*C_{CB} needed by BDDC application in KSP and in preproc */
    4091:     MatMatMult(M3,C_B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);
    4092:     MatDestroy(&C_B);
    4093:     MatCopy(M3,S_CC,SAME_NONZERO_PATTERN); /* S_CC can have a different LDA, MatMatSolve doesn't support it */
    4094:     MatDestroy(&M3);
    4095:   }

    4097:   /* Get submatrices from subdomain matrix */
    4098:   if (n_vertices) {
    4099: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    4100:     PetscBool oldpin;
    4101: #endif
    4102:     PetscBool isaij;
    4103:     IS        is_aux;

    4105:     if (sub_schurs && sub_schurs->reuse_solver) { /* is_R_local is not sorted, ISComplement doesn't like it */
    4106:       IS tis;

    4108:       ISDuplicate(pcbddc->is_R_local,&tis);
    4109:       ISSort(tis);
    4110:       ISComplement(tis,0,pcis->n,&is_aux);
    4111:       ISDestroy(&tis);
    4112:     } else {
    4113:       ISComplement(pcbddc->is_R_local,0,pcis->n,&is_aux);
    4114:     }
    4115: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    4116:     oldpin = pcbddc->local_mat->boundtocpu;
    4117: #endif
    4118:     MatBindToCPU(pcbddc->local_mat,PETSC_TRUE);
    4119:     MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);
    4120:     MatCreateSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);
    4121:     PetscObjectBaseTypeCompare((PetscObject)A_VR,MATSEQAIJ,&isaij);
    4122:     if (!isaij) { /* TODO REMOVE: MatMatMult(A_VR,A_RRmA_RV) below may raise an error */
    4123:       MatConvert(A_VR,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_VR);
    4124:     }
    4125:     MatCreateSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);
    4126: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    4127:     MatBindToCPU(pcbddc->local_mat,oldpin);
    4128: #endif
    4129:     ISDestroy(&is_aux);
    4130:   }

    4132:   /* Matrix of coarse basis functions (local) */
    4133:   if (pcbddc->coarse_phi_B) {
    4134:     PetscInt on_B,on_primal,on_D=n_D;
    4135:     if (pcbddc->coarse_phi_D) {
    4136:       MatGetSize(pcbddc->coarse_phi_D,&on_D,NULL);
    4137:     }
    4138:     MatGetSize(pcbddc->coarse_phi_B,&on_B,&on_primal);
    4139:     if (on_B != n_B || on_primal != pcbddc->local_primal_size || on_D != n_D) {
    4140:       PetscScalar *marray;

    4142:       MatDenseGetArray(pcbddc->coarse_phi_B,&marray);
    4143:       PetscFree(marray);
    4144:       MatDestroy(&pcbddc->coarse_phi_B);
    4145:       MatDestroy(&pcbddc->coarse_psi_B);
    4146:       MatDestroy(&pcbddc->coarse_phi_D);
    4147:       MatDestroy(&pcbddc->coarse_psi_D);
    4148:     }
    4149:   }

    4151:   if (!pcbddc->coarse_phi_B) {
    4152:     PetscScalar *marr;

    4154:     /* memory size */
    4155:     n = n_B*pcbddc->local_primal_size;
    4156:     if (pcbddc->switch_static || pcbddc->dbg_flag) n += n_D*pcbddc->local_primal_size;
    4157:     if (!pcbddc->symmetric_primal) n *= 2;
    4158:     PetscCalloc1(n,&marr);
    4159:     MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marr,&pcbddc->coarse_phi_B);
    4160:     marr += n_B*pcbddc->local_primal_size;
    4161:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
    4162:       MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marr,&pcbddc->coarse_phi_D);
    4163:       marr += n_D*pcbddc->local_primal_size;
    4164:     }
    4165:     if (!pcbddc->symmetric_primal) {
    4166:       MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marr,&pcbddc->coarse_psi_B);
    4167:       marr += n_B*pcbddc->local_primal_size;
    4168:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    4169:         MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marr,&pcbddc->coarse_psi_D);
    4170:       }
    4171:     } else {
    4172:       PetscObjectReference((PetscObject)pcbddc->coarse_phi_B);
    4173:       pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
    4174:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    4175:         PetscObjectReference((PetscObject)pcbddc->coarse_phi_D);
    4176:         pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
    4177:       }
    4178:     }
    4179:   }

    4181:   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
    4182:   p0_lidx_I = NULL;
    4183:   if (pcbddc->benign_n && (pcbddc->switch_static || pcbddc->dbg_flag)) {
    4184:     const PetscInt *idxs;

    4186:     ISGetIndices(pcis->is_I_local,&idxs);
    4187:     PetscMalloc1(pcbddc->benign_n,&p0_lidx_I);
    4188:     for (i=0;i<pcbddc->benign_n;i++) {
    4189:       PetscFindInt(pcbddc->benign_p0_lidx[i],pcis->n-pcis->n_B,idxs,&p0_lidx_I[i]);
    4190:     }
    4191:     ISRestoreIndices(pcis->is_I_local,&idxs);
    4192:   }

    4194:   /* vertices */
    4195:   if (n_vertices) {
    4196:     PetscBool restoreavr = PETSC_FALSE;

    4198:     MatConvert(A_VV,MATDENSE,MAT_INPLACE_MATRIX,&A_VV);

    4200:     if (n_R) {
    4201:       Mat               A_RRmA_RV,A_RV_bcorr=NULL,S_VVt; /* S_VVt with LDA=N */
    4202:       PetscBLASInt      B_N,B_one = 1;
    4203:       const PetscScalar *x;
    4204:       PetscScalar       *y;

    4206:       MatScale(A_RV,m_one);
    4207:       if (need_benign_correction) {
    4208:         ISLocalToGlobalMapping RtoN;
    4209:         IS                     is_p0;
    4210:         PetscInt               *idxs_p0,n;

    4212:         PetscMalloc1(pcbddc->benign_n,&idxs_p0);
    4213:         ISLocalToGlobalMappingCreateIS(pcbddc->is_R_local,&RtoN);
    4214:         ISGlobalToLocalMappingApply(RtoN,IS_GTOLM_DROP,pcbddc->benign_n,pcbddc->benign_p0_lidx,&n,idxs_p0);
    4216:         ISLocalToGlobalMappingDestroy(&RtoN);
    4217:         ISCreateGeneral(PETSC_COMM_SELF,n,idxs_p0,PETSC_OWN_POINTER,&is_p0);
    4218:         MatCreateSubMatrix(A_RV,is_p0,NULL,MAT_INITIAL_MATRIX,&A_RV_bcorr);
    4219:         ISDestroy(&is_p0);
    4220:       }

    4222:       MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,work,&A_RRmA_RV);
    4223:       if (!sparserhs || need_benign_correction) {
    4224:         if (lda_rhs == n_R) {
    4225:           MatConvert(A_RV,MATDENSE,MAT_INPLACE_MATRIX,&A_RV);
    4226:         } else {
    4227:           PetscScalar    *av,*array;
    4228:           const PetscInt *xadj,*adjncy;
    4229:           PetscInt       n;
    4230:           PetscBool      flg_row;

    4232:           array = work+lda_rhs*n_vertices;
    4233:           PetscArrayzero(array,lda_rhs*n_vertices);
    4234:           MatConvert(A_RV,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_RV);
    4235:           MatGetRowIJ(A_RV,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
    4236:           MatSeqAIJGetArray(A_RV,&av);
    4237:           for (i=0;i<n;i++) {
    4238:             PetscInt j;
    4239:             for (j=xadj[i];j<xadj[i+1];j++) array[lda_rhs*adjncy[j]+i] = av[j];
    4240:           }
    4241:           MatRestoreRowIJ(A_RV,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
    4242:           MatDestroy(&A_RV);
    4243:           MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,array,&A_RV);
    4244:         }
    4245:         if (need_benign_correction) {
    4246:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
    4247:           PetscScalar        *marr;

    4249:           MatDenseGetArray(A_RV,&marr);
    4250:           /* need \Phi^T A_RV = (I+L)A_RV, L given by

    4252:                  | 0 0  0 | (V)
    4253:              L = | 0 0 -1 | (P-p0)
    4254:                  | 0 0 -1 | (p0)

    4256:           */
    4257:           for (i=0;i<reuse_solver->benign_n;i++) {
    4258:             const PetscScalar *vals;
    4259:             const PetscInt    *idxs,*idxs_zero;
    4260:             PetscInt          n,j,nz;

    4262:             ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i],&nz);
    4263:             ISGetIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
    4264:             MatGetRow(A_RV_bcorr,i,&n,&idxs,&vals);
    4265:             for (j=0;j<n;j++) {
    4266:               PetscScalar val = vals[j];
    4267:               PetscInt    k,col = idxs[j];
    4268:               for (k=0;k<nz;k++) marr[idxs_zero[k]+lda_rhs*col] -= val;
    4269:             }
    4270:             MatRestoreRow(A_RV_bcorr,i,&n,&idxs,&vals);
    4271:             ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
    4272:           }
    4273:           MatDenseRestoreArray(A_RV,&marr);
    4274:         }
    4275:         PetscObjectReference((PetscObject)A_RV);
    4276:         Brhs = A_RV;
    4277:       } else {
    4278:         Mat tA_RVT,A_RVT;

    4280:         if (!pcbddc->symmetric_primal) {
    4281:           /* A_RV already scaled by -1 */
    4282:           MatTranspose(A_RV,MAT_INITIAL_MATRIX,&A_RVT);
    4283:         } else {
    4284:           restoreavr = PETSC_TRUE;
    4285:           MatScale(A_VR,-1.0);
    4286:           PetscObjectReference((PetscObject)A_VR);
    4287:           A_RVT = A_VR;
    4288:         }
    4289:         if (lda_rhs != n_R) {
    4290:           PetscScalar *aa;
    4291:           PetscInt    r,*ii,*jj;
    4292:           PetscBool   done;

    4294:           MatGetRowIJ(A_RVT,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
    4296:           MatSeqAIJGetArray(A_RVT,&aa);
    4297:           MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,n_vertices,lda_rhs,ii,jj,aa,&tA_RVT);
    4298:           MatRestoreRowIJ(A_RVT,0,PETSC_FALSE,PETSC_FALSE,&r,(const PetscInt**)&ii,(const PetscInt**)&jj,&done);
    4300:         } else {
    4301:           PetscObjectReference((PetscObject)A_RVT);
    4302:           tA_RVT = A_RVT;
    4303:         }
    4304:         MatCreateTranspose(tA_RVT,&Brhs);
    4305:         MatDestroy(&tA_RVT);
    4306:         MatDestroy(&A_RVT);
    4307:       }
    4308:       if (F) {
    4309:         /* need to correct the rhs */
    4310:         if (need_benign_correction) {
    4311:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
    4312:           PetscScalar        *marr;

    4314:           MatDenseGetArray(Brhs,&marr);
    4315:           if (lda_rhs != n_R) {
    4316:             for (i=0;i<n_vertices;i++) {
    4317:               VecPlaceArray(dummy_vec,marr+i*lda_rhs);
    4318:               PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_FALSE,PETSC_TRUE);
    4319:               VecResetArray(dummy_vec);
    4320:             }
    4321:           } else {
    4322:             for (i=0;i<n_vertices;i++) {
    4323:               VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
    4324:               PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_FALSE,PETSC_TRUE);
    4325:               VecResetArray(pcbddc->vec1_R);
    4326:             }
    4327:           }
    4328:           MatDenseRestoreArray(Brhs,&marr);
    4329:         }
    4330:         MatMatSolve(F,Brhs,A_RRmA_RV);
    4331:         if (restoreavr) {
    4332:           MatScale(A_VR,-1.0);
    4333:         }
    4334:         /* need to correct the solution */
    4335:         if (need_benign_correction) {
    4336:           PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
    4337:           PetscScalar        *marr;

    4339:           MatDenseGetArray(A_RRmA_RV,&marr);
    4340:           if (lda_rhs != n_R) {
    4341:             for (i=0;i<n_vertices;i++) {
    4342:               VecPlaceArray(dummy_vec,marr+i*lda_rhs);
    4343:               PCBDDCReuseSolversBenignAdapt(reuse_solver,dummy_vec,NULL,PETSC_TRUE,PETSC_TRUE);
    4344:               VecResetArray(dummy_vec);
    4345:             }
    4346:           } else {
    4347:             for (i=0;i<n_vertices;i++) {
    4348:               VecPlaceArray(pcbddc->vec1_R,marr+i*lda_rhs);
    4349:               PCBDDCReuseSolversBenignAdapt(reuse_solver,pcbddc->vec1_R,NULL,PETSC_TRUE,PETSC_TRUE);
    4350:               VecResetArray(pcbddc->vec1_R);
    4351:             }
    4352:           }
    4353:           MatDenseRestoreArray(A_RRmA_RV,&marr);
    4354:         }
    4355:       } else {
    4356:         MatDenseGetArray(Brhs,&y);
    4357:         for (i=0;i<n_vertices;i++) {
    4358:           VecPlaceArray(pcbddc->vec1_R,y+i*lda_rhs);
    4359:           VecPlaceArray(pcbddc->vec2_R,work+i*lda_rhs);
    4360:           KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
    4361:           KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
    4362:           VecResetArray(pcbddc->vec1_R);
    4363:           VecResetArray(pcbddc->vec2_R);
    4364:         }
    4365:         MatDenseRestoreArray(Brhs,&y);
    4366:       }
    4367:       MatDestroy(&A_RV);
    4368:       MatDestroy(&Brhs);
    4369:       /* S_VV and S_CV */
    4370:       if (n_constraints) {
    4371:         Mat B;

    4373:         PetscArrayzero(work+lda_rhs*n_vertices,n_B*n_vertices);
    4374:         for (i=0;i<n_vertices;i++) {
    4375:           VecPlaceArray(pcbddc->vec1_R,work+i*lda_rhs);
    4376:           VecPlaceArray(pcis->vec1_B,work+lda_rhs*n_vertices+i*n_B);
    4377:           VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    4378:           VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    4379:           VecResetArray(pcis->vec1_B);
    4380:           VecResetArray(pcbddc->vec1_R);
    4381:         }
    4382:         MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_vertices,work+lda_rhs*n_vertices,&B);
    4383:         /* Reuse dense S_C = pcbddc->local_auxmat1 * B */
    4384:         MatProductCreateWithMat(pcbddc->local_auxmat1,B,NULL,S_CV);
    4385:         MatProductSetType(S_CV,MATPRODUCT_AB);
    4386:         MatProductSetFromOptions(S_CV);
    4387:         MatProductSymbolic(S_CV);
    4388:         MatProductNumeric(S_CV);
    4389:         MatProductClear(S_CV);

    4391:         MatDestroy(&B);
    4392:         MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_vertices,work+lda_rhs*n_vertices,&B);
    4393:         /* Reuse B = local_auxmat2_R * S_CV */
    4394:         MatProductCreateWithMat(local_auxmat2_R,S_CV,NULL,B);
    4395:         MatProductSetType(B,MATPRODUCT_AB);
    4396:         MatProductSetFromOptions(B);
    4397:         MatProductSymbolic(B);
    4398:         MatProductNumeric(B);

    4400:         MatScale(S_CV,m_one);
    4401:         PetscBLASIntCast(lda_rhs*n_vertices,&B_N);
    4402:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,work+lda_rhs*n_vertices,&B_one,work,&B_one));
    4403:         MatDestroy(&B);
    4404:       }
    4405:       if (lda_rhs != n_R) {
    4406:         MatDestroy(&A_RRmA_RV);
    4407:         MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&A_RRmA_RV);
    4408:         MatDenseSetLDA(A_RRmA_RV,lda_rhs);
    4409:       }
    4410:       MatMatMult(A_VR,A_RRmA_RV,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VVt);
    4411:       /* need A_VR * \Phi * A_RRmA_RV = A_VR * (I+L)^T * A_RRmA_RV, L given as before */
    4412:       if (need_benign_correction) {
    4413:         PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
    4414:         PetscScalar        *marr,*sums;

    4416:         PetscMalloc1(n_vertices,&sums);
    4417:         MatDenseGetArray(S_VVt,&marr);
    4418:         for (i=0;i<reuse_solver->benign_n;i++) {
    4419:           const PetscScalar *vals;
    4420:           const PetscInt    *idxs,*idxs_zero;
    4421:           PetscInt          n,j,nz;

    4423:           ISGetLocalSize(reuse_solver->benign_zerodiag_subs[i],&nz);
    4424:           ISGetIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
    4425:           for (j=0;j<n_vertices;j++) {
    4426:             PetscInt k;
    4427:             sums[j] = 0.;
    4428:             for (k=0;k<nz;k++) sums[j] += work[idxs_zero[k]+j*lda_rhs];
    4429:           }
    4430:           MatGetRow(A_RV_bcorr,i,&n,&idxs,&vals);
    4431:           for (j=0;j<n;j++) {
    4432:             PetscScalar val = vals[j];
    4433:             PetscInt k;
    4434:             for (k=0;k<n_vertices;k++) {
    4435:               marr[idxs[j]+k*n_vertices] += val*sums[k];
    4436:             }
    4437:           }
    4438:           MatRestoreRow(A_RV_bcorr,i,&n,&idxs,&vals);
    4439:           ISRestoreIndices(reuse_solver->benign_zerodiag_subs[i],&idxs_zero);
    4440:         }
    4441:         PetscFree(sums);
    4442:         MatDenseRestoreArray(S_VVt,&marr);
    4443:         MatDestroy(&A_RV_bcorr);
    4444:       }
    4445:       MatDestroy(&A_RRmA_RV);
    4446:       PetscBLASIntCast(n_vertices*n_vertices,&B_N);
    4447:       MatDenseGetArrayRead(A_VV,&x);
    4448:       MatDenseGetArray(S_VVt,&y);
    4449:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,x,&B_one,y,&B_one));
    4450:       MatDenseRestoreArrayRead(A_VV,&x);
    4451:       MatDenseRestoreArray(S_VVt,&y);
    4452:       MatCopy(S_VVt,S_VV,SAME_NONZERO_PATTERN);
    4453:       MatDestroy(&S_VVt);
    4454:     } else {
    4455:       MatCopy(A_VV,S_VV,SAME_NONZERO_PATTERN);
    4456:     }
    4457:     MatDestroy(&A_VV);

    4459:     /* coarse basis functions */
    4460:     for (i=0;i<n_vertices;i++) {
    4461:       Vec         v;
    4462:       PetscScalar one = 1.0,zero = 0.0;

    4464:       VecPlaceArray(pcbddc->vec1_R,work+lda_rhs*i);
    4465:       MatDenseGetColumnVec(pcbddc->coarse_phi_B,i,&v);
    4466:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4467:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4468:       if (PetscDefined(USE_DEBUG)) { /* The following VecSetValues() expects a sequential matrix */
    4469:         PetscMPIInt rank;
    4470:         MPI_Comm_rank(PetscObjectComm((PetscObject)pcbddc->coarse_phi_B),&rank);
    4472:       }
    4473:       VecSetValues(v,1,&idx_V_B[i],&one,INSERT_VALUES);
    4474:       VecAssemblyBegin(v); /* If v is on device, hope VecSetValues() eventually implemented by a host to device memcopy */
    4475:       VecAssemblyEnd(v);
    4476:       MatDenseRestoreColumnVec(pcbddc->coarse_phi_B,i,&v);

    4478:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    4479:         PetscInt j;

    4481:         MatDenseGetColumnVec(pcbddc->coarse_phi_D,i,&v);
    4482:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4483:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4484:         if (PetscDefined(USE_DEBUG)) { /* The following VecSetValues() expects a sequential matrix */
    4485:           PetscMPIInt rank;
    4486:           MPI_Comm_rank(PetscObjectComm((PetscObject)pcbddc->coarse_phi_D),&rank);
    4488:         }
    4489:         for (j=0;j<pcbddc->benign_n;j++) VecSetValues(v,1,&p0_lidx_I[j],&zero,INSERT_VALUES);
    4490:         VecAssemblyBegin(v);
    4491:         VecAssemblyEnd(v);
    4492:         MatDenseRestoreColumnVec(pcbddc->coarse_phi_D,i,&v);
    4493:       }
    4494:       VecResetArray(pcbddc->vec1_R);
    4495:     }
    4496:     /* if n_R == 0 the object is not destroyed */
    4497:     MatDestroy(&A_RV);
    4498:   }
    4499:   VecDestroy(&dummy_vec);

    4501:   if (n_constraints) {
    4502:     Mat B;

    4504:     MatCreateSeqDense(PETSC_COMM_SELF,lda_rhs,n_constraints,work,&B);
    4505:     MatScale(S_CC,m_one);
    4506:     MatProductCreateWithMat(local_auxmat2_R,S_CC,NULL,B);
    4507:     MatProductSetType(B,MATPRODUCT_AB);
    4508:     MatProductSetFromOptions(B);
    4509:     MatProductSymbolic(B);
    4510:     MatProductNumeric(B);

    4512:     MatScale(S_CC,m_one);
    4513:     if (n_vertices) {
    4514:       if (isCHOL || need_benign_correction) { /* if we can solve the interior problem with cholesky, we should also be fine with transposing here */
    4515:         MatTranspose(S_CV,MAT_REUSE_MATRIX,&S_VC);
    4516:       } else {
    4517:         Mat S_VCt;

    4519:         if (lda_rhs != n_R) {
    4520:           MatDestroy(&B);
    4521:           MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work,&B);
    4522:           MatDenseSetLDA(B,lda_rhs);
    4523:         }
    4524:         MatMatMult(A_VR,B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VCt);
    4525:         MatCopy(S_VCt,S_VC,SAME_NONZERO_PATTERN);
    4526:         MatDestroy(&S_VCt);
    4527:       }
    4528:     }
    4529:     MatDestroy(&B);
    4530:     /* coarse basis functions */
    4531:     for (i=0;i<n_constraints;i++) {
    4532:       Vec v;

    4534:       VecPlaceArray(pcbddc->vec1_R,work+lda_rhs*i);
    4535:       MatDenseGetColumnVec(pcbddc->coarse_phi_B,i+n_vertices,&v);
    4536:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4537:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4538:       MatDenseRestoreColumnVec(pcbddc->coarse_phi_B,i+n_vertices,&v);
    4539:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    4540:         PetscInt    j;
    4541:         PetscScalar zero = 0.0;
    4542:         MatDenseGetColumnVec(pcbddc->coarse_phi_D,i+n_vertices,&v);
    4543:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4544:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4545:         for (j=0;j<pcbddc->benign_n;j++) VecSetValues(v,1,&p0_lidx_I[j],&zero,INSERT_VALUES);
    4546:         VecAssemblyBegin(v);
    4547:         VecAssemblyEnd(v);
    4548:         MatDenseRestoreColumnVec(pcbddc->coarse_phi_D,i+n_vertices,&v);
    4549:       }
    4550:       VecResetArray(pcbddc->vec1_R);
    4551:     }
    4552:   }
    4553:   if (n_constraints) {
    4554:     MatDestroy(&local_auxmat2_R);
    4555:   }
    4556:   PetscFree(p0_lidx_I);

    4558:   /* coarse matrix entries relative to B_0 */
    4559:   if (pcbddc->benign_n) {
    4560:     Mat               B0_B,B0_BPHI;
    4561:     IS                is_dummy;
    4562:     const PetscScalar *data;
    4563:     PetscInt          j;

    4565:     ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy);
    4566:     MatCreateSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
    4567:     ISDestroy(&is_dummy);
    4568:     MatMatMult(B0_B,pcbddc->coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&B0_BPHI);
    4569:     MatConvert(B0_BPHI,MATSEQDENSE,MAT_INPLACE_MATRIX,&B0_BPHI);
    4570:     MatDenseGetArrayRead(B0_BPHI,&data);
    4571:     for (j=0;j<pcbddc->benign_n;j++) {
    4572:       PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
    4573:       for (i=0;i<pcbddc->local_primal_size;i++) {
    4574:         coarse_submat_vals[primal_idx*pcbddc->local_primal_size+i] = data[i*pcbddc->benign_n+j];
    4575:         coarse_submat_vals[i*pcbddc->local_primal_size+primal_idx] = data[i*pcbddc->benign_n+j];
    4576:       }
    4577:     }
    4578:     MatDenseRestoreArrayRead(B0_BPHI,&data);
    4579:     MatDestroy(&B0_B);
    4580:     MatDestroy(&B0_BPHI);
    4581:   }

    4583:   /* compute other basis functions for non-symmetric problems */
    4584:   if (!pcbddc->symmetric_primal) {
    4585:     Mat         B_V=NULL,B_C=NULL;
    4586:     PetscScalar *marray;

    4588:     if (n_constraints) {
    4589:       Mat S_CCT,C_CRT;

    4591:       MatTranspose(C_CR,MAT_INITIAL_MATRIX,&C_CRT);
    4592:       MatTranspose(S_CC,MAT_INITIAL_MATRIX,&S_CCT);
    4593:       MatMatMult(C_CRT,S_CCT,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B_C);
    4594:       MatDestroy(&S_CCT);
    4595:       if (n_vertices) {
    4596:         Mat S_VCT;

    4598:         MatTranspose(S_VC,MAT_INITIAL_MATRIX,&S_VCT);
    4599:         MatMatMult(C_CRT,S_VCT,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&B_V);
    4600:         MatDestroy(&S_VCT);
    4601:       }
    4602:       MatDestroy(&C_CRT);
    4603:     } else {
    4604:       MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,NULL,&B_V);
    4605:     }
    4606:     if (n_vertices && n_R) {
    4607:       PetscScalar    *av,*marray;
    4608:       const PetscInt *xadj,*adjncy;
    4609:       PetscInt       n;
    4610:       PetscBool      flg_row;

    4612:       /* B_V = B_V - A_VR^T */
    4613:       MatConvert(A_VR,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_VR);
    4614:       MatGetRowIJ(A_VR,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
    4615:       MatSeqAIJGetArray(A_VR,&av);
    4616:       MatDenseGetArray(B_V,&marray);
    4617:       for (i=0;i<n;i++) {
    4618:         PetscInt j;
    4619:         for (j=xadj[i];j<xadj[i+1];j++) marray[i*n_R + adjncy[j]] -= av[j];
    4620:       }
    4621:       MatDenseRestoreArray(B_V,&marray);
    4622:       MatRestoreRowIJ(A_VR,0,PETSC_FALSE,PETSC_FALSE,&n,&xadj,&adjncy,&flg_row);
    4623:       MatDestroy(&A_VR);
    4624:     }

    4626:     /* currently there's no support for MatTransposeMatSolve(F,B,X) */
    4627:     if (n_vertices) {
    4628:       MatDenseGetArray(B_V,&marray);
    4629:       for (i=0;i<n_vertices;i++) {
    4630:         VecPlaceArray(pcbddc->vec1_R,marray+i*n_R);
    4631:         VecPlaceArray(pcbddc->vec2_R,work+i*n_R);
    4632:         KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
    4633:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
    4634:         VecResetArray(pcbddc->vec1_R);
    4635:         VecResetArray(pcbddc->vec2_R);
    4636:       }
    4637:       MatDenseRestoreArray(B_V,&marray);
    4638:     }
    4639:     if (B_C) {
    4640:       MatDenseGetArray(B_C,&marray);
    4641:       for (i=n_vertices;i<n_constraints+n_vertices;i++) {
    4642:         VecPlaceArray(pcbddc->vec1_R,marray+(i-n_vertices)*n_R);
    4643:         VecPlaceArray(pcbddc->vec2_R,work+i*n_R);
    4644:         KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
    4645:         KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
    4646:         VecResetArray(pcbddc->vec1_R);
    4647:         VecResetArray(pcbddc->vec2_R);
    4648:       }
    4649:       MatDenseRestoreArray(B_C,&marray);
    4650:     }
    4651:     /* coarse basis functions */
    4652:     for (i=0;i<pcbddc->local_primal_size;i++) {
    4653:       Vec  v;

    4655:       VecPlaceArray(pcbddc->vec1_R,work+i*n_R);
    4656:       MatDenseGetColumnVec(pcbddc->coarse_psi_B,i,&v);
    4657:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4658:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4659:       if (i<n_vertices) {
    4660:         PetscScalar one = 1.0;
    4661:         VecSetValues(v,1,&idx_V_B[i],&one,INSERT_VALUES);
    4662:         VecAssemblyBegin(v);
    4663:         VecAssemblyEnd(v);
    4664:       }
    4665:       MatDenseRestoreColumnVec(pcbddc->coarse_psi_B,i,&v);

    4667:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    4668:         MatDenseGetColumnVec(pcbddc->coarse_psi_D,i,&v);
    4669:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4670:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,v,INSERT_VALUES,SCATTER_FORWARD);
    4671:         MatDenseRestoreColumnVec(pcbddc->coarse_psi_D,i,&v);
    4672:       }
    4673:       VecResetArray(pcbddc->vec1_R);
    4674:     }
    4675:     MatDestroy(&B_V);
    4676:     MatDestroy(&B_C);
    4677:   }

    4679:   /* free memory */
    4680:   PetscFree(idx_V_B);
    4681:   MatDestroy(&S_VV);
    4682:   MatDestroy(&S_CV);
    4683:   MatDestroy(&S_VC);
    4684:   MatDestroy(&S_CC);
    4685:   PetscFree(work);
    4686:   if (n_vertices) {
    4687:     MatDestroy(&A_VR);
    4688:   }
    4689:   if (n_constraints) {
    4690:     MatDestroy(&C_CR);
    4691:   }
    4692:   PetscLogEventEnd(PC_BDDC_CorrectionSetUp[pcbddc->current_level],pc,0,0,0);

    4694:   /* Checking coarse_sub_mat and coarse basis functios */
    4695:   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
    4696:   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
    4697:   if (pcbddc->dbg_flag) {
    4698:     Mat         coarse_sub_mat;
    4699:     Mat         AUXMAT,TM1,TM2,TM3,TM4;
    4700:     Mat         coarse_phi_D,coarse_phi_B;
    4701:     Mat         coarse_psi_D,coarse_psi_B;
    4702:     Mat         A_II,A_BB,A_IB,A_BI;
    4703:     Mat         C_B,CPHI;
    4704:     IS          is_dummy;
    4705:     Vec         mones;
    4706:     MatType     checkmattype=MATSEQAIJ;
    4707:     PetscReal   real_value;

    4709:     if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
    4710:       Mat A;
    4711:       PCBDDCBenignProject(pc,NULL,NULL,&A);
    4712:       MatCreateSubMatrix(A,pcis->is_I_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&A_II);
    4713:       MatCreateSubMatrix(A,pcis->is_I_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&A_IB);
    4714:       MatCreateSubMatrix(A,pcis->is_B_local,pcis->is_I_local,MAT_INITIAL_MATRIX,&A_BI);
    4715:       MatCreateSubMatrix(A,pcis->is_B_local,pcis->is_B_local,MAT_INITIAL_MATRIX,&A_BB);
    4716:       MatDestroy(&A);
    4717:     } else {
    4718:       MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);
    4719:       MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);
    4720:       MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);
    4721:       MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);
    4722:     }
    4723:     MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);
    4724:     MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);
    4725:     if (!pcbddc->symmetric_primal) {
    4726:       MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);
    4727:       MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);
    4728:     }
    4729:     MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);

    4731:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    4732:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat computation (symmetric %d)\n",pcbddc->symmetric_primal);
    4733:     PetscViewerFlush(pcbddc->dbg_viewer);
    4734:     if (!pcbddc->symmetric_primal) {
    4735:       MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    4736:       MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);
    4737:       MatDestroy(&AUXMAT);
    4738:       MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    4739:       MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);
    4740:       MatDestroy(&AUXMAT);
    4741:       MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    4742:       MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);
    4743:       MatDestroy(&AUXMAT);
    4744:       MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    4745:       MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);
    4746:       MatDestroy(&AUXMAT);
    4747:     } else {
    4748:       MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);
    4749:       MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);
    4750:       MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    4751:       MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);
    4752:       MatDestroy(&AUXMAT);
    4753:       MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    4754:       MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);
    4755:       MatDestroy(&AUXMAT);
    4756:     }
    4757:     MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);
    4758:     MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);
    4759:     MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);
    4760:     MatConvert(TM1,MATSEQDENSE,MAT_INPLACE_MATRIX,&TM1);
    4761:     if (pcbddc->benign_n) {
    4762:       Mat               B0_B,B0_BPHI;
    4763:       const PetscScalar *data2;
    4764:       PetscScalar       *data;
    4765:       PetscInt          j;

    4767:       ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy);
    4768:       MatCreateSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
    4769:       MatMatMult(B0_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&B0_BPHI);
    4770:       MatConvert(B0_BPHI,MATSEQDENSE,MAT_INPLACE_MATRIX,&B0_BPHI);
    4771:       MatDenseGetArray(TM1,&data);
    4772:       MatDenseGetArrayRead(B0_BPHI,&data2);
    4773:       for (j=0;j<pcbddc->benign_n;j++) {
    4774:         PetscInt primal_idx = pcbddc->local_primal_size - pcbddc->benign_n + j;
    4775:         for (i=0;i<pcbddc->local_primal_size;i++) {
    4776:           data[primal_idx*pcbddc->local_primal_size+i] += data2[i*pcbddc->benign_n+j];
    4777:           data[i*pcbddc->local_primal_size+primal_idx] += data2[i*pcbddc->benign_n+j];
    4778:         }
    4779:       }
    4780:       MatDenseRestoreArray(TM1,&data);
    4781:       MatDenseRestoreArrayRead(B0_BPHI,&data2);
    4782:       MatDestroy(&B0_B);
    4783:       ISDestroy(&is_dummy);
    4784:       MatDestroy(&B0_BPHI);
    4785:     }
    4786: #if 0
    4787:   {
    4788:     PetscViewer viewer;
    4789:     char filename[256];
    4790:     sprintf(filename,"details_local_coarse_mat%d_level%d.m",PetscGlobalRank,pcbddc->current_level);
    4791:     PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);
    4792:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    4793:     PetscObjectSetName((PetscObject)coarse_sub_mat,"computed");
    4794:     MatView(coarse_sub_mat,viewer);
    4795:     PetscObjectSetName((PetscObject)TM1,"projected");
    4796:     MatView(TM1,viewer);
    4797:     if (pcbddc->coarse_phi_B) {
    4798:       PetscObjectSetName((PetscObject)pcbddc->coarse_phi_B,"phi_B");
    4799:       MatView(pcbddc->coarse_phi_B,viewer);
    4800:     }
    4801:     if (pcbddc->coarse_phi_D) {
    4802:       PetscObjectSetName((PetscObject)pcbddc->coarse_phi_D,"phi_D");
    4803:       MatView(pcbddc->coarse_phi_D,viewer);
    4804:     }
    4805:     if (pcbddc->coarse_psi_B) {
    4806:       PetscObjectSetName((PetscObject)pcbddc->coarse_psi_B,"psi_B");
    4807:       MatView(pcbddc->coarse_psi_B,viewer);
    4808:     }
    4809:     if (pcbddc->coarse_psi_D) {
    4810:       PetscObjectSetName((PetscObject)pcbddc->coarse_psi_D,"psi_D");
    4811:       MatView(pcbddc->coarse_psi_D,viewer);
    4812:     }
    4813:     PetscObjectSetName((PetscObject)pcbddc->local_mat,"A");
    4814:     MatView(pcbddc->local_mat,viewer);
    4815:     PetscObjectSetName((PetscObject)pcbddc->ConstraintMatrix,"C");
    4816:     MatView(pcbddc->ConstraintMatrix,viewer);
    4817:     PetscObjectSetName((PetscObject)pcis->is_I_local,"I");
    4818:     ISView(pcis->is_I_local,viewer);
    4819:     PetscObjectSetName((PetscObject)pcis->is_B_local,"B");
    4820:     ISView(pcis->is_B_local,viewer);
    4821:     PetscObjectSetName((PetscObject)pcbddc->is_R_local,"R");
    4822:     ISView(pcbddc->is_R_local,viewer);
    4823:     PetscViewerDestroy(&viewer);
    4824:   }
    4825: #endif
    4826:     MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);
    4827:     MatNorm(TM1,NORM_FROBENIUS,&real_value);
    4828:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    4829:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d          matrix error % 1.14e\n",PetscGlobalRank,real_value);

    4831:     /* check constraints */
    4832:     ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size-pcbddc->benign_n,0,1,&is_dummy);
    4833:     MatCreateSubMatrix(pcbddc->ConstraintMatrix,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);
    4834:     if (!pcbddc->benign_n) { /* TODO: add benign case */
    4835:       MatMatMult(C_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&CPHI);
    4836:     } else {
    4837:       PetscScalar *data;
    4838:       Mat         tmat;
    4839:       MatDenseGetArray(pcbddc->coarse_phi_B,&data);
    4840:       MatCreateSeqDense(PETSC_COMM_SELF,pcis->n_B,pcbddc->local_primal_size-pcbddc->benign_n,data,&tmat);
    4841:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&data);
    4842:       MatMatMult(C_B,tmat,MAT_INITIAL_MATRIX,1.0,&CPHI);
    4843:       MatDestroy(&tmat);
    4844:     }
    4845:     MatCreateVecs(CPHI,&mones,NULL);
    4846:     VecSet(mones,-1.0);
    4847:     MatDiagonalSet(CPHI,mones,ADD_VALUES);
    4848:     MatNorm(CPHI,NORM_FROBENIUS,&real_value);
    4849:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d phi constraints error % 1.14e\n",PetscGlobalRank,real_value);
    4850:     if (!pcbddc->symmetric_primal) {
    4851:       MatMatMult(C_B,coarse_psi_B,MAT_REUSE_MATRIX,1.0,&CPHI);
    4852:       VecSet(mones,-1.0);
    4853:       MatDiagonalSet(CPHI,mones,ADD_VALUES);
    4854:       MatNorm(CPHI,NORM_FROBENIUS,&real_value);
    4855:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d psi constraints error % 1.14e\n",PetscGlobalRank,real_value);
    4856:     }
    4857:     MatDestroy(&C_B);
    4858:     MatDestroy(&CPHI);
    4859:     ISDestroy(&is_dummy);
    4860:     VecDestroy(&mones);
    4861:     PetscViewerFlush(pcbddc->dbg_viewer);
    4862:     MatDestroy(&A_II);
    4863:     MatDestroy(&A_BB);
    4864:     MatDestroy(&A_IB);
    4865:     MatDestroy(&A_BI);
    4866:     MatDestroy(&TM1);
    4867:     MatDestroy(&TM2);
    4868:     MatDestroy(&TM3);
    4869:     MatDestroy(&TM4);
    4870:     MatDestroy(&coarse_phi_D);
    4871:     MatDestroy(&coarse_phi_B);
    4872:     if (!pcbddc->symmetric_primal) {
    4873:       MatDestroy(&coarse_psi_D);
    4874:       MatDestroy(&coarse_psi_B);
    4875:     }
    4876:     MatDestroy(&coarse_sub_mat);
    4877:   }
    4878:   /* FINAL CUDA support (we cannot currently mix viennacl and cuda vectors */
    4879:   {
    4880:     PetscBool gpu;

    4882:     PetscObjectTypeCompare((PetscObject)pcis->vec1_N,VECSEQCUDA,&gpu);
    4883:     if (gpu) {
    4884:       if (pcbddc->local_auxmat1) {
    4885:         MatConvert(pcbddc->local_auxmat1,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->local_auxmat1);
    4886:       }
    4887:       if (pcbddc->local_auxmat2) {
    4888:         MatConvert(pcbddc->local_auxmat2,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->local_auxmat2);
    4889:       }
    4890:       if (pcbddc->coarse_phi_B) {
    4891:         MatConvert(pcbddc->coarse_phi_B,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_phi_B);
    4892:       }
    4893:       if (pcbddc->coarse_phi_D) {
    4894:         MatConvert(pcbddc->coarse_phi_D,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_phi_D);
    4895:       }
    4896:       if (pcbddc->coarse_psi_B) {
    4897:         MatConvert(pcbddc->coarse_psi_B,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_psi_B);
    4898:       }
    4899:       if (pcbddc->coarse_psi_D) {
    4900:         MatConvert(pcbddc->coarse_psi_D,MATSEQDENSECUDA,MAT_INPLACE_MATRIX,&pcbddc->coarse_psi_D);
    4901:       }
    4902:     }
    4903:   }
    4904:   /* get back data */
    4905:   *coarse_submat_vals_n = coarse_submat_vals;
    4906:   return 0;
    4907: }

    4909: PetscErrorCode MatCreateSubMatrixUnsorted(Mat A, IS isrow, IS iscol, Mat* B)
    4910: {
    4911:   Mat            *work_mat;
    4912:   IS             isrow_s,iscol_s;
    4913:   PetscBool      rsorted,csorted;
    4914:   PetscInt       rsize,*idxs_perm_r=NULL,csize,*idxs_perm_c=NULL;

    4916:   ISSorted(isrow,&rsorted);
    4917:   ISSorted(iscol,&csorted);
    4918:   ISGetLocalSize(isrow,&rsize);
    4919:   ISGetLocalSize(iscol,&csize);

    4921:   if (!rsorted) {
    4922:     const PetscInt *idxs;
    4923:     PetscInt *idxs_sorted,i;

    4925:     PetscMalloc1(rsize,&idxs_perm_r);
    4926:     PetscMalloc1(rsize,&idxs_sorted);
    4927:     for (i=0;i<rsize;i++) {
    4928:       idxs_perm_r[i] = i;
    4929:     }
    4930:     ISGetIndices(isrow,&idxs);
    4931:     PetscSortIntWithPermutation(rsize,idxs,idxs_perm_r);
    4932:     for (i=0;i<rsize;i++) {
    4933:       idxs_sorted[i] = idxs[idxs_perm_r[i]];
    4934:     }
    4935:     ISRestoreIndices(isrow,&idxs);
    4936:     ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_sorted,PETSC_OWN_POINTER,&isrow_s);
    4937:   } else {
    4938:     PetscObjectReference((PetscObject)isrow);
    4939:     isrow_s = isrow;
    4940:   }

    4942:   if (!csorted) {
    4943:     if (isrow == iscol) {
    4944:       PetscObjectReference((PetscObject)isrow_s);
    4945:       iscol_s = isrow_s;
    4946:     } else {
    4947:       const PetscInt *idxs;
    4948:       PetscInt       *idxs_sorted,i;

    4950:       PetscMalloc1(csize,&idxs_perm_c);
    4951:       PetscMalloc1(csize,&idxs_sorted);
    4952:       for (i=0;i<csize;i++) {
    4953:         idxs_perm_c[i] = i;
    4954:       }
    4955:       ISGetIndices(iscol,&idxs);
    4956:       PetscSortIntWithPermutation(csize,idxs,idxs_perm_c);
    4957:       for (i=0;i<csize;i++) {
    4958:         idxs_sorted[i] = idxs[idxs_perm_c[i]];
    4959:       }
    4960:       ISRestoreIndices(iscol,&idxs);
    4961:       ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_sorted,PETSC_OWN_POINTER,&iscol_s);
    4962:     }
    4963:   } else {
    4964:     PetscObjectReference((PetscObject)iscol);
    4965:     iscol_s = iscol;
    4966:   }

    4968:   MatCreateSubMatrices(A,1,&isrow_s,&iscol_s,MAT_INITIAL_MATRIX,&work_mat);

    4970:   if (!rsorted || !csorted) {
    4971:     Mat      new_mat;
    4972:     IS       is_perm_r,is_perm_c;

    4974:     if (!rsorted) {
    4975:       PetscInt *idxs_r,i;
    4976:       PetscMalloc1(rsize,&idxs_r);
    4977:       for (i=0;i<rsize;i++) {
    4978:         idxs_r[idxs_perm_r[i]] = i;
    4979:       }
    4980:       PetscFree(idxs_perm_r);
    4981:       ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_r,PETSC_OWN_POINTER,&is_perm_r);
    4982:     } else {
    4983:       ISCreateStride(PETSC_COMM_SELF,rsize,0,1,&is_perm_r);
    4984:     }
    4985:     ISSetPermutation(is_perm_r);

    4987:     if (!csorted) {
    4988:       if (isrow_s == iscol_s) {
    4989:         PetscObjectReference((PetscObject)is_perm_r);
    4990:         is_perm_c = is_perm_r;
    4991:       } else {
    4992:         PetscInt *idxs_c,i;
    4994:         PetscMalloc1(csize,&idxs_c);
    4995:         for (i=0;i<csize;i++) {
    4996:           idxs_c[idxs_perm_c[i]] = i;
    4997:         }
    4998:         PetscFree(idxs_perm_c);
    4999:         ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_c,PETSC_OWN_POINTER,&is_perm_c);
    5000:       }
    5001:     } else {
    5002:       ISCreateStride(PETSC_COMM_SELF,csize,0,1,&is_perm_c);
    5003:     }
    5004:     ISSetPermutation(is_perm_c);

    5006:     MatPermute(work_mat[0],is_perm_r,is_perm_c,&new_mat);
    5007:     MatDestroy(&work_mat[0]);
    5008:     work_mat[0] = new_mat;
    5009:     ISDestroy(&is_perm_r);
    5010:     ISDestroy(&is_perm_c);
    5011:   }

    5013:   PetscObjectReference((PetscObject)work_mat[0]);
    5014:   *B = work_mat[0];
    5015:   MatDestroyMatrices(1,&work_mat);
    5016:   ISDestroy(&isrow_s);
    5017:   ISDestroy(&iscol_s);
    5018:   return 0;
    5019: }

    5021: PetscErrorCode PCBDDCComputeLocalMatrix(PC pc, Mat ChangeOfBasisMatrix)
    5022: {
    5023:   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
    5024:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
    5025:   Mat            new_mat,lA;
    5026:   IS             is_local,is_global;
    5027:   PetscInt       local_size;
    5028:   PetscBool      isseqaij;

    5030:   MatDestroy(&pcbddc->local_mat);
    5031:   MatGetSize(matis->A,&local_size,NULL);
    5032:   ISCreateStride(PetscObjectComm((PetscObject)matis->A),local_size,0,1,&is_local);
    5033:   ISLocalToGlobalMappingApplyIS(matis->rmapping,is_local,&is_global);
    5034:   ISDestroy(&is_local);
    5035:   MatCreateSubMatrixUnsorted(ChangeOfBasisMatrix,is_global,is_global,&new_mat);
    5036:   ISDestroy(&is_global);

    5038:   if (pcbddc->dbg_flag) {
    5039:     Vec       x,x_change;
    5040:     PetscReal error;

    5042:     MatCreateVecs(ChangeOfBasisMatrix,&x,&x_change);
    5043:     VecSetRandom(x,NULL);
    5044:     MatMult(ChangeOfBasisMatrix,x,x_change);
    5045:     VecScatterBegin(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);
    5046:     VecScatterEnd(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);
    5047:     MatMult(new_mat,matis->x,matis->y);
    5048:     if (!pcbddc->change_interior) {
    5049:       const PetscScalar *x,*y,*v;
    5050:       PetscReal         lerror = 0.;
    5051:       PetscInt          i;

    5053:       VecGetArrayRead(matis->x,&x);
    5054:       VecGetArrayRead(matis->y,&y);
    5055:       VecGetArrayRead(matis->counter,&v);
    5056:       for (i=0;i<local_size;i++)
    5057:         if (PetscRealPart(v[i]) < 1.5 && PetscAbsScalar(x[i]-y[i]) > lerror)
    5058:           lerror = PetscAbsScalar(x[i]-y[i]);
    5059:       VecRestoreArrayRead(matis->x,&x);
    5060:       VecRestoreArrayRead(matis->y,&y);
    5061:       VecRestoreArrayRead(matis->counter,&v);
    5062:       MPIU_Allreduce(&lerror,&error,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)pc));
    5063:       if (error > PETSC_SMALL) {
    5064:         if (!pcbddc->user_ChangeOfBasisMatrix || pcbddc->current_level) {
    5065:           SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on I: %1.6e",error);
    5066:         } else {
    5067:           SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_USER,"Error global vs local change on I: %1.6e",error);
    5068:         }
    5069:       }
    5070:     }
    5071:     VecScatterBegin(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);
    5072:     VecScatterEnd(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);
    5073:     VecAXPY(x,-1.0,x_change);
    5074:     VecNorm(x,NORM_INFINITY,&error);
    5075:     if (error > PETSC_SMALL) {
    5076:       if (!pcbddc->user_ChangeOfBasisMatrix || pcbddc->current_level) {
    5077:         SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on N: %1.6e",error);
    5078:       } else {
    5079:         SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_USER,"Error global vs local change on N: %1.6e",error);
    5080:       }
    5081:     }
    5082:     VecDestroy(&x);
    5083:     VecDestroy(&x_change);
    5084:   }

    5086:   /* lA is present if we are setting up an inner BDDC for a saddle point FETI-DP */
    5087:   PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject*)&lA);

    5089:   /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
    5090:   PetscObjectBaseTypeCompare((PetscObject)matis->A,MATSEQAIJ,&isseqaij);
    5091:   if (isseqaij) {
    5092:     MatDestroy(&pcbddc->local_mat);
    5093:     MatPtAP(matis->A,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);
    5094:     if (lA) {
    5095:       Mat work;
    5096:       MatPtAP(lA,new_mat,MAT_INITIAL_MATRIX,2.0,&work);
    5097:       PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject)work);
    5098:       MatDestroy(&work);
    5099:     }
    5100:   } else {
    5101:     Mat work_mat;

    5103:     MatDestroy(&pcbddc->local_mat);
    5104:     MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);
    5105:     MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);
    5106:     MatDestroy(&work_mat);
    5107:     if (lA) {
    5108:       Mat work;
    5109:       MatConvert(lA,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);
    5110:       MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&work);
    5111:       PetscObjectCompose((PetscObject)pc,"__KSPFETIDP_lA" ,(PetscObject)work);
    5112:       MatDestroy(&work);
    5113:     }
    5114:   }
    5115:   if (matis->A->symmetric_set) {
    5116:     MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);
    5117: #if !defined(PETSC_USE_COMPLEX)
    5118:     MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);
    5119: #endif
    5120:   }
    5121:   MatDestroy(&new_mat);
    5122:   return 0;
    5123: }

    5125: PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
    5126: {
    5127:   PC_IS*          pcis = (PC_IS*)(pc->data);
    5128:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
    5129:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    5130:   PetscInt        *idx_R_local=NULL;
    5131:   PetscInt        n_vertices,i,j,n_R,n_D,n_B;
    5132:   PetscInt        vbs,bs;
    5133:   PetscBT         bitmask=NULL;

    5135:   /*
    5136:     No need to setup local scatters if
    5137:       - primal space is unchanged
    5138:         AND
    5139:       - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
    5140:         AND
    5141:       - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
    5142:   */
    5143:   if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) {
    5144:     return 0;
    5145:   }
    5146:   /* destroy old objects */
    5147:   ISDestroy(&pcbddc->is_R_local);
    5148:   VecScatterDestroy(&pcbddc->R_to_B);
    5149:   VecScatterDestroy(&pcbddc->R_to_D);
    5150:   /* Set Non-overlapping dimensions */
    5151:   n_B = pcis->n_B;
    5152:   n_D = pcis->n - n_B;
    5153:   n_vertices = pcbddc->n_vertices;

    5155:   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */

    5157:   /* create auxiliary bitmask and allocate workspace */
    5158:   if (!sub_schurs || !sub_schurs->reuse_solver) {
    5159:     PetscMalloc1(pcis->n-n_vertices,&idx_R_local);
    5160:     PetscBTCreate(pcis->n,&bitmask);
    5161:     for (i=0;i<n_vertices;i++) {
    5162:       PetscBTSet(bitmask,pcbddc->local_primal_ref_node[i]);
    5163:     }

    5165:     for (i=0, n_R=0; i<pcis->n; i++) {
    5166:       if (!PetscBTLookup(bitmask,i)) {
    5167:         idx_R_local[n_R++] = i;
    5168:       }
    5169:     }
    5170:   } else { /* A different ordering (already computed) is present if we are reusing the Schur solver */
    5171:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    5173:     ISGetIndices(reuse_solver->is_R,(const PetscInt**)&idx_R_local);
    5174:     ISGetLocalSize(reuse_solver->is_R,&n_R);
    5175:   }

    5177:   /* Block code */
    5178:   vbs = 1;
    5179:   MatGetBlockSize(pcbddc->local_mat,&bs);
    5180:   if (bs>1 && !(n_vertices%bs)) {
    5181:     PetscBool is_blocked = PETSC_TRUE;
    5182:     PetscInt  *vary;
    5183:     if (!sub_schurs || !sub_schurs->reuse_solver) {
    5184:       PetscMalloc1(pcis->n/bs,&vary);
    5185:       PetscArrayzero(vary,pcis->n/bs);
    5186:       /* Verify that the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
    5187:       /* 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 */
    5188:       for (i=0; i<n_vertices; i++) vary[pcbddc->local_primal_ref_node[i]/bs]++;
    5189:       for (i=0; i<pcis->n/bs; i++) {
    5190:         if (vary[i]!=0 && vary[i]!=bs) {
    5191:           is_blocked = PETSC_FALSE;
    5192:           break;
    5193:         }
    5194:       }
    5195:       PetscFree(vary);
    5196:     } else {
    5197:       /* Verify directly the R set */
    5198:       for (i=0; i<n_R/bs; i++) {
    5199:         PetscInt j,node=idx_R_local[bs*i];
    5200:         for (j=1; j<bs; j++) {
    5201:           if (node != idx_R_local[bs*i+j]-j) {
    5202:             is_blocked = PETSC_FALSE;
    5203:             break;
    5204:           }
    5205:         }
    5206:       }
    5207:     }
    5208:     if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
    5209:       vbs = bs;
    5210:       for (i=0;i<n_R/vbs;i++) {
    5211:         idx_R_local[i] = idx_R_local[vbs*i]/vbs;
    5212:       }
    5213:     }
    5214:   }
    5215:   ISCreateBlock(PETSC_COMM_SELF,vbs,n_R/vbs,idx_R_local,PETSC_COPY_VALUES,&pcbddc->is_R_local);
    5216:   if (sub_schurs && sub_schurs->reuse_solver) {
    5217:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    5219:     ISRestoreIndices(reuse_solver->is_R,(const PetscInt**)&idx_R_local);
    5220:     ISDestroy(&reuse_solver->is_R);
    5221:     PetscObjectReference((PetscObject)pcbddc->is_R_local);
    5222:     reuse_solver->is_R = pcbddc->is_R_local;
    5223:   } else {
    5224:     PetscFree(idx_R_local);
    5225:   }

    5227:   /* print some info if requested */
    5228:   if (pcbddc->dbg_flag) {
    5229:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    5230:     PetscViewerFlush(pcbddc->dbg_viewer);
    5231:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    5232:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);
    5233:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %D, dirichlet_size = %D, boundary_size = %D\n",pcis->n,n_D,n_B);
    5234:     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);
    5235:     PetscViewerFlush(pcbddc->dbg_viewer);
    5236:   }

    5238:   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
    5239:   if (!sub_schurs || !sub_schurs->reuse_solver) {
    5240:     IS       is_aux1,is_aux2;
    5241:     PetscInt *aux_array1,*aux_array2,*is_indices,*idx_R_local;

    5243:     ISGetIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);
    5244:     PetscMalloc1(pcis->n_B-n_vertices,&aux_array1);
    5245:     PetscMalloc1(pcis->n_B-n_vertices,&aux_array2);
    5246:     ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);
    5247:     for (i=0; i<n_D; i++) {
    5248:       PetscBTSet(bitmask,is_indices[i]);
    5249:     }
    5250:     ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);
    5251:     for (i=0, j=0; i<n_R; i++) {
    5252:       if (!PetscBTLookup(bitmask,idx_R_local[i])) {
    5253:         aux_array1[j++] = i;
    5254:       }
    5255:     }
    5256:     ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);
    5257:     ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);
    5258:     for (i=0, j=0; i<n_B; i++) {
    5259:       if (!PetscBTLookup(bitmask,is_indices[i])) {
    5260:         aux_array2[j++] = i;
    5261:       }
    5262:     }
    5263:     ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);
    5264:     ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);
    5265:     VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);
    5266:     ISDestroy(&is_aux1);
    5267:     ISDestroy(&is_aux2);

    5269:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
    5270:       PetscMalloc1(n_D,&aux_array1);
    5271:       for (i=0, j=0; i<n_R; i++) {
    5272:         if (PetscBTLookup(bitmask,idx_R_local[i])) {
    5273:           aux_array1[j++] = i;
    5274:         }
    5275:       }
    5276:       ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);
    5277:       VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);
    5278:       ISDestroy(&is_aux1);
    5279:     }
    5280:     PetscBTDestroy(&bitmask);
    5281:     ISRestoreIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);
    5282:   } else {
    5283:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;
    5284:     IS                 tis;
    5285:     PetscInt           schur_size;

    5287:     ISGetLocalSize(reuse_solver->is_B,&schur_size);
    5288:     ISCreateStride(PETSC_COMM_SELF,schur_size,n_D,1,&tis);
    5289:     VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_B,reuse_solver->is_B,&pcbddc->R_to_B);
    5290:     ISDestroy(&tis);
    5291:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
    5292:       ISCreateStride(PETSC_COMM_SELF,n_D,0,1,&tis);
    5293:       VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);
    5294:       ISDestroy(&tis);
    5295:     }
    5296:   }
    5297:   return 0;
    5298: }

    5300: static PetscErrorCode MatNullSpacePropagateAny_Private(Mat A, IS is, Mat B)
    5301: {
    5302:   MatNullSpace   NullSpace;
    5303:   Mat            dmat;
    5304:   const Vec      *nullvecs;
    5305:   Vec            v,v2,*nullvecs2;
    5306:   VecScatter     sct = NULL;
    5307:   PetscContainer c;
    5308:   PetscScalar    *ddata;
    5309:   PetscInt       k,nnsp_size,bsiz,bsiz2,n,N,bs;
    5310:   PetscBool      nnsp_has_cnst;

    5312:   if (!is && !B) { /* MATIS */
    5313:     Mat_IS* matis = (Mat_IS*)A->data;

    5315:     if (!B) {
    5316:       MatISGetLocalMat(A,&B);
    5317:     }
    5318:     sct  = matis->cctx;
    5319:     PetscObjectReference((PetscObject)sct);
    5320:   } else {
    5321:     MatGetNullSpace(B,&NullSpace);
    5322:     if (!NullSpace) {
    5323:       MatGetNearNullSpace(B,&NullSpace);
    5324:     }
    5325:     if (NullSpace) return 0;
    5326:   }
    5327:   MatGetNullSpace(A,&NullSpace);
    5328:   if (!NullSpace) {
    5329:     MatGetNearNullSpace(A,&NullSpace);
    5330:   }
    5331:   if (!NullSpace) return 0;

    5333:   MatCreateVecs(A,&v,NULL);
    5334:   MatCreateVecs(B,&v2,NULL);
    5335:   if (!sct) {
    5336:     VecScatterCreate(v,is,v2,NULL,&sct);
    5337:   }
    5338:   MatNullSpaceGetVecs(NullSpace,&nnsp_has_cnst,&nnsp_size,(const Vec**)&nullvecs);
    5339:   bsiz = bsiz2 = nnsp_size+!!nnsp_has_cnst;
    5340:   PetscMalloc1(bsiz,&nullvecs2);
    5341:   VecGetBlockSize(v2,&bs);
    5342:   VecGetSize(v2,&N);
    5343:   VecGetLocalSize(v2,&n);
    5344:   PetscMalloc1(n*bsiz,&ddata);
    5345:   for (k=0;k<nnsp_size;k++) {
    5346:     VecCreateMPIWithArray(PetscObjectComm((PetscObject)B),bs,n,N,ddata + n*k,&nullvecs2[k]);
    5347:     VecScatterBegin(sct,nullvecs[k],nullvecs2[k],INSERT_VALUES,SCATTER_FORWARD);
    5348:     VecScatterEnd(sct,nullvecs[k],nullvecs2[k],INSERT_VALUES,SCATTER_FORWARD);
    5349:   }
    5350:   if (nnsp_has_cnst) {
    5351:     VecCreateMPIWithArray(PetscObjectComm((PetscObject)B),bs,n,N,ddata + n*nnsp_size,&nullvecs2[nnsp_size]);
    5352:     VecSet(nullvecs2[nnsp_size],1.0);
    5353:   }
    5354:   PCBDDCOrthonormalizeVecs(&bsiz2,nullvecs2);
    5355:   MatNullSpaceCreate(PetscObjectComm((PetscObject)B),PETSC_FALSE,bsiz2,nullvecs2,&NullSpace);

    5357:   MatCreateDense(PetscObjectComm((PetscObject)B),n,PETSC_DECIDE,N,bsiz2,ddata,&dmat);
    5358:   PetscContainerCreate(PetscObjectComm((PetscObject)B),&c);
    5359:   PetscContainerSetPointer(c,ddata);
    5360:   PetscContainerSetUserDestroy(c,PetscContainerUserDestroyDefault);
    5361:   PetscObjectCompose((PetscObject)dmat,"_PBDDC_Null_dmat_arr",(PetscObject)c);
    5362:   PetscContainerDestroy(&c);
    5363:   PetscObjectCompose((PetscObject)NullSpace,"_PBDDC_Null_dmat",(PetscObject)dmat);
    5364:   MatDestroy(&dmat);

    5366:   for (k=0;k<bsiz;k++) {
    5367:     VecDestroy(&nullvecs2[k]);
    5368:   }
    5369:   PetscFree(nullvecs2);
    5370:   MatSetNearNullSpace(B,NullSpace);
    5371:   MatNullSpaceDestroy(&NullSpace);
    5372:   VecDestroy(&v);
    5373:   VecDestroy(&v2);
    5374:   VecScatterDestroy(&sct);
    5375:   return 0;
    5376: }

    5378: PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, PetscBool dirichlet, PetscBool neumann)
    5379: {
    5380:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
    5381:   PC_IS          *pcis = (PC_IS*)pc->data;
    5382:   PC             pc_temp;
    5383:   Mat            A_RR;
    5384:   MatNullSpace   nnsp;
    5385:   MatReuse       reuse;
    5386:   PetscScalar    m_one = -1.0;
    5387:   PetscReal      value;
    5388:   PetscInt       n_D,n_R;
    5389:   PetscBool      issbaij,opts;
    5390:   void           (*f)(void) = NULL;
    5391:   char           dir_prefix[256],neu_prefix[256],str_level[16];
    5392:   size_t         len;

    5394:   PetscLogEventBegin(PC_BDDC_LocalSolvers[pcbddc->current_level],pc,0,0,0);
    5395:   /* approximate solver, propagate NearNullSpace if needed */
    5396:   if (!pc->setupcalled && (pcbddc->NullSpace_corr[0] || pcbddc->NullSpace_corr[2])) {
    5397:     MatNullSpace gnnsp1,gnnsp2;
    5398:     PetscBool    lhas,ghas;

    5400:     MatGetNearNullSpace(pcbddc->local_mat,&nnsp);
    5401:     MatGetNearNullSpace(pc->pmat,&gnnsp1);
    5402:     MatGetNullSpace(pc->pmat,&gnnsp2);
    5403:     lhas = nnsp ? PETSC_TRUE : PETSC_FALSE;
    5404:     MPIU_Allreduce(&lhas,&ghas,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
    5405:     if (!ghas && (gnnsp1 || gnnsp2)) {
    5406:       MatNullSpacePropagateAny_Private(pc->pmat,NULL,NULL);
    5407:     }
    5408:   }

    5410:   /* compute prefixes */
    5411:   PetscStrcpy(dir_prefix,"");
    5412:   PetscStrcpy(neu_prefix,"");
    5413:   if (!pcbddc->current_level) {
    5414:     PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,sizeof(dir_prefix));
    5415:     PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,sizeof(neu_prefix));
    5416:     PetscStrlcat(dir_prefix,"pc_bddc_dirichlet_",sizeof(dir_prefix));
    5417:     PetscStrlcat(neu_prefix,"pc_bddc_neumann_",sizeof(neu_prefix));
    5418:   } else {
    5419:     PetscSNPrintf(str_level,sizeof(str_level),"l%d_",(int)(pcbddc->current_level));
    5420:     PetscStrlen(((PetscObject)pc)->prefix,&len);
    5421:     len -= 15; /* remove "pc_bddc_coarse_" */
    5422:     if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
    5423:     if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
    5424:     /* Nonstandard use of PetscStrncpy() to only copy a portion of the input string */
    5425:     PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,len+1);
    5426:     PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len+1);
    5427:     PetscStrlcat(dir_prefix,"pc_bddc_dirichlet_",sizeof(dir_prefix));
    5428:     PetscStrlcat(neu_prefix,"pc_bddc_neumann_",sizeof(neu_prefix));
    5429:     PetscStrlcat(dir_prefix,str_level,sizeof(dir_prefix));
    5430:     PetscStrlcat(neu_prefix,str_level,sizeof(neu_prefix));
    5431:   }

    5433:   /* DIRICHLET PROBLEM */
    5434:   if (dirichlet) {
    5435:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    5436:     if (pcbddc->benign_n && !pcbddc->benign_change_explicit) {
    5438:       if (pcbddc->dbg_flag) {
    5439:         Mat    A_IIn;

    5441:         PCBDDCBenignProject(pc,pcis->is_I_local,pcis->is_I_local,&A_IIn);
    5442:         MatDestroy(&pcis->A_II);
    5443:         pcis->A_II = A_IIn;
    5444:       }
    5445:     }
    5446:     if (pcbddc->local_mat->symmetric_set) {
    5447:       MatSetOption(pcis->A_II,MAT_SYMMETRIC,pcbddc->local_mat->symmetric);
    5448:     }
    5449:     /* Matrix for Dirichlet problem is pcis->A_II */
    5450:     n_D  = pcis->n - pcis->n_B;
    5451:     opts = PETSC_FALSE;
    5452:     if (!pcbddc->ksp_D) { /* create object if not yet build */
    5453:       opts = PETSC_TRUE;
    5454:       KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);
    5455:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);
    5456:       /* default */
    5457:       KSPSetType(pcbddc->ksp_D,KSPPREONLY);
    5458:       KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);
    5459:       PetscObjectTypeCompare((PetscObject)pcis->pA_II,MATSEQSBAIJ,&issbaij);
    5460:       KSPGetPC(pcbddc->ksp_D,&pc_temp);
    5461:       if (issbaij) {
    5462:         PCSetType(pc_temp,PCCHOLESKY);
    5463:       } else {
    5464:         PCSetType(pc_temp,PCLU);
    5465:       }
    5466:       KSPSetErrorIfNotConverged(pcbddc->ksp_D,pc->erroriffailure);
    5467:     }
    5468:     MatSetOptionsPrefix(pcis->pA_II,((PetscObject)pcbddc->ksp_D)->prefix);
    5469:     KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->pA_II);
    5470:     /* Allow user's customization */
    5471:     if (opts) {
    5472:       KSPSetFromOptions(pcbddc->ksp_D);
    5473:     }
    5474:     MatGetNearNullSpace(pcis->pA_II,&nnsp);
    5475:     if (pcbddc->NullSpace_corr[0] && !nnsp) { /* approximate solver, propagate NearNullSpace */
    5476:       MatNullSpacePropagateAny_Private(pcbddc->local_mat,pcis->is_I_local,pcis->pA_II);
    5477:     }
    5478:     MatGetNearNullSpace(pcis->pA_II,&nnsp);
    5479:     KSPGetPC(pcbddc->ksp_D,&pc_temp);
    5480:     PetscObjectQueryFunction((PetscObject)pc_temp,"PCSetCoordinates_C",&f);
    5481:     if (f && pcbddc->mat_graph->cloc && !nnsp) {
    5482:       PetscReal      *coords = pcbddc->mat_graph->coords,*scoords;
    5483:       const PetscInt *idxs;
    5484:       PetscInt       cdim = pcbddc->mat_graph->cdim,nl,i,d;

    5486:       ISGetLocalSize(pcis->is_I_local,&nl);
    5487:       ISGetIndices(pcis->is_I_local,&idxs);
    5488:       PetscMalloc1(nl*cdim,&scoords);
    5489:       for (i=0;i<nl;i++) {
    5490:         for (d=0;d<cdim;d++) {
    5491:           scoords[i*cdim+d] = coords[idxs[i]*cdim+d];
    5492:         }
    5493:       }
    5494:       ISRestoreIndices(pcis->is_I_local,&idxs);
    5495:       PCSetCoordinates(pc_temp,cdim,nl,scoords);
    5496:       PetscFree(scoords);
    5497:     }
    5498:     if (sub_schurs && sub_schurs->reuse_solver) {
    5499:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    5501:       KSPSetPC(pcbddc->ksp_D,reuse_solver->interior_solver);
    5502:     }

    5504:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
    5505:     if (!n_D) {
    5506:       KSPGetPC(pcbddc->ksp_D,&pc_temp);
    5507:       PCSetType(pc_temp,PCNONE);
    5508:     }
    5509:     KSPSetUp(pcbddc->ksp_D);
    5510:     /* set ksp_D into pcis data */
    5511:     PetscObjectReference((PetscObject)pcbddc->ksp_D);
    5512:     KSPDestroy(&pcis->ksp_D);
    5513:     pcis->ksp_D = pcbddc->ksp_D;
    5514:   }

    5516:   /* NEUMANN PROBLEM */
    5517:   A_RR = NULL;
    5518:   if (neumann) {
    5519:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    5520:     PetscInt        ibs,mbs;
    5521:     PetscBool       issbaij, reuse_neumann_solver;
    5522:     Mat_IS*         matis = (Mat_IS*)pc->pmat->data;

    5524:     reuse_neumann_solver = PETSC_FALSE;
    5525:     if (sub_schurs && sub_schurs->reuse_solver) {
    5526:       IS iP;

    5528:       reuse_neumann_solver = PETSC_TRUE;
    5529:       PetscObjectQuery((PetscObject)sub_schurs->A,"__KSPFETIDP_iP",(PetscObject*)&iP);
    5530:       if (iP) reuse_neumann_solver = PETSC_FALSE;
    5531:     }
    5532:     /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
    5533:     ISGetSize(pcbddc->is_R_local,&n_R);
    5534:     if (pcbddc->ksp_R) { /* already created ksp */
    5535:       PetscInt nn_R;
    5536:       KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);
    5537:       PetscObjectReference((PetscObject)A_RR);
    5538:       MatGetSize(A_RR,&nn_R,NULL);
    5539:       if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
    5540:         KSPReset(pcbddc->ksp_R);
    5541:         MatDestroy(&A_RR);
    5542:         reuse = MAT_INITIAL_MATRIX;
    5543:       } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
    5544:         if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
    5545:           MatDestroy(&A_RR);
    5546:           reuse = MAT_INITIAL_MATRIX;
    5547:         } else { /* safe to reuse the matrix */
    5548:           reuse = MAT_REUSE_MATRIX;
    5549:         }
    5550:       }
    5551:       /* last check */
    5552:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
    5553:         MatDestroy(&A_RR);
    5554:         reuse = MAT_INITIAL_MATRIX;
    5555:       }
    5556:     } else { /* first time, so we need to create the matrix */
    5557:       reuse = MAT_INITIAL_MATRIX;
    5558:     }
    5559:     /* convert pcbddc->local_mat if needed later in PCBDDCSetUpCorrection
    5560:        TODO: Get Rid of these conversions */
    5561:     MatGetBlockSize(pcbddc->local_mat,&mbs);
    5562:     ISGetBlockSize(pcbddc->is_R_local,&ibs);
    5563:     PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);
    5564:     if (ibs != mbs) { /* need to convert to SEQAIJ to extract any submatrix with is_R_local */
    5565:       if (matis->A == pcbddc->local_mat) {
    5566:         MatDestroy(&pcbddc->local_mat);
    5567:         MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
    5568:       } else {
    5569:         MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
    5570:       }
    5571:     } else if (issbaij) { /* need to convert to BAIJ to get offdiagonal blocks */
    5572:       if (matis->A == pcbddc->local_mat) {
    5573:         MatDestroy(&pcbddc->local_mat);
    5574:         MatConvert(matis->A,mbs > 1 ? MATSEQBAIJ : MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
    5575:       } else {
    5576:         MatConvert(pcbddc->local_mat,mbs > 1 ? MATSEQBAIJ : MATSEQAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
    5577:       }
    5578:     }
    5579:     /* extract A_RR */
    5580:     if (reuse_neumann_solver) {
    5581:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    5583:       if (pcbddc->dbg_flag) { /* we need A_RR to test the solver later */
    5584:         MatDestroy(&A_RR);
    5585:         if (reuse_solver->benign_n) { /* we are not using the explicit change of basis on the pressures */
    5586:           PCBDDCBenignProject(pc,pcbddc->is_R_local,pcbddc->is_R_local,&A_RR);
    5587:         } else {
    5588:           MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_RR);
    5589:         }
    5590:       } else {
    5591:         MatDestroy(&A_RR);
    5592:         PCGetOperators(reuse_solver->correction_solver,&A_RR,NULL);
    5593:         PetscObjectReference((PetscObject)A_RR);
    5594:       }
    5595:     } else { /* we have to build the neumann solver, so we need to extract the relevant matrix */
    5596:       MatCreateSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);
    5597:     }
    5598:     if (pcbddc->local_mat->symmetric_set) {
    5599:       MatSetOption(A_RR,MAT_SYMMETRIC,pcbddc->local_mat->symmetric);
    5600:     }
    5601:     opts = PETSC_FALSE;
    5602:     if (!pcbddc->ksp_R) { /* create object if not present */
    5603:       opts = PETSC_TRUE;
    5604:       KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);
    5605:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);
    5606:       /* default */
    5607:       KSPSetType(pcbddc->ksp_R,KSPPREONLY);
    5608:       KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);
    5609:       KSPGetPC(pcbddc->ksp_R,&pc_temp);
    5610:       PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);
    5611:       if (issbaij) {
    5612:         PCSetType(pc_temp,PCCHOLESKY);
    5613:       } else {
    5614:         PCSetType(pc_temp,PCLU);
    5615:       }
    5616:       KSPSetErrorIfNotConverged(pcbddc->ksp_R,pc->erroriffailure);
    5617:     }
    5618:     KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);
    5619:     MatSetOptionsPrefix(A_RR,((PetscObject)pcbddc->ksp_R)->prefix);
    5620:     if (opts) { /* Allow user's customization once */
    5621:       KSPSetFromOptions(pcbddc->ksp_R);
    5622:     }
    5623:     MatGetNearNullSpace(A_RR,&nnsp);
    5624:     if (pcbddc->NullSpace_corr[2] && !nnsp) { /* approximate solver, propagate NearNullSpace */
    5625:       MatNullSpacePropagateAny_Private(pcbddc->local_mat,pcbddc->is_R_local,A_RR);
    5626:     }
    5627:     MatGetNearNullSpace(A_RR,&nnsp);
    5628:     KSPGetPC(pcbddc->ksp_R,&pc_temp);
    5629:     PetscObjectQueryFunction((PetscObject)pc_temp,"PCSetCoordinates_C",&f);
    5630:     if (f && pcbddc->mat_graph->cloc && !nnsp) {
    5631:       PetscReal      *coords = pcbddc->mat_graph->coords,*scoords;
    5632:       const PetscInt *idxs;
    5633:       PetscInt       cdim = pcbddc->mat_graph->cdim,nl,i,d;

    5635:       ISGetLocalSize(pcbddc->is_R_local,&nl);
    5636:       ISGetIndices(pcbddc->is_R_local,&idxs);
    5637:       PetscMalloc1(nl*cdim,&scoords);
    5638:       for (i=0;i<nl;i++) {
    5639:         for (d=0;d<cdim;d++) {
    5640:           scoords[i*cdim+d] = coords[idxs[i]*cdim+d];
    5641:         }
    5642:       }
    5643:       ISRestoreIndices(pcbddc->is_R_local,&idxs);
    5644:       PCSetCoordinates(pc_temp,cdim,nl,scoords);
    5645:       PetscFree(scoords);
    5646:     }

    5648:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
    5649:     if (!n_R) {
    5650:       KSPGetPC(pcbddc->ksp_R,&pc_temp);
    5651:       PCSetType(pc_temp,PCNONE);
    5652:     }
    5653:     /* Reuse solver if it is present */
    5654:     if (reuse_neumann_solver) {
    5655:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    5657:       KSPSetPC(pcbddc->ksp_R,reuse_solver->correction_solver);
    5658:     }
    5659:     KSPSetUp(pcbddc->ksp_R);
    5660:   }

    5662:   if (pcbddc->dbg_flag) {
    5663:     PetscViewerFlush(pcbddc->dbg_viewer);
    5664:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    5665:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    5666:   }
    5667:   PetscLogEventEnd(PC_BDDC_LocalSolvers[pcbddc->current_level],pc,0,0,0);

    5669:   /* adapt Dirichlet and Neumann solvers if a nullspace correction has been requested */
    5670:   if (pcbddc->NullSpace_corr[0]) {
    5671:     PCBDDCSetUseExactDirichlet(pc,PETSC_FALSE);
    5672:   }
    5673:   if (dirichlet && pcbddc->NullSpace_corr[0] && !pcbddc->switch_static) {
    5674:     PCBDDCNullSpaceAssembleCorrection(pc,PETSC_TRUE,pcbddc->NullSpace_corr[1]);
    5675:   }
    5676:   if (neumann && pcbddc->NullSpace_corr[2]) {
    5677:     PCBDDCNullSpaceAssembleCorrection(pc,PETSC_FALSE,pcbddc->NullSpace_corr[3]);
    5678:   }
    5679:   /* check Dirichlet and Neumann solvers */
    5680:   if (pcbddc->dbg_flag) {
    5681:     if (dirichlet) { /* Dirichlet */
    5682:       VecSetRandom(pcis->vec1_D,NULL);
    5683:       MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);
    5684:       KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);
    5685:       KSPCheckSolve(pcbddc->ksp_D,pc,pcis->vec2_D);
    5686:       VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);
    5687:       VecNorm(pcis->vec1_D,NORM_INFINITY,&value);
    5688:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve (%s) = % 1.14e \n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_D))->prefix,value);
    5689:       PetscViewerFlush(pcbddc->dbg_viewer);
    5690:     }
    5691:     if (neumann) { /* Neumann */
    5692:       VecSetRandom(pcbddc->vec1_R,NULL);
    5693:       MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);
    5694:       KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);
    5695:       KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec2_R);
    5696:       VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);
    5697:       VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);
    5698:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann solve (%s) = % 1.14e\n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_R))->prefix,value);
    5699:       PetscViewerFlush(pcbddc->dbg_viewer);
    5700:     }
    5701:   }
    5702:   /* free Neumann problem's matrix */
    5703:   MatDestroy(&A_RR);
    5704:   return 0;
    5705: }

    5707: static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec inout_B, Vec inout_D, PetscBool applytranspose)
    5708: {
    5709:   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
    5710:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    5711:   PetscBool       reuse_solver = sub_schurs ? ( sub_schurs->reuse_solver ? PETSC_TRUE : PETSC_FALSE) : PETSC_FALSE;

    5713:   if (!reuse_solver) {
    5714:     VecSet(pcbddc->vec1_R,0.);
    5715:   }
    5716:   if (!pcbddc->switch_static) {
    5717:     if (applytranspose && pcbddc->local_auxmat1) {
    5718:       MatMultTranspose(pcbddc->local_auxmat2,inout_B,pcbddc->vec1_C);
    5719:       MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);
    5720:     }
    5721:     if (!reuse_solver) {
    5722:       VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    5723:       VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    5724:     } else {
    5725:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    5727:       VecScatterBegin(reuse_solver->correction_scatter_B,inout_B,reuse_solver->rhs_B,INSERT_VALUES,SCATTER_FORWARD);
    5728:       VecScatterEnd(reuse_solver->correction_scatter_B,inout_B,reuse_solver->rhs_B,INSERT_VALUES,SCATTER_FORWARD);
    5729:     }
    5730:   } else {
    5731:     VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    5732:     VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    5733:     VecScatterBegin(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    5734:     VecScatterEnd(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    5735:     if (applytranspose && pcbddc->local_auxmat1) {
    5736:       MatMultTranspose(pcbddc->local_auxmat2,pcbddc->vec1_R,pcbddc->vec1_C);
    5737:       MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);
    5738:       VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    5739:       VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    5740:     }
    5741:   }
    5742:   PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][1],pc,0,0,0);
    5743:   if (!reuse_solver || pcbddc->switch_static) {
    5744:     if (applytranspose) {
    5745:       KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);
    5746:     } else {
    5747:       KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);
    5748:     }
    5749:     KSPCheckSolve(pcbddc->ksp_R,pc,pcbddc->vec1_R);
    5750:   } else {
    5751:     PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    5753:     if (applytranspose) {
    5754:       MatFactorSolveSchurComplementTranspose(reuse_solver->F,reuse_solver->rhs_B,reuse_solver->sol_B);
    5755:     } else {
    5756:       MatFactorSolveSchurComplement(reuse_solver->F,reuse_solver->rhs_B,reuse_solver->sol_B);
    5757:     }
    5758:   }
    5759:   PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][1],pc,0,0,0);
    5760:   VecSet(inout_B,0.);
    5761:   if (!pcbddc->switch_static) {
    5762:     if (!reuse_solver) {
    5763:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    5764:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    5765:     } else {
    5766:       PCBDDCReuseSolvers reuse_solver = sub_schurs->reuse_solver;

    5768:       VecScatterBegin(reuse_solver->correction_scatter_B,reuse_solver->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);
    5769:       VecScatterEnd(reuse_solver->correction_scatter_B,reuse_solver->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);
    5770:     }
    5771:     if (!applytranspose && pcbddc->local_auxmat1) {
    5772:       MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);
    5773:       MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,inout_B,inout_B);
    5774:     }
    5775:   } else {
    5776:     VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    5777:     VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    5778:     VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
    5779:     VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
    5780:     if (!applytranspose && pcbddc->local_auxmat1) {
    5781:       MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);
    5782:       MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);
    5783:     }
    5784:     VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    5785:     VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    5786:     VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
    5787:     VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
    5788:   }
    5789:   return 0;
    5790: }

    5792: /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
    5793: PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
    5794: {
    5795:   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
    5796:   PC_IS*            pcis = (PC_IS*)  (pc->data);
    5797:   const PetscScalar zero = 0.0;

    5799:   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
    5800:   if (!pcbddc->benign_apply_coarse_only) {
    5801:     if (applytranspose) {
    5802:       MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);
    5803:       if (pcbddc->switch_static) MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);
    5804:     } else {
    5805:       MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);
    5806:       if (pcbddc->switch_static) MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P);
    5807:     }
    5808:   } else {
    5809:     VecSet(pcbddc->vec1_P,zero);
    5810:   }

    5812:   /* add p0 to the last value of vec1_P holding the coarse dof relative to p0 */
    5813:   if (pcbddc->benign_n) {
    5814:     PetscScalar *array;
    5815:     PetscInt    j;

    5817:     VecGetArray(pcbddc->vec1_P,&array);
    5818:     for (j=0;j<pcbddc->benign_n;j++) array[pcbddc->local_primal_size-pcbddc->benign_n+j] += pcbddc->benign_p0[j];
    5819:     VecRestoreArray(pcbddc->vec1_P,&array);
    5820:   }

    5822:   /* start communications from local primal nodes to rhs of coarse solver */
    5823:   VecSet(pcbddc->coarse_vec,zero);
    5824:   PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);
    5825:   PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);

    5827:   /* Coarse solution -> rhs and sol updated inside PCBDDCScattarCoarseDataBegin/End */
    5828:   if (pcbddc->coarse_ksp) {
    5829:     Mat          coarse_mat;
    5830:     Vec          rhs,sol;
    5831:     MatNullSpace nullsp;
    5832:     PetscBool    isbddc = PETSC_FALSE;

    5834:     if (pcbddc->benign_have_null) {
    5835:       PC        coarse_pc;

    5837:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
    5838:       PetscObjectTypeCompare((PetscObject)coarse_pc,PCBDDC,&isbddc);
    5839:       /* we need to propagate to coarser levels the need for a possible benign correction */
    5840:       if (isbddc && pcbddc->benign_apply_coarse_only && !pcbddc->benign_skip_correction) {
    5841:         PC_BDDC* coarsepcbddc = (PC_BDDC*)(coarse_pc->data);
    5842:         coarsepcbddc->benign_skip_correction = PETSC_FALSE;
    5843:         coarsepcbddc->benign_apply_coarse_only = PETSC_TRUE;
    5844:       }
    5845:     }
    5846:     KSPGetRhs(pcbddc->coarse_ksp,&rhs);
    5847:     KSPGetSolution(pcbddc->coarse_ksp,&sol);
    5848:     KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);
    5849:     if (applytranspose) {
    5851:       PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][2],pc,0,0,0);
    5852:       KSPSolveTranspose(pcbddc->coarse_ksp,rhs,sol);
    5853:       PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][2],pc,0,0,0);
    5854:       KSPCheckSolve(pcbddc->coarse_ksp,pc,sol);
    5855:       MatGetTransposeNullSpace(coarse_mat,&nullsp);
    5856:       if (nullsp) {
    5857:         MatNullSpaceRemove(nullsp,sol);
    5858:       }
    5859:     } else {
    5860:       MatGetNullSpace(coarse_mat,&nullsp);
    5861:       if (pcbddc->benign_apply_coarse_only && isbddc) { /* need just to apply the coarse preconditioner during presolve */
    5862:         PC        coarse_pc;

    5864:         if (nullsp) {
    5865:           MatNullSpaceRemove(nullsp,rhs);
    5866:         }
    5867:         KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
    5868:         PCPreSolve(coarse_pc,pcbddc->coarse_ksp);
    5869:         PCBDDCBenignRemoveInterior(coarse_pc,rhs,sol);
    5870:         PCPostSolve(coarse_pc,pcbddc->coarse_ksp);
    5871:       } else {
    5872:         PetscLogEventBegin(PC_BDDC_Solves[pcbddc->current_level][2],pc,0,0,0);
    5873:         KSPSolve(pcbddc->coarse_ksp,rhs,sol);
    5874:         PetscLogEventEnd(PC_BDDC_Solves[pcbddc->current_level][2],pc,0,0,0);
    5875:         KSPCheckSolve(pcbddc->coarse_ksp,pc,sol);
    5876:         if (nullsp) {
    5877:           MatNullSpaceRemove(nullsp,sol);
    5878:         }
    5879:       }
    5880:     }
    5881:     /* we don't need the benign correction at coarser levels anymore */
    5882:     if (pcbddc->benign_have_null && isbddc) {
    5883:       PC        coarse_pc;
    5884:       PC_BDDC*  coarsepcbddc;

    5886:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
    5887:       coarsepcbddc = (PC_BDDC*)(coarse_pc->data);
    5888:       coarsepcbddc->benign_skip_correction = PETSC_TRUE;
    5889:       coarsepcbddc->benign_apply_coarse_only = PETSC_FALSE;
    5890:     }
    5891:   }

    5893:   /* Local solution on R nodes */
    5894:   if (pcis->n && !pcbddc->benign_apply_coarse_only) {
    5895:     PCBDDCSolveSubstructureCorrection(pc,pcis->vec1_B,pcis->vec1_D,applytranspose);
    5896:   }
    5897:   /* communications from coarse sol to local primal nodes */
    5898:   PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);
    5899:   PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);

    5901:   /* Sum contributions from the two levels */
    5902:   if (!pcbddc->benign_apply_coarse_only) {
    5903:     if (applytranspose) {
    5904:       MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);
    5905:       if (pcbddc->switch_static) MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);
    5906:     } else {
    5907:       MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);
    5908:       if (pcbddc->switch_static) MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D);
    5909:     }
    5910:     /* store p0 */
    5911:     if (pcbddc->benign_n) {
    5912:       PetscScalar *array;
    5913:       PetscInt    j;

    5915:       VecGetArray(pcbddc->vec1_P,&array);
    5916:       for (j=0;j<pcbddc->benign_n;j++) pcbddc->benign_p0[j] = array[pcbddc->local_primal_size-pcbddc->benign_n+j];
    5917:       VecRestoreArray(pcbddc->vec1_P,&array);
    5918:     }
    5919:   } else { /* expand the coarse solution */
    5920:     if (applytranspose) {
    5921:       MatMult(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B);
    5922:     } else {
    5923:       MatMult(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B);
    5924:     }
    5925:   }
    5926:   return 0;
    5927: }

    5929: PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
    5930: {
    5931:   PC_BDDC*          pcbddc = (PC_BDDC*)(pc->data);
    5932:   Vec               from,to;
    5933:   const PetscScalar *array;

    5935:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
    5936:     from = pcbddc->coarse_vec;
    5937:     to = pcbddc->vec1_P;
    5938:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
    5939:       Vec tvec;

    5941:       KSPGetRhs(pcbddc->coarse_ksp,&tvec);
    5942:       VecResetArray(tvec);
    5943:       KSPGetSolution(pcbddc->coarse_ksp,&tvec);
    5944:       VecGetArrayRead(tvec,&array);
    5945:       VecPlaceArray(from,array);
    5946:       VecRestoreArrayRead(tvec,&array);
    5947:     }
    5948:   } else { /* from local to global -> put data in coarse right hand side */
    5949:     from = pcbddc->vec1_P;
    5950:     to = pcbddc->coarse_vec;
    5951:   }
    5952:   VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);
    5953:   return 0;
    5954: }

    5956: PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
    5957: {
    5958:   PC_BDDC*          pcbddc = (PC_BDDC*)(pc->data);
    5959:   Vec               from,to;
    5960:   const PetscScalar *array;

    5962:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
    5963:     from = pcbddc->coarse_vec;
    5964:     to = pcbddc->vec1_P;
    5965:   } else { /* from local to global -> put data in coarse right hand side */
    5966:     from = pcbddc->vec1_P;
    5967:     to = pcbddc->coarse_vec;
    5968:   }
    5969:   VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);
    5970:   if (smode == SCATTER_FORWARD) {
    5971:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
    5972:       Vec tvec;

    5974:       KSPGetRhs(pcbddc->coarse_ksp,&tvec);
    5975:       VecGetArrayRead(to,&array);
    5976:       VecPlaceArray(tvec,array);
    5977:       VecRestoreArrayRead(to,&array);
    5978:     }
    5979:   } else {
    5980:     if (pcbddc->coarse_ksp) { /* restore array of pcbddc->coarse_vec */
    5981:      VecResetArray(from);
    5982:     }
    5983:   }
    5984:   return 0;
    5985: }

    5987: PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
    5988: {
    5989:   PetscErrorCode    ierr;
    5990:   PC_IS*            pcis = (PC_IS*)(pc->data);
    5991:   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
    5992:   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
    5993:   /* one and zero */
    5994:   PetscScalar       one=1.0,zero=0.0;
    5995:   /* space to store constraints and their local indices */
    5996:   PetscScalar       *constraints_data;
    5997:   PetscInt          *constraints_idxs,*constraints_idxs_B;
    5998:   PetscInt          *constraints_idxs_ptr,*constraints_data_ptr;
    5999:   PetscInt          *constraints_n;
    6000:   /* iterators */
    6001:   PetscInt          i,j,k,total_counts,total_counts_cc,cum;
    6002:   /* BLAS integers */
    6003:   PetscBLASInt      lwork,lierr;
    6004:   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
    6005:   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
    6006:   /* reuse */
    6007:   PetscInt          olocal_primal_size,olocal_primal_size_cc;
    6008:   PetscInt          *olocal_primal_ref_node,*olocal_primal_ref_mult;
    6009:   /* change of basis */
    6010:   PetscBool         qr_needed;
    6011:   PetscBT           change_basis,qr_needed_idx;
    6012:   /* auxiliary stuff */
    6013:   PetscInt          *nnz,*is_indices;
    6014:   PetscInt          ncc;
    6015:   /* some quantities */
    6016:   PetscInt          n_vertices,total_primal_vertices,valid_constraints;
    6017:   PetscInt          size_of_constraint,max_size_of_constraint=0,max_constraints,temp_constraints;
    6018:   PetscReal         tol; /* tolerance for retaining eigenmodes */

    6020:   tol  = PetscSqrtReal(PETSC_SMALL);
    6021:   /* Destroy Mat objects computed previously */
    6022:   MatDestroy(&pcbddc->ChangeOfBasisMatrix);
    6023:   MatDestroy(&pcbddc->ConstraintMatrix);
    6024:   MatDestroy(&pcbddc->switch_static_change);
    6025:   /* save info on constraints from previous setup (if any) */
    6026:   olocal_primal_size = pcbddc->local_primal_size;
    6027:   olocal_primal_size_cc = pcbddc->local_primal_size_cc;
    6028:   PetscMalloc2(olocal_primal_size_cc,&olocal_primal_ref_node,olocal_primal_size_cc,&olocal_primal_ref_mult);
    6029:   PetscArraycpy(olocal_primal_ref_node,pcbddc->local_primal_ref_node,olocal_primal_size_cc);
    6030:   PetscArraycpy(olocal_primal_ref_mult,pcbddc->local_primal_ref_mult,olocal_primal_size_cc);
    6031:   PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);
    6032:   PetscFree(pcbddc->primal_indices_local_idxs);

    6034:   if (!pcbddc->adaptive_selection) {
    6035:     IS           ISForVertices,*ISForFaces,*ISForEdges;
    6036:     MatNullSpace nearnullsp;
    6037:     const Vec    *nearnullvecs;
    6038:     Vec          *localnearnullsp;
    6039:     PetscScalar  *array;
    6040:     PetscInt     n_ISForFaces,n_ISForEdges,nnsp_size;
    6041:     PetscBool    nnsp_has_cnst;
    6042:     /* LAPACK working arrays for SVD or POD */
    6043:     PetscBool    skip_lapack,boolforchange;
    6044:     PetscScalar  *work;
    6045:     PetscReal    *singular_vals;
    6046: #if defined(PETSC_USE_COMPLEX)
    6047:     PetscReal    *rwork;
    6048: #endif
    6049:     PetscScalar  *temp_basis = NULL,*correlation_mat = NULL;
    6050:     PetscBLASInt dummy_int=1;
    6051:     PetscScalar  dummy_scalar=1.;
    6052:     PetscBool    use_pod = PETSC_FALSE;

    6054:     /* MKL SVD with same input gives different results on different processes! */
    6055: #if defined(PETSC_MISSING_LAPACK_GESVD) || defined(PETSC_HAVE_MKL_LIBS)
    6056:     use_pod = PETSC_TRUE;
    6057: #endif
    6058:     /* Get index sets for faces, edges and vertices from graph */
    6059:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
    6060:     /* print some info */
    6061:     if (pcbddc->dbg_flag && (!pcbddc->sub_schurs || pcbddc->sub_schurs_rebuild)) {
    6062:       PetscInt nv;

    6064:       PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);
    6065:       ISGetSize(ISForVertices,&nv);
    6066:       PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    6067:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
    6068:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%D)\n",PetscGlobalRank,nv,pcbddc->use_vertices);
    6069:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%D)\n",PetscGlobalRank,n_ISForEdges,pcbddc->use_edges);
    6070:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%D)\n",PetscGlobalRank,n_ISForFaces,pcbddc->use_faces);
    6071:       PetscViewerFlush(pcbddc->dbg_viewer);
    6072:       PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);
    6073:     }

    6075:     /* free unneeded index sets */
    6076:     if (!pcbddc->use_vertices) {
    6077:       ISDestroy(&ISForVertices);
    6078:     }
    6079:     if (!pcbddc->use_edges) {
    6080:       for (i=0;i<n_ISForEdges;i++) {
    6081:         ISDestroy(&ISForEdges[i]);
    6082:       }
    6083:       PetscFree(ISForEdges);
    6084:       n_ISForEdges = 0;
    6085:     }
    6086:     if (!pcbddc->use_faces) {
    6087:       for (i=0;i<n_ISForFaces;i++) {
    6088:         ISDestroy(&ISForFaces[i]);
    6089:       }
    6090:       PetscFree(ISForFaces);
    6091:       n_ISForFaces = 0;
    6092:     }

    6094:     /* check if near null space is attached to global mat */
    6095:     if (pcbddc->use_nnsp) {
    6096:       MatGetNearNullSpace(pc->pmat,&nearnullsp);
    6097:     } else nearnullsp = NULL;

    6099:     if (nearnullsp) {
    6100:       MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);
    6101:       /* remove any stored info */
    6102:       MatNullSpaceDestroy(&pcbddc->onearnullspace);
    6103:       PetscFree(pcbddc->onearnullvecs_state);
    6104:       /* store information for BDDC solver reuse */
    6105:       PetscObjectReference((PetscObject)nearnullsp);
    6106:       pcbddc->onearnullspace = nearnullsp;
    6107:       PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);
    6108:       for (i=0;i<nnsp_size;i++) {
    6109:         PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);
    6110:       }
    6111:     } else { /* if near null space is not provided BDDC uses constants by default */
    6112:       nnsp_size = 0;
    6113:       nnsp_has_cnst = PETSC_TRUE;
    6114:     }
    6115:     /* get max number of constraints on a single cc */
    6116:     max_constraints = nnsp_size;
    6117:     if (nnsp_has_cnst) max_constraints++;

    6119:     /*
    6120:          Evaluate maximum storage size needed by the procedure
    6121:          - Indices for connected component i stored at "constraints_idxs + constraints_idxs_ptr[i]"
    6122:          - Values for constraints on connected component i stored at "constraints_data + constraints_data_ptr[i]"
    6123:          There can be multiple constraints per connected component
    6124:                                                                                                                                                            */
    6125:     n_vertices = 0;
    6126:     if (ISForVertices) {
    6127:       ISGetSize(ISForVertices,&n_vertices);
    6128:     }
    6129:     ncc = n_vertices+n_ISForFaces+n_ISForEdges;
    6130:     PetscMalloc3(ncc+1,&constraints_idxs_ptr,ncc+1,&constraints_data_ptr,ncc,&constraints_n);

    6132:     total_counts = n_ISForFaces+n_ISForEdges;
    6133:     total_counts *= max_constraints;
    6134:     total_counts += n_vertices;
    6135:     PetscBTCreate(total_counts,&change_basis);

    6137:     total_counts = 0;
    6138:     max_size_of_constraint = 0;
    6139:     for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
    6140:       IS used_is;
    6141:       if (i<n_ISForEdges) {
    6142:         used_is = ISForEdges[i];
    6143:       } else {
    6144:         used_is = ISForFaces[i-n_ISForEdges];
    6145:       }
    6146:       ISGetSize(used_is,&j);
    6147:       total_counts += j;
    6148:       max_size_of_constraint = PetscMax(j,max_size_of_constraint);
    6149:     }
    6150:     PetscMalloc3(total_counts*max_constraints+n_vertices,&constraints_data,total_counts+n_vertices,&constraints_idxs,total_counts+n_vertices,&constraints_idxs_B);

    6152:     /* get local part of global near null space vectors */
    6153:     PetscMalloc1(nnsp_size,&localnearnullsp);
    6154:     for (k=0;k<nnsp_size;k++) {
    6155:       VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);
    6156:       VecScatterBegin(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);
    6157:       VecScatterEnd(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);
    6158:     }

    6160:     /* whether or not to skip lapack calls */
    6161:     skip_lapack = PETSC_TRUE;
    6162:     if (n_ISForFaces+n_ISForEdges && max_constraints > 1 && !pcbddc->use_nnsp_true) skip_lapack = PETSC_FALSE;

    6164:     /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
    6165:     if (!skip_lapack) {
    6166:       PetscScalar temp_work;

    6168:       if (use_pod) {
    6169:         /* Proper Orthogonal Decomposition (POD) using the snapshot method */
    6170:         PetscMalloc1(max_constraints*max_constraints,&correlation_mat);
    6171:         PetscMalloc1(max_constraints,&singular_vals);
    6172:         PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);
    6173: #if defined(PETSC_USE_COMPLEX)
    6174:         PetscMalloc1(3*max_constraints,&rwork);
    6175: #endif
    6176:         /* now we evaluate the optimal workspace using query with lwork=-1 */
    6177:         PetscBLASIntCast(max_constraints,&Blas_N);
    6178:         PetscBLASIntCast(max_constraints,&Blas_LDA);
    6179:         lwork = -1;
    6180:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6181: #if !defined(PETSC_USE_COMPLEX)
    6182:         PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
    6183: #else
    6184:         PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
    6185: #endif
    6186:         PetscFPTrapPop();
    6188:       } else {
    6189: #if !defined(PETSC_MISSING_LAPACK_GESVD)
    6190:         /* SVD */
    6191:         PetscInt max_n,min_n;
    6192:         max_n = max_size_of_constraint;
    6193:         min_n = max_constraints;
    6194:         if (max_size_of_constraint < max_constraints) {
    6195:           min_n = max_size_of_constraint;
    6196:           max_n = max_constraints;
    6197:         }
    6198:         PetscMalloc1(min_n,&singular_vals);
    6199: #if defined(PETSC_USE_COMPLEX)
    6200:         PetscMalloc1(5*min_n,&rwork);
    6201: #endif
    6202:         /* now we evaluate the optimal workspace using query with lwork=-1 */
    6203:         lwork = -1;
    6204:         PetscBLASIntCast(max_n,&Blas_M);
    6205:         PetscBLASIntCast(min_n,&Blas_N);
    6206:         PetscBLASIntCast(max_n,&Blas_LDA);
    6207:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6208: #if !defined(PETSC_USE_COMPLEX)
    6209:         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));
    6210: #else
    6211:         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));
    6212: #endif
    6213:         PetscFPTrapPop();
    6215: #else
    6216:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"This should not happen");
    6217: #endif /* on missing GESVD */
    6218:       }
    6219:       /* Allocate optimal workspace */
    6220:       PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);
    6221:       PetscMalloc1(lwork,&work);
    6222:     }
    6223:     /* Now we can loop on constraining sets */
    6224:     total_counts = 0;
    6225:     constraints_idxs_ptr[0] = 0;
    6226:     constraints_data_ptr[0] = 0;
    6227:     /* vertices */
    6228:     if (n_vertices) {
    6229:       ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);
    6230:       PetscArraycpy(constraints_idxs,is_indices,n_vertices);
    6231:       for (i=0;i<n_vertices;i++) {
    6232:         constraints_n[total_counts] = 1;
    6233:         constraints_data[total_counts] = 1.0;
    6234:         constraints_idxs_ptr[total_counts+1] = constraints_idxs_ptr[total_counts]+1;
    6235:         constraints_data_ptr[total_counts+1] = constraints_data_ptr[total_counts]+1;
    6236:         total_counts++;
    6237:       }
    6238:       ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);
    6239:       n_vertices = total_counts;
    6240:     }

    6242:     /* edges and faces */
    6243:     total_counts_cc = total_counts;
    6244:     for (ncc=0;ncc<n_ISForEdges+n_ISForFaces;ncc++) {
    6245:       IS        used_is;
    6246:       PetscBool idxs_copied = PETSC_FALSE;

    6248:       if (ncc<n_ISForEdges) {
    6249:         used_is = ISForEdges[ncc];
    6250:         boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
    6251:       } else {
    6252:         used_is = ISForFaces[ncc-n_ISForEdges];
    6253:         boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
    6254:       }
    6255:       temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */

    6257:       ISGetSize(used_is,&size_of_constraint);
    6258:       ISGetIndices(used_is,(const PetscInt**)&is_indices);
    6259:       /* change of basis should not be performed on local periodic nodes */
    6260:       if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
    6261:       if (nnsp_has_cnst) {
    6262:         PetscScalar quad_value;

    6264:         PetscArraycpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint);
    6265:         idxs_copied = PETSC_TRUE;

    6267:         if (!pcbddc->use_nnsp_true) {
    6268:           quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
    6269:         } else {
    6270:           quad_value = 1.0;
    6271:         }
    6272:         for (j=0;j<size_of_constraint;j++) {
    6273:           constraints_data[constraints_data_ptr[total_counts_cc]+j] = quad_value;
    6274:         }
    6275:         temp_constraints++;
    6276:         total_counts++;
    6277:       }
    6278:       for (k=0;k<nnsp_size;k++) {
    6279:         PetscReal real_value;
    6280:         PetscScalar *ptr_to_data;

    6282:         VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
    6283:         ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]+temp_constraints*size_of_constraint];
    6284:         for (j=0;j<size_of_constraint;j++) {
    6285:           ptr_to_data[j] = array[is_indices[j]];
    6286:         }
    6287:         VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
    6288:         /* check if array is null on the connected component */
    6289:         PetscBLASIntCast(size_of_constraint,&Blas_N);
    6290:         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,ptr_to_data,&Blas_one));
    6291:         if (real_value > tol*size_of_constraint) { /* keep indices and values */
    6292:           temp_constraints++;
    6293:           total_counts++;
    6294:           if (!idxs_copied) {
    6295:             PetscArraycpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint);
    6296:             idxs_copied = PETSC_TRUE;
    6297:           }
    6298:         }
    6299:       }
    6300:       ISRestoreIndices(used_is,(const PetscInt**)&is_indices);
    6301:       valid_constraints = temp_constraints;
    6302:       if (!pcbddc->use_nnsp_true && temp_constraints) {
    6303:         if (temp_constraints == 1) { /* just normalize the constraint */
    6304:           PetscScalar norm,*ptr_to_data;

    6306:           ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];
    6307:           PetscBLASIntCast(size_of_constraint,&Blas_N);
    6308:           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,ptr_to_data,&Blas_one,ptr_to_data,&Blas_one));
    6309:           norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
    6310:           PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,ptr_to_data,&Blas_one));
    6311:         } else { /* perform SVD */
    6312:           PetscScalar *ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];

    6314:           if (use_pod) {
    6315:             /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
    6316:                POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
    6317:                -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
    6318:                   the constraints basis will differ (by a complex factor with absolute value equal to 1)
    6319:                   from that computed using LAPACKgesvd
    6320:                -> This is due to a different computation of eigenvectors in LAPACKheev
    6321:                -> The quality of the POD-computed basis will be the same */
    6322:             PetscArrayzero(correlation_mat,temp_constraints*temp_constraints);
    6323:             /* Store upper triangular part of correlation matrix */
    6324:             PetscBLASIntCast(size_of_constraint,&Blas_N);
    6325:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6326:             for (j=0;j<temp_constraints;j++) {
    6327:               for (k=0;k<j+1;k++) {
    6328:                 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));
    6329:               }
    6330:             }
    6331:             /* compute eigenvalues and eigenvectors of correlation matrix */
    6332:             PetscBLASIntCast(temp_constraints,&Blas_N);
    6333:             PetscBLASIntCast(temp_constraints,&Blas_LDA);
    6334: #if !defined(PETSC_USE_COMPLEX)
    6335:             PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
    6336: #else
    6337:             PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
    6338: #endif
    6339:             PetscFPTrapPop();
    6341:             /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
    6342:             j = 0;
    6343:             while (j < temp_constraints && singular_vals[j]/singular_vals[temp_constraints-1] < tol) j++;
    6344:             total_counts = total_counts-j;
    6345:             valid_constraints = temp_constraints-j;
    6346:             /* scale and copy POD basis into used quadrature memory */
    6347:             PetscBLASIntCast(size_of_constraint,&Blas_M);
    6348:             PetscBLASIntCast(temp_constraints,&Blas_N);
    6349:             PetscBLASIntCast(temp_constraints,&Blas_K);
    6350:             PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    6351:             PetscBLASIntCast(temp_constraints,&Blas_LDB);
    6352:             PetscBLASIntCast(size_of_constraint,&Blas_LDC);
    6353:             if (j<temp_constraints) {
    6354:               PetscInt ii;
    6355:               for (k=j;k<temp_constraints;k++) singular_vals[k] = 1.0/PetscSqrtReal(singular_vals[k]);
    6356:               PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6357:               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));
    6358:               PetscFPTrapPop();
    6359:               for (k=0;k<temp_constraints-j;k++) {
    6360:                 for (ii=0;ii<size_of_constraint;ii++) {
    6361:                   ptr_to_data[k*size_of_constraint+ii] = singular_vals[temp_constraints-1-k]*temp_basis[(temp_constraints-1-k)*size_of_constraint+ii];
    6362:                 }
    6363:               }
    6364:             }
    6365:           } else {
    6366: #if !defined(PETSC_MISSING_LAPACK_GESVD)
    6367:             PetscBLASIntCast(size_of_constraint,&Blas_M);
    6368:             PetscBLASIntCast(temp_constraints,&Blas_N);
    6369:             PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    6370:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6371: #if !defined(PETSC_USE_COMPLEX)
    6372:             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));
    6373: #else
    6374:             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));
    6375: #endif
    6377:             PetscFPTrapPop();
    6378:             /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
    6379:             k = temp_constraints;
    6380:             if (k > size_of_constraint) k = size_of_constraint;
    6381:             j = 0;
    6382:             while (j < k && singular_vals[k-j-1]/singular_vals[0] < tol) j++;
    6383:             valid_constraints = k-j;
    6384:             total_counts = total_counts-temp_constraints+valid_constraints;
    6385: #else
    6386:             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"This should not happen");
    6387: #endif /* on missing GESVD */
    6388:           }
    6389:         }
    6390:       }
    6391:       /* update pointers information */
    6392:       if (valid_constraints) {
    6393:         constraints_n[total_counts_cc] = valid_constraints;
    6394:         constraints_idxs_ptr[total_counts_cc+1] = constraints_idxs_ptr[total_counts_cc]+size_of_constraint;
    6395:         constraints_data_ptr[total_counts_cc+1] = constraints_data_ptr[total_counts_cc]+size_of_constraint*valid_constraints;
    6396:         /* set change_of_basis flag */
    6397:         if (boolforchange) {
    6398:           PetscBTSet(change_basis,total_counts_cc);
    6399:         }
    6400:         total_counts_cc++;
    6401:       }
    6402:     }
    6403:     /* free workspace */
    6404:     if (!skip_lapack) {
    6405:       PetscFree(work);
    6406: #if defined(PETSC_USE_COMPLEX)
    6407:       PetscFree(rwork);
    6408: #endif
    6409:       PetscFree(singular_vals);
    6410:       PetscFree(correlation_mat);
    6411:       PetscFree(temp_basis);
    6412:     }
    6413:     for (k=0;k<nnsp_size;k++) {
    6414:       VecDestroy(&localnearnullsp[k]);
    6415:     }
    6416:     PetscFree(localnearnullsp);
    6417:     /* free index sets of faces, edges and vertices */
    6418:     for (i=0;i<n_ISForFaces;i++) {
    6419:       ISDestroy(&ISForFaces[i]);
    6420:     }
    6421:     if (n_ISForFaces) {
    6422:       PetscFree(ISForFaces);
    6423:     }
    6424:     for (i=0;i<n_ISForEdges;i++) {
    6425:       ISDestroy(&ISForEdges[i]);
    6426:     }
    6427:     if (n_ISForEdges) {
    6428:       PetscFree(ISForEdges);
    6429:     }
    6430:     ISDestroy(&ISForVertices);
    6431:   } else {
    6432:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

    6434:     total_counts = 0;
    6435:     n_vertices = 0;
    6436:     if (sub_schurs->is_vertices && pcbddc->use_vertices) {
    6437:       ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);
    6438:     }
    6439:     max_constraints = 0;
    6440:     total_counts_cc = 0;
    6441:     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
    6442:       total_counts += pcbddc->adaptive_constraints_n[i];
    6443:       if (pcbddc->adaptive_constraints_n[i]) total_counts_cc++;
    6444:       max_constraints = PetscMax(max_constraints,pcbddc->adaptive_constraints_n[i]);
    6445:     }
    6446:     constraints_idxs_ptr = pcbddc->adaptive_constraints_idxs_ptr;
    6447:     constraints_data_ptr = pcbddc->adaptive_constraints_data_ptr;
    6448:     constraints_idxs = pcbddc->adaptive_constraints_idxs;
    6449:     constraints_data = pcbddc->adaptive_constraints_data;
    6450:     /* constraints_n differs from pcbddc->adaptive_constraints_n */
    6451:     PetscMalloc1(total_counts_cc,&constraints_n);
    6452:     total_counts_cc = 0;
    6453:     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
    6454:       if (pcbddc->adaptive_constraints_n[i]) {
    6455:         constraints_n[total_counts_cc++] = pcbddc->adaptive_constraints_n[i];
    6456:       }
    6457:     }

    6459:     max_size_of_constraint = 0;
    6460:     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]);
    6461:     PetscMalloc1(constraints_idxs_ptr[total_counts_cc],&constraints_idxs_B);
    6462:     /* Change of basis */
    6463:     PetscBTCreate(total_counts_cc,&change_basis);
    6464:     if (pcbddc->use_change_of_basis) {
    6465:       for (i=0;i<sub_schurs->n_subs;i++) {
    6466:         if (PetscBTLookup(sub_schurs->is_edge,i) || pcbddc->use_change_on_faces) {
    6467:           PetscBTSet(change_basis,i+n_vertices);
    6468:         }
    6469:       }
    6470:     }
    6471:   }
    6472:   pcbddc->local_primal_size = total_counts;
    6473:   PetscMalloc1(pcbddc->local_primal_size+pcbddc->benign_n,&pcbddc->primal_indices_local_idxs);

    6475:   /* map constraints_idxs in boundary numbering */
    6476:   ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,constraints_idxs_ptr[total_counts_cc],constraints_idxs,&i,constraints_idxs_B);

    6479:   /* Create constraint matrix */
    6480:   MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);
    6481:   MatSetType(pcbddc->ConstraintMatrix,MATAIJ);
    6482:   MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);

    6484:   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
    6485:   /* determine if a QR strategy is needed for change of basis */
    6486:   qr_needed = pcbddc->use_qr_single;
    6487:   PetscBTCreate(total_counts_cc,&qr_needed_idx);
    6488:   total_primal_vertices=0;
    6489:   pcbddc->local_primal_size_cc = 0;
    6490:   for (i=0;i<total_counts_cc;i++) {
    6491:     size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    6492:     if (size_of_constraint == 1 && pcbddc->mat_graph->custom_minimal_size) {
    6493:       pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]];
    6494:       pcbddc->local_primal_size_cc += 1;
    6495:     } else if (PetscBTLookup(change_basis,i)) {
    6496:       for (k=0;k<constraints_n[i];k++) {
    6497:         pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]+k];
    6498:       }
    6499:       pcbddc->local_primal_size_cc += constraints_n[i];
    6500:       if (constraints_n[i] > 1 || pcbddc->use_qr_single) {
    6501:         PetscBTSet(qr_needed_idx,i);
    6502:         qr_needed = PETSC_TRUE;
    6503:       }
    6504:     } else {
    6505:       pcbddc->local_primal_size_cc += 1;
    6506:     }
    6507:   }
    6508:   /* note that the local variable n_vertices used below stores the number of pointwise constraints */
    6509:   pcbddc->n_vertices = total_primal_vertices;
    6510:   /* permute indices in order to have a sorted set of vertices */
    6511:   PetscSortInt(total_primal_vertices,pcbddc->primal_indices_local_idxs);
    6512:   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);
    6513:   PetscArraycpy(pcbddc->local_primal_ref_node,pcbddc->primal_indices_local_idxs,total_primal_vertices);
    6514:   for (i=0;i<total_primal_vertices;i++) pcbddc->local_primal_ref_mult[i] = 1;

    6516:   /* nonzero structure of constraint matrix */
    6517:   /* and get reference dof for local constraints */
    6518:   PetscMalloc1(pcbddc->local_primal_size,&nnz);
    6519:   for (i=0;i<total_primal_vertices;i++) nnz[i] = 1;

    6521:   j = total_primal_vertices;
    6522:   total_counts = total_primal_vertices;
    6523:   cum = total_primal_vertices;
    6524:   for (i=n_vertices;i<total_counts_cc;i++) {
    6525:     if (!PetscBTLookup(change_basis,i)) {
    6526:       pcbddc->local_primal_ref_node[cum] = constraints_idxs[constraints_idxs_ptr[i]];
    6527:       pcbddc->local_primal_ref_mult[cum] = constraints_n[i];
    6528:       cum++;
    6529:       size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    6530:       for (k=0;k<constraints_n[i];k++) {
    6531:         pcbddc->primal_indices_local_idxs[total_counts++] = constraints_idxs[constraints_idxs_ptr[i]+k];
    6532:         nnz[j+k] = size_of_constraint;
    6533:       }
    6534:       j += constraints_n[i];
    6535:     }
    6536:   }
    6537:   MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);
    6538:   MatSetOption(pcbddc->ConstraintMatrix,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
    6539:   PetscFree(nnz);

    6541:   /* set values in constraint matrix */
    6542:   for (i=0;i<total_primal_vertices;i++) {
    6543:     MatSetValue(pcbddc->ConstraintMatrix,i,pcbddc->local_primal_ref_node[i],1.0,INSERT_VALUES);
    6544:   }
    6545:   total_counts = total_primal_vertices;
    6546:   for (i=n_vertices;i<total_counts_cc;i++) {
    6547:     if (!PetscBTLookup(change_basis,i)) {
    6548:       PetscInt *cols;

    6550:       size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    6551:       cols = constraints_idxs+constraints_idxs_ptr[i];
    6552:       for (k=0;k<constraints_n[i];k++) {
    6553:         PetscInt    row = total_counts+k;
    6554:         PetscScalar *vals;

    6556:         vals = constraints_data+constraints_data_ptr[i]+k*size_of_constraint;
    6557:         MatSetValues(pcbddc->ConstraintMatrix,1,&row,size_of_constraint,cols,vals,INSERT_VALUES);
    6558:       }
    6559:       total_counts += constraints_n[i];
    6560:     }
    6561:   }
    6562:   /* assembling */
    6563:   MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);
    6564:   MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);
    6565:   MatViewFromOptions(pcbddc->ConstraintMatrix,(PetscObject)pc,"-pc_bddc_constraint_mat_view");

    6567:   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
    6568:   if (pcbddc->use_change_of_basis) {
    6569:     /* dual and primal dofs on a single cc */
    6570:     PetscInt     dual_dofs,primal_dofs;
    6571:     /* working stuff for GEQRF */
    6572:     PetscScalar  *qr_basis = NULL,*qr_tau = NULL,*qr_work = NULL,lqr_work_t;
    6573:     PetscBLASInt lqr_work;
    6574:     /* working stuff for UNGQR */
    6575:     PetscScalar  *gqr_work = NULL,lgqr_work_t=0.0;
    6576:     PetscBLASInt lgqr_work;
    6577:     /* working stuff for TRTRS */
    6578:     PetscScalar  *trs_rhs = NULL;
    6579:     PetscBLASInt Blas_NRHS;
    6580:     /* pointers for values insertion into change of basis matrix */
    6581:     PetscInt     *start_rows,*start_cols;
    6582:     PetscScalar  *start_vals;
    6583:     /* working stuff for values insertion */
    6584:     PetscBT      is_primal;
    6585:     PetscInt     *aux_primal_numbering_B;
    6586:     /* matrix sizes */
    6587:     PetscInt     global_size,local_size;
    6588:     /* temporary change of basis */
    6589:     Mat          localChangeOfBasisMatrix;
    6590:     /* extra space for debugging */
    6591:     PetscScalar  *dbg_work = NULL;

    6593:     /* local temporary change of basis acts on local interfaces -> dimension is n_B x n_B */
    6594:     MatCreate(PETSC_COMM_SELF,&localChangeOfBasisMatrix);
    6595:     MatSetType(localChangeOfBasisMatrix,MATAIJ);
    6596:     MatSetSizes(localChangeOfBasisMatrix,pcis->n,pcis->n,pcis->n,pcis->n);
    6597:     /* nonzeros for local mat */
    6598:     PetscMalloc1(pcis->n,&nnz);
    6599:     if (!pcbddc->benign_change || pcbddc->fake_change) {
    6600:       for (i=0;i<pcis->n;i++) nnz[i]=1;
    6601:     } else {
    6602:       const PetscInt *ii;
    6603:       PetscInt       n;
    6604:       PetscBool      flg_row;
    6605:       MatGetRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,NULL,&flg_row);
    6606:       for (i=0;i<n;i++) nnz[i] = ii[i+1]-ii[i];
    6607:       MatRestoreRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,NULL,&flg_row);
    6608:     }
    6609:     for (i=n_vertices;i<total_counts_cc;i++) {
    6610:       if (PetscBTLookup(change_basis,i)) {
    6611:         size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    6612:         if (PetscBTLookup(qr_needed_idx,i)) {
    6613:           for (j=0;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = size_of_constraint;
    6614:         } else {
    6615:           nnz[constraints_idxs[constraints_idxs_ptr[i]]] = size_of_constraint;
    6616:           for (j=1;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = 2;
    6617:         }
    6618:       }
    6619:     }
    6620:     MatSeqAIJSetPreallocation(localChangeOfBasisMatrix,0,nnz);
    6621:     MatSetOption(localChangeOfBasisMatrix,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
    6622:     PetscFree(nnz);
    6623:     /* Set interior change in the matrix */
    6624:     if (!pcbddc->benign_change || pcbddc->fake_change) {
    6625:       for (i=0;i<pcis->n;i++) {
    6626:         MatSetValue(localChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);
    6627:       }
    6628:     } else {
    6629:       const PetscInt *ii,*jj;
    6630:       PetscScalar    *aa;
    6631:       PetscInt       n;
    6632:       PetscBool      flg_row;
    6633:       MatGetRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&jj,&flg_row);
    6634:       MatSeqAIJGetArray(pcbddc->benign_change,&aa);
    6635:       for (i=0;i<n;i++) {
    6636:         MatSetValues(localChangeOfBasisMatrix,1,&i,ii[i+1]-ii[i],jj+ii[i],aa+ii[i],INSERT_VALUES);
    6637:       }
    6638:       MatSeqAIJRestoreArray(pcbddc->benign_change,&aa);
    6639:       MatRestoreRowIJ(pcbddc->benign_change,0,PETSC_FALSE,PETSC_FALSE,&n,&ii,&jj,&flg_row);
    6640:     }

    6642:     if (pcbddc->dbg_flag) {
    6643:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
    6644:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);
    6645:     }

    6647:     /* Now we loop on the constraints which need a change of basis */
    6648:     /*
    6649:        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
    6650:        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)

    6652:        Basic blocks of change of basis matrix T computed by

    6654:           - Using the following block transformation if there is only a primal dof on the cc (and -pc_bddc_use_qr_single is not specified)

    6656:             | 1        0   ...        0         s_1/S |
    6657:             | 0        1   ...        0         s_2/S |
    6658:             |              ...                        |
    6659:             | 0        ...            1     s_{n-1}/S |
    6660:             | -s_1/s_n ...    -s_{n-1}/s_n      s_n/S |

    6662:             with S = \sum_{i=1}^n s_i^2
    6663:             NOTE: in the above example, the primal dof is the last one of the edge in LOCAL ordering
    6664:                   in the current implementation, the primal dof is the first one of the edge in GLOBAL ordering

    6666:           - QR decomposition of constraints otherwise
    6667:     */
    6668:     if (qr_needed && max_size_of_constraint) {
    6669:       /* space to store Q */
    6670:       PetscMalloc1(max_size_of_constraint*max_size_of_constraint,&qr_basis);
    6671:       /* array to store scaling factors for reflectors */
    6672:       PetscMalloc1(max_constraints,&qr_tau);
    6673:       /* first we issue queries for optimal work */
    6674:       PetscBLASIntCast(max_size_of_constraint,&Blas_M);
    6675:       PetscBLASIntCast(max_constraints,&Blas_N);
    6676:       PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);
    6677:       lqr_work = -1;
    6678:       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
    6680:       PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);
    6681:       PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);
    6682:       lgqr_work = -1;
    6683:       PetscBLASIntCast(max_size_of_constraint,&Blas_M);
    6684:       PetscBLASIntCast(max_size_of_constraint,&Blas_N);
    6685:       PetscBLASIntCast(max_constraints,&Blas_K);
    6686:       PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);
    6687:       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
    6688:       PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
    6690:       PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);
    6691:       PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);
    6692:       /* array to store rhs and solution of triangular solver */
    6693:       PetscMalloc1(max_constraints*max_constraints,&trs_rhs);
    6694:       /* allocating workspace for check */
    6695:       if (pcbddc->dbg_flag) {
    6696:         PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&dbg_work);
    6697:       }
    6698:     }
    6699:     /* array to store whether a node is primal or not */
    6700:     PetscBTCreate(pcis->n_B,&is_primal);
    6701:     PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);
    6702:     ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,pcbddc->local_primal_ref_node,&i,aux_primal_numbering_B);
    6704:     for (i=0;i<total_primal_vertices;i++) {
    6705:       PetscBTSet(is_primal,aux_primal_numbering_B[i]);
    6706:     }
    6707:     PetscFree(aux_primal_numbering_B);

    6709:     /* loop on constraints and see whether or not they need a change of basis and compute it */
    6710:     for (total_counts=n_vertices;total_counts<total_counts_cc;total_counts++) {
    6711:       size_of_constraint = constraints_idxs_ptr[total_counts+1]-constraints_idxs_ptr[total_counts];
    6712:       if (PetscBTLookup(change_basis,total_counts)) {
    6713:         /* get constraint info */
    6714:         primal_dofs = constraints_n[total_counts];
    6715:         dual_dofs = size_of_constraint-primal_dofs;

    6717:         if (pcbddc->dbg_flag) {
    6718:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraints %D: %D need a change of basis (size %D)\n",total_counts,primal_dofs,size_of_constraint);
    6719:         }

    6721:         if (PetscBTLookup(qr_needed_idx,total_counts)) { /* QR */

    6723:           /* copy quadrature constraints for change of basis check */
    6724:           if (pcbddc->dbg_flag) {
    6725:             PetscArraycpy(dbg_work,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);
    6726:           }
    6727:           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
    6728:           PetscArraycpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);

    6730:           /* compute QR decomposition of constraints */
    6731:           PetscBLASIntCast(size_of_constraint,&Blas_M);
    6732:           PetscBLASIntCast(primal_dofs,&Blas_N);
    6733:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    6734:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6735:           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
    6737:           PetscFPTrapPop();

    6739:           /* explicitly compute R^-T */
    6740:           PetscArrayzero(trs_rhs,primal_dofs*primal_dofs);
    6741:           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
    6742:           PetscBLASIntCast(primal_dofs,&Blas_N);
    6743:           PetscBLASIntCast(primal_dofs,&Blas_NRHS);
    6744:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    6745:           PetscBLASIntCast(primal_dofs,&Blas_LDB);
    6746:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6747:           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
    6749:           PetscFPTrapPop();

    6751:           /* explicitly compute all columns of Q (Q = [Q1 | Q2]) overwriting QR factorization in qr_basis */
    6752:           PetscBLASIntCast(size_of_constraint,&Blas_M);
    6753:           PetscBLASIntCast(size_of_constraint,&Blas_N);
    6754:           PetscBLASIntCast(primal_dofs,&Blas_K);
    6755:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    6756:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6757:           PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
    6759:           PetscFPTrapPop();

    6761:           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
    6762:              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
    6763:              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
    6764:           PetscBLASIntCast(size_of_constraint,&Blas_M);
    6765:           PetscBLASIntCast(primal_dofs,&Blas_N);
    6766:           PetscBLASIntCast(primal_dofs,&Blas_K);
    6767:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    6768:           PetscBLASIntCast(primal_dofs,&Blas_LDB);
    6769:           PetscBLASIntCast(size_of_constraint,&Blas_LDC);
    6770:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6771:           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));
    6772:           PetscFPTrapPop();
    6773:           PetscArraycpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs);

    6775:           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
    6776:           start_rows = &constraints_idxs[constraints_idxs_ptr[total_counts]];
    6777:           /* insert cols for primal dofs */
    6778:           for (j=0;j<primal_dofs;j++) {
    6779:             start_vals = &qr_basis[j*size_of_constraint];
    6780:             start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+j];
    6781:             MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);
    6782:           }
    6783:           /* insert cols for dual dofs */
    6784:           for (j=0,k=0;j<dual_dofs;k++) {
    6785:             if (!PetscBTLookup(is_primal,constraints_idxs_B[constraints_idxs_ptr[total_counts]+k])) {
    6786:               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
    6787:               start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+k];
    6788:               MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);
    6789:               j++;
    6790:             }
    6791:           }

    6793:           /* check change of basis */
    6794:           if (pcbddc->dbg_flag) {
    6795:             PetscInt   ii,jj;
    6796:             PetscBool valid_qr=PETSC_TRUE;
    6797:             PetscBLASIntCast(primal_dofs,&Blas_M);
    6798:             PetscBLASIntCast(size_of_constraint,&Blas_N);
    6799:             PetscBLASIntCast(size_of_constraint,&Blas_K);
    6800:             PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    6801:             PetscBLASIntCast(size_of_constraint,&Blas_LDB);
    6802:             PetscBLASIntCast(primal_dofs,&Blas_LDC);
    6803:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    6804:             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));
    6805:             PetscFPTrapPop();
    6806:             for (jj=0;jj<size_of_constraint;jj++) {
    6807:               for (ii=0;ii<primal_dofs;ii++) {
    6808:                 if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
    6809:                 if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-(PetscReal)1) > 1.e-12) valid_qr = PETSC_FALSE;
    6810:               }
    6811:             }
    6812:             if (!valid_qr) {
    6813:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");
    6814:               for (jj=0;jj<size_of_constraint;jj++) {
    6815:                 for (ii=0;ii<primal_dofs;ii++) {
    6816:                   if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
    6817:                     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]));
    6818:                   }
    6819:                   if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-(PetscReal)1) > 1.e-12) {
    6820:                     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]));
    6821:                   }
    6822:                 }
    6823:               }
    6824:             } else {
    6825:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");
    6826:             }
    6827:           }
    6828:         } else { /* simple transformation block */
    6829:           PetscInt    row,col;
    6830:           PetscScalar val,norm;

    6832:           PetscBLASIntCast(size_of_constraint,&Blas_N);
    6833:           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,constraints_data+constraints_data_ptr[total_counts],&Blas_one,constraints_data+constraints_data_ptr[total_counts],&Blas_one));
    6834:           for (j=0;j<size_of_constraint;j++) {
    6835:             PetscInt row_B = constraints_idxs_B[constraints_idxs_ptr[total_counts]+j];
    6836:             row = constraints_idxs[constraints_idxs_ptr[total_counts]+j];
    6837:             if (!PetscBTLookup(is_primal,row_B)) {
    6838:               col = constraints_idxs[constraints_idxs_ptr[total_counts]];
    6839:               MatSetValue(localChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);
    6840:               MatSetValue(localChangeOfBasisMatrix,row,col,constraints_data[constraints_data_ptr[total_counts]+j]/norm,INSERT_VALUES);
    6841:             } else {
    6842:               for (k=0;k<size_of_constraint;k++) {
    6843:                 col = constraints_idxs[constraints_idxs_ptr[total_counts]+k];
    6844:                 if (row != col) {
    6845:                   val = -constraints_data[constraints_data_ptr[total_counts]+k]/constraints_data[constraints_data_ptr[total_counts]];
    6846:                 } else {
    6847:                   val = constraints_data[constraints_data_ptr[total_counts]]/norm;
    6848:                 }
    6849:                 MatSetValue(localChangeOfBasisMatrix,row,col,val,INSERT_VALUES);
    6850:               }
    6851:             }
    6852:           }
    6853:           if (pcbddc->dbg_flag) {
    6854:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");
    6855:           }
    6856:         }
    6857:       } else {
    6858:         if (pcbddc->dbg_flag) {
    6859:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %D does not need a change of basis (size %D)\n",total_counts,size_of_constraint);
    6860:         }
    6861:       }
    6862:     }

    6864:     /* free workspace */
    6865:     if (qr_needed) {
    6866:       if (pcbddc->dbg_flag) {
    6867:         PetscFree(dbg_work);
    6868:       }
    6869:       PetscFree(trs_rhs);
    6870:       PetscFree(qr_tau);
    6871:       PetscFree(qr_work);
    6872:       PetscFree(gqr_work);
    6873:       PetscFree(qr_basis);
    6874:     }
    6875:     PetscBTDestroy(&is_primal);
    6876:     MatAssemblyBegin(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);
    6877:     MatAssemblyEnd(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);

    6879:     /* assembling of global change of variable */
    6880:     if (!pcbddc->fake_change) {
    6881:       Mat      tmat;
    6882:       PetscInt bs;

    6884:       VecGetSize(pcis->vec1_global,&global_size);
    6885:       VecGetLocalSize(pcis->vec1_global,&local_size);
    6886:       MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&tmat);
    6887:       MatISSetLocalMat(tmat,localChangeOfBasisMatrix);
    6888:       MatAssemblyBegin(tmat,MAT_FINAL_ASSEMBLY);
    6889:       MatAssemblyEnd(tmat,MAT_FINAL_ASSEMBLY);
    6890:       MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->ChangeOfBasisMatrix);
    6891:       MatSetType(pcbddc->ChangeOfBasisMatrix,MATAIJ);
    6892:       MatGetBlockSize(pc->pmat,&bs);
    6893:       MatSetBlockSize(pcbddc->ChangeOfBasisMatrix,bs);
    6894:       MatSetSizes(pcbddc->ChangeOfBasisMatrix,local_size,local_size,global_size,global_size);
    6895:       MatISSetMPIXAIJPreallocation_Private(tmat,pcbddc->ChangeOfBasisMatrix,PETSC_TRUE);
    6896:       MatConvert(tmat,MATAIJ,MAT_REUSE_MATRIX,&pcbddc->ChangeOfBasisMatrix);
    6897:       MatDestroy(&tmat);
    6898:       VecSet(pcis->vec1_global,0.0);
    6899:       VecSet(pcis->vec1_N,1.0);
    6900:       VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    6901:       VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    6902:       VecReciprocal(pcis->vec1_global);
    6903:       MatDiagonalScale(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,NULL);

    6905:       /* check */
    6906:       if (pcbddc->dbg_flag) {
    6907:         PetscReal error;
    6908:         Vec       x,x_change;

    6910:         VecDuplicate(pcis->vec1_global,&x);
    6911:         VecDuplicate(pcis->vec1_global,&x_change);
    6912:         VecSetRandom(x,NULL);
    6913:         VecCopy(x,pcis->vec1_global);
    6914:         VecScatterBegin(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    6915:         VecScatterEnd(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    6916:         MatMult(localChangeOfBasisMatrix,pcis->vec1_N,pcis->vec2_N);
    6917:         VecScatterBegin(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);
    6918:         VecScatterEnd(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);
    6919:         MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);
    6920:         VecAXPY(x,-1.0,x_change);
    6921:         VecNorm(x,NORM_INFINITY,&error);
    6922:         if (error > PETSC_SMALL) {
    6923:           SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Error global vs local change on N: %1.6e",error);
    6924:         }
    6925:         VecDestroy(&x);
    6926:         VecDestroy(&x_change);
    6927:       }
    6928:       /* adapt sub_schurs computed (if any) */
    6929:       if (pcbddc->use_deluxe_scaling) {
    6930:         PCBDDCSubSchurs sub_schurs=pcbddc->sub_schurs;

    6933:         if (sub_schurs && sub_schurs->S_Ej_all) {
    6934:           Mat                    S_new,tmat;
    6935:           IS                     is_all_N,is_V_Sall = NULL;

    6937:           ISLocalToGlobalMappingApplyIS(pcis->BtoNmap,sub_schurs->is_Ej_all,&is_all_N);
    6938:           MatCreateSubMatrix(localChangeOfBasisMatrix,is_all_N,is_all_N,MAT_INITIAL_MATRIX,&tmat);
    6939:           if (pcbddc->deluxe_zerorows) {
    6940:             ISLocalToGlobalMapping NtoSall;
    6941:             IS                     is_V;
    6942:             ISCreateGeneral(PETSC_COMM_SELF,pcbddc->n_vertices,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&is_V);
    6943:             ISLocalToGlobalMappingCreateIS(is_all_N,&NtoSall);
    6944:             ISGlobalToLocalMappingApplyIS(NtoSall,IS_GTOLM_DROP,is_V,&is_V_Sall);
    6945:             ISLocalToGlobalMappingDestroy(&NtoSall);
    6946:             ISDestroy(&is_V);
    6947:           }
    6948:           ISDestroy(&is_all_N);
    6949:           MatPtAP(sub_schurs->S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);
    6950:           MatDestroy(&sub_schurs->S_Ej_all);
    6951:           PetscObjectReference((PetscObject)S_new);
    6952:           if (pcbddc->deluxe_zerorows) {
    6953:             const PetscScalar *array;
    6954:             const PetscInt    *idxs_V,*idxs_all;
    6955:             PetscInt          i,n_V;

    6957:             MatZeroRowsColumnsIS(S_new,is_V_Sall,1.,NULL,NULL);
    6958:             ISGetLocalSize(is_V_Sall,&n_V);
    6959:             ISGetIndices(is_V_Sall,&idxs_V);
    6960:             ISGetIndices(sub_schurs->is_Ej_all,&idxs_all);
    6961:             VecGetArrayRead(pcis->D,&array);
    6962:             for (i=0;i<n_V;i++) {
    6963:               PetscScalar val;
    6964:               PetscInt    idx;

    6966:               idx = idxs_V[i];
    6967:               val = array[idxs_all[idxs_V[i]]];
    6968:               MatSetValue(S_new,idx,idx,val,INSERT_VALUES);
    6969:             }
    6970:             MatAssemblyBegin(S_new,MAT_FINAL_ASSEMBLY);
    6971:             MatAssemblyEnd(S_new,MAT_FINAL_ASSEMBLY);
    6972:             VecRestoreArrayRead(pcis->D,&array);
    6973:             ISRestoreIndices(sub_schurs->is_Ej_all,&idxs_all);
    6974:             ISRestoreIndices(is_V_Sall,&idxs_V);
    6975:           }
    6976:           sub_schurs->S_Ej_all = S_new;
    6977:           MatDestroy(&S_new);
    6978:           if (sub_schurs->sum_S_Ej_all) {
    6979:             MatPtAP(sub_schurs->sum_S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);
    6980:             MatDestroy(&sub_schurs->sum_S_Ej_all);
    6981:             PetscObjectReference((PetscObject)S_new);
    6982:             if (pcbddc->deluxe_zerorows) {
    6983:               MatZeroRowsColumnsIS(S_new,is_V_Sall,1.,NULL,NULL);
    6984:             }
    6985:             sub_schurs->sum_S_Ej_all = S_new;
    6986:             MatDestroy(&S_new);
    6987:           }
    6988:           ISDestroy(&is_V_Sall);
    6989:           MatDestroy(&tmat);
    6990:         }
    6991:         /* destroy any change of basis context in sub_schurs */
    6992:         if (sub_schurs && sub_schurs->change) {
    6993:           PetscInt i;

    6995:           for (i=0;i<sub_schurs->n_subs;i++) {
    6996:             KSPDestroy(&sub_schurs->change[i]);
    6997:           }
    6998:           PetscFree(sub_schurs->change);
    6999:         }
    7000:       }
    7001:       if (pcbddc->switch_static) { /* need to save the local change */
    7002:         pcbddc->switch_static_change = localChangeOfBasisMatrix;
    7003:       } else {
    7004:         MatDestroy(&localChangeOfBasisMatrix);
    7005:       }
    7006:       /* determine if any process has changed the pressures locally */
    7007:       pcbddc->change_interior = pcbddc->benign_have_null;
    7008:     } else { /* fake change (get back change of basis into ConstraintMatrix and info on qr) */
    7009:       MatDestroy(&pcbddc->ConstraintMatrix);
    7010:       pcbddc->ConstraintMatrix = localChangeOfBasisMatrix;
    7011:       pcbddc->use_qr_single = qr_needed;
    7012:     }
    7013:   } else if (pcbddc->user_ChangeOfBasisMatrix || pcbddc->benign_saddle_point) {
    7014:     if (!pcbddc->benign_have_null && pcbddc->user_ChangeOfBasisMatrix) {
    7015:       PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);
    7016:       pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
    7017:     } else {
    7018:       Mat benign_global = NULL;
    7019:       if (pcbddc->benign_have_null) {
    7020:         Mat M;

    7022:         pcbddc->change_interior = PETSC_TRUE;
    7023:         VecCopy(matis->counter,pcis->vec1_N);
    7024:         VecReciprocal(pcis->vec1_N);
    7025:         MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&benign_global);
    7026:         if (pcbddc->benign_change) {
    7027:           MatDuplicate(pcbddc->benign_change,MAT_COPY_VALUES,&M);
    7028:           MatDiagonalScale(M,pcis->vec1_N,NULL);
    7029:         } else {
    7030:           MatCreateSeqAIJ(PETSC_COMM_SELF,pcis->n,pcis->n,1,NULL,&M);
    7031:           MatDiagonalSet(M,pcis->vec1_N,INSERT_VALUES);
    7032:         }
    7033:         MatISSetLocalMat(benign_global,M);
    7034:         MatDestroy(&M);
    7035:         MatAssemblyBegin(benign_global,MAT_FINAL_ASSEMBLY);
    7036:         MatAssemblyEnd(benign_global,MAT_FINAL_ASSEMBLY);
    7037:       }
    7038:       if (pcbddc->user_ChangeOfBasisMatrix) {
    7039:         MatMatMult(pcbddc->user_ChangeOfBasisMatrix,benign_global,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->ChangeOfBasisMatrix);
    7040:         MatDestroy(&benign_global);
    7041:       } else if (pcbddc->benign_have_null) {
    7042:         pcbddc->ChangeOfBasisMatrix = benign_global;
    7043:       }
    7044:     }
    7045:     if (pcbddc->switch_static && pcbddc->ChangeOfBasisMatrix) { /* need to save the local change */
    7046:       IS             is_global;
    7047:       const PetscInt *gidxs;

    7049:       ISLocalToGlobalMappingGetIndices(matis->rmapping,&gidxs);
    7050:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcis->n,gidxs,PETSC_COPY_VALUES,&is_global);
    7051:       ISLocalToGlobalMappingRestoreIndices(matis->rmapping,&gidxs);
    7052:       MatCreateSubMatrixUnsorted(pcbddc->ChangeOfBasisMatrix,is_global,is_global,&pcbddc->switch_static_change);
    7053:       ISDestroy(&is_global);
    7054:     }
    7055:   }
    7056:   if (!pcbddc->fake_change && pcbddc->ChangeOfBasisMatrix && !pcbddc->work_change) {
    7057:     VecDuplicate(pcis->vec1_global,&pcbddc->work_change);
    7058:   }

    7060:   if (!pcbddc->fake_change) {
    7061:     /* add pressure dofs to set of primal nodes for numbering purposes */
    7062:     for (i=0;i<pcbddc->benign_n;i++) {
    7063:       pcbddc->local_primal_ref_node[pcbddc->local_primal_size_cc] = pcbddc->benign_p0_lidx[i];
    7064:       pcbddc->primal_indices_local_idxs[pcbddc->local_primal_size] = pcbddc->benign_p0_lidx[i];
    7065:       pcbddc->local_primal_ref_mult[pcbddc->local_primal_size_cc] = 1;
    7066:       pcbddc->local_primal_size_cc++;
    7067:       pcbddc->local_primal_size++;
    7068:     }

    7070:     /* check if a new primal space has been introduced (also take into account benign trick) */
    7071:     pcbddc->new_primal_space_local = PETSC_TRUE;
    7072:     if (olocal_primal_size == pcbddc->local_primal_size) {
    7073:       PetscArraycmp(pcbddc->local_primal_ref_node,olocal_primal_ref_node,olocal_primal_size_cc,&pcbddc->new_primal_space_local);
    7074:       pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
    7075:       if (!pcbddc->new_primal_space_local) {
    7076:         PetscArraycmp(pcbddc->local_primal_ref_mult,olocal_primal_ref_mult,olocal_primal_size_cc,&pcbddc->new_primal_space_local);
    7077:         pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
    7078:       }
    7079:     }
    7080:     /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
    7081:     MPIU_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
    7082:   }
    7083:   PetscFree2(olocal_primal_ref_node,olocal_primal_ref_mult);

    7085:   /* flush dbg viewer */
    7086:   if (pcbddc->dbg_flag) {
    7087:     PetscViewerFlush(pcbddc->dbg_viewer);
    7088:   }

    7090:   /* free workspace */
    7091:   PetscBTDestroy(&qr_needed_idx);
    7092:   PetscBTDestroy(&change_basis);
    7093:   if (!pcbddc->adaptive_selection) {
    7094:     PetscFree3(constraints_idxs_ptr,constraints_data_ptr,constraints_n);
    7095:     PetscFree3(constraints_data,constraints_idxs,constraints_idxs_B);
    7096:   } else {
    7097:     PetscFree5(pcbddc->adaptive_constraints_n,
    7098:                       pcbddc->adaptive_constraints_idxs_ptr,
    7099:                       pcbddc->adaptive_constraints_data_ptr,
    7100:                       pcbddc->adaptive_constraints_idxs,
    7101:                       pcbddc->adaptive_constraints_data);
    7102:     PetscFree(constraints_n);
    7103:     PetscFree(constraints_idxs_B);
    7104:   }
    7105:   return 0;
    7106: }

    7108: PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
    7109: {
    7110:   ISLocalToGlobalMapping map;
    7111:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
    7112:   Mat_IS                 *matis  = (Mat_IS*)pc->pmat->data;
    7113:   PetscInt               i,N;
    7114:   PetscBool              rcsr = PETSC_FALSE;

    7116:   if (pcbddc->recompute_topography) {
    7117:     pcbddc->graphanalyzed = PETSC_FALSE;
    7118:     /* Reset previously computed graph */
    7119:     PCBDDCGraphReset(pcbddc->mat_graph);
    7120:     /* Init local Graph struct */
    7121:     MatGetSize(pc->pmat,&N,NULL);
    7122:     MatISGetLocalToGlobalMapping(pc->pmat,&map,NULL);
    7123:     PCBDDCGraphInit(pcbddc->mat_graph,map,N,pcbddc->graphmaxcount);

    7125:     if (pcbddc->user_primal_vertices_local && !pcbddc->user_primal_vertices) {
    7126:       PCBDDCConsistencyCheckIS(pc,MPI_LOR,&pcbddc->user_primal_vertices_local);
    7127:     }
    7128:     /* Check validity of the csr graph passed in by the user */

    7131:     /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
    7132:     if (!pcbddc->mat_graph->xadj && pcbddc->use_local_adj) {
    7133:       PetscInt  *xadj,*adjncy;
    7134:       PetscInt  nvtxs;
    7135:       PetscBool flg_row=PETSC_FALSE;

    7137:       MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
    7138:       if (flg_row) {
    7139:         PCBDDCSetLocalAdjacencyGraph(pc,nvtxs,xadj,adjncy,PETSC_COPY_VALUES);
    7140:         pcbddc->computed_rowadj = PETSC_TRUE;
    7141:       }
    7142:       MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
    7143:       rcsr = PETSC_TRUE;
    7144:     }
    7145:     if (pcbddc->dbg_flag) {
    7146:       PetscViewerFlush(pcbddc->dbg_viewer);
    7147:     }

    7149:     if (pcbddc->mat_graph->cdim && !pcbddc->mat_graph->cloc) {
    7150:       PetscReal    *lcoords;
    7151:       PetscInt     n;
    7152:       MPI_Datatype dimrealtype;

    7154:       /* TODO: support for blocked */
    7156:       MatGetLocalSize(matis->A,&n,NULL);
    7157:       PetscMalloc1(pcbddc->mat_graph->cdim*n,&lcoords);
    7158:       MPI_Type_contiguous(pcbddc->mat_graph->cdim,MPIU_REAL,&dimrealtype);
    7159:       MPI_Type_commit(&dimrealtype);
    7160:       PetscSFBcastBegin(matis->sf,dimrealtype,pcbddc->mat_graph->coords,lcoords,MPI_REPLACE);
    7161:       PetscSFBcastEnd(matis->sf,dimrealtype,pcbddc->mat_graph->coords,lcoords,MPI_REPLACE);
    7162:       MPI_Type_free(&dimrealtype);
    7163:       PetscFree(pcbddc->mat_graph->coords);

    7165:       pcbddc->mat_graph->coords = lcoords;
    7166:       pcbddc->mat_graph->cloc   = PETSC_TRUE;
    7167:       pcbddc->mat_graph->cnloc  = n;
    7168:     }
    7170:     pcbddc->mat_graph->active_coords = (PetscBool)(pcbddc->corner_selection && pcbddc->mat_graph->cdim && !pcbddc->corner_selected);

    7172:     /* Setup of Graph */
    7173:     pcbddc->mat_graph->commsizelimit = 0; /* don't use the COMM_SELF variant of the graph */
    7174:     PCBDDCGraphSetUp(pcbddc->mat_graph,pcbddc->vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices_local);

    7176:     /* attach info on disconnected subdomains if present */
    7177:     if (pcbddc->n_local_subs) {
    7178:       PetscInt *local_subs,n,totn;

    7180:       MatGetLocalSize(matis->A,&n,NULL);
    7181:       PetscMalloc1(n,&local_subs);
    7182:       for (i=0;i<n;i++) local_subs[i] = pcbddc->n_local_subs;
    7183:       for (i=0;i<pcbddc->n_local_subs;i++) {
    7184:         const PetscInt *idxs;
    7185:         PetscInt       nl,j;

    7187:         ISGetLocalSize(pcbddc->local_subs[i],&nl);
    7188:         ISGetIndices(pcbddc->local_subs[i],&idxs);
    7189:         for (j=0;j<nl;j++) local_subs[idxs[j]] = i;
    7190:         ISRestoreIndices(pcbddc->local_subs[i],&idxs);
    7191:       }
    7192:       for (i=0,totn=0;i<n;i++) totn = PetscMax(totn,local_subs[i]);
    7193:       pcbddc->mat_graph->n_local_subs = totn + 1;
    7194:       pcbddc->mat_graph->local_subs = local_subs;
    7195:     }
    7196:   }

    7198:   if (!pcbddc->graphanalyzed) {
    7199:     /* Graph's connected components analysis */
    7200:     PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);
    7201:     pcbddc->graphanalyzed = PETSC_TRUE;
    7202:     pcbddc->corner_selected = pcbddc->corner_selection;
    7203:   }
    7204:   if (rcsr) pcbddc->mat_graph->nvtxs_csr = 0;
    7205:   return 0;
    7206: }

    7208: PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt *nio, Vec vecs[])
    7209: {
    7210:   PetscInt       i,j,n;
    7211:   PetscScalar    *alphas;
    7212:   PetscReal      norm,*onorms;

    7214:   n = *nio;
    7215:   if (!n) return 0;
    7216:   PetscMalloc2(n,&alphas,n,&onorms);
    7217:   VecNormalize(vecs[0],&norm);
    7218:   if (norm < PETSC_SMALL) {
    7219:     onorms[0] = 0.0;
    7220:     VecSet(vecs[0],0.0);
    7221:   } else {
    7222:     onorms[0] = norm;
    7223:   }

    7225:   for (i=1;i<n;i++) {
    7226:     VecMDot(vecs[i],i,vecs,alphas);
    7227:     for (j=0;j<i;j++) alphas[j] = PetscConj(-alphas[j]);
    7228:     VecMAXPY(vecs[i],i,alphas,vecs);
    7229:     VecNormalize(vecs[i],&norm);
    7230:     if (norm < PETSC_SMALL) {
    7231:       onorms[i] = 0.0;
    7232:       VecSet(vecs[i],0.0);
    7233:     } else {
    7234:       onorms[i] = norm;
    7235:     }
    7236:   }
    7237:   /* push nonzero vectors at the beginning */
    7238:   for (i=0;i<n;i++) {
    7239:     if (onorms[i] == 0.0) {
    7240:       for (j=i+1;j<n;j++) {
    7241:         if (onorms[j] != 0.0) {
    7242:           VecCopy(vecs[j],vecs[i]);
    7243:           onorms[j] = 0.0;
    7244:         }
    7245:       }
    7246:     }
    7247:   }
    7248:   for (i=0,*nio=0;i<n;i++) *nio += onorms[i] != 0.0 ? 1 : 0;
    7249:   PetscFree2(alphas,onorms);
    7250:   return 0;
    7251: }

    7253: PetscErrorCode PCBDDCMatISGetSubassemblingPattern(Mat mat, PetscInt *n_subdomains, PetscInt redprocs, IS* is_sends, PetscBool *have_void)
    7254: {
    7255:   ISLocalToGlobalMapping mapping;
    7256:   Mat                    A;
    7257:   PetscInt               n_neighs,*neighs,*n_shared,**shared;
    7258:   PetscMPIInt            size,rank,color;
    7259:   PetscInt               *xadj,*adjncy;
    7260:   PetscInt               *adjncy_wgt,*v_wgt,*ranks_send_to_idx;
    7261:   PetscInt               im_active,active_procs,N,n,i,j,threshold = 2;
    7262:   PetscInt               void_procs,*procs_candidates = NULL;
    7263:   PetscInt               xadj_count,*count;
    7264:   PetscBool              ismatis,use_vwgt=PETSC_FALSE;
    7265:   PetscSubcomm           psubcomm;
    7266:   MPI_Comm               subcomm;

    7269:   PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);

    7275:   if (have_void) *have_void = PETSC_FALSE;
    7276:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    7277:   MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);
    7278:   MatISGetLocalMat(mat,&A);
    7279:   MatGetLocalSize(A,&n,NULL);
    7280:   im_active = !!n;
    7281:   MPIU_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)mat));
    7282:   void_procs = size - active_procs;
    7283:   /* get ranks of of non-active processes in mat communicator */
    7284:   if (void_procs) {
    7285:     PetscInt ncand;

    7287:     if (have_void) *have_void = PETSC_TRUE;
    7288:     PetscMalloc1(size,&procs_candidates);
    7289:     MPI_Allgather(&im_active,1,MPIU_INT,procs_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)mat));
    7290:     for (i=0,ncand=0;i<size;i++) {
    7291:       if (!procs_candidates[i]) {
    7292:         procs_candidates[ncand++] = i;
    7293:       }
    7294:     }
    7295:     /* force n_subdomains to be not greater that the number of non-active processes */
    7296:     *n_subdomains = PetscMin(void_procs,*n_subdomains);
    7297:   }

    7299:   /* number of subdomains requested greater than active processes or matrix size -> just shift the matrix
    7300:      number of subdomains requested 1 -> send to rank-0 or first candidate in voids  */
    7301:   MatGetSize(mat,&N,NULL);
    7302:   if (active_procs < *n_subdomains || *n_subdomains == 1 || N <= *n_subdomains) {
    7303:     PetscInt issize,isidx,dest;
    7304:     if (*n_subdomains == 1) dest = 0;
    7305:     else dest = rank;
    7306:     if (im_active) {
    7307:       issize = 1;
    7308:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
    7309:         isidx = procs_candidates[dest];
    7310:       } else {
    7311:         isidx = dest;
    7312:       }
    7313:     } else {
    7314:       issize = 0;
    7315:       isidx = -1;
    7316:     }
    7317:     if (*n_subdomains != 1) *n_subdomains = active_procs;
    7318:     ISCreateGeneral(PetscObjectComm((PetscObject)mat),issize,&isidx,PETSC_COPY_VALUES,is_sends);
    7319:     PetscFree(procs_candidates);
    7320:     return 0;
    7321:   }
    7322:   PetscOptionsGetBool(NULL,NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);
    7323:   PetscOptionsGetInt(NULL,NULL,"-matis_partitioning_threshold",&threshold,NULL);
    7324:   threshold = PetscMax(threshold,2);

    7326:   /* Get info on mapping */
    7327:   MatISGetLocalToGlobalMapping(mat,&mapping,NULL);
    7328:   ISLocalToGlobalMappingGetInfo(mapping,&n_neighs,&neighs,&n_shared,&shared);

    7330:   /* build local CSR graph of subdomains' connectivity */
    7331:   PetscMalloc1(2,&xadj);
    7332:   xadj[0] = 0;
    7333:   xadj[1] = PetscMax(n_neighs-1,0);
    7334:   PetscMalloc1(xadj[1],&adjncy);
    7335:   PetscMalloc1(xadj[1],&adjncy_wgt);
    7336:   PetscCalloc1(n,&count);
    7337:   for (i=1;i<n_neighs;i++)
    7338:     for (j=0;j<n_shared[i];j++)
    7339:       count[shared[i][j]] += 1;

    7341:   xadj_count = 0;
    7342:   for (i=1;i<n_neighs;i++) {
    7343:     for (j=0;j<n_shared[i];j++) {
    7344:       if (count[shared[i][j]] < threshold) {
    7345:         adjncy[xadj_count] = neighs[i];
    7346:         adjncy_wgt[xadj_count] = n_shared[i];
    7347:         xadj_count++;
    7348:         break;
    7349:       }
    7350:     }
    7351:   }
    7352:   xadj[1] = xadj_count;
    7353:   PetscFree(count);
    7354:   ISLocalToGlobalMappingRestoreInfo(mapping,&n_neighs,&neighs,&n_shared,&shared);
    7355:   PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);

    7357:   PetscMalloc1(1,&ranks_send_to_idx);

    7359:   /* Restrict work on active processes only */
    7360:   PetscMPIIntCast(im_active,&color);
    7361:   if (void_procs) {
    7362:     PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&psubcomm);
    7363:     PetscSubcommSetNumber(psubcomm,2); /* 2 groups, active process and not active processes */
    7364:     PetscSubcommSetTypeGeneral(psubcomm,color,rank);
    7365:     subcomm = PetscSubcommChild(psubcomm);
    7366:   } else {
    7367:     psubcomm = NULL;
    7368:     subcomm = PetscObjectComm((PetscObject)mat);
    7369:   }

    7371:   v_wgt = NULL;
    7372:   if (!color) {
    7373:     PetscFree(xadj);
    7374:     PetscFree(adjncy);
    7375:     PetscFree(adjncy_wgt);
    7376:   } else {
    7377:     Mat             subdomain_adj;
    7378:     IS              new_ranks,new_ranks_contig;
    7379:     MatPartitioning partitioner;
    7380:     PetscInt        rstart=0,rend=0;
    7381:     PetscInt        *is_indices,*oldranks;
    7382:     PetscMPIInt     size;
    7383:     PetscBool       aggregate;

    7385:     MPI_Comm_size(subcomm,&size);
    7386:     if (void_procs) {
    7387:       PetscInt prank = rank;
    7388:       PetscMalloc1(size,&oldranks);
    7389:       MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,subcomm);
    7390:       for (i=0;i<xadj[1];i++) {
    7391:         PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);
    7392:       }
    7393:       PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);
    7394:     } else {
    7395:       oldranks = NULL;
    7396:     }
    7397:     aggregate = ((redprocs > 0 && redprocs < size) ? PETSC_TRUE : PETSC_FALSE);
    7398:     if (aggregate) { /* TODO: all this part could be made more efficient */
    7399:       PetscInt    lrows,row,ncols,*cols;
    7400:       PetscMPIInt nrank;
    7401:       PetscScalar *vals;

    7403:       MPI_Comm_rank(subcomm,&nrank);
    7404:       lrows = 0;
    7405:       if (nrank<redprocs) {
    7406:         lrows = size/redprocs;
    7407:         if (nrank<size%redprocs) lrows++;
    7408:       }
    7409:       MatCreateAIJ(subcomm,lrows,lrows,size,size,50,NULL,50,NULL,&subdomain_adj);
    7410:       MatGetOwnershipRange(subdomain_adj,&rstart,&rend);
    7411:       MatSetOption(subdomain_adj,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
    7412:       MatSetOption(subdomain_adj,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
    7413:       row = nrank;
    7414:       ncols = xadj[1]-xadj[0];
    7415:       cols = adjncy;
    7416:       PetscMalloc1(ncols,&vals);
    7417:       for (i=0;i<ncols;i++) vals[i] = adjncy_wgt[i];
    7418:       MatSetValues(subdomain_adj,1,&row,ncols,cols,vals,INSERT_VALUES);
    7419:       MatAssemblyBegin(subdomain_adj,MAT_FINAL_ASSEMBLY);
    7420:       MatAssemblyEnd(subdomain_adj,MAT_FINAL_ASSEMBLY);
    7421:       PetscFree(xadj);
    7422:       PetscFree(adjncy);
    7423:       PetscFree(adjncy_wgt);
    7424:       PetscFree(vals);
    7425:       if (use_vwgt) {
    7426:         Vec               v;
    7427:         const PetscScalar *array;
    7428:         PetscInt          nl;

    7430:         MatCreateVecs(subdomain_adj,&v,NULL);
    7431:         VecSetValue(v,row,(PetscScalar)n,INSERT_VALUES);
    7432:         VecAssemblyBegin(v);
    7433:         VecAssemblyEnd(v);
    7434:         VecGetLocalSize(v,&nl);
    7435:         VecGetArrayRead(v,&array);
    7436:         PetscMalloc1(nl,&v_wgt);
    7437:         for (i=0;i<nl;i++) v_wgt[i] = (PetscInt)PetscRealPart(array[i]);
    7438:         VecRestoreArrayRead(v,&array);
    7439:         VecDestroy(&v);
    7440:       }
    7441:     } else {
    7442:       MatCreateMPIAdj(subcomm,1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);
    7443:       if (use_vwgt) {
    7444:         PetscMalloc1(1,&v_wgt);
    7445:         v_wgt[0] = n;
    7446:       }
    7447:     }
    7448:     /* MatView(subdomain_adj,0); */

    7450:     /* Partition */
    7451:     MatPartitioningCreate(subcomm,&partitioner);
    7452: #if defined(PETSC_HAVE_PTSCOTCH)
    7453:     MatPartitioningSetType(partitioner,MATPARTITIONINGPTSCOTCH);
    7454: #elif defined(PETSC_HAVE_PARMETIS)
    7455:     MatPartitioningSetType(partitioner,MATPARTITIONINGPARMETIS);
    7456: #else
    7457:     MatPartitioningSetType(partitioner,MATPARTITIONINGAVERAGE);
    7458: #endif
    7459:     MatPartitioningSetAdjacency(partitioner,subdomain_adj);
    7460:     if (v_wgt) {
    7461:       MatPartitioningSetVertexWeights(partitioner,v_wgt);
    7462:     }
    7463:     *n_subdomains = PetscMin((PetscInt)size,*n_subdomains);
    7464:     MatPartitioningSetNParts(partitioner,*n_subdomains);
    7465:     MatPartitioningSetFromOptions(partitioner);
    7466:     MatPartitioningApply(partitioner,&new_ranks);
    7467:     /* MatPartitioningView(partitioner,0); */

    7469:     /* renumber new_ranks to avoid "holes" in new set of processors */
    7470:     ISRenumber(new_ranks,NULL,NULL,&new_ranks_contig);
    7471:     ISDestroy(&new_ranks);
    7472:     ISGetIndices(new_ranks_contig,(const PetscInt**)&is_indices);
    7473:     if (!aggregate) {
    7474:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
    7475:         PetscAssert(oldranks,PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
    7476:         ranks_send_to_idx[0] = procs_candidates[oldranks[is_indices[0]]];
    7477:       } else if (oldranks) {
    7478:         ranks_send_to_idx[0] = oldranks[is_indices[0]];
    7479:       } else {
    7480:         ranks_send_to_idx[0] = is_indices[0];
    7481:       }
    7482:     } else {
    7483:       PetscInt    idx = 0;
    7484:       PetscMPIInt tag;
    7485:       MPI_Request *reqs;

    7487:       PetscObjectGetNewTag((PetscObject)subdomain_adj,&tag);
    7488:       PetscMalloc1(rend-rstart,&reqs);
    7489:       for (i=rstart;i<rend;i++) {
    7490:         MPI_Isend(is_indices+i-rstart,1,MPIU_INT,i,tag,subcomm,&reqs[i-rstart]);
    7491:       }
    7492:       MPI_Recv(&idx,1,MPIU_INT,MPI_ANY_SOURCE,tag,subcomm,MPI_STATUS_IGNORE);
    7493:       MPI_Waitall(rend-rstart,reqs,MPI_STATUSES_IGNORE);
    7494:       PetscFree(reqs);
    7495:       if (procs_candidates) { /* shift the pattern on non-active candidates (if any) */
    7496:         PetscAssert(oldranks,PETSC_COMM_SELF,PETSC_ERR_PLIB,"This should not happen");
    7497:         ranks_send_to_idx[0] = procs_candidates[oldranks[idx]];
    7498:       } else if (oldranks) {
    7499:         ranks_send_to_idx[0] = oldranks[idx];
    7500:       } else {
    7501:         ranks_send_to_idx[0] = idx;
    7502:       }
    7503:     }
    7504:     ISRestoreIndices(new_ranks_contig,(const PetscInt**)&is_indices);
    7505:     /* clean up */
    7506:     PetscFree(oldranks);
    7507:     ISDestroy(&new_ranks_contig);
    7508:     MatDestroy(&subdomain_adj);
    7509:     MatPartitioningDestroy(&partitioner);
    7510:   }
    7511:   PetscSubcommDestroy(&psubcomm);
    7512:   PetscFree(procs_candidates);

    7514:   /* assemble parallel IS for sends */
    7515:   i = 1;
    7516:   if (!color) i=0;
    7517:   ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,is_sends);
    7518:   return 0;
    7519: }

    7521: typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;

    7523: 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[])
    7524: {
    7525:   Mat                    local_mat;
    7526:   IS                     is_sends_internal;
    7527:   PetscInt               rows,cols,new_local_rows;
    7528:   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals,buf_size_vecs;
    7529:   PetscBool              ismatis,isdense,newisdense,destroy_mat;
    7530:   ISLocalToGlobalMapping l2gmap;
    7531:   PetscInt*              l2gmap_indices;
    7532:   const PetscInt*        is_indices;
    7533:   MatType                new_local_type;
    7534:   /* buffers */
    7535:   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
    7536:   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
    7537:   PetscInt               *recv_buffer_idxs_local;
    7538:   PetscScalar            *ptr_vals,*recv_buffer_vals;
    7539:   const PetscScalar      *send_buffer_vals;
    7540:   PetscScalar            *ptr_vecs,*send_buffer_vecs,*recv_buffer_vecs;
    7541:   /* MPI */
    7542:   MPI_Comm               comm,comm_n;
    7543:   PetscSubcomm           subcomm;
    7544:   PetscMPIInt            n_sends,n_recvs,size;
    7545:   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
    7546:   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
    7547:   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,tag_vecs,source_dest;
    7548:   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals,*send_req_vecs;
    7549:   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals,*recv_req_vecs;

    7552:   PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);
    7560:   if (nvecs) {
    7563:   }
    7564:   /* further checks */
    7565:   MatISGetLocalMat(mat,&local_mat);
    7566:   PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);
    7568:   MatGetSize(local_mat,&rows,&cols);
    7570:   if (reuse && *mat_n) {
    7571:     PetscInt mrows,mcols,mnrows,mncols;
    7573:     PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);
    7575:     MatGetSize(mat,&mrows,&mcols);
    7576:     MatGetSize(*mat_n,&mnrows,&mncols);
    7579:   }
    7580:   MatGetBlockSize(local_mat,&bs);

    7583:   /* prepare IS for sending if not provided */
    7584:   if (!is_sends) {
    7586:     PCBDDCMatISGetSubassemblingPattern(mat,&n_subdomains,0,&is_sends_internal,NULL);
    7587:   } else {
    7588:     PetscObjectReference((PetscObject)is_sends);
    7589:     is_sends_internal = is_sends;
    7590:   }

    7592:   /* get comm */
    7593:   PetscObjectGetComm((PetscObject)mat,&comm);

    7595:   /* compute number of sends */
    7596:   ISGetLocalSize(is_sends_internal,&i);
    7597:   PetscMPIIntCast(i,&n_sends);

    7599:   /* compute number of receives */
    7600:   MPI_Comm_size(comm,&size);
    7601:   PetscMalloc1(size,&iflags);
    7602:   PetscArrayzero(iflags,size);
    7603:   ISGetIndices(is_sends_internal,&is_indices);
    7604:   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
    7605:   PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);
    7606:   PetscFree(iflags);

    7608:   /* restrict comm if requested */
    7609:   subcomm = NULL;
    7610:   destroy_mat = PETSC_FALSE;
    7611:   if (restrict_comm) {
    7612:     PetscMPIInt color,subcommsize;

    7614:     color = 0;
    7615:     if (restrict_full) {
    7616:       if (!n_recvs) color = 1; /* processes not receiving anything will not participate in new comm (full restriction) */
    7617:     } else {
    7618:       if (!n_recvs && n_sends) color = 1; /* just those processes that are sending but not receiving anything will not participate in new comm */
    7619:     }
    7620:     MPIU_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);
    7621:     subcommsize = size - subcommsize;
    7622:     /* check if reuse has been requested */
    7623:     if (reuse) {
    7624:       if (*mat_n) {
    7625:         PetscMPIInt subcommsize2;
    7626:         MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);
    7628:         comm_n = PetscObjectComm((PetscObject)*mat_n);
    7629:       } else {
    7630:         comm_n = PETSC_COMM_SELF;
    7631:       }
    7632:     } else { /* MAT_INITIAL_MATRIX */
    7633:       PetscMPIInt rank;

    7635:       MPI_Comm_rank(comm,&rank);
    7636:       PetscSubcommCreate(comm,&subcomm);
    7637:       PetscSubcommSetNumber(subcomm,2);
    7638:       PetscSubcommSetTypeGeneral(subcomm,color,rank);
    7639:       comm_n = PetscSubcommChild(subcomm);
    7640:     }
    7641:     /* flag to destroy *mat_n if not significative */
    7642:     if (color) destroy_mat = PETSC_TRUE;
    7643:   } else {
    7644:     comm_n = comm;
    7645:   }

    7647:   /* prepare send/receive buffers */
    7648:   PetscMalloc1(size,&ilengths_idxs);
    7649:   PetscArrayzero(ilengths_idxs,size);
    7650:   PetscMalloc1(size,&ilengths_vals);
    7651:   PetscArrayzero(ilengths_vals,size);
    7652:   if (nis) {
    7653:     PetscCalloc1(size,&ilengths_idxs_is);
    7654:   }

    7656:   /* Get data from local matrices */
    7658:     /* TODO: See below some guidelines on how to prepare the local buffers */
    7659:     /*
    7660:        send_buffer_vals should contain the raw values of the local matrix
    7661:        send_buffer_idxs should contain:
    7662:        - MatType_PRIVATE type
    7663:        - PetscInt        size_of_l2gmap
    7664:        - PetscInt        global_row_indices[size_of_l2gmap]
    7665:        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
    7666:     */
    7667:   {
    7668:     ISLocalToGlobalMapping mapping;

    7670:     MatISGetLocalToGlobalMapping(mat,&mapping,NULL);
    7671:     MatDenseGetArrayRead(local_mat,&send_buffer_vals);
    7672:     ISLocalToGlobalMappingGetSize(mapping,&i);
    7673:     PetscMalloc1(i+2,&send_buffer_idxs);
    7674:     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
    7675:     send_buffer_idxs[1] = i;
    7676:     ISLocalToGlobalMappingGetIndices(mapping,(const PetscInt**)&ptr_idxs);
    7677:     PetscArraycpy(&send_buffer_idxs[2],ptr_idxs,i);
    7678:     ISLocalToGlobalMappingRestoreIndices(mapping,(const PetscInt**)&ptr_idxs);
    7679:     PetscMPIIntCast(i,&len);
    7680:     for (i=0;i<n_sends;i++) {
    7681:       ilengths_vals[is_indices[i]] = len*len;
    7682:       ilengths_idxs[is_indices[i]] = len+2;
    7683:     }
    7684:   }
    7685:   PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);
    7686:   /* additional is (if any) */
    7687:   if (nis) {
    7688:     PetscMPIInt psum;
    7689:     PetscInt j;
    7690:     for (j=0,psum=0;j<nis;j++) {
    7691:       PetscInt plen;
    7692:       ISGetLocalSize(isarray[j],&plen);
    7693:       PetscMPIIntCast(plen,&len);
    7694:       psum += len+1; /* indices + length */
    7695:     }
    7696:     PetscMalloc1(psum,&send_buffer_idxs_is);
    7697:     for (j=0,psum=0;j<nis;j++) {
    7698:       PetscInt plen;
    7699:       const PetscInt *is_array_idxs;
    7700:       ISGetLocalSize(isarray[j],&plen);
    7701:       send_buffer_idxs_is[psum] = plen;
    7702:       ISGetIndices(isarray[j],&is_array_idxs);
    7703:       PetscArraycpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen);
    7704:       ISRestoreIndices(isarray[j],&is_array_idxs);
    7705:       psum += plen+1; /* indices + length */
    7706:     }
    7707:     for (i=0;i<n_sends;i++) {
    7708:       ilengths_idxs_is[is_indices[i]] = psum;
    7709:     }
    7710:     PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);
    7711:   }
    7712:   MatISRestoreLocalMat(mat,&local_mat);

    7714:   buf_size_idxs = 0;
    7715:   buf_size_vals = 0;
    7716:   buf_size_idxs_is = 0;
    7717:   buf_size_vecs = 0;
    7718:   for (i=0;i<n_recvs;i++) {
    7719:     buf_size_idxs += (PetscInt)olengths_idxs[i];
    7720:     buf_size_vals += (PetscInt)olengths_vals[i];
    7721:     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
    7722:     if (nvecs) buf_size_vecs += (PetscInt)olengths_idxs[i];
    7723:   }
    7724:   PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);
    7725:   PetscMalloc1(buf_size_vals,&recv_buffer_vals);
    7726:   PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);
    7727:   PetscMalloc1(buf_size_vecs,&recv_buffer_vecs);

    7729:   /* get new tags for clean communications */
    7730:   PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);
    7731:   PetscObjectGetNewTag((PetscObject)mat,&tag_vals);
    7732:   PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);
    7733:   PetscObjectGetNewTag((PetscObject)mat,&tag_vecs);

    7735:   /* allocate for requests */
    7736:   PetscMalloc1(n_sends,&send_req_idxs);
    7737:   PetscMalloc1(n_sends,&send_req_vals);
    7738:   PetscMalloc1(n_sends,&send_req_idxs_is);
    7739:   PetscMalloc1(n_sends,&send_req_vecs);
    7740:   PetscMalloc1(n_recvs,&recv_req_idxs);
    7741:   PetscMalloc1(n_recvs,&recv_req_vals);
    7742:   PetscMalloc1(n_recvs,&recv_req_idxs_is);
    7743:   PetscMalloc1(n_recvs,&recv_req_vecs);

    7745:   /* communications */
    7746:   ptr_idxs = recv_buffer_idxs;
    7747:   ptr_vals = recv_buffer_vals;
    7748:   ptr_idxs_is = recv_buffer_idxs_is;
    7749:   ptr_vecs = recv_buffer_vecs;
    7750:   for (i=0;i<n_recvs;i++) {
    7751:     source_dest = onodes[i];
    7752:     MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);
    7753:     MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);
    7754:     ptr_idxs += olengths_idxs[i];
    7755:     ptr_vals += olengths_vals[i];
    7756:     if (nis) {
    7757:       source_dest = onodes_is[i];
    7758:       MPI_Irecv(ptr_idxs_is,olengths_idxs_is[i],MPIU_INT,source_dest,tag_idxs_is,comm,&recv_req_idxs_is[i]);
    7759:       ptr_idxs_is += olengths_idxs_is[i];
    7760:     }
    7761:     if (nvecs) {
    7762:       source_dest = onodes[i];
    7763:       MPI_Irecv(ptr_vecs,olengths_idxs[i]-2,MPIU_SCALAR,source_dest,tag_vecs,comm,&recv_req_vecs[i]);
    7764:       ptr_vecs += olengths_idxs[i]-2;
    7765:     }
    7766:   }
    7767:   for (i=0;i<n_sends;i++) {
    7768:     PetscMPIIntCast(is_indices[i],&source_dest);
    7769:     MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);
    7770:     MPI_Isend((PetscScalar*)send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);
    7771:     if (nis) {
    7772:       MPI_Isend(send_buffer_idxs_is,ilengths_idxs_is[source_dest],MPIU_INT,source_dest,tag_idxs_is,comm,&send_req_idxs_is[i]);
    7773:     }
    7774:     if (nvecs) {
    7775:       VecGetArray(nnsp_vec[0],&send_buffer_vecs);
    7776:       MPI_Isend(send_buffer_vecs,ilengths_idxs[source_dest]-2,MPIU_SCALAR,source_dest,tag_vecs,comm,&send_req_vecs[i]);
    7777:     }
    7778:   }
    7779:   ISRestoreIndices(is_sends_internal,&is_indices);
    7780:   ISDestroy(&is_sends_internal);

    7782:   /* assemble new l2g map */
    7783:   MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);
    7784:   ptr_idxs = recv_buffer_idxs;
    7785:   new_local_rows = 0;
    7786:   for (i=0;i<n_recvs;i++) {
    7787:     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
    7788:     ptr_idxs += olengths_idxs[i];
    7789:   }
    7790:   PetscMalloc1(new_local_rows,&l2gmap_indices);
    7791:   ptr_idxs = recv_buffer_idxs;
    7792:   new_local_rows = 0;
    7793:   for (i=0;i<n_recvs;i++) {
    7794:     PetscArraycpy(&l2gmap_indices[new_local_rows],ptr_idxs+2,*(ptr_idxs+1));
    7795:     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
    7796:     ptr_idxs += olengths_idxs[i];
    7797:   }
    7798:   PetscSortRemoveDupsInt(&new_local_rows,l2gmap_indices);
    7799:   ISLocalToGlobalMappingCreate(comm_n,1,new_local_rows,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);
    7800:   PetscFree(l2gmap_indices);

    7802:   /* infer new local matrix type from received local matrices type */
    7803:   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
    7804:   /* 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) */
    7805:   if (n_recvs) {
    7806:     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
    7807:     ptr_idxs = recv_buffer_idxs;
    7808:     for (i=0;i<n_recvs;i++) {
    7809:       if ((PetscInt)new_local_type_private != *ptr_idxs) {
    7810:         new_local_type_private = MATAIJ_PRIVATE;
    7811:         break;
    7812:       }
    7813:       ptr_idxs += olengths_idxs[i];
    7814:     }
    7815:     switch (new_local_type_private) {
    7816:       case MATDENSE_PRIVATE:
    7817:         new_local_type = MATSEQAIJ;
    7818:         bs = 1;
    7819:         break;
    7820:       case MATAIJ_PRIVATE:
    7821:         new_local_type = MATSEQAIJ;
    7822:         bs = 1;
    7823:         break;
    7824:       case MATBAIJ_PRIVATE:
    7825:         new_local_type = MATSEQBAIJ;
    7826:         break;
    7827:       case MATSBAIJ_PRIVATE:
    7828:         new_local_type = MATSEQSBAIJ;
    7829:         break;
    7830:       default:
    7831:         SETERRQ(comm,PETSC_ERR_SUP,"Unsupported private type %d in %s",new_local_type_private,PETSC_FUNCTION_NAME);
    7832:     }
    7833:   } else { /* by default, new_local_type is seqaij */
    7834:     new_local_type = MATSEQAIJ;
    7835:     bs = 1;
    7836:   }

    7838:   /* create MATIS object if needed */
    7839:   if (!reuse) {
    7840:     MatGetSize(mat,&rows,&cols);
    7841:     MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,l2gmap,mat_n);
    7842:   } else {
    7843:     /* it also destroys the local matrices */
    7844:     if (*mat_n) {
    7845:       MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);
    7846:     } else { /* this is a fake object */
    7847:       MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,l2gmap,mat_n);
    7848:     }
    7849:   }
    7850:   MatISGetLocalMat(*mat_n,&local_mat);
    7851:   MatSetType(local_mat,new_local_type);

    7853:   MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);

    7855:   /* Global to local map of received indices */
    7856:   PetscMalloc1(buf_size_idxs,&recv_buffer_idxs_local); /* needed for values insertion */
    7857:   ISGlobalToLocalMappingApply(l2gmap,IS_GTOLM_MASK,buf_size_idxs,recv_buffer_idxs,&i,recv_buffer_idxs_local);
    7858:   ISLocalToGlobalMappingDestroy(&l2gmap);

    7860:   /* restore attributes -> type of incoming data and its size */
    7861:   buf_size_idxs = 0;
    7862:   for (i=0;i<n_recvs;i++) {
    7863:     recv_buffer_idxs_local[buf_size_idxs] = recv_buffer_idxs[buf_size_idxs];
    7864:     recv_buffer_idxs_local[buf_size_idxs+1] = recv_buffer_idxs[buf_size_idxs+1];
    7865:     buf_size_idxs += (PetscInt)olengths_idxs[i];
    7866:   }
    7867:   PetscFree(recv_buffer_idxs);

    7869:   /* set preallocation */
    7870:   PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&newisdense);
    7871:   if (!newisdense) {
    7872:     PetscInt *new_local_nnz=NULL;

    7874:     ptr_idxs = recv_buffer_idxs_local;
    7875:     if (n_recvs) {
    7876:       PetscCalloc1(new_local_rows,&new_local_nnz);
    7877:     }
    7878:     for (i=0;i<n_recvs;i++) {
    7879:       PetscInt j;
    7880:       if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
    7881:         for (j=0;j<*(ptr_idxs+1);j++) {
    7882:           new_local_nnz[*(ptr_idxs+2+j)] += *(ptr_idxs+1);
    7883:         }
    7884:       } else {
    7885:         /* TODO */
    7886:       }
    7887:       ptr_idxs += olengths_idxs[i];
    7888:     }
    7889:     if (new_local_nnz) {
    7890:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMin(new_local_nnz[i],new_local_rows);
    7891:       MatSeqAIJSetPreallocation(local_mat,0,new_local_nnz);
    7892:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] /= bs;
    7893:       MatSeqBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);
    7894:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMax(new_local_nnz[i]-i,0);
    7895:       MatSeqSBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);
    7896:     } else {
    7897:       MatSetUp(local_mat);
    7898:     }
    7899:     PetscFree(new_local_nnz);
    7900:   } else {
    7901:     MatSetUp(local_mat);
    7902:   }

    7904:   /* set values */
    7905:   ptr_vals = recv_buffer_vals;
    7906:   ptr_idxs = recv_buffer_idxs_local;
    7907:   for (i=0;i<n_recvs;i++) {
    7908:     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
    7909:       MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);
    7910:       MatSetValues(local_mat,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);
    7911:       MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);
    7912:       MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);
    7913:       MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);
    7914:     } else {
    7915:       /* TODO */
    7916:     }
    7917:     ptr_idxs += olengths_idxs[i];
    7918:     ptr_vals += olengths_vals[i];
    7919:   }
    7920:   MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);
    7921:   MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);
    7922:   MatISRestoreLocalMat(*mat_n,&local_mat);
    7923:   MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);
    7924:   MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);
    7925:   PetscFree(recv_buffer_vals);

    7927: #if 0
    7928:   if (!restrict_comm) { /* check */
    7929:     Vec       lvec,rvec;
    7930:     PetscReal infty_error;

    7932:     MatCreateVecs(mat,&rvec,&lvec);
    7933:     VecSetRandom(rvec,NULL);
    7934:     MatMult(mat,rvec,lvec);
    7935:     VecScale(lvec,-1.0);
    7936:     MatMultAdd(*mat_n,rvec,lvec,lvec);
    7937:     VecNorm(lvec,NORM_INFINITY,&infty_error);
    7938:     PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
    7939:     VecDestroy(&rvec);
    7940:     VecDestroy(&lvec);
    7941:   }
    7942: #endif

    7944:   /* assemble new additional is (if any) */
    7945:   if (nis) {
    7946:     PetscInt **temp_idxs,*count_is,j,psum;

    7948:     MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);
    7949:     PetscCalloc1(nis,&count_is);
    7950:     ptr_idxs = recv_buffer_idxs_is;
    7951:     psum = 0;
    7952:     for (i=0;i<n_recvs;i++) {
    7953:       for (j=0;j<nis;j++) {
    7954:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
    7955:         count_is[j] += plen; /* increment counting of buffer for j-th IS */
    7956:         psum += plen;
    7957:         ptr_idxs += plen+1; /* shift pointer to received data */
    7958:       }
    7959:     }
    7960:     PetscMalloc1(nis,&temp_idxs);
    7961:     PetscMalloc1(psum,&temp_idxs[0]);
    7962:     for (i=1;i<nis;i++) {
    7963:       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
    7964:     }
    7965:     PetscArrayzero(count_is,nis);
    7966:     ptr_idxs = recv_buffer_idxs_is;
    7967:     for (i=0;i<n_recvs;i++) {
    7968:       for (j=0;j<nis;j++) {
    7969:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
    7970:         PetscArraycpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen);
    7971:         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
    7972:         ptr_idxs += plen+1; /* shift pointer to received data */
    7973:       }
    7974:     }
    7975:     for (i=0;i<nis;i++) {
    7976:       ISDestroy(&isarray[i]);
    7977:       PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);
    7978:       ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);
    7979:     }
    7980:     PetscFree(count_is);
    7981:     PetscFree(temp_idxs[0]);
    7982:     PetscFree(temp_idxs);
    7983:   }
    7984:   /* free workspace */
    7985:   PetscFree(recv_buffer_idxs_is);
    7986:   MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);
    7987:   PetscFree(send_buffer_idxs);
    7988:   MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);
    7989:   if (isdense) {
    7990:     MatISGetLocalMat(mat,&local_mat);
    7991:     MatDenseRestoreArrayRead(local_mat,&send_buffer_vals);
    7992:     MatISRestoreLocalMat(mat,&local_mat);
    7993:   } else {
    7994:     /* PetscFree(send_buffer_vals); */
    7995:   }
    7996:   if (nis) {
    7997:     MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);
    7998:     PetscFree(send_buffer_idxs_is);
    7999:   }

    8001:   if (nvecs) {
    8002:     MPI_Waitall(n_recvs,recv_req_vecs,MPI_STATUSES_IGNORE);
    8003:     MPI_Waitall(n_sends,send_req_vecs,MPI_STATUSES_IGNORE);
    8004:     VecRestoreArray(nnsp_vec[0],&send_buffer_vecs);
    8005:     VecDestroy(&nnsp_vec[0]);
    8006:     VecCreate(comm_n,&nnsp_vec[0]);
    8007:     VecSetSizes(nnsp_vec[0],new_local_rows,PETSC_DECIDE);
    8008:     VecSetType(nnsp_vec[0],VECSTANDARD);
    8009:     /* set values */
    8010:     ptr_vals = recv_buffer_vecs;
    8011:     ptr_idxs = recv_buffer_idxs_local;
    8012:     VecGetArray(nnsp_vec[0],&send_buffer_vecs);
    8013:     for (i=0;i<n_recvs;i++) {
    8014:       PetscInt j;
    8015:       for (j=0;j<*(ptr_idxs+1);j++) {
    8016:         send_buffer_vecs[*(ptr_idxs+2+j)] += *(ptr_vals + j);
    8017:       }
    8018:       ptr_idxs += olengths_idxs[i];
    8019:       ptr_vals += olengths_idxs[i]-2;
    8020:     }
    8021:     VecRestoreArray(nnsp_vec[0],&send_buffer_vecs);
    8022:     VecAssemblyBegin(nnsp_vec[0]);
    8023:     VecAssemblyEnd(nnsp_vec[0]);
    8024:   }

    8026:   PetscFree(recv_buffer_vecs);
    8027:   PetscFree(recv_buffer_idxs_local);
    8028:   PetscFree(recv_req_idxs);
    8029:   PetscFree(recv_req_vals);
    8030:   PetscFree(recv_req_vecs);
    8031:   PetscFree(recv_req_idxs_is);
    8032:   PetscFree(send_req_idxs);
    8033:   PetscFree(send_req_vals);
    8034:   PetscFree(send_req_vecs);
    8035:   PetscFree(send_req_idxs_is);
    8036:   PetscFree(ilengths_vals);
    8037:   PetscFree(ilengths_idxs);
    8038:   PetscFree(olengths_vals);
    8039:   PetscFree(olengths_idxs);
    8040:   PetscFree(onodes);
    8041:   if (nis) {
    8042:     PetscFree(ilengths_idxs_is);
    8043:     PetscFree(olengths_idxs_is);
    8044:     PetscFree(onodes_is);
    8045:   }
    8046:   PetscSubcommDestroy(&subcomm);
    8047:   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not participate */
    8048:     MatDestroy(mat_n);
    8049:     for (i=0;i<nis;i++) {
    8050:       ISDestroy(&isarray[i]);
    8051:     }
    8052:     if (nvecs) { /* need to match VecDestroy nnsp_vec called in the other code path */
    8053:       VecDestroy(&nnsp_vec[0]);
    8054:     }
    8055:     *mat_n = NULL;
    8056:   }
    8057:   return 0;
    8058: }

    8060: /* temporary hack into ksp private data structure */
    8061: #include <petsc/private/kspimpl.h>

    8063: PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
    8064: {
    8065:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
    8066:   PC_IS                  *pcis = (PC_IS*)pc->data;
    8067:   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
    8068:   Mat                    coarsedivudotp = NULL;
    8069:   Mat                    coarseG,t_coarse_mat_is;
    8070:   MatNullSpace           CoarseNullSpace = NULL;
    8071:   ISLocalToGlobalMapping coarse_islg;
    8072:   IS                     coarse_is,*isarray,corners;
    8073:   PetscInt               i,im_active=-1,active_procs=-1;
    8074:   PetscInt               nis,nisdofs,nisneu,nisvert;
    8075:   PetscInt               coarse_eqs_per_proc;
    8076:   PC                     pc_temp;
    8077:   PCType                 coarse_pc_type;
    8078:   KSPType                coarse_ksp_type;
    8079:   PetscBool              multilevel_requested,multilevel_allowed;
    8080:   PetscBool              coarse_reuse;
    8081:   PetscInt               ncoarse,nedcfield;
    8082:   PetscBool              compute_vecs = PETSC_FALSE;
    8083:   PetscScalar            *array;
    8084:   MatReuse               coarse_mat_reuse;
    8085:   PetscBool              restr, full_restr, have_void;
    8086:   PetscMPIInt            size;
    8087:   PetscErrorCode         ierr;

    8089:   PetscLogEventBegin(PC_BDDC_CoarseSetUp[pcbddc->current_level],pc,0,0,0);
    8090:   /* Assign global numbering to coarse dofs */
    8091:   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 */
    8092:     PetscInt ocoarse_size;
    8093:     compute_vecs = PETSC_TRUE;

    8095:     pcbddc->new_primal_space = PETSC_TRUE;
    8096:     ocoarse_size = pcbddc->coarse_size;
    8097:     PetscFree(pcbddc->global_primal_indices);
    8098:     PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);
    8099:     /* see if we can avoid some work */
    8100:     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
    8101:       /* if the coarse size is different or we are using adaptive selection, better to not reuse the coarse matrix */
    8102:       if (ocoarse_size != pcbddc->coarse_size || pcbddc->adaptive_selection) {
    8103:         KSPReset(pcbddc->coarse_ksp);
    8104:         coarse_reuse = PETSC_FALSE;
    8105:       } else { /* we can safely reuse already computed coarse matrix */
    8106:         coarse_reuse = PETSC_TRUE;
    8107:       }
    8108:     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
    8109:       coarse_reuse = PETSC_FALSE;
    8110:     }
    8111:     /* reset any subassembling information */
    8112:     if (!coarse_reuse || pcbddc->recompute_topography) {
    8113:       ISDestroy(&pcbddc->coarse_subassembling);
    8114:     }
    8115:   } else { /* primal space is unchanged, so we can reuse coarse matrix */
    8116:     coarse_reuse = PETSC_TRUE;
    8117:   }
    8118:   if (coarse_reuse && pcbddc->coarse_ksp) {
    8119:     KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);
    8120:     PetscObjectReference((PetscObject)coarse_mat);
    8121:     coarse_mat_reuse = MAT_REUSE_MATRIX;
    8122:   } else {
    8123:     coarse_mat = NULL;
    8124:     coarse_mat_reuse = MAT_INITIAL_MATRIX;
    8125:   }

    8127:   /* creates temporary l2gmap and IS for coarse indexes */
    8128:   ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);
    8129:   ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);

    8131:   /* creates temporary MATIS object for coarse matrix */
    8132:   MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_submat_dense);
    8133:   MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,coarse_islg,&t_coarse_mat_is);
    8134:   MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);
    8135:   MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);
    8136:   MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);
    8137:   MatDestroy(&coarse_submat_dense);

    8139:   /* count "active" (i.e. with positive local size) and "void" processes */
    8140:   im_active = !!(pcis->n);
    8141:   MPIU_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));

    8143:   /* determine number of processes partecipating to coarse solver and compute subassembling pattern */
    8144:   /* restr : whether we want to exclude senders (which are not receivers) from the subassembling pattern */
    8145:   /* full_restr : just use the receivers from the subassembling pattern */
    8146:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    8147:   coarse_mat_is        = NULL;
    8148:   multilevel_allowed   = PETSC_FALSE;
    8149:   multilevel_requested = PETSC_FALSE;
    8150:   coarse_eqs_per_proc  = PetscMin(PetscMax(pcbddc->coarse_size,1),pcbddc->coarse_eqs_per_proc);
    8151:   if (coarse_eqs_per_proc < 0) coarse_eqs_per_proc = pcbddc->coarse_size;
    8152:   if (pcbddc->current_level < pcbddc->max_levels) multilevel_requested = PETSC_TRUE;
    8153:   if (pcbddc->coarse_size <= pcbddc->coarse_eqs_limit) multilevel_requested = PETSC_FALSE;
    8154:   if (multilevel_requested) {
    8155:     ncoarse    = active_procs/pcbddc->coarsening_ratio;
    8156:     restr      = PETSC_FALSE;
    8157:     full_restr = PETSC_FALSE;
    8158:   } else {
    8159:     ncoarse    = pcbddc->coarse_size/coarse_eqs_per_proc + !!(pcbddc->coarse_size%coarse_eqs_per_proc);
    8160:     restr      = PETSC_TRUE;
    8161:     full_restr = PETSC_TRUE;
    8162:   }
    8163:   if (!pcbddc->coarse_size || size == 1) multilevel_allowed = multilevel_requested = restr = full_restr = PETSC_FALSE;
    8164:   ncoarse = PetscMax(1,ncoarse);
    8165:   if (!pcbddc->coarse_subassembling) {
    8166:     if (pcbddc->coarsening_ratio > 1) {
    8167:       if (multilevel_requested) {
    8168:         PCBDDCMatISGetSubassemblingPattern(pc->pmat,&ncoarse,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling,&have_void);
    8169:       } else {
    8170:         PCBDDCMatISGetSubassemblingPattern(t_coarse_mat_is,&ncoarse,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling,&have_void);
    8171:       }
    8172:     } else {
    8173:       PetscMPIInt rank;

    8175:       MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
    8176:       have_void = (active_procs == (PetscInt)size) ? PETSC_FALSE : PETSC_TRUE;
    8177:       ISCreateStride(PetscObjectComm((PetscObject)pc),1,rank,1,&pcbddc->coarse_subassembling);
    8178:     }
    8179:   } else { /* if a subassembling pattern exists, then we can reuse the coarse ksp and compute the number of process involved */
    8180:     PetscInt    psum;
    8181:     if (pcbddc->coarse_ksp) psum = 1;
    8182:     else psum = 0;
    8183:     MPIU_Allreduce(&psum,&ncoarse,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
    8184:     have_void = ncoarse < size ? PETSC_TRUE : PETSC_FALSE;
    8185:   }
    8186:   /* determine if we can go multilevel */
    8187:   if (multilevel_requested) {
    8188:     if (ncoarse > 1) multilevel_allowed = PETSC_TRUE; /* found enough processes */
    8189:     else restr = full_restr = PETSC_TRUE; /* 1 subdomain, use a direct solver */
    8190:   }
    8191:   if (multilevel_allowed && have_void) restr = PETSC_TRUE;

    8193:   /* dump subassembling pattern */
    8194:   if (pcbddc->dbg_flag && multilevel_allowed) {
    8195:     ISView(pcbddc->coarse_subassembling,pcbddc->dbg_viewer);
    8196:   }
    8197:   /* compute dofs splitting and neumann boundaries for coarse dofs */
    8198:   nedcfield = -1;
    8199:   corners = NULL;
    8200:   if (multilevel_allowed && !coarse_reuse && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal || pcbddc->nedclocal || pcbddc->corner_selected)) { /* protects from unneeded computations */
    8201:     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
    8202:     const PetscInt         *idxs;
    8203:     ISLocalToGlobalMapping tmap;

    8205:     /* create map between primal indices (in local representative ordering) and local primal numbering */
    8206:     ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);
    8207:     /* allocate space for temporary storage */
    8208:     PetscMalloc1(pcbddc->local_primal_size,&tidxs);
    8209:     PetscMalloc1(pcbddc->local_primal_size,&tidxs2);
    8210:     /* allocate for IS array */
    8211:     nisdofs = pcbddc->n_ISForDofsLocal;
    8212:     if (pcbddc->nedclocal) {
    8213:       if (pcbddc->nedfield > -1) {
    8214:         nedcfield = pcbddc->nedfield;
    8215:       } else {
    8216:         nedcfield = 0;
    8218:         nisdofs = 1;
    8219:       }
    8220:     }
    8221:     nisneu = !!pcbddc->NeumannBoundariesLocal;
    8222:     nisvert = 0; /* nisvert is not used */
    8223:     nis = nisdofs + nisneu + nisvert;
    8224:     PetscMalloc1(nis,&isarray);
    8225:     /* dofs splitting */
    8226:     for (i=0;i<nisdofs;i++) {
    8227:       /* ISView(pcbddc->ISForDofsLocal[i],0); */
    8228:       if (nedcfield != i) {
    8229:         ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);
    8230:         ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);
    8231:         ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
    8232:         ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);
    8233:       } else {
    8234:         ISGetLocalSize(pcbddc->nedclocal,&tsize);
    8235:         ISGetIndices(pcbddc->nedclocal,&idxs);
    8236:         ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
    8238:         ISRestoreIndices(pcbddc->nedclocal,&idxs);
    8239:       }
    8240:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
    8241:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);
    8242:       /* ISView(isarray[i],0); */
    8243:     }
    8244:     /* neumann boundaries */
    8245:     if (pcbddc->NeumannBoundariesLocal) {
    8246:       /* ISView(pcbddc->NeumannBoundariesLocal,0); */
    8247:       ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);
    8248:       ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);
    8249:       ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
    8250:       ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);
    8251:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
    8252:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);
    8253:       /* ISView(isarray[nisdofs],0); */
    8254:     }
    8255:     /* coordinates */
    8256:     if (pcbddc->corner_selected) {
    8257:       PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&corners);
    8258:       ISGetLocalSize(corners,&tsize);
    8259:       ISGetIndices(corners,&idxs);
    8260:       ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
    8262:       ISRestoreIndices(corners,&idxs);
    8263:       PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&corners);
    8264:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
    8265:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),nout,tidxs2,PETSC_COPY_VALUES,&corners);
    8266:     }
    8267:     PetscFree(tidxs);
    8268:     PetscFree(tidxs2);
    8269:     ISLocalToGlobalMappingDestroy(&tmap);
    8270:   } else {
    8271:     nis = 0;
    8272:     nisdofs = 0;
    8273:     nisneu = 0;
    8274:     nisvert = 0;
    8275:     isarray = NULL;
    8276:   }
    8277:   /* destroy no longer needed map */
    8278:   ISLocalToGlobalMappingDestroy(&coarse_islg);

    8280:   /* subassemble */
    8281:   if (multilevel_allowed) {
    8282:     Vec       vp[1];
    8283:     PetscInt  nvecs = 0;
    8284:     PetscBool reuse,reuser;

    8286:     if (coarse_mat) reuse = PETSC_TRUE;
    8287:     else reuse = PETSC_FALSE;
    8288:     MPIU_Allreduce(&reuse,&reuser,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
    8289:     vp[0] = NULL;
    8290:     if (pcbddc->benign_have_null) { /* propagate no-net-flux quadrature to coarser level */
    8291:       VecCreate(PetscObjectComm((PetscObject)pc),&vp[0]);
    8292:       VecSetSizes(vp[0],pcbddc->local_primal_size,PETSC_DECIDE);
    8293:       VecSetType(vp[0],VECSTANDARD);
    8294:       nvecs = 1;

    8296:       if (pcbddc->divudotp) {
    8297:         Mat      B,loc_divudotp;
    8298:         Vec      v,p;
    8299:         IS       dummy;
    8300:         PetscInt np;

    8302:         MatISGetLocalMat(pcbddc->divudotp,&loc_divudotp);
    8303:         MatGetSize(loc_divudotp,&np,NULL);
    8304:         ISCreateStride(PETSC_COMM_SELF,np,0,1,&dummy);
    8305:         MatCreateSubMatrix(loc_divudotp,dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B);
    8306:         MatCreateVecs(B,&v,&p);
    8307:         VecSet(p,1.);
    8308:         MatMultTranspose(B,p,v);
    8309:         VecDestroy(&p);
    8310:         MatDestroy(&B);
    8311:         VecGetArray(vp[0],&array);
    8312:         VecPlaceArray(pcbddc->vec1_P,array);
    8313:         MatMultTranspose(pcbddc->coarse_phi_B,v,pcbddc->vec1_P);
    8314:         VecResetArray(pcbddc->vec1_P);
    8315:         VecRestoreArray(vp[0],&array);
    8316:         ISDestroy(&dummy);
    8317:         VecDestroy(&v);
    8318:       }
    8319:     }
    8320:     if (reuser) {
    8321:       PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_TRUE,&coarse_mat,nis,isarray,nvecs,vp);
    8322:     } else {
    8323:       PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_FALSE,&coarse_mat_is,nis,isarray,nvecs,vp);
    8324:     }
    8325:     if (vp[0]) { /* vp[0] could have been placed on a different set of processes */
    8326:       PetscScalar       *arraym;
    8327:       const PetscScalar *arrayv;
    8328:       PetscInt          nl;
    8329:       VecGetLocalSize(vp[0],&nl);
    8330:       MatCreateSeqDense(PETSC_COMM_SELF,1,nl,NULL,&coarsedivudotp);
    8331:       MatDenseGetArray(coarsedivudotp,&arraym);
    8332:       VecGetArrayRead(vp[0],&arrayv);
    8333:       PetscArraycpy(arraym,arrayv,nl);
    8334:       VecRestoreArrayRead(vp[0],&arrayv);
    8335:       MatDenseRestoreArray(coarsedivudotp,&arraym);
    8336:       VecDestroy(&vp[0]);
    8337:     } else {
    8338:       MatCreateSeqAIJ(PETSC_COMM_SELF,0,0,1,NULL,&coarsedivudotp);
    8339:     }
    8340:   } else {
    8341:     PCBDDCMatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling,0,restr,full_restr,PETSC_FALSE,&coarse_mat_is,0,NULL,0,NULL);
    8342:   }
    8343:   if (coarse_mat_is || coarse_mat) {
    8344:     if (!multilevel_allowed) {
    8345:       MatConvert(coarse_mat_is,MATAIJ,coarse_mat_reuse,&coarse_mat);
    8346:     } else {
    8347:       /* if this matrix is present, it means we are not reusing the coarse matrix */
    8348:       if (coarse_mat_is) {
    8350:         PetscObjectReference((PetscObject)coarse_mat_is);
    8351:         coarse_mat = coarse_mat_is;
    8352:       }
    8353:     }
    8354:   }
    8355:   MatDestroy(&t_coarse_mat_is);
    8356:   MatDestroy(&coarse_mat_is);

    8358:   /* create local to global scatters for coarse problem */
    8359:   if (compute_vecs) {
    8360:     PetscInt lrows;
    8361:     VecDestroy(&pcbddc->coarse_vec);
    8362:     if (coarse_mat) {
    8363:       MatGetLocalSize(coarse_mat,&lrows,NULL);
    8364:     } else {
    8365:       lrows = 0;
    8366:     }
    8367:     VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);
    8368:     VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);
    8369:     VecSetType(pcbddc->coarse_vec,coarse_mat ? coarse_mat->defaultvectype : VECSTANDARD);
    8370:     VecScatterDestroy(&pcbddc->coarse_loc_to_glob);
    8371:     VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);
    8372:   }
    8373:   ISDestroy(&coarse_is);

    8375:   /* set defaults for coarse KSP and PC */
    8376:   if (multilevel_allowed) {
    8377:     coarse_ksp_type = KSPRICHARDSON;
    8378:     coarse_pc_type  = PCBDDC;
    8379:   } else {
    8380:     coarse_ksp_type = KSPPREONLY;
    8381:     coarse_pc_type  = PCREDUNDANT;
    8382:   }

    8384:   /* print some info if requested */
    8385:   if (pcbddc->dbg_flag) {
    8386:     if (!multilevel_allowed) {
    8387:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    8388:       if (multilevel_requested) {
    8389:         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);
    8390:       } else if (pcbddc->max_levels) {
    8391:         PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%D)\n",pcbddc->max_levels);
    8392:       }
    8393:       PetscViewerFlush(pcbddc->dbg_viewer);
    8394:     }
    8395:   }

    8397:   /* communicate coarse discrete gradient */
    8398:   coarseG = NULL;
    8399:   if (pcbddc->nedcG && multilevel_allowed) {
    8400:     MPI_Comm ccomm;
    8401:     if (coarse_mat) {
    8402:       ccomm = PetscObjectComm((PetscObject)coarse_mat);
    8403:     } else {
    8404:       ccomm = MPI_COMM_NULL;
    8405:     }
    8406:     MatMPIAIJRestrict(pcbddc->nedcG,ccomm,&coarseG);
    8407:   }

    8409:   /* create the coarse KSP object only once with defaults */
    8410:   if (coarse_mat) {
    8411:     PetscBool   isredundant,isbddc,force,valid;
    8412:     PetscViewer dbg_viewer = NULL;

    8414:     if (pcbddc->dbg_flag) {
    8415:       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat));
    8416:       PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);
    8417:     }
    8418:     if (!pcbddc->coarse_ksp) {
    8419:       char   prefix[256],str_level[16];
    8420:       size_t len;

    8422:       KSPCreate(PetscObjectComm((PetscObject)coarse_mat),&pcbddc->coarse_ksp);
    8423:       KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,pc->erroriffailure);
    8424:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);
    8425:       KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);
    8426:       KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);
    8427:       KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);
    8428:       KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);
    8429:       KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
    8430:       /* TODO is this logic correct? should check for coarse_mat type */
    8431:       PCSetType(pc_temp,coarse_pc_type);
    8432:       /* prefix */
    8433:       PetscStrcpy(prefix,"");
    8434:       PetscStrcpy(str_level,"");
    8435:       if (!pcbddc->current_level) {
    8436:         PetscStrncpy(prefix,((PetscObject)pc)->prefix,sizeof(prefix));
    8437:         PetscStrlcat(prefix,"pc_bddc_coarse_",sizeof(prefix));
    8438:       } else {
    8439:         PetscStrlen(((PetscObject)pc)->prefix,&len);
    8440:         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
    8441:         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
    8442:         /* Nonstandard use of PetscStrncpy() to copy only a portion of the string */
    8443:         PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);
    8444:         PetscSNPrintf(str_level,sizeof(str_level),"l%d_",(int)(pcbddc->current_level));
    8445:         PetscStrlcat(prefix,str_level,sizeof(prefix));
    8446:       }
    8447:       KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);
    8448:       /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
    8449:       PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);
    8450:       PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);
    8451:       PCBDDCSetLevels(pc_temp,pcbddc->max_levels);
    8452:       /* allow user customization */
    8453:       KSPSetFromOptions(pcbddc->coarse_ksp);
    8454:       /* get some info after set from options */
    8455:       KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
    8456:       /* multilevel cannot be done with coarse PC different from BDDC, NN, HPDDM, unless forced to */
    8457:       force = PETSC_FALSE;
    8458:       PetscOptionsGetBool(NULL,((PetscObject)pc_temp)->prefix,"-pc_type_forced",&force,NULL);
    8459:       PetscObjectTypeCompareAny((PetscObject)pc_temp,&valid,PCBDDC,PCNN,PCHPDDM,"");
    8460:       PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);
    8461:       if (multilevel_allowed && !force && !valid) {
    8462:         isbddc = PETSC_TRUE;
    8463:         PCSetType(pc_temp,PCBDDC);
    8464:         PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);
    8465:         PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);
    8466:         PCBDDCSetLevels(pc_temp,pcbddc->max_levels);
    8467:         if (pc_temp->ops->setfromoptions) { /* need to setfromoptions again, skipping the pc_type */
    8468:           PetscObjectOptionsBegin((PetscObject)pc_temp);
    8469:           (*pc_temp->ops->setfromoptions)(PetscOptionsObject,pc_temp);
    8470:           PetscObjectProcessOptionsHandlers(PetscOptionsObject,(PetscObject)pc_temp);
    8471:           PetscOptionsEnd();
    8472:           pc_temp->setfromoptionscalled++;
    8473:         }
    8474:       }
    8475:     }
    8476:     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
    8477:     KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
    8478:     if (nisdofs) {
    8479:       PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);
    8480:       for (i=0;i<nisdofs;i++) {
    8481:         ISDestroy(&isarray[i]);
    8482:       }
    8483:     }
    8484:     if (nisneu) {
    8485:       PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);
    8486:       ISDestroy(&isarray[nisdofs]);
    8487:     }
    8488:     if (nisvert) {
    8489:       PCBDDCSetPrimalVerticesIS(pc_temp,isarray[nis-1]);
    8490:       ISDestroy(&isarray[nis-1]);
    8491:     }
    8492:     if (coarseG) {
    8493:       PCBDDCSetDiscreteGradient(pc_temp,coarseG,1,nedcfield,PETSC_FALSE,PETSC_TRUE);
    8494:     }

    8496:     /* get some info after set from options */
    8497:     PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);

    8499:     /* multilevel can only be requested via -pc_bddc_levels or PCBDDCSetLevels */
    8500:     if (isbddc && !multilevel_allowed) {
    8501:       PCSetType(pc_temp,coarse_pc_type);
    8502:     }
    8503:     /* multilevel cannot be done with coarse PC different from BDDC, NN, HPDDM, unless forced to */
    8504:     force = PETSC_FALSE;
    8505:     PetscOptionsGetBool(NULL,((PetscObject)pc_temp)->prefix,"-pc_type_forced",&force,NULL);
    8506:     PetscObjectTypeCompareAny((PetscObject)pc_temp,&valid,PCBDDC,PCNN,PCHPDDM,"");
    8507:     if (multilevel_requested && multilevel_allowed && !valid && !force) {
    8508:       PCSetType(pc_temp,PCBDDC);
    8509:     }
    8510:     PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);
    8511:     if (isredundant) {
    8512:       KSP inner_ksp;
    8513:       PC  inner_pc;

    8515:       PCRedundantGetKSP(pc_temp,&inner_ksp);
    8516:       KSPGetPC(inner_ksp,&inner_pc);
    8517:     }

    8519:     /* parameters which miss an API */
    8520:     PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);
    8521:     if (isbddc) {
    8522:       PC_BDDC* pcbddc_coarse = (PC_BDDC*)pc_temp->data;

    8524:       pcbddc_coarse->detect_disconnected = PETSC_TRUE;
    8525:       pcbddc_coarse->coarse_eqs_per_proc = pcbddc->coarse_eqs_per_proc;
    8526:       pcbddc_coarse->coarse_eqs_limit    = pcbddc->coarse_eqs_limit;
    8527:       pcbddc_coarse->benign_saddle_point = pcbddc->benign_have_null;
    8528:       if (pcbddc_coarse->benign_saddle_point) {
    8529:         Mat                    coarsedivudotp_is;
    8530:         ISLocalToGlobalMapping l2gmap,rl2g,cl2g;
    8531:         IS                     row,col;
    8532:         const PetscInt         *gidxs;
    8533:         PetscInt               n,st,M,N;

    8535:         MatGetSize(coarsedivudotp,&n,NULL);
    8536:         MPI_Scan(&n,&st,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)coarse_mat));
    8537:         st   = st-n;
    8538:         ISCreateStride(PetscObjectComm((PetscObject)coarse_mat),1,st,1,&row);
    8539:         MatISGetLocalToGlobalMapping(coarse_mat,&l2gmap,NULL);
    8540:         ISLocalToGlobalMappingGetSize(l2gmap,&n);
    8541:         ISLocalToGlobalMappingGetIndices(l2gmap,&gidxs);
    8542:         ISCreateGeneral(PetscObjectComm((PetscObject)coarse_mat),n,gidxs,PETSC_COPY_VALUES,&col);
    8543:         ISLocalToGlobalMappingRestoreIndices(l2gmap,&gidxs);
    8544:         ISLocalToGlobalMappingCreateIS(row,&rl2g);
    8545:         ISLocalToGlobalMappingCreateIS(col,&cl2g);
    8546:         ISGetSize(row,&M);
    8547:         MatGetSize(coarse_mat,&N,NULL);
    8548:         ISDestroy(&row);
    8549:         ISDestroy(&col);
    8550:         MatCreate(PetscObjectComm((PetscObject)coarse_mat),&coarsedivudotp_is);
    8551:         MatSetType(coarsedivudotp_is,MATIS);
    8552:         MatSetSizes(coarsedivudotp_is,PETSC_DECIDE,PETSC_DECIDE,M,N);
    8553:         MatSetLocalToGlobalMapping(coarsedivudotp_is,rl2g,cl2g);
    8554:         ISLocalToGlobalMappingDestroy(&rl2g);
    8555:         ISLocalToGlobalMappingDestroy(&cl2g);
    8556:         MatISSetLocalMat(coarsedivudotp_is,coarsedivudotp);
    8557:         MatDestroy(&coarsedivudotp);
    8558:         PCBDDCSetDivergenceMat(pc_temp,coarsedivudotp_is,PETSC_FALSE,NULL);
    8559:         MatDestroy(&coarsedivudotp_is);
    8560:         pcbddc_coarse->adaptive_userdefined = PETSC_TRUE;
    8561:         if (pcbddc->adaptive_threshold[0] == 0.0) pcbddc_coarse->deluxe_zerorows = PETSC_TRUE;
    8562:       }
    8563:     }

    8565:     /* propagate symmetry info of coarse matrix */
    8566:     MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);
    8567:     if (pc->pmat->symmetric_set) {
    8568:       MatSetOption(coarse_mat,MAT_SYMMETRIC,pc->pmat->symmetric);
    8569:     }
    8570:     if (pc->pmat->hermitian_set) {
    8571:       MatSetOption(coarse_mat,MAT_HERMITIAN,pc->pmat->hermitian);
    8572:     }
    8573:     if (pc->pmat->spd_set) {
    8574:       MatSetOption(coarse_mat,MAT_SPD,pc->pmat->spd);
    8575:     }
    8576:     if (pcbddc->benign_saddle_point && !pcbddc->benign_have_null) {
    8577:       MatSetOption(coarse_mat,MAT_SPD,PETSC_TRUE);
    8578:     }
    8579:     /* set operators */
    8580:     MatViewFromOptions(coarse_mat,(PetscObject)pc,"-pc_bddc_coarse_mat_view");
    8581:     MatSetOptionsPrefix(coarse_mat,((PetscObject)pcbddc->coarse_ksp)->prefix);
    8582:     KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);
    8583:     if (pcbddc->dbg_flag) {
    8584:       PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);
    8585:     }
    8586:   }
    8587:   MatDestroy(&coarseG);
    8588:   PetscFree(isarray);
    8589: #if 0
    8590:   {
    8591:     PetscViewer viewer;
    8592:     char filename[256];
    8593:     sprintf(filename,"coarse_mat_level%d.m",pcbddc->current_level);
    8594:     PetscViewerASCIIOpen(PetscObjectComm((PetscObject)coarse_mat),filename,&viewer);
    8595:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    8596:     MatView(coarse_mat,viewer);
    8597:     PetscViewerPopFormat(viewer);
    8598:     PetscViewerDestroy(&viewer);
    8599:   }
    8600: #endif

    8602:   if (corners) {
    8603:     Vec            gv;
    8604:     IS             is;
    8605:     const PetscInt *idxs;
    8606:     PetscInt       i,d,N,n,cdim = pcbddc->mat_graph->cdim;
    8607:     PetscScalar    *coords;

    8610:     VecGetSize(pcbddc->coarse_vec,&N);
    8611:     VecGetLocalSize(pcbddc->coarse_vec,&n);
    8612:     VecCreate(PetscObjectComm((PetscObject)pcbddc->coarse_vec),&gv);
    8613:     VecSetBlockSize(gv,cdim);
    8614:     VecSetSizes(gv,n*cdim,N*cdim);
    8615:     VecSetType(gv,VECSTANDARD);
    8616:     VecSetFromOptions(gv);
    8617:     VecSet(gv,PETSC_MAX_REAL); /* we only propagate coordinates from vertices constraints */

    8619:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&is);
    8620:     ISGetLocalSize(is,&n);
    8621:     ISGetIndices(is,&idxs);
    8622:     PetscMalloc1(n*cdim,&coords);
    8623:     for (i=0;i<n;i++) {
    8624:       for (d=0;d<cdim;d++) {
    8625:         coords[cdim*i+d] = pcbddc->mat_graph->coords[cdim*idxs[i]+d];
    8626:       }
    8627:     }
    8628:     ISRestoreIndices(is,&idxs);
    8629:     PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&is);

    8631:     ISGetLocalSize(corners,&n);
    8632:     ISGetIndices(corners,&idxs);
    8633:     VecSetValuesBlocked(gv,n,idxs,coords,INSERT_VALUES);
    8634:     ISRestoreIndices(corners,&idxs);
    8635:     PetscFree(coords);
    8636:     VecAssemblyBegin(gv);
    8637:     VecAssemblyEnd(gv);
    8638:     VecGetArray(gv,&coords);
    8639:     if (pcbddc->coarse_ksp) {
    8640:       PC        coarse_pc;
    8641:       PetscBool isbddc;

    8643:       KSPGetPC(pcbddc->coarse_ksp,&coarse_pc);
    8644:       PetscObjectTypeCompare((PetscObject)coarse_pc,PCBDDC,&isbddc);
    8645:       if (isbddc) { /* coarse coordinates have PETSC_MAX_REAL, specific for BDDC */
    8646:         PetscReal *realcoords;

    8648:         VecGetLocalSize(gv,&n);
    8649: #if defined(PETSC_USE_COMPLEX)
    8650:         PetscMalloc1(n,&realcoords);
    8651:         for (i=0;i<n;i++) realcoords[i] = PetscRealPart(coords[i]);
    8652: #else
    8653:         realcoords = coords;
    8654: #endif
    8655:         PCSetCoordinates(coarse_pc,cdim,n/cdim,realcoords);
    8656: #if defined(PETSC_USE_COMPLEX)
    8657:         PetscFree(realcoords);
    8658: #endif
    8659:       }
    8660:     }
    8661:     VecRestoreArray(gv,&coords);
    8662:     VecDestroy(&gv);
    8663:   }
    8664:   ISDestroy(&corners);

    8666:   if (pcbddc->coarse_ksp) {
    8667:     Vec crhs,csol;

    8669:     KSPGetSolution(pcbddc->coarse_ksp,&csol);
    8670:     KSPGetRhs(pcbddc->coarse_ksp,&crhs);
    8671:     if (!csol) {
    8672:       MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);
    8673:     }
    8674:     if (!crhs) {
    8675:       MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));
    8676:     }
    8677:   }
    8678:   MatDestroy(&coarsedivudotp);

    8680:   /* compute null space for coarse solver if the benign trick has been requested */
    8681:   if (pcbddc->benign_null) {

    8683:     VecSet(pcbddc->vec1_P,0.);
    8684:     for (i=0;i<pcbddc->benign_n;i++) {
    8685:       VecSetValue(pcbddc->vec1_P,pcbddc->local_primal_size-pcbddc->benign_n+i,1.0,INSERT_VALUES);
    8686:     }
    8687:     VecAssemblyBegin(pcbddc->vec1_P);
    8688:     VecAssemblyEnd(pcbddc->vec1_P);
    8689:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,INSERT_VALUES,SCATTER_FORWARD);
    8690:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,INSERT_VALUES,SCATTER_FORWARD);
    8691:     if (coarse_mat) {
    8692:       Vec         nullv;
    8693:       PetscScalar *array,*array2;
    8694:       PetscInt    nl;

    8696:       MatCreateVecs(coarse_mat,&nullv,NULL);
    8697:       VecGetLocalSize(nullv,&nl);
    8698:       VecGetArrayRead(pcbddc->coarse_vec,(const PetscScalar**)&array);
    8699:       VecGetArray(nullv,&array2);
    8700:       PetscArraycpy(array2,array,nl);
    8701:       VecRestoreArray(nullv,&array2);
    8702:       VecRestoreArrayRead(pcbddc->coarse_vec,(const PetscScalar**)&array);
    8703:       VecNormalize(nullv,NULL);
    8704:       MatNullSpaceCreate(PetscObjectComm((PetscObject)coarse_mat),PETSC_FALSE,1,&nullv,&CoarseNullSpace);
    8705:       VecDestroy(&nullv);
    8706:     }
    8707:   }
    8708:   PetscLogEventEnd(PC_BDDC_CoarseSetUp[pcbddc->current_level],pc,0,0,0);

    8710:   PetscLogEventBegin(PC_BDDC_CoarseSolver[pcbddc->current_level],pc,0,0,0);
    8711:   if (pcbddc->coarse_ksp) {
    8712:     PetscBool ispreonly;

    8714:     if (CoarseNullSpace) {
    8715:       PetscBool isnull;
    8716:       MatNullSpaceTest(CoarseNullSpace,coarse_mat,&isnull);
    8717:       if (isnull) {
    8718:         MatSetNullSpace(coarse_mat,CoarseNullSpace);
    8719:       }
    8720:       /* TODO: add local nullspaces (if any) */
    8721:     }
    8722:     /* setup coarse ksp */
    8723:     KSPSetUp(pcbddc->coarse_ksp);
    8724:     /* Check coarse problem if in debug mode or if solving with an iterative method */
    8725:     PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);
    8726:     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates)) {
    8727:       KSP       check_ksp;
    8728:       KSPType   check_ksp_type;
    8729:       PC        check_pc;
    8730:       Vec       check_vec,coarse_vec;
    8731:       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
    8732:       PetscInt  its;
    8733:       PetscBool compute_eigs;
    8734:       PetscReal *eigs_r,*eigs_c;
    8735:       PetscInt  neigs;
    8736:       const char *prefix;

    8738:       /* Create ksp object suitable for estimation of extreme eigenvalues */
    8739:       KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);
    8740:       PetscObjectIncrementTabLevel((PetscObject)check_ksp,(PetscObject)pcbddc->coarse_ksp,0);
    8741:       KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,PETSC_FALSE);
    8742:       KSPSetOperators(check_ksp,coarse_mat,coarse_mat);
    8743:       KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);
    8744:       /* prevent from setup unneeded object */
    8745:       KSPGetPC(check_ksp,&check_pc);
    8746:       PCSetType(check_pc,PCNONE);
    8747:       if (ispreonly) {
    8748:         check_ksp_type = KSPPREONLY;
    8749:         compute_eigs = PETSC_FALSE;
    8750:       } else {
    8751:         check_ksp_type = KSPGMRES;
    8752:         compute_eigs = PETSC_TRUE;
    8753:       }
    8754:       KSPSetType(check_ksp,check_ksp_type);
    8755:       KSPSetComputeSingularValues(check_ksp,compute_eigs);
    8756:       KSPSetComputeEigenvalues(check_ksp,compute_eigs);
    8757:       KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);
    8758:       KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);
    8759:       KSPSetOptionsPrefix(check_ksp,prefix);
    8760:       KSPAppendOptionsPrefix(check_ksp,"check_");
    8761:       KSPSetFromOptions(check_ksp);
    8762:       KSPSetUp(check_ksp);
    8763:       KSPGetPC(pcbddc->coarse_ksp,&check_pc);
    8764:       KSPSetPC(check_ksp,check_pc);
    8765:       /* create random vec */
    8766:       MatCreateVecs(coarse_mat,&coarse_vec,&check_vec);
    8767:       VecSetRandom(check_vec,NULL);
    8768:       MatMult(coarse_mat,check_vec,coarse_vec);
    8769:       /* solve coarse problem */
    8770:       KSPSolve(check_ksp,coarse_vec,coarse_vec);
    8771:       KSPCheckSolve(check_ksp,pc,coarse_vec);
    8772:       /* set eigenvalue estimation if preonly has not been requested */
    8773:       if (compute_eigs) {
    8774:         PetscMalloc1(pcbddc->coarse_size+1,&eigs_r);
    8775:         PetscMalloc1(pcbddc->coarse_size+1,&eigs_c);
    8776:         KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);
    8777:         if (neigs) {
    8778:           lambda_max = eigs_r[neigs-1];
    8779:           lambda_min = eigs_r[0];
    8780:           if (pcbddc->use_coarse_estimates) {
    8781:             if (lambda_max>=lambda_min) { /* using PETSC_SMALL since lambda_max == lambda_min is not allowed by KSPChebyshevSetEigenvalues */
    8782:               KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max+PETSC_SMALL,lambda_min);
    8783:               KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));
    8784:             }
    8785:           }
    8786:         }
    8787:       }

    8789:       /* check coarse problem residual error */
    8790:       if (pcbddc->dbg_flag) {
    8791:         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
    8792:         PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));
    8793:         VecAXPY(check_vec,-1.0,coarse_vec);
    8794:         VecNorm(check_vec,NORM_INFINITY,&infty_error);
    8795:         MatMult(coarse_mat,check_vec,coarse_vec);
    8796:         VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);
    8797:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (use estimates %d)\n",pcbddc->use_coarse_estimates);
    8798:         PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);
    8799:         PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);
    8800:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);
    8801:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);
    8802:         if (CoarseNullSpace) {
    8803:           PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem is singular\n");
    8804:         }
    8805:         if (compute_eigs) {
    8806:           PetscReal          lambda_max_s,lambda_min_s;
    8807:           KSPConvergedReason reason;
    8808:           KSPGetType(check_ksp,&check_ksp_type);
    8809:           KSPGetIterationNumber(check_ksp,&its);
    8810:           KSPGetConvergedReason(check_ksp,&reason);
    8811:           KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);
    8812:           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);
    8813:           for (i=0;i<neigs;i++) {
    8814:             PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);
    8815:           }
    8816:         }
    8817:         PetscViewerFlush(dbg_viewer);
    8818:         PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));
    8819:       }
    8820:       VecDestroy(&check_vec);
    8821:       VecDestroy(&coarse_vec);
    8822:       KSPDestroy(&check_ksp);
    8823:       if (compute_eigs) {
    8824:         PetscFree(eigs_r);
    8825:         PetscFree(eigs_c);
    8826:       }
    8827:     }
    8828:   }
    8829:   MatNullSpaceDestroy(&CoarseNullSpace);
    8830:   /* print additional info */
    8831:   if (pcbddc->dbg_flag) {
    8832:     /* waits until all processes reaches this point */
    8833:     PetscBarrier((PetscObject)pc);
    8834:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %D\n",pcbddc->current_level);
    8835:     PetscViewerFlush(pcbddc->dbg_viewer);
    8836:   }

    8838:   /* free memory */
    8839:   MatDestroy(&coarse_mat);
    8840:   PetscLogEventEnd(PC_BDDC_CoarseSolver[pcbddc->current_level],pc,0,0,0);
    8841:   return 0;
    8842: }

    8844: PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
    8845: {
    8846:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
    8847:   PC_IS*         pcis = (PC_IS*)pc->data;
    8848:   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
    8849:   IS             subset,subset_mult,subset_n;
    8850:   PetscInt       local_size,coarse_size=0;
    8851:   PetscInt       *local_primal_indices=NULL;
    8852:   const PetscInt *t_local_primal_indices;

    8854:   /* Compute global number of coarse dofs */
    8856:   ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&subset_n);
    8857:   ISLocalToGlobalMappingApplyIS(pcis->mapping,subset_n,&subset);
    8858:   ISDestroy(&subset_n);
    8859:   ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_mult,PETSC_COPY_VALUES,&subset_mult);
    8860:   ISRenumber(subset,subset_mult,&coarse_size,&subset_n);
    8861:   ISDestroy(&subset);
    8862:   ISDestroy(&subset_mult);
    8863:   ISGetLocalSize(subset_n,&local_size);
    8865:   PetscMalloc1(local_size,&local_primal_indices);
    8866:   ISGetIndices(subset_n,&t_local_primal_indices);
    8867:   PetscArraycpy(local_primal_indices,t_local_primal_indices,local_size);
    8868:   ISRestoreIndices(subset_n,&t_local_primal_indices);
    8869:   ISDestroy(&subset_n);

    8871:   /* check numbering */
    8872:   if (pcbddc->dbg_flag) {
    8873:     PetscScalar coarsesum,*array,*array2;
    8874:     PetscInt    i;
    8875:     PetscBool   set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;

    8877:     PetscViewerFlush(pcbddc->dbg_viewer);
    8878:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    8879:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");
    8880:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    8881:     /* counter */
    8882:     VecSet(pcis->vec1_global,0.0);
    8883:     VecSet(pcis->vec1_N,1.0);
    8884:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    8885:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    8886:     VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);
    8887:     VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec2_N,INSERT_VALUES,SCATTER_FORWARD);
    8888:     VecSet(pcis->vec1_N,0.0);
    8889:     for (i=0;i<pcbddc->local_primal_size;i++) {
    8890:       VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);
    8891:     }
    8892:     VecAssemblyBegin(pcis->vec1_N);
    8893:     VecAssemblyEnd(pcis->vec1_N);
    8894:     VecSet(pcis->vec1_global,0.0);
    8895:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    8896:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    8897:     VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    8898:     VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    8899:     VecGetArray(pcis->vec1_N,&array);
    8900:     VecGetArray(pcis->vec2_N,&array2);
    8901:     for (i=0;i<pcis->n;i++) {
    8902:       if (array[i] != 0.0 && array[i] != array2[i]) {
    8903:         PetscInt owned = (PetscInt)PetscRealPart(array[i]),gi;
    8904:         PetscInt neigh = (PetscInt)PetscRealPart(array2[i]);
    8905:         set_error = PETSC_TRUE;
    8906:         ISLocalToGlobalMappingApply(pcis->mapping,1,&i,&gi);
    8907:         PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %D (gid %D) owned by %D processes instead of %D!\n",PetscGlobalRank,i,gi,owned,neigh);
    8908:       }
    8909:     }
    8910:     VecRestoreArray(pcis->vec2_N,&array2);
    8911:     MPIU_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
    8912:     PetscViewerFlush(pcbddc->dbg_viewer);
    8913:     for (i=0;i<pcis->n;i++) {
    8914:       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
    8915:     }
    8916:     VecRestoreArray(pcis->vec1_N,&array);
    8917:     VecSet(pcis->vec1_global,0.0);
    8918:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    8919:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    8920:     VecSum(pcis->vec1_global,&coarsesum);
    8921:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %D (%lf)\n",coarse_size,PetscRealPart(coarsesum));
    8922:     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
    8923:       PetscInt *gidxs;

    8925:       PetscMalloc1(pcbddc->local_primal_size,&gidxs);
    8926:       ISLocalToGlobalMappingApply(pcis->mapping,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,gidxs);
    8927:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");
    8928:       PetscViewerFlush(pcbddc->dbg_viewer);
    8929:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);
    8930:       for (i=0;i<pcbddc->local_primal_size;i++) {
    8931:         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]);
    8932:       }
    8933:       PetscViewerFlush(pcbddc->dbg_viewer);
    8934:       PetscFree(gidxs);
    8935:     }
    8936:     PetscViewerFlush(pcbddc->dbg_viewer);
    8937:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    8939:   }

    8941:   /* get back data */
    8942:   *coarse_size_n = coarse_size;
    8943:   *local_primal_indices_n = local_primal_indices;
    8944:   return 0;
    8945: }

    8947: PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
    8948: {
    8949:   IS             localis_t;
    8950:   PetscInt       i,lsize,*idxs,n;
    8951:   PetscScalar    *vals;

    8953:   /* get indices in local ordering exploiting local to global map */
    8954:   ISGetLocalSize(globalis,&lsize);
    8955:   PetscMalloc1(lsize,&vals);
    8956:   for (i=0;i<lsize;i++) vals[i] = 1.0;
    8957:   ISGetIndices(globalis,(const PetscInt**)&idxs);
    8958:   VecSet(gwork,0.0);
    8959:   VecSet(lwork,0.0);
    8960:   if (idxs) { /* multilevel guard */
    8961:     VecSetOption(gwork,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);
    8962:     VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);
    8963:   }
    8964:   VecAssemblyBegin(gwork);
    8965:   ISRestoreIndices(globalis,(const PetscInt**)&idxs);
    8966:   PetscFree(vals);
    8967:   VecAssemblyEnd(gwork);
    8968:   /* now compute set in local ordering */
    8969:   VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);
    8970:   VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);
    8971:   VecGetArrayRead(lwork,(const PetscScalar**)&vals);
    8972:   VecGetSize(lwork,&n);
    8973:   for (i=0,lsize=0;i<n;i++) {
    8974:     if (PetscRealPart(vals[i]) > 0.5) {
    8975:       lsize++;
    8976:     }
    8977:   }
    8978:   PetscMalloc1(lsize,&idxs);
    8979:   for (i=0,lsize=0;i<n;i++) {
    8980:     if (PetscRealPart(vals[i]) > 0.5) {
    8981:       idxs[lsize++] = i;
    8982:     }
    8983:   }
    8984:   VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);
    8985:   ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);
    8986:   *localis = localis_t;
    8987:   return 0;
    8988: }

    8990: PetscErrorCode PCBDDCSetUpSubSchurs(PC pc)
    8991: {
    8992:   PC_IS               *pcis=(PC_IS*)pc->data;
    8993:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
    8994:   PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
    8995:   Mat                 S_j;
    8996:   PetscInt            *used_xadj,*used_adjncy;
    8997:   PetscBool           free_used_adj;
    8998:   PetscErrorCode      ierr;

    9000:   PetscLogEventBegin(PC_BDDC_Schurs[pcbddc->current_level],pc,0,0,0);
    9001:   /* decide the adjacency to be used for determining internal problems for local schur on subsets */
    9002:   free_used_adj = PETSC_FALSE;
    9003:   if (pcbddc->sub_schurs_layers == -1) {
    9004:     used_xadj = NULL;
    9005:     used_adjncy = NULL;
    9006:   } else {
    9007:     if (pcbddc->sub_schurs_use_useradj && pcbddc->mat_graph->xadj) {
    9008:       used_xadj = pcbddc->mat_graph->xadj;
    9009:       used_adjncy = pcbddc->mat_graph->adjncy;
    9010:     } else if (pcbddc->computed_rowadj) {
    9011:       used_xadj = pcbddc->mat_graph->xadj;
    9012:       used_adjncy = pcbddc->mat_graph->adjncy;
    9013:     } else {
    9014:       PetscBool      flg_row=PETSC_FALSE;
    9015:       const PetscInt *xadj,*adjncy;
    9016:       PetscInt       nvtxs;

    9018:       MatGetRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);
    9019:       if (flg_row) {
    9020:         PetscMalloc2(nvtxs+1,&used_xadj,xadj[nvtxs],&used_adjncy);
    9021:         PetscArraycpy(used_xadj,xadj,nvtxs+1);
    9022:         PetscArraycpy(used_adjncy,adjncy,xadj[nvtxs]);
    9023:         free_used_adj = PETSC_TRUE;
    9024:       } else {
    9025:         pcbddc->sub_schurs_layers = -1;
    9026:         used_xadj = NULL;
    9027:         used_adjncy = NULL;
    9028:       }
    9029:       MatRestoreRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);
    9030:     }
    9031:   }

    9033:   /* setup sub_schurs data */
    9034:   MatCreateSchurComplement(pcis->A_II,pcis->pA_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);
    9035:   if (!sub_schurs->schur_explicit) {
    9036:     /* pcbddc->ksp_D up to date only if not using MatFactor with Schur complement support */
    9037:     MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);
    9038:     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);
    9039:   } else {
    9040:     Mat       change = NULL;
    9041:     Vec       scaling = NULL;
    9042:     IS        change_primal = NULL, iP;
    9043:     PetscInt  benign_n;
    9044:     PetscBool reuse_solvers = (PetscBool)!pcbddc->use_change_of_basis;
    9045:     PetscBool need_change = PETSC_FALSE;
    9046:     PetscBool discrete_harmonic = PETSC_FALSE;

    9048:     if (!pcbddc->use_vertices && reuse_solvers) {
    9049:       PetscInt n_vertices;

    9051:       ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);
    9052:       reuse_solvers = (PetscBool)!n_vertices;
    9053:     }
    9054:     if (!pcbddc->benign_change_explicit) {
    9055:       benign_n = pcbddc->benign_n;
    9056:     } else {
    9057:       benign_n = 0;
    9058:     }
    9059:     /* sub_schurs->change is a local object; instead, PCBDDCConstraintsSetUp and the quantities used in the test below are logically collective on pc.
    9060:        We need a global reduction to avoid possible deadlocks.
    9061:        We assume that sub_schurs->change is created once, and then reused for different solves, unless the topography has been recomputed */
    9062:     if (pcbddc->adaptive_userdefined || (pcbddc->deluxe_zerorows && !pcbddc->use_change_of_basis)) {
    9063:       PetscBool have_loc_change = (PetscBool)(!!sub_schurs->change);
    9064:       MPIU_Allreduce(&have_loc_change,&need_change,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
    9065:       need_change = (PetscBool)(!need_change);
    9066:     }
    9067:     /* If the user defines additional constraints, we import them here.
    9068:        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 */
    9069:     if (need_change) {
    9070:       PC_IS   *pcisf;
    9071:       PC_BDDC *pcbddcf;
    9072:       PC      pcf;

    9075:       PCCreate(PetscObjectComm((PetscObject)pc),&pcf);
    9076:       PCSetOperators(pcf,pc->mat,pc->pmat);
    9077:       PCSetType(pcf,PCBDDC);

    9079:       /* hacks */
    9080:       pcisf                        = (PC_IS*)pcf->data;
    9081:       pcisf->is_B_local            = pcis->is_B_local;
    9082:       pcisf->vec1_N                = pcis->vec1_N;
    9083:       pcisf->BtoNmap               = pcis->BtoNmap;
    9084:       pcisf->n                     = pcis->n;
    9085:       pcisf->n_B                   = pcis->n_B;
    9086:       pcbddcf                      = (PC_BDDC*)pcf->data;
    9087:       PetscFree(pcbddcf->mat_graph);
    9088:       pcbddcf->mat_graph           = pcbddc->mat_graph;
    9089:       pcbddcf->use_faces           = PETSC_TRUE;
    9090:       pcbddcf->use_change_of_basis = PETSC_TRUE;
    9091:       pcbddcf->use_change_on_faces = PETSC_TRUE;
    9092:       pcbddcf->use_qr_single       = PETSC_TRUE;
    9093:       pcbddcf->fake_change         = PETSC_TRUE;

    9095:       /* setup constraints so that we can get information on primal vertices and change of basis (in local numbering) */
    9096:       PCBDDCConstraintsSetUp(pcf);
    9097:       sub_schurs->change_with_qr = pcbddcf->use_qr_single;
    9098:       ISCreateGeneral(PETSC_COMM_SELF,pcbddcf->n_vertices,pcbddcf->local_primal_ref_node,PETSC_COPY_VALUES,&change_primal);
    9099:       change = pcbddcf->ConstraintMatrix;
    9100:       pcbddcf->ConstraintMatrix = NULL;

    9102:       /* free unneeded memory allocated in PCBDDCConstraintsSetUp */
    9103:       PetscFree(pcbddcf->sub_schurs);
    9104:       MatNullSpaceDestroy(&pcbddcf->onearnullspace);
    9105:       PetscFree2(pcbddcf->local_primal_ref_node,pcbddcf->local_primal_ref_mult);
    9106:       PetscFree(pcbddcf->primal_indices_local_idxs);
    9107:       PetscFree(pcbddcf->onearnullvecs_state);
    9108:       PetscFree(pcf->data);
    9109:       pcf->ops->destroy = NULL;
    9110:       pcf->ops->reset   = NULL;
    9111:       PCDestroy(&pcf);
    9112:     }
    9113:     if (!pcbddc->use_deluxe_scaling) scaling = pcis->D;

    9115:     PetscObjectQuery((PetscObject)pc,"__KSPFETIDP_iP",(PetscObject*)&iP);
    9116:     if (iP) {
    9117:       PetscOptionsBegin(PetscObjectComm((PetscObject)iP),sub_schurs->prefix,"BDDC sub_schurs options","PC");
    9118:       PetscOptionsBool("-sub_schurs_discrete_harmonic",NULL,NULL,discrete_harmonic,&discrete_harmonic,NULL);
    9119:       PetscOptionsEnd();
    9120:     }
    9121:     if (discrete_harmonic) {
    9122:       Mat A;
    9123:       MatDuplicate(pcbddc->local_mat,MAT_COPY_VALUES,&A);
    9124:       MatZeroRowsColumnsIS(A,iP,1.0,NULL,NULL);
    9125:       PetscObjectCompose((PetscObject)A,"__KSPFETIDP_iP",(PetscObject)iP);
    9126:       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);
    9127:       MatDestroy(&A);
    9128:     } else {
    9129:       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);
    9130:     }
    9131:     MatDestroy(&change);
    9132:     ISDestroy(&change_primal);
    9133:   }
    9134:   MatDestroy(&S_j);

    9136:   /* free adjacency */
    9137:   if (free_used_adj) {
    9138:     PetscFree2(used_xadj,used_adjncy);
    9139:   }
    9140:   PetscLogEventEnd(PC_BDDC_Schurs[pcbddc->current_level],pc,0,0,0);
    9141:   return 0;
    9142: }

    9144: PetscErrorCode PCBDDCInitSubSchurs(PC pc)
    9145: {
    9146:   PC_IS               *pcis=(PC_IS*)pc->data;
    9147:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
    9148:   PCBDDCGraph         graph;

    9150:   /* attach interface graph for determining subsets */
    9151:   if (pcbddc->sub_schurs_rebuild) { /* in case rebuild has been requested, it uses a graph generated only by the neighbouring information */
    9152:     IS       verticesIS,verticescomm;
    9153:     PetscInt vsize,*idxs;

    9155:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);
    9156:     ISGetSize(verticesIS,&vsize);
    9157:     ISGetIndices(verticesIS,(const PetscInt**)&idxs);
    9158:     ISCreateGeneral(PetscObjectComm((PetscObject)pc),vsize,idxs,PETSC_COPY_VALUES,&verticescomm);
    9159:     ISRestoreIndices(verticesIS,(const PetscInt**)&idxs);
    9160:     PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);
    9161:     PCBDDCGraphCreate(&graph);
    9162:     PCBDDCGraphInit(graph,pcbddc->mat_graph->l2gmap,pcbddc->mat_graph->nvtxs_global,pcbddc->graphmaxcount);
    9163:     PCBDDCGraphSetUp(graph,pcbddc->mat_graph->custom_minimal_size,NULL,pcbddc->DirichletBoundariesLocal,0,NULL,verticescomm);
    9164:     ISDestroy(&verticescomm);
    9165:     PCBDDCGraphComputeConnectedComponents(graph);
    9166:   } else {
    9167:     graph = pcbddc->mat_graph;
    9168:   }
    9169:   /* print some info */
    9170:   if (pcbddc->dbg_flag && !pcbddc->sub_schurs_rebuild) {
    9171:     IS       vertices;
    9172:     PetscInt nv,nedges,nfaces;
    9173:     PCBDDCGraphASCIIView(graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);
    9174:     PCBDDCGraphGetCandidatesIS(graph,&nfaces,NULL,&nedges,NULL,&vertices);
    9175:     ISGetSize(vertices,&nv);
    9176:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    9177:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
    9178:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%D)\n",PetscGlobalRank,(int)nv,pcbddc->use_vertices);
    9179:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%D)\n",PetscGlobalRank,(int)nedges,pcbddc->use_edges);
    9180:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%D)\n",PetscGlobalRank,(int)nfaces,pcbddc->use_faces);
    9181:     PetscViewerFlush(pcbddc->dbg_viewer);
    9182:     PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);
    9183:     PCBDDCGraphRestoreCandidatesIS(graph,&nfaces,NULL,&nedges,NULL,&vertices);
    9184:   }

    9186:   /* sub_schurs init */
    9187:   if (!pcbddc->sub_schurs) {
    9188:     PCBDDCSubSchursCreate(&pcbddc->sub_schurs);
    9189:   }
    9190:   PCBDDCSubSchursInit(pcbddc->sub_schurs,((PetscObject)pc)->prefix,pcis->is_I_local,pcis->is_B_local,graph,pcis->BtoNmap,pcbddc->sub_schurs_rebuild);

    9192:   /* free graph struct */
    9193:   if (pcbddc->sub_schurs_rebuild) {
    9194:     PCBDDCGraphDestroy(&graph);
    9195:   }
    9196:   return 0;
    9197: }

    9199: PetscErrorCode PCBDDCCheckOperator(PC pc)
    9200: {
    9201:   PC_IS               *pcis=(PC_IS*)pc->data;
    9202:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;

    9204:   if (pcbddc->n_vertices == pcbddc->local_primal_size) {
    9205:     IS             zerodiag = NULL;
    9206:     Mat            S_j,B0_B=NULL;
    9207:     Vec            dummy_vec=NULL,vec_check_B,vec_scale_P;
    9208:     PetscScalar    *p0_check,*array,*array2;
    9209:     PetscReal      norm;
    9210:     PetscInt       i;

    9212:     /* B0 and B0_B */
    9213:     if (zerodiag) {
    9214:       IS       dummy;

    9216:       ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&dummy);
    9217:       MatCreateSubMatrix(pcbddc->benign_B0,dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);
    9218:       MatCreateVecs(B0_B,NULL,&dummy_vec);
    9219:       ISDestroy(&dummy);
    9220:     }
    9221:     /* I need a primal vector to scale primal nodes since BDDC sums contibutions */
    9222:     VecDuplicate(pcbddc->vec1_P,&vec_scale_P);
    9223:     VecSet(pcbddc->vec1_P,1.0);
    9224:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
    9225:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
    9226:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);
    9227:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,vec_scale_P,INSERT_VALUES,SCATTER_REVERSE);
    9228:     VecReciprocal(vec_scale_P);
    9229:     /* S_j */
    9230:     MatCreateSchurComplement(pcis->A_II,pcis->pA_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);
    9231:     MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);

    9233:     /* mimic vector in \widetilde{W}_\Gamma */
    9234:     VecSetRandom(pcis->vec1_N,NULL);
    9235:     /* continuous in primal space */
    9236:     VecSetRandom(pcbddc->coarse_vec,NULL);
    9237:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
    9238:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
    9239:     VecGetArray(pcbddc->vec1_P,&array);
    9240:     PetscCalloc1(pcbddc->benign_n,&p0_check);
    9241:     for (i=0;i<pcbddc->benign_n;i++) p0_check[i] = array[pcbddc->local_primal_size-pcbddc->benign_n+i];
    9242:     VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);
    9243:     VecRestoreArray(pcbddc->vec1_P,&array);
    9244:     VecAssemblyBegin(pcis->vec1_N);
    9245:     VecAssemblyEnd(pcis->vec1_N);
    9246:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    9247:     VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    9248:     VecDuplicate(pcis->vec2_B,&vec_check_B);
    9249:     VecCopy(pcis->vec2_B,vec_check_B);

    9251:     /* assemble rhs for coarse problem */
    9252:     /* widetilde{S}_\Gamma w_\Gamma + \widetilde{B0}^T_B p0 */
    9253:     /* local with Schur */
    9254:     MatMult(S_j,pcis->vec2_B,pcis->vec1_B);
    9255:     if (zerodiag) {
    9256:       VecGetArray(dummy_vec,&array);
    9257:       for (i=0;i<pcbddc->benign_n;i++) array[i] = p0_check[i];
    9258:       VecRestoreArray(dummy_vec,&array);
    9259:       MatMultTransposeAdd(B0_B,dummy_vec,pcis->vec1_B,pcis->vec1_B);
    9260:     }
    9261:     /* sum on primal nodes the local contributions */
    9262:     VecScatterBegin(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);
    9263:     VecScatterEnd(pcis->N_to_B,pcis->vec1_B,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);
    9264:     VecGetArray(pcis->vec1_N,&array);
    9265:     VecGetArray(pcbddc->vec1_P,&array2);
    9266:     for (i=0;i<pcbddc->local_primal_size;i++) array2[i] = array[pcbddc->local_primal_ref_node[i]];
    9267:     VecRestoreArray(pcbddc->vec1_P,&array2);
    9268:     VecRestoreArray(pcis->vec1_N,&array);
    9269:     VecSet(pcbddc->coarse_vec,0.);
    9270:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
    9271:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->vec1_P,pcbddc->coarse_vec,ADD_VALUES,SCATTER_FORWARD);
    9272:     VecScatterBegin(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
    9273:     VecScatterEnd(pcbddc->coarse_loc_to_glob,pcbddc->coarse_vec,pcbddc->vec1_P,INSERT_VALUES,SCATTER_REVERSE);
    9274:     VecGetArray(pcbddc->vec1_P,&array);
    9275:     /* scale primal nodes (BDDC sums contibutions) */
    9276:     VecPointwiseMult(pcbddc->vec1_P,vec_scale_P,pcbddc->vec1_P);
    9277:     VecSetValues(pcis->vec1_N,pcbddc->local_primal_size,pcbddc->local_primal_ref_node,array,INSERT_VALUES);
    9278:     VecRestoreArray(pcbddc->vec1_P,&array);
    9279:     VecAssemblyBegin(pcis->vec1_N);
    9280:     VecAssemblyEnd(pcis->vec1_N);
    9281:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    9282:     VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    9283:     /* global: \widetilde{B0}_B w_\Gamma */
    9284:     if (zerodiag) {
    9285:       MatMult(B0_B,pcis->vec2_B,dummy_vec);
    9286:       VecGetArray(dummy_vec,&array);
    9287:       for (i=0;i<pcbddc->benign_n;i++) pcbddc->benign_p0[i] = array[i];
    9288:       VecRestoreArray(dummy_vec,&array);
    9289:     }
    9290:     /* BDDC */
    9291:     VecSet(pcis->vec1_D,0.);
    9292:     PCBDDCApplyInterfacePreconditioner(pc,PETSC_FALSE);

    9294:     VecCopy(pcis->vec1_B,pcis->vec2_B);
    9295:     VecAXPY(pcis->vec1_B,-1.0,vec_check_B);
    9296:     VecNorm(pcis->vec1_B,NORM_INFINITY,&norm);
    9297:     PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC local error is %1.4e\n",PetscGlobalRank,norm);
    9298:     for (i=0;i<pcbddc->benign_n;i++) {
    9299:       PetscPrintf(PETSC_COMM_SELF,"[%d] BDDC p0[%D] error is %1.4e\n",PetscGlobalRank,i,PetscAbsScalar(pcbddc->benign_p0[i]-p0_check[i]));
    9300:     }
    9301:     PetscFree(p0_check);
    9302:     VecDestroy(&vec_scale_P);
    9303:     VecDestroy(&vec_check_B);
    9304:     VecDestroy(&dummy_vec);
    9305:     MatDestroy(&S_j);
    9306:     MatDestroy(&B0_B);
    9307:   }
    9308:   return 0;
    9309: }

    9311: #include <../src/mat/impls/aij/mpi/mpiaij.h>
    9312: PetscErrorCode MatMPIAIJRestrict(Mat A, MPI_Comm ccomm, Mat *B)
    9313: {
    9314:   Mat            At;
    9315:   IS             rows;
    9316:   PetscInt       rst,ren;
    9317:   PetscLayout    rmap;

    9319:   rst = ren = 0;
    9320:   if (ccomm != MPI_COMM_NULL) {
    9321:     PetscLayoutCreate(ccomm,&rmap);
    9322:     PetscLayoutSetSize(rmap,A->rmap->N);
    9323:     PetscLayoutSetBlockSize(rmap,1);
    9324:     PetscLayoutSetUp(rmap);
    9325:     PetscLayoutGetRange(rmap,&rst,&ren);
    9326:   }
    9327:   ISCreateStride(PetscObjectComm((PetscObject)A),ren-rst,rst,1,&rows);
    9328:   MatCreateSubMatrix(A,rows,NULL,MAT_INITIAL_MATRIX,&At);
    9329:   ISDestroy(&rows);

    9331:   if (ccomm != MPI_COMM_NULL) {
    9332:     Mat_MPIAIJ *a,*b;
    9333:     IS         from,to;
    9334:     Vec        gvec;
    9335:     PetscInt   lsize;

    9337:     MatCreate(ccomm,B);
    9338:     MatSetSizes(*B,ren-rst,PETSC_DECIDE,PETSC_DECIDE,At->cmap->N);
    9339:     MatSetType(*B,MATAIJ);
    9340:     PetscLayoutDestroy(&((*B)->rmap));
    9341:     PetscLayoutSetUp((*B)->cmap);
    9342:     a    = (Mat_MPIAIJ*)At->data;
    9343:     b    = (Mat_MPIAIJ*)(*B)->data;
    9344:     MPI_Comm_size(ccomm,&b->size);
    9345:     MPI_Comm_rank(ccomm,&b->rank);
    9346:     PetscObjectReference((PetscObject)a->A);
    9347:     PetscObjectReference((PetscObject)a->B);
    9348:     b->A = a->A;
    9349:     b->B = a->B;

    9351:     b->donotstash      = a->donotstash;
    9352:     b->roworiented     = a->roworiented;
    9353:     b->rowindices      = NULL;
    9354:     b->rowvalues       = NULL;
    9355:     b->getrowactive    = PETSC_FALSE;

    9357:     (*B)->rmap         = rmap;
    9358:     (*B)->factortype   = A->factortype;
    9359:     (*B)->assembled    = PETSC_TRUE;
    9360:     (*B)->insertmode   = NOT_SET_VALUES;
    9361:     (*B)->preallocated = PETSC_TRUE;

    9363:     if (a->colmap) {
    9364: #if defined(PETSC_USE_CTABLE)
    9365:       PetscTableCreateCopy(a->colmap,&b->colmap);
    9366: #else
    9367:       PetscMalloc1(At->cmap->N,&b->colmap);
    9368:       PetscLogObjectMemory((PetscObject)*B,At->cmap->N*sizeof(PetscInt));
    9369:       PetscArraycpy(b->colmap,a->colmap,At->cmap->N);
    9370: #endif
    9371:     } else b->colmap = NULL;
    9372:     if (a->garray) {
    9373:       PetscInt len;
    9374:       len  = a->B->cmap->n;
    9375:       PetscMalloc1(len+1,&b->garray);
    9376:       PetscLogObjectMemory((PetscObject)(*B),len*sizeof(PetscInt));
    9377:       if (len) PetscArraycpy(b->garray,a->garray,len);
    9378:     } else b->garray = NULL;

    9380:     PetscObjectReference((PetscObject)a->lvec);
    9381:     b->lvec = a->lvec;
    9382:     PetscLogObjectParent((PetscObject)*B,(PetscObject)b->lvec);

    9384:     /* cannot use VecScatterCopy */
    9385:     VecGetLocalSize(b->lvec,&lsize);
    9386:     ISCreateGeneral(ccomm,lsize,b->garray,PETSC_USE_POINTER,&from);
    9387:     ISCreateStride(PETSC_COMM_SELF,lsize,0,1,&to);
    9388:     MatCreateVecs(*B,&gvec,NULL);
    9389:     VecScatterCreate(gvec,from,b->lvec,to,&b->Mvctx);
    9390:     PetscLogObjectParent((PetscObject)*B,(PetscObject)b->Mvctx);
    9391:     ISDestroy(&from);
    9392:     ISDestroy(&to);
    9393:     VecDestroy(&gvec);
    9394:   }
    9395:   MatDestroy(&At);
    9396:   return 0;
    9397: }