Date: 2016-07-24T17:05:12+00:00

Actual source code: bddcprivate.c
petsc-3.7.3 2016-07-24
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      1: #include <../src/ksp/pc/impls/bddc/bddc.h>
      2: #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
      3: #include <petscblaslapack.h>

      5: static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y);
      6: static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y);

     10: PetscErrorCode PCBDDCAdaptiveSelection(PC pc)
     11: {
     12:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
     13:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
     14:   PetscBLASInt    B_dummyint,B_neigs,B_ierr,B_lwork;
     15:   PetscBLASInt    *B_iwork,*B_ifail;
     16:   PetscScalar     *work,lwork;
     17:   PetscScalar     *St,*S,*eigv;
     18:   PetscScalar     *Sarray,*Starray;
     19:   PetscReal       *eigs,thresh;
     20:   PetscInt        i,nmax,nmin,nv,cum,mss,cum2,cumarray,maxneigs;
     21:   PetscBool       allocated_S_St;
     22: #if defined(PETSC_USE_COMPLEX)
     23:   PetscReal       *rwork;
     24: #endif
     25:   PetscErrorCode  ierr;

     28:   if (!sub_schurs->use_mumps) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Adaptive selection of constraints requires MUMPS");

     30:   if (pcbddc->dbg_flag) {
     31:     PetscViewerFlush(pcbddc->dbg_viewer);
     32:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
     33:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check adaptive selection of constraints\n");
     34:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
     35:   }

     37:   if (pcbddc->dbg_flag) {
     38:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d cc %d (%d,%d).\n",PetscGlobalRank,sub_schurs->n_subs,sub_schurs->is_hermitian,sub_schurs->is_posdef);
     39:   }

     41:   if (sub_schurs->n_subs && (!sub_schurs->is_hermitian || !sub_schurs->is_posdef)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Adaptive selection not yet implemented for general matrix pencils (herm %d, posdef %d)\n",sub_schurs->is_hermitian,sub_schurs->is_posdef);

     43:   /* max size of subsets */
     44:   mss = 0;
     45:   for (i=0;i<sub_schurs->n_subs;i++) {
     46:     PetscInt subset_size;

     48:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
     49:     mss = PetscMax(mss,subset_size);
     50:   }

     52:   /* min/max and threshold */
     53:   nmax = pcbddc->adaptive_nmax > 0 ? pcbddc->adaptive_nmax : mss;
     54:   nmin = pcbddc->adaptive_nmin > 0 ? pcbddc->adaptive_nmin : 0;
     55:   nmax = PetscMax(nmin,nmax);
     56:   allocated_S_St = PETSC_FALSE;
     57:   if (nmin) {
     58:     allocated_S_St = PETSC_TRUE;
     59:   }

     61:   /* allocate lapack workspace */
     62:   cum = cum2 = 0;
     63:   maxneigs = 0;
     64:   for (i=0;i<sub_schurs->n_subs;i++) {
     65:     PetscInt n,subset_size;

     67:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
     68:     n = PetscMin(subset_size,nmax);
     69:     cum += subset_size;
     70:     cum2 += subset_size*n;
     71:     maxneigs = PetscMax(maxneigs,n);
     72:   }
     73:   if (mss) {
     74:     if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
     75:       PetscBLASInt B_itype = 1;
     76:       PetscBLASInt B_N = mss;
     77:       PetscReal    zero = 0.0;
     78:       PetscReal    eps = 0.0; /* dlamch? */

     80:       B_lwork = -1;
     81:       S = NULL;
     82:       St = NULL;
     83:       eigs = NULL;
     84:       eigv = NULL;
     85:       B_iwork = NULL;
     86:       B_ifail = NULL;
     87: #if defined(PETSC_USE_COMPLEX)
     88:       rwork = NULL;
     89: #endif
     90:       thresh = 1.0;
     91:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
     92: #if defined(PETSC_USE_COMPLEX)
     93:       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));
     94: #else
     95:       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));
     96: #endif
     97:       if (B_ierr != 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYGVX Lapack routine %d",(int)B_ierr);
     98:       PetscFPTrapPop();
     99:     } else {
    100:         /* TODO */
    101:     }
    102:   } else {
    103:     lwork = 0;
    104:   }

    106:   nv = 0;
    107:   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) */
    108:     ISGetLocalSize(sub_schurs->is_vertices,&nv);
    109:   }
    110:   PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);
    111:   if (allocated_S_St) {
    112:     PetscMalloc2(mss*mss,&S,mss*mss,&St);
    113:   }
    114:   PetscMalloc5(mss*mss,&eigv,mss,&eigs,B_lwork,&work,5*mss,&B_iwork,mss,&B_ifail);
    115: #if defined(PETSC_USE_COMPLEX)
    116:   PetscMalloc1(7*mss,&rwork);
    117: #endif
    118:   PetscMalloc5(nv+sub_schurs->n_subs,&pcbddc->adaptive_constraints_n,
    119:                       nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_idxs_ptr,
    120:                       nv+sub_schurs->n_subs+1,&pcbddc->adaptive_constraints_data_ptr,
    121:                       nv+cum,&pcbddc->adaptive_constraints_idxs,
    122:                       nv+cum2,&pcbddc->adaptive_constraints_data);
    123:   PetscMemzero(pcbddc->adaptive_constraints_n,(nv+sub_schurs->n_subs)*sizeof(PetscInt));

    125:   maxneigs = 0;
    126:   cum = cumarray = 0;
    127:   pcbddc->adaptive_constraints_idxs_ptr[0] = 0;
    128:   pcbddc->adaptive_constraints_data_ptr[0] = 0;
    129:   if (sub_schurs->is_vertices && pcbddc->use_vertices) {
    130:     const PetscInt *idxs;

    132:     ISGetIndices(sub_schurs->is_vertices,&idxs);
    133:     for (cum=0;cum<nv;cum++) {
    134:       pcbddc->adaptive_constraints_n[cum] = 1;
    135:       pcbddc->adaptive_constraints_idxs[cum] = idxs[cum];
    136:       pcbddc->adaptive_constraints_data[cum] = 1.0;
    137:       pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum]+1;
    138:       pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum]+1;
    139:     }
    140:     ISRestoreIndices(sub_schurs->is_vertices,&idxs);
    141:   }

    143:   if (mss) { /* multilevel */
    144:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);
    145:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);
    146:   }

    148:   for (i=0;i<sub_schurs->n_subs;i++) {

    150:     const PetscInt *idxs;
    151:     PetscReal      infty = PETSC_MAX_REAL;
    152:     PetscInt       j,subset_size,eigs_start = 0;
    153:     PetscBLASInt   B_N;
    154:     PetscBool      same_data = PETSC_FALSE;

    156:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    157:     PetscBLASIntCast(subset_size,&B_N);
    158:     if (allocated_S_St) { /* S and S_t should be copied since we could need them later */
    159:       if (sub_schurs->is_hermitian) {
    160:         PetscInt j,k;
    161:         if (sub_schurs->n_subs == 1) { /* zeroing memory to use PetscMemcmp later */
    162:           PetscMemzero(S,subset_size*subset_size*sizeof(PetscScalar));
    163:           PetscMemzero(St,subset_size*subset_size*sizeof(PetscScalar));
    164:         }
    165:         for (j=0;j<subset_size;j++) {
    166:           for (k=j;k<subset_size;k++) {
    167:             S [j*subset_size+k] = Sarray [cumarray+j*subset_size+k];
    168:             St[j*subset_size+k] = Starray[cumarray+j*subset_size+k];
    169:           }
    170:         }
    171:       } else {
    172:         PetscMemcpy(S,Sarray+cumarray,subset_size*subset_size*sizeof(PetscScalar));
    173:         PetscMemcpy(St,Starray+cumarray,subset_size*subset_size*sizeof(PetscScalar));
    174:       }
    175:     } else {
    176:       S = Sarray + cumarray;
    177:       St = Starray + cumarray;
    178:     }

    180:     ISGetIndices(sub_schurs->is_subs[i],&idxs);
    181:     /* see if we can save some work */
    182:     if (sub_schurs->n_subs == 1) {
    183:       PetscMemcmp(S,St,subset_size*subset_size*sizeof(PetscScalar),&same_data);
    184:     }

    186:     if (same_data) { /* there's no need of constraints here, deluxe scaling is enough */
    187:       B_neigs = 0;
    188:     } else {
    189:       /* Threshold: this is an heuristic for edges */
    190:       thresh = pcbddc->mat_graph->count[idxs[0]]*pcbddc->adaptive_threshold;

    192:       if (sub_schurs->is_hermitian && sub_schurs->is_posdef) {
    193:         PetscBLASInt B_itype = 1;
    194:         PetscBLASInt B_IL, B_IU;
    195:         PetscReal    eps = -1.0; /* dlamch? */
    196:         PetscInt     nmin_s;

    198:         /* ask for eigenvalues larger than thresh */
    199:         if (pcbddc->dbg_flag) {
    200:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Computing for sub %d/%d %d %d.\n",i,sub_schurs->n_subs,subset_size,pcbddc->mat_graph->count[idxs[0]]);
    201:         }
    202:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    203: #if defined(PETSC_USE_COMPLEX)
    204:         PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,rwork,B_iwork,B_ifail,&B_ierr));
    205: #else
    206:         PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","V","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&B_IL,&B_IU,&eps,&B_neigs,eigs,eigv,&B_N,work,&B_lwork,B_iwork,B_ifail,&B_ierr));
    207: #endif
    208:         PetscFPTrapPop();
    209:         if (B_ierr) {
    210:           if (B_ierr < 0 ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
    211:           else if (B_ierr <= B_N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: %d eigenvalues failed to converge",(int)B_ierr);
    212:           else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: leading minor of order %d is not positive definite",(int)B_ierr-B_N-1);
    213:         }

    215:         if (B_neigs > nmax) {
    216:           if (pcbddc->dbg_flag) {
    217:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   found %d eigs, more than maximum required %d.\n",B_neigs,nmax);
    218:           }
    219:           eigs_start = B_neigs -nmax;
    220:           B_neigs = nmax;
    221:         }

    223:         nmin_s = PetscMin(nmin,B_N);
    224:         if (B_neigs < nmin_s) {
    225:           PetscBLASInt B_neigs2;

    227:           B_IU = B_N - B_neigs;
    228:           B_IL = B_N - nmin_s + 1;
    229:           if (pcbddc->dbg_flag) {
    230:             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);
    231:           }
    232:           if (sub_schurs->is_hermitian) {
    233:             PetscInt j;
    234:             for (j=0;j<subset_size;j++) {
    235:               PetscMemcpy(S+j*(subset_size+1),Sarray+cumarray+j*(subset_size+1),(subset_size-j)*sizeof(PetscScalar));
    236:             }
    237:             for (j=0;j<subset_size;j++) {
    238:               PetscMemcpy(St+j*(subset_size+1),Starray+cumarray+j*(subset_size+1),(subset_size-j)*sizeof(PetscScalar));
    239:             }
    240:           } else {
    241:             PetscMemcpy(S,Sarray+cumarray,subset_size*subset_size*sizeof(PetscScalar));
    242:             PetscMemcpy(St,Starray+cumarray,subset_size*subset_size*sizeof(PetscScalar));
    243:           }
    244:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    245: #if defined(PETSC_USE_COMPLEX)
    246:           PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&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));
    247: #else
    248:           PetscStackCallBLAS("LAPACKsygvx",LAPACKsygvx_(&B_itype,"V","I","L",&B_N,St,&B_N,S,&B_N,&thresh,&infty,&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));
    249: #endif
    250:           PetscFPTrapPop();
    251:           B_neigs += B_neigs2;
    252:         }
    253:         if (B_ierr) {
    254:           if (B_ierr < 0 ) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: illegal value for argument %d",-(int)B_ierr);
    255:           else if (B_ierr <= B_N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: %d eigenvalues failed to converge",(int)B_ierr);
    256:           else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYGVX Lapack routine: leading minor of order %d is not positive definite",(int)B_ierr-B_N-1);
    257:         }
    258:         if (pcbddc->dbg_flag) {
    259:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Got %d eigs\n",B_neigs);
    260:           for (j=0;j<B_neigs;j++) {
    261:             if (eigs[j] == 0.0) {
    262:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     Inf\n");
    263:             } else {
    264:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"     %1.6e\n",eigs[j+eigs_start]);
    265:             }
    266:           }
    267:         }
    268:       } else {
    269:           /* TODO */
    270:       }
    271:     }
    272:     maxneigs = PetscMax(B_neigs,maxneigs);
    273:     pcbddc->adaptive_constraints_n[i+nv] = B_neigs;
    274:     if (B_neigs) {
    275:       PetscMemcpy(pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum],eigv+eigs_start*subset_size,B_neigs*subset_size*sizeof(PetscScalar));

    277:       if (pcbddc->dbg_flag > 1) {
    278:         PetscInt ii;
    279:         for (ii=0;ii<B_neigs;ii++) {
    280:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"   -> Eigenvector %d/%d (%d)\n",ii,B_neigs,B_N);
    281:           for (j=0;j<B_N;j++) {
    282: #if defined(PETSC_USE_COMPLEX)
    283:             PetscReal r = PetscRealPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
    284:             PetscReal c = PetscImaginaryPart(pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
    285:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e + %1.4e i\n",r,c);
    286: #else
    287:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"       %1.4e\n",pcbddc->adaptive_constraints_data[ii*subset_size+j+pcbddc->adaptive_constraints_data_ptr[cum]]);
    288: #endif
    289:           }
    290:         }
    291:       }
    292: #if 0
    293:       for (j=0;j<B_neigs;j++) {
    294:         PetscBLASInt Blas_N,Blas_one = 1.0;
    295:         PetscScalar norm;
    296:         PetscBLASIntCast(subset_size,&Blas_N);
    297:         PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum]+j*subset_size,
    298:                                                    &Blas_one,pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum]+j*subset_size,&Blas_one));
    299:         if (pcbddc->adaptive_constraints_data[cum] > 0.0) {
    300:           norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
    301:         } else {
    302:           norm = -1.0/PetscSqrtReal(PetscRealPart(norm));
    303:         }
    304:         PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,pcbddc->adaptive_constraints_data+pcbddc->adaptive_constraints_data_ptr[cum]+j*subset_size,&Blas_one));
    305:       }
    306: #endif
    307:       PetscMemcpy(pcbddc->adaptive_constraints_idxs+pcbddc->adaptive_constraints_idxs_ptr[cum],idxs,subset_size*sizeof(PetscInt));
    308:       pcbddc->adaptive_constraints_idxs_ptr[cum+1] = pcbddc->adaptive_constraints_idxs_ptr[cum] + subset_size;
    309:       pcbddc->adaptive_constraints_data_ptr[cum+1] = pcbddc->adaptive_constraints_data_ptr[cum] + subset_size*B_neigs;
    310:       cum++;
    311:     }
    312:     ISRestoreIndices(sub_schurs->is_subs[i],&idxs);
    313:     /* shift for next computation */
    314:     cumarray += subset_size*subset_size;
    315:   }
    316:   if (pcbddc->dbg_flag) {
    317:     PetscViewerFlush(pcbddc->dbg_viewer);
    318:   }

    320:   if (mss) {
    321:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&Sarray);
    322:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&Starray);
    323:     /* destroy matrices (junk) */
    324:     MatDestroy(&sub_schurs->sum_S_Ej_inv_all);
    325:     MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);
    326:   }
    327:   if (allocated_S_St) {
    328:     PetscFree2(S,St);
    329:   }
    330:   PetscFree5(eigv,eigs,work,B_iwork,B_ifail);
    331: #if defined(PETSC_USE_COMPLEX)
    332:   PetscFree(rwork);
    333: #endif
    334:   if (pcbddc->dbg_flag) {
    335:     PetscInt maxneigs_r;
    336:     MPIU_Allreduce(&maxneigs,&maxneigs_r,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));
    337:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of constraints per cc %d\n",maxneigs_r);
    338:   }
    339:   return(0);
    340: }

    344: PetscErrorCode PCBDDCSetUpSolvers(PC pc)
    345: {
    346:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
    347:   PetscScalar    *coarse_submat_vals;

    351:   /* Setup local scatters R_to_B and (optionally) R_to_D */
    352:   /* PCBDDCSetUpLocalWorkVectors should be called first! */
    353:   PCBDDCSetUpLocalScatters(pc);

    355:   /* Setup local neumann solver ksp_R */
    356:   /* PCBDDCSetUpLocalScatters should be called first! */
    357:   PCBDDCSetUpLocalSolvers(pc,PETSC_FALSE,PETSC_TRUE);

    359:   /* Change global null space passed in by the user if change of basis has been requested */
    360:   if (pcbddc->NullSpace && pcbddc->ChangeOfBasisMatrix) {
    361:     PCBDDCNullSpaceAdaptGlobal(pc);
    362:   }

    364:   /*
    365:      Setup local correction and local part of coarse basis.
    366:      Gives back the dense local part of the coarse matrix in column major ordering
    367:   */
    368:   PCBDDCSetUpCorrection(pc,&coarse_submat_vals);

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

    373:   /* free */
    374:   PetscFree(coarse_submat_vals);
    375:   return(0);
    376: }

    380: PetscErrorCode PCBDDCResetCustomization(PC pc)
    381: {
    382:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

    386:   PCBDDCGraphResetCSR(pcbddc->mat_graph);
    387:   ISDestroy(&pcbddc->user_primal_vertices);
    388:   MatNullSpaceDestroy(&pcbddc->NullSpace);
    389:   ISDestroy(&pcbddc->NeumannBoundaries);
    390:   ISDestroy(&pcbddc->NeumannBoundariesLocal);
    391:   ISDestroy(&pcbddc->DirichletBoundaries);
    392:   MatNullSpaceDestroy(&pcbddc->onearnullspace);
    393:   PetscFree(pcbddc->onearnullvecs_state);
    394:   ISDestroy(&pcbddc->DirichletBoundariesLocal);
    395:   PCBDDCSetDofsSplitting(pc,0,NULL);
    396:   PCBDDCSetDofsSplittingLocal(pc,0,NULL);
    397:   return(0);
    398: }

    402: PetscErrorCode PCBDDCResetTopography(PC pc)
    403: {
    404:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;

    408:   MatDestroy(&pcbddc->user_ChangeOfBasisMatrix);
    409:   MatDestroy(&pcbddc->ChangeOfBasisMatrix);
    410:   MatDestroy(&pcbddc->ConstraintMatrix);
    411:   PCBDDCGraphReset(pcbddc->mat_graph);
    412:   PCBDDCSubSchursReset(pcbddc->sub_schurs);
    413:   return(0);
    414: }

    418: PetscErrorCode PCBDDCResetSolvers(PC pc)
    419: {
    420:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
    421:   PetscScalar    *array;

    425:   VecDestroy(&pcbddc->coarse_vec);
    426:   if (pcbddc->coarse_phi_B) {
    427:     MatDenseGetArray(pcbddc->coarse_phi_B,&array);
    428:     PetscFree(array);
    429:   }
    430:   MatDestroy(&pcbddc->coarse_phi_B);
    431:   MatDestroy(&pcbddc->coarse_phi_D);
    432:   MatDestroy(&pcbddc->coarse_psi_B);
    433:   MatDestroy(&pcbddc->coarse_psi_D);
    434:   VecDestroy(&pcbddc->vec1_P);
    435:   VecDestroy(&pcbddc->vec1_C);
    436:   MatDestroy(&pcbddc->local_auxmat2);
    437:   MatDestroy(&pcbddc->local_auxmat1);
    438:   VecDestroy(&pcbddc->vec1_R);
    439:   VecDestroy(&pcbddc->vec2_R);
    440:   ISDestroy(&pcbddc->is_R_local);
    441:   VecScatterDestroy(&pcbddc->R_to_B);
    442:   VecScatterDestroy(&pcbddc->R_to_D);
    443:   VecScatterDestroy(&pcbddc->coarse_loc_to_glob);
    444:   KSPDestroy(&pcbddc->ksp_D);
    445:   KSPDestroy(&pcbddc->ksp_R);
    446:   KSPDestroy(&pcbddc->coarse_ksp);
    447:   MatDestroy(&pcbddc->local_mat);
    448:   PetscFree(pcbddc->primal_indices_local_idxs);
    449:   PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);
    450:   PetscFree(pcbddc->global_primal_indices);
    451:   ISDestroy(&pcbddc->coarse_subassembling);
    452:   ISDestroy(&pcbddc->coarse_subassembling_init);
    453:   return(0);
    454: }

    458: PetscErrorCode PCBDDCSetUpLocalWorkVectors(PC pc)
    459: {
    460:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
    461:   PC_IS          *pcis = (PC_IS*)pc->data;
    462:   VecType        impVecType;
    463:   PetscInt       n_constraints,n_R,old_size;

    467:   if (!pcbddc->ConstraintMatrix) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Constraint matrix has not been created");
    468:   /* get sizes */
    469:   n_constraints = pcbddc->local_primal_size - pcbddc->n_vertices;
    470:   n_R = pcis->n-pcbddc->n_vertices;
    471:   VecGetType(pcis->vec1_N,&impVecType);
    472:   /* local work vectors (try to avoid unneeded work)*/
    473:   /* R nodes */
    474:   old_size = -1;
    475:   if (pcbddc->vec1_R) {
    476:     VecGetSize(pcbddc->vec1_R,&old_size);
    477:   }
    478:   if (n_R != old_size) {
    479:     VecDestroy(&pcbddc->vec1_R);
    480:     VecDestroy(&pcbddc->vec2_R);
    481:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_R);
    482:     VecSetSizes(pcbddc->vec1_R,PETSC_DECIDE,n_R);
    483:     VecSetType(pcbddc->vec1_R,impVecType);
    484:     VecDuplicate(pcbddc->vec1_R,&pcbddc->vec2_R);
    485:   }
    486:   /* local primal dofs */
    487:   old_size = -1;
    488:   if (pcbddc->vec1_P) {
    489:     VecGetSize(pcbddc->vec1_P,&old_size);
    490:   }
    491:   if (pcbddc->local_primal_size != old_size) {
    492:     VecDestroy(&pcbddc->vec1_P);
    493:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_P);
    494:     VecSetSizes(pcbddc->vec1_P,PETSC_DECIDE,pcbddc->local_primal_size);
    495:     VecSetType(pcbddc->vec1_P,impVecType);
    496:   }
    497:   /* local explicit constraints */
    498:   old_size = -1;
    499:   if (pcbddc->vec1_C) {
    500:     VecGetSize(pcbddc->vec1_C,&old_size);
    501:   }
    502:   if (n_constraints && n_constraints != old_size) {
    503:     VecDestroy(&pcbddc->vec1_C);
    504:     VecCreate(PetscObjectComm((PetscObject)pcis->vec1_N),&pcbddc->vec1_C);
    505:     VecSetSizes(pcbddc->vec1_C,PETSC_DECIDE,n_constraints);
    506:     VecSetType(pcbddc->vec1_C,impVecType);
    507:   }
    508:   return(0);
    509: }

    513: PetscErrorCode PCBDDCSetUpCorrection(PC pc, PetscScalar **coarse_submat_vals_n)
    514: {
    515:   PetscErrorCode  ierr;
    516:   /* pointers to pcis and pcbddc */
    517:   PC_IS*          pcis = (PC_IS*)pc->data;
    518:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
    519:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    520:   /* submatrices of local problem */
    521:   Mat             A_RV,A_VR,A_VV,local_auxmat2_R;
    522:   /* submatrices of local coarse problem */
    523:   Mat             S_VV,S_CV,S_VC,S_CC;
    524:   /* working matrices */
    525:   Mat             C_CR;
    526:   /* additional working stuff */
    527:   PC              pc_R;
    528:   Mat             F;
    529:   PetscBool       isLU,isCHOL,isILU;

    531:   PetscScalar     *coarse_submat_vals; /* TODO: use a PETSc matrix */
    532:   PetscScalar     *work;
    533:   PetscInt        *idx_V_B;
    534:   PetscInt        n,n_vertices,n_constraints;
    535:   PetscInt        i,n_R,n_D,n_B;
    536:   PetscBool       unsymmetric_check;
    537:   /* matrix type (vector type propagated downstream from vec1_C and local matrix type) */
    538:   MatType         impMatType;
    539:   /* some shortcuts to scalars */
    540:   PetscScalar     one=1.0,m_one=-1.0;

    543:   n_vertices = pcbddc->n_vertices;
    544:   n_constraints = pcbddc->local_primal_size-n_vertices;
    545:   /* Set Non-overlapping dimensions */
    546:   n_B = pcis->n_B;
    547:   n_D = pcis->n - n_B;
    548:   n_R = pcis->n - n_vertices;

    550:   /* Set types for local objects needed by BDDC precondtioner */
    551:   impMatType = MATSEQDENSE;

    553:   /* vertices in boundary numbering */
    554:   PetscMalloc1(n_vertices,&idx_V_B);
    555:   ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,n_vertices,pcbddc->local_primal_ref_node,&i,idx_V_B);
    556:   if (i != n_vertices) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Error in boundary numbering for BDDC vertices! %D != %D\n",n_vertices,i);

    558:   /* Subdomain contribution (Non-overlapping) to coarse matrix  */
    559:   PetscMalloc1(pcbddc->local_primal_size*pcbddc->local_primal_size,&coarse_submat_vals);
    560:   MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_vertices,coarse_submat_vals,&S_VV);
    561:   MatSeqDenseSetLDA(S_VV,pcbddc->local_primal_size);
    562:   MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_vertices,coarse_submat_vals+n_vertices,&S_CV);
    563:   MatSeqDenseSetLDA(S_CV,pcbddc->local_primal_size);
    564:   MatCreateSeqDense(PETSC_COMM_SELF,n_vertices,n_constraints,coarse_submat_vals+pcbddc->local_primal_size*n_vertices,&S_VC);
    565:   MatSeqDenseSetLDA(S_VC,pcbddc->local_primal_size);
    566:   MatCreateSeqDense(PETSC_COMM_SELF,n_constraints,n_constraints,coarse_submat_vals+(pcbddc->local_primal_size+1)*n_vertices,&S_CC);
    567:   MatSeqDenseSetLDA(S_CC,pcbddc->local_primal_size);

    569:   unsymmetric_check = PETSC_FALSE;
    570:   /* allocate workspace */
    571:   n = 0;
    572:   if (n_constraints) {
    573:     n += n_R*n_constraints;
    574:   }
    575:   if (n_vertices) {
    576:     n = PetscMax(2*n_R*n_vertices,n);
    577:     n = PetscMax((n_R+n_B)*n_vertices,n);
    578:   }
    579:   if (!pcbddc->symmetric_primal) {
    580:     n = PetscMax(2*n_R*pcbddc->local_primal_size,n);
    581:     unsymmetric_check = PETSC_TRUE;
    582:   }
    583:   PetscMalloc1(n,&work);

    585:   /* determine if can use MatSolve routines instead of calling KSPSolve on ksp_R */
    586:   KSPGetPC(pcbddc->ksp_R,&pc_R);
    587:   PetscObjectTypeCompare((PetscObject)pc_R,PCLU,&isLU);
    588:   PetscObjectTypeCompare((PetscObject)pc_R,PCILU,&isILU);
    589:   PetscObjectTypeCompare((PetscObject)pc_R,PCCHOLESKY,&isCHOL);
    590:   if (isLU || isILU || isCHOL) {
    591:     PCFactorGetMatrix(pc_R,&F);
    592:   } else if (sub_schurs->reuse_mumps) {
    593:     PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;
    594:     MatFactorType type;

    596:     F = reuse_mumps->F;
    597:     MatGetFactorType(F,&type);
    598:     if (type == MAT_FACTOR_CHOLESKY) isCHOL = PETSC_TRUE;
    599:   } else {
    600:     F = NULL;
    601:   }

    603:   /* Precompute stuffs needed for preprocessing and application of BDDC*/
    604:   if (n_constraints) {
    605:     Mat         M1,M2,M3;
    606:     Mat         auxmat;
    607:     IS          is_aux;
    608:     PetscScalar *array,*array2;

    610:     MatDestroy(&pcbddc->local_auxmat1);
    611:     MatDestroy(&pcbddc->local_auxmat2);

    613:     /* Extract constraints on R nodes: C_{CR}  */
    614:     ISCreateStride(PETSC_COMM_SELF,n_constraints,n_vertices,1,&is_aux);
    615:     MatGetSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&C_CR);
    616:     MatGetSubMatrix(pcbddc->ConstraintMatrix,is_aux,pcis->is_B_local,MAT_INITIAL_MATRIX,&auxmat);

    618:     /* Assemble         local_auxmat2_R =        (- A_{RR}^{-1} C^T_{CR}) needed by BDDC setup */
    619:     /* Assemble pcbddc->local_auxmat2   = R_to_B (- A_{RR}^{-1} C^T_{CR}) needed by BDDC application */
    620:     PetscMemzero(work,n_R*n_constraints*sizeof(PetscScalar));
    621:     for (i=0;i<n_constraints;i++) {
    622:       const PetscScalar *row_cmat_values;
    623:       const PetscInt    *row_cmat_indices;
    624:       PetscInt          size_of_constraint,j;

    626:       MatGetRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);
    627:       for (j=0;j<size_of_constraint;j++) {
    628:         work[row_cmat_indices[j]+i*n_R] = -row_cmat_values[j];
    629:       }
    630:       MatRestoreRow(C_CR,i,&size_of_constraint,&row_cmat_indices,&row_cmat_values);
    631:     }
    632:     MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,NULL,&local_auxmat2_R);
    633:     if (F) {
    634:       Mat B;

    636:       MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work,&B);
    637:       MatMatSolve(F,B,local_auxmat2_R);
    638:       MatDestroy(&B);
    639:     } else {
    640:       PetscScalar *marr;

    642:       MatDenseGetArray(local_auxmat2_R,&marr);
    643:       for (i=0;i<n_constraints;i++) {
    644:         VecPlaceArray(pcbddc->vec1_R,work+i*n_R);
    645:         VecPlaceArray(pcbddc->vec2_R,marr+i*n_R);
    646:         KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
    647:         VecResetArray(pcbddc->vec1_R);
    648:         VecResetArray(pcbddc->vec2_R);
    649:       }
    650:       MatDenseRestoreArray(local_auxmat2_R,&marr);
    651:     }
    652:     if (!pcbddc->switch_static) {
    653:       MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_constraints,NULL,&pcbddc->local_auxmat2);
    654:       MatDenseGetArray(pcbddc->local_auxmat2,&array);
    655:       MatDenseGetArray(local_auxmat2_R,&array2);
    656:       for (i=0;i<n_constraints;i++) {
    657:         VecPlaceArray(pcbddc->vec1_R,array2+i*n_R);
    658:         VecPlaceArray(pcis->vec1_B,array+i*n_B);
    659:         VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    660:         VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    661:         VecResetArray(pcis->vec1_B);
    662:         VecResetArray(pcbddc->vec1_R);
    663:       }
    664:       MatDenseRestoreArray(local_auxmat2_R,&array2);
    665:       MatDenseRestoreArray(pcbddc->local_auxmat2,&array);
    666:       MatMatMult(auxmat,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);
    667:     } else {
    668:       PetscObjectReference((PetscObject)local_auxmat2_R);
    669:       pcbddc->local_auxmat2 = local_auxmat2_R;
    670:       MatMatMult(C_CR,pcbddc->local_auxmat2,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&M3);
    671:     }
    672:     ISDestroy(&is_aux);
    673:     /* Assemble explicitly S_CC = ( C_{CR} A_{RR}^{-1} C^T_{CR} )^{-1}  */
    674:     MatScale(M3,m_one);
    675:     MatDuplicate(M3,MAT_DO_NOT_COPY_VALUES,&M1);
    676:     MatDuplicate(M3,MAT_DO_NOT_COPY_VALUES,&M2);
    677:     if (isCHOL) {
    678:       MatCholeskyFactor(M3,NULL,NULL);
    679:     } else {
    680:       MatLUFactor(M3,NULL,NULL,NULL);
    681:     }
    682:     VecSet(pcbddc->vec1_C,one);
    683:     MatDiagonalSet(M2,pcbddc->vec1_C,INSERT_VALUES);
    684:     MatMatSolve(M3,M2,M1);
    685:     MatDestroy(&M2);
    686:     MatDestroy(&M3);
    687:     /* Assemble local_auxmat1 = S_CC*C_{CB} needed by BDDC application in KSP and in preproc */
    688:     MatMatMult(M1,auxmat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&pcbddc->local_auxmat1);
    689:     MatDestroy(&auxmat);
    690:     MatCopy(M1,S_CC,SAME_NONZERO_PATTERN); /* S_CC can have a different LDA, MatMatSolve doesn't support it */
    691:     MatDestroy(&M1);
    692:   }
    693:   /* Get submatrices from subdomain matrix */
    694:   if (n_vertices) {
    695:     IS is_aux;

    697:     if (sub_schurs->reuse_mumps) { /* is_R_local is not sorted, ISComplement doesn't like it */
    698:       IS tis;

    700:       ISDuplicate(pcbddc->is_R_local,&tis);
    701:       ISSort(tis);
    702:       ISComplement(tis,0,pcis->n,&is_aux);
    703:       ISDestroy(&tis);
    704:     } else {
    705:       ISComplement(pcbddc->is_R_local,0,pcis->n,&is_aux);
    706:     }
    707:     MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,is_aux,MAT_INITIAL_MATRIX,&A_RV);
    708:     MatGetSubMatrix(pcbddc->local_mat,is_aux,pcbddc->is_R_local,MAT_INITIAL_MATRIX,&A_VR);
    709:     MatGetSubMatrix(pcbddc->local_mat,is_aux,is_aux,MAT_INITIAL_MATRIX,&A_VV);
    710:     ISDestroy(&is_aux);
    711:   }

    713:   /* Matrix of coarse basis functions (local) */
    714:   if (pcbddc->coarse_phi_B) {
    715:     PetscInt on_B,on_primal,on_D=n_D;
    716:     if (pcbddc->coarse_phi_D) {
    717:       MatGetSize(pcbddc->coarse_phi_D,&on_D,NULL);
    718:     }
    719:     MatGetSize(pcbddc->coarse_phi_B,&on_B,&on_primal);
    720:     if (on_B != n_B || on_primal != pcbddc->local_primal_size || on_D != n_D) {
    721:       PetscScalar *marray;

    723:       MatDenseGetArray(pcbddc->coarse_phi_B,&marray);
    724:       PetscFree(marray);
    725:       MatDestroy(&pcbddc->coarse_phi_B);
    726:       MatDestroy(&pcbddc->coarse_psi_B);
    727:       MatDestroy(&pcbddc->coarse_phi_D);
    728:       MatDestroy(&pcbddc->coarse_psi_D);
    729:     }
    730:   }

    732:   if (!pcbddc->coarse_phi_B) {
    733:     PetscScalar *marray;

    735:     n = n_B*pcbddc->local_primal_size;
    736:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
    737:       n += n_D*pcbddc->local_primal_size;
    738:     }
    739:     if (!pcbddc->symmetric_primal) {
    740:       n *= 2;
    741:     }
    742:     PetscCalloc1(n,&marray);
    743:     MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marray,&pcbddc->coarse_phi_B);
    744:     n = n_B*pcbddc->local_primal_size;
    745:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
    746:       MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_phi_D);
    747:       n += n_D*pcbddc->local_primal_size;
    748:     }
    749:     if (!pcbddc->symmetric_primal) {
    750:       MatCreateSeqDense(PETSC_COMM_SELF,n_B,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_psi_B);
    751:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    752:         n = n_B*pcbddc->local_primal_size;
    753:         MatCreateSeqDense(PETSC_COMM_SELF,n_D,pcbddc->local_primal_size,marray+n,&pcbddc->coarse_psi_D);
    754:       }
    755:     } else {
    756:       PetscObjectReference((PetscObject)pcbddc->coarse_phi_B);
    757:       pcbddc->coarse_psi_B = pcbddc->coarse_phi_B;
    758:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    759:         PetscObjectReference((PetscObject)pcbddc->coarse_phi_D);
    760:         pcbddc->coarse_psi_D = pcbddc->coarse_phi_D;
    761:       }
    762:     }
    763:   }
    764:   /* We are now ready to evaluate coarse basis functions and subdomain contribution to coarse problem */
    765:   /* vertices */
    766:   if (n_vertices) {

    768:     MatConvert(A_VV,impMatType,MAT_INPLACE_MATRIX,&A_VV);

    770:     if (n_R) {
    771:       Mat          A_RRmA_RV,S_VVt; /* S_VVt with LDA=N */
    772:       PetscBLASInt B_N,B_one = 1;
    773:       PetscScalar  *x,*y;
    774:       PetscBool    isseqaij;

    776:       MatScale(A_RV,m_one);
    777:       MatConvert(A_RV,impMatType,MAT_INPLACE_MATRIX,&A_RV);
    778:       MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&A_RRmA_RV);
    779:       if (F) { /* TODO could be optimized for symmetric problems */
    780:         MatMatSolve(F,A_RV,A_RRmA_RV);
    781:       } else {
    782:         MatDenseGetArray(A_RV,&y);
    783:         for (i=0;i<n_vertices;i++) {
    784:           VecPlaceArray(pcbddc->vec1_R,y+i*n_R);
    785:           VecPlaceArray(pcbddc->vec2_R,work+i*n_R);
    786:           KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
    787:           VecResetArray(pcbddc->vec1_R);
    788:           VecResetArray(pcbddc->vec2_R);
    789:         }
    790:         MatDenseRestoreArray(A_RV,&y);
    791:       }
    792:       MatDestroy(&A_RV);
    793:       /* S_VV and S_CV are the subdomain contribution to coarse matrix. WARNING -> column major ordering */
    794:       if (n_constraints) {
    795:         Mat B;

    797:         PetscMemzero(work+n_R*n_vertices,n_B*n_vertices*sizeof(PetscScalar));
    798:         for (i=0;i<n_vertices;i++) {
    799:           VecPlaceArray(pcbddc->vec1_R,work+i*n_R);
    800:           VecPlaceArray(pcis->vec1_B,work+n_R*n_vertices+i*n_B);
    801:           VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    802:           VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    803:           VecResetArray(pcis->vec1_B);
    804:           VecResetArray(pcbddc->vec1_R);
    805:         }
    806:         MatCreateSeqDense(PETSC_COMM_SELF,n_B,n_vertices,work+n_R*n_vertices,&B);
    807:         MatMatMult(pcbddc->local_auxmat1,B,MAT_REUSE_MATRIX,PETSC_DEFAULT,&S_CV);
    808:         MatDestroy(&B);
    809:         MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work+n_R*n_vertices,&B);
    810:         MatMatMult(local_auxmat2_R,S_CV,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B);
    811:         MatScale(S_CV,m_one);
    812:         PetscBLASIntCast(n_R*n_vertices,&B_N);
    813:         PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,work+n_R*n_vertices,&B_one,work,&B_one));
    814:         MatDestroy(&B);
    815:       }
    816:       PetscObjectTypeCompare((PetscObject)A_VR,MATSEQAIJ,&isseqaij);
    817:       if (!isseqaij) { /* MatMatMult with SEQ(S)BAIJ below will raise an error */
    818:         MatConvert(A_VR,MATSEQAIJ,MAT_INPLACE_MATRIX,&A_VR);
    819:       }
    820:       MatMatMult(A_VR,A_RRmA_RV,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VVt);
    821:       MatDestroy(&A_RRmA_RV);
    822:       PetscBLASIntCast(n_vertices*n_vertices,&B_N);
    823:       MatDenseGetArray(A_VV,&x);
    824:       MatDenseGetArray(S_VVt,&y);
    825:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&one,x,&B_one,y,&B_one));
    826:       MatDenseRestoreArray(A_VV,&x);
    827:       MatDenseRestoreArray(S_VVt,&y);
    828:       MatCopy(S_VVt,S_VV,SAME_NONZERO_PATTERN);
    829:       MatDestroy(&S_VVt);
    830:     } else {
    831:       MatCopy(A_VV,S_VV,SAME_NONZERO_PATTERN);
    832:     }
    833:     MatDestroy(&A_VV);
    834:     /* coarse basis functions */
    835:     for (i=0;i<n_vertices;i++) {
    836:       PetscScalar *y;

    838:       VecPlaceArray(pcbddc->vec1_R,work+n_R*i);
    839:       MatDenseGetArray(pcbddc->coarse_phi_B,&y);
    840:       VecPlaceArray(pcis->vec1_B,y+n_B*i);
    841:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    842:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    843:       y[n_B*i+idx_V_B[i]] = 1.0;
    844:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);
    845:       VecResetArray(pcis->vec1_B);

    847:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    848:         MatDenseGetArray(pcbddc->coarse_phi_D,&y);
    849:         VecPlaceArray(pcis->vec1_D,y+n_D*i);
    850:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
    851:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
    852:         VecResetArray(pcis->vec1_D);
    853:         MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);
    854:       }
    855:       VecResetArray(pcbddc->vec1_R);
    856:     }
    857:     /* if n_R == 0 the object is not destroyed */
    858:     MatDestroy(&A_RV);
    859:   }

    861:   if (n_constraints) {
    862:     Mat B;

    864:     MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work,&B);
    865:     MatScale(S_CC,m_one);
    866:     MatMatMult(local_auxmat2_R,S_CC,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B);
    867:     MatScale(S_CC,m_one);
    868:     if (n_vertices) {
    869:       if (isCHOL) { /* if we can solve the interior problem with cholesky, we should also be fine with transposing here */
    870:         MatTranspose(S_CV,MAT_REUSE_MATRIX,&S_VC);
    871:       } else {
    872:         Mat S_VCt;

    874:         MatMatMult(A_VR,B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&S_VCt);
    875:         MatCopy(S_VCt,S_VC,SAME_NONZERO_PATTERN);
    876:         MatDestroy(&S_VCt);
    877:       }
    878:     }
    879:     MatDestroy(&B);
    880:     /* coarse basis functions */
    881:     for (i=0;i<n_constraints;i++) {
    882:       PetscScalar *y;

    884:       VecPlaceArray(pcbddc->vec1_R,work+n_R*i);
    885:       MatDenseGetArray(pcbddc->coarse_phi_B,&y);
    886:       VecPlaceArray(pcis->vec1_B,y+n_B*(i+n_vertices));
    887:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    888:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    889:       MatDenseRestoreArray(pcbddc->coarse_phi_B,&y);
    890:       VecResetArray(pcis->vec1_B);
    891:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    892:         MatDenseGetArray(pcbddc->coarse_phi_D,&y);
    893:         VecPlaceArray(pcis->vec1_D,y+n_D*(i+n_vertices));
    894:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
    895:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
    896:         VecResetArray(pcis->vec1_D);
    897:         MatDenseRestoreArray(pcbddc->coarse_phi_D,&y);
    898:       }
    899:       VecResetArray(pcbddc->vec1_R);
    900:     }
    901:   }
    902:   if (n_constraints) {
    903:     MatDestroy(&local_auxmat2_R);
    904:   }

    906:   /* compute other basis functions for non-symmetric problems */
    907:   if (!pcbddc->symmetric_primal) {

    909:     if (n_constraints) {
    910:       Mat S_CCT,B_C;

    912:       /* this is a lazy thing */
    913:       MatConvert(C_CR,impMatType,MAT_INPLACE_MATRIX,&C_CR);
    914:       MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_constraints,work+n_vertices*n_R,&B_C);
    915:       MatTranspose(S_CC,MAT_INITIAL_MATRIX,&S_CCT);
    916:       MatTransposeMatMult(C_CR,S_CCT,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B_C);
    917:       MatDestroy(&S_CCT);
    918:       if (n_vertices) {
    919:         Mat B_V,S_VCT;

    921:         MatCreateSeqDense(PETSC_COMM_SELF,n_R,n_vertices,work,&B_V);
    922:         MatTranspose(S_VC,MAT_INITIAL_MATRIX,&S_VCT);
    923:         MatTransposeMatMult(C_CR,S_VCT,MAT_REUSE_MATRIX,PETSC_DEFAULT,&B_V);
    924:         MatDestroy(&B_V);
    925:         MatDestroy(&S_VCT);
    926:       }
    927:       MatDestroy(&B_C);
    928:     } else { /* if there are no constraints, reset work */
    929:       PetscMemzero(work,n_R*pcbddc->local_primal_size*sizeof(PetscScalar));
    930:     }
    931:     if (n_vertices && n_R) {
    932:       Mat          A_VRT;
    933:       PetscScalar  *marray;
    934:       PetscBLASInt B_N,B_one = 1;

    936:       MatTranspose(A_VR,MAT_INITIAL_MATRIX,&A_VRT);
    937:       MatConvert(A_VRT,impMatType,MAT_INPLACE_MATRIX,&A_VRT);
    938:       MatDenseGetArray(A_VRT,&marray);
    939:       PetscBLASIntCast(n_vertices*n_R,&B_N);
    940:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&B_N,&m_one,marray,&B_one,work,&B_one));
    941:       MatDenseRestoreArray(A_VRT,&marray);
    942:       MatDestroy(&A_VRT);
    943:     }

    945:     if (F) { /* currently there's no support for MatTransposeMatSolve(F,B,X) */
    946:       for (i=0;i<pcbddc->local_primal_size;i++) {
    947:         VecPlaceArray(pcbddc->vec1_R,work+i*n_R);
    948:         VecPlaceArray(pcbddc->vec2_R,work+(i+pcbddc->local_primal_size)*n_R);
    949:         MatSolveTranspose(F,pcbddc->vec1_R,pcbddc->vec2_R);
    950:         VecResetArray(pcbddc->vec1_R);
    951:         VecResetArray(pcbddc->vec2_R);
    952:       }
    953:     } else {
    954:       for (i=0;i<pcbddc->local_primal_size;i++) {
    955:         VecPlaceArray(pcbddc->vec1_R,work+i*n_R);
    956:         VecPlaceArray(pcbddc->vec2_R,work+(i+pcbddc->local_primal_size)*n_R);
    957:         KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec2_R);
    958:         VecResetArray(pcbddc->vec1_R);
    959:         VecResetArray(pcbddc->vec2_R);
    960:       }
    961:     }
    962:     /* coarse basis functions */
    963:     for (i=0;i<pcbddc->local_primal_size;i++) {
    964:       PetscScalar *y;

    966:       VecPlaceArray(pcbddc->vec1_R,work+n_R*(i+pcbddc->local_primal_size));
    967:       MatDenseGetArray(pcbddc->coarse_psi_B,&y);
    968:       VecPlaceArray(pcis->vec1_B,y+n_B*i);
    969:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    970:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    971:       if (i<n_vertices) {
    972:         y[n_B*i+idx_V_B[i]] = 1.0;
    973:       }
    974:       MatDenseRestoreArray(pcbddc->coarse_psi_B,&y);
    975:       VecResetArray(pcis->vec1_B);

    977:       if (pcbddc->switch_static || pcbddc->dbg_flag) {
    978:         MatDenseGetArray(pcbddc->coarse_psi_D,&y);
    979:         VecPlaceArray(pcis->vec1_D,y+n_D*i);
    980:         VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
    981:         VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
    982:         VecResetArray(pcis->vec1_D);
    983:         MatDenseRestoreArray(pcbddc->coarse_psi_D,&y);
    984:       }
    985:       VecResetArray(pcbddc->vec1_R);
    986:     }
    987:   }
    988:   /* free memory */
    989:   PetscFree(idx_V_B);
    990:   MatDestroy(&S_VV);
    991:   MatDestroy(&S_CV);
    992:   MatDestroy(&S_VC);
    993:   MatDestroy(&S_CC);
    994:   PetscFree(work);
    995:   if (n_vertices) {
    996:     MatDestroy(&A_VR);
    997:   }
    998:   if (n_constraints) {
    999:     MatDestroy(&C_CR);
    1000:   }
    1001:   /* Checking coarse_sub_mat and coarse basis functios */
    1002:   /* Symmetric case     : It should be \Phi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
    1003:   /* Non-symmetric case : It should be \Psi^{(j)^T} A^{(j)} \Phi^{(j)}=coarse_sub_mat */
    1004:   if (pcbddc->dbg_flag) {
    1005:     Mat         coarse_sub_mat;
    1006:     Mat         AUXMAT,TM1,TM2,TM3,TM4;
    1007:     Mat         coarse_phi_D,coarse_phi_B;
    1008:     Mat         coarse_psi_D,coarse_psi_B;
    1009:     Mat         A_II,A_BB,A_IB,A_BI;
    1010:     Mat         C_B,CPHI;
    1011:     IS          is_dummy;
    1012:     Vec         mones;
    1013:     MatType     checkmattype=MATSEQAIJ;
    1014:     PetscReal   real_value;

    1016:     MatConvert(pcis->A_II,checkmattype,MAT_INITIAL_MATRIX,&A_II);
    1017:     MatConvert(pcis->A_IB,checkmattype,MAT_INITIAL_MATRIX,&A_IB);
    1018:     MatConvert(pcis->A_BI,checkmattype,MAT_INITIAL_MATRIX,&A_BI);
    1019:     MatConvert(pcis->A_BB,checkmattype,MAT_INITIAL_MATRIX,&A_BB);
    1020:     MatConvert(pcbddc->coarse_phi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_D);
    1021:     MatConvert(pcbddc->coarse_phi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_phi_B);
    1022:     if (unsymmetric_check) {
    1023:       MatConvert(pcbddc->coarse_psi_D,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_D);
    1024:       MatConvert(pcbddc->coarse_psi_B,checkmattype,MAT_INITIAL_MATRIX,&coarse_psi_B);
    1025:     }
    1026:     MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,coarse_submat_vals,&coarse_sub_mat);

    1028:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    1029:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse sub mat computation (symmetric %d)\n",pcbddc->symmetric_primal);
    1030:     PetscViewerFlush(pcbddc->dbg_viewer);
    1031:     if (unsymmetric_check) {
    1032:       MatMatMult(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    1033:       MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM1);
    1034:       MatDestroy(&AUXMAT);
    1035:       MatMatMult(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    1036:       MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM2);
    1037:       MatDestroy(&AUXMAT);
    1038:       MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    1039:       MatTransposeMatMult(coarse_psi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);
    1040:       MatDestroy(&AUXMAT);
    1041:       MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    1042:       MatTransposeMatMult(coarse_psi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);
    1043:       MatDestroy(&AUXMAT);
    1044:     } else {
    1045:       MatPtAP(A_II,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&TM1);
    1046:       MatPtAP(A_BB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&TM2);
    1047:       MatMatMult(A_IB,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    1048:       MatTransposeMatMult(coarse_phi_D,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM3);
    1049:       MatDestroy(&AUXMAT);
    1050:       MatMatMult(A_BI,coarse_phi_D,MAT_INITIAL_MATRIX,1.0,&AUXMAT);
    1051:       MatTransposeMatMult(coarse_phi_B,AUXMAT,MAT_INITIAL_MATRIX,1.0,&TM4);
    1052:       MatDestroy(&AUXMAT);
    1053:     }
    1054:     MatAXPY(TM1,one,TM2,DIFFERENT_NONZERO_PATTERN);
    1055:     MatAXPY(TM1,one,TM3,DIFFERENT_NONZERO_PATTERN);
    1056:     MatAXPY(TM1,one,TM4,DIFFERENT_NONZERO_PATTERN);
    1057:     MatConvert(TM1,MATSEQDENSE,MAT_INPLACE_MATRIX,&TM1);
    1058:     MatAXPY(TM1,m_one,coarse_sub_mat,DIFFERENT_NONZERO_PATTERN);
    1059:     MatNorm(TM1,NORM_FROBENIUS,&real_value);
    1060:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    1061:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d          matrix error % 1.14e\n",PetscGlobalRank,real_value);

    1063:     /* check constraints */
    1064:     ISCreateStride(PETSC_COMM_SELF,pcbddc->local_primal_size,0,1,&is_dummy);
    1065:     MatGetSubMatrix(pcbddc->ConstraintMatrix,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&C_B);
    1066:     MatMatMult(C_B,coarse_phi_B,MAT_INITIAL_MATRIX,1.0,&CPHI);
    1067:     MatCreateVecs(CPHI,&mones,NULL);
    1068:     VecSet(mones,-1.0);
    1069:     MatDiagonalSet(CPHI,mones,ADD_VALUES);
    1070:     MatNorm(CPHI,NORM_FROBENIUS,&real_value);
    1071:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d phi constraints error % 1.14e\n",PetscGlobalRank,real_value);
    1072:     if (unsymmetric_check) {
    1073:       MatMatMult(C_B,coarse_psi_B,MAT_REUSE_MATRIX,1.0,&CPHI);
    1074:       VecSet(mones,-1.0);
    1075:       MatDiagonalSet(CPHI,mones,ADD_VALUES);
    1076:       MatNorm(CPHI,NORM_FROBENIUS,&real_value);
    1077:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d psi constraints error % 1.14e\n",PetscGlobalRank,real_value);
    1078:     }
    1079:     MatDestroy(&C_B);
    1080:     MatDestroy(&CPHI);
    1081:     ISDestroy(&is_dummy);
    1082:     VecDestroy(&mones);

    1084:     PetscViewerFlush(pcbddc->dbg_viewer);
    1085:     MatDestroy(&A_II);
    1086:     MatDestroy(&A_BB);
    1087:     MatDestroy(&A_IB);
    1088:     MatDestroy(&A_BI);
    1089:     MatDestroy(&TM1);
    1090:     MatDestroy(&TM2);
    1091:     MatDestroy(&TM3);
    1092:     MatDestroy(&TM4);
    1093:     MatDestroy(&coarse_phi_D);
    1094:     MatDestroy(&coarse_phi_B);
    1095:     if (unsymmetric_check) {
    1096:       MatDestroy(&coarse_psi_D);
    1097:       MatDestroy(&coarse_psi_B);
    1098:     }
    1099:     MatDestroy(&coarse_sub_mat);
    1100:   }
    1101:   /* get back data */
    1102:   *coarse_submat_vals_n = coarse_submat_vals;
    1103:   return(0);
    1104: }

    1108: PetscErrorCode MatGetSubMatrixUnsorted(Mat A, IS isrow, IS iscol, Mat* B)
    1109: {
    1110:   Mat            *work_mat;
    1111:   IS             isrow_s,iscol_s;
    1112:   PetscBool      rsorted,csorted;
    1113:   PetscInt       rsize,*idxs_perm_r=NULL,csize,*idxs_perm_c=NULL;

    1117:   ISSorted(isrow,&rsorted);
    1118:   ISSorted(iscol,&csorted);
    1119:   ISGetLocalSize(isrow,&rsize);
    1120:   ISGetLocalSize(iscol,&csize);

    1122:   if (!rsorted) {
    1123:     const PetscInt *idxs;
    1124:     PetscInt *idxs_sorted,i;

    1126:     PetscMalloc1(rsize,&idxs_perm_r);
    1127:     PetscMalloc1(rsize,&idxs_sorted);
    1128:     for (i=0;i<rsize;i++) {
    1129:       idxs_perm_r[i] = i;
    1130:     }
    1131:     ISGetIndices(isrow,&idxs);
    1132:     PetscSortIntWithPermutation(rsize,idxs,idxs_perm_r);
    1133:     for (i=0;i<rsize;i++) {
    1134:       idxs_sorted[i] = idxs[idxs_perm_r[i]];
    1135:     }
    1136:     ISRestoreIndices(isrow,&idxs);
    1137:     ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_sorted,PETSC_OWN_POINTER,&isrow_s);
    1138:   } else {
    1139:     PetscObjectReference((PetscObject)isrow);
    1140:     isrow_s = isrow;
    1141:   }

    1143:   if (!csorted) {
    1144:     if (isrow == iscol) {
    1145:       PetscObjectReference((PetscObject)isrow_s);
    1146:       iscol_s = isrow_s;
    1147:     } else {
    1148:       const PetscInt *idxs;
    1149:       PetscInt       *idxs_sorted,i;

    1151:       PetscMalloc1(csize,&idxs_perm_c);
    1152:       PetscMalloc1(csize,&idxs_sorted);
    1153:       for (i=0;i<csize;i++) {
    1154:         idxs_perm_c[i] = i;
    1155:       }
    1156:       ISGetIndices(iscol,&idxs);
    1157:       PetscSortIntWithPermutation(csize,idxs,idxs_perm_c);
    1158:       for (i=0;i<csize;i++) {
    1159:         idxs_sorted[i] = idxs[idxs_perm_c[i]];
    1160:       }
    1161:       ISRestoreIndices(iscol,&idxs);
    1162:       ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_sorted,PETSC_OWN_POINTER,&iscol_s);
    1163:     }
    1164:   } else {
    1165:     PetscObjectReference((PetscObject)iscol);
    1166:     iscol_s = iscol;
    1167:   }

    1169:   MatGetSubMatrices(A,1,&isrow_s,&iscol_s,MAT_INITIAL_MATRIX,&work_mat);

    1171:   if (!rsorted || !csorted) {
    1172:     Mat      new_mat;
    1173:     IS       is_perm_r,is_perm_c;

    1175:     if (!rsorted) {
    1176:       PetscInt *idxs_r,i;
    1177:       PetscMalloc1(rsize,&idxs_r);
    1178:       for (i=0;i<rsize;i++) {
    1179:         idxs_r[idxs_perm_r[i]] = i;
    1180:       }
    1181:       PetscFree(idxs_perm_r);
    1182:       ISCreateGeneral(PETSC_COMM_SELF,rsize,idxs_r,PETSC_OWN_POINTER,&is_perm_r);
    1183:     } else {
    1184:       ISCreateStride(PETSC_COMM_SELF,rsize,0,1,&is_perm_r);
    1185:     }
    1186:     ISSetPermutation(is_perm_r);

    1188:     if (!csorted) {
    1189:       if (isrow_s == iscol_s) {
    1190:         PetscObjectReference((PetscObject)is_perm_r);
    1191:         is_perm_c = is_perm_r;
    1192:       } else {
    1193:         PetscInt *idxs_c,i;
    1194:         PetscMalloc1(csize,&idxs_c);
    1195:         for (i=0;i<csize;i++) {
    1196:           idxs_c[idxs_perm_c[i]] = i;
    1197:         }
    1198:         PetscFree(idxs_perm_c);
    1199:         ISCreateGeneral(PETSC_COMM_SELF,csize,idxs_c,PETSC_OWN_POINTER,&is_perm_c);
    1200:       }
    1201:     } else {
    1202:       ISCreateStride(PETSC_COMM_SELF,csize,0,1,&is_perm_c);
    1203:     }
    1204:     ISSetPermutation(is_perm_c);

    1206:     MatPermute(work_mat[0],is_perm_r,is_perm_c,&new_mat);
    1207:     MatDestroy(&work_mat[0]);
    1208:     work_mat[0] = new_mat;
    1209:     ISDestroy(&is_perm_r);
    1210:     ISDestroy(&is_perm_c);
    1211:   }

    1213:   PetscObjectReference((PetscObject)work_mat[0]);
    1214:   *B = work_mat[0];
    1215:   MatDestroyMatrices(1,&work_mat);
    1216:   ISDestroy(&isrow_s);
    1217:   ISDestroy(&iscol_s);
    1218:   return(0);
    1219: }

    1223: PetscErrorCode PCBDDCComputeLocalMatrix(PC pc, Mat ChangeOfBasisMatrix)
    1224: {
    1225:   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
    1226:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
    1227:   Mat            new_mat;
    1228:   IS             is_local,is_global;
    1229:   PetscInt       local_size;
    1230:   PetscBool      isseqaij;

    1234:   MatDestroy(&pcbddc->local_mat);
    1235:   MatGetSize(matis->A,&local_size,NULL);
    1236:   ISCreateStride(PetscObjectComm((PetscObject)matis->A),local_size,0,1,&is_local);
    1237:   ISLocalToGlobalMappingApplyIS(pc->pmat->rmap->mapping,is_local,&is_global);
    1238:   ISDestroy(&is_local);
    1239:   MatGetSubMatrixUnsorted(ChangeOfBasisMatrix,is_global,is_global,&new_mat);
    1240:   ISDestroy(&is_global);

    1242:   /* check */
    1243:   if (pcbddc->dbg_flag) {
    1244:     Vec       x,x_change;
    1245:     PetscReal error;

    1247:     MatCreateVecs(ChangeOfBasisMatrix,&x,&x_change);
    1248:     VecSetRandom(x,NULL);
    1249:     MatMult(ChangeOfBasisMatrix,x,x_change);
    1250:     VecScatterBegin(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);
    1251:     VecScatterEnd(matis->cctx,x,matis->x,INSERT_VALUES,SCATTER_FORWARD);
    1252:     MatMult(new_mat,matis->x,matis->y);
    1253:     VecScatterBegin(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);
    1254:     VecScatterEnd(matis->rctx,matis->y,x,INSERT_VALUES,SCATTER_REVERSE);
    1255:     VecAXPY(x,-1.0,x_change);
    1256:     VecNorm(x,NORM_INFINITY,&error);
    1257:     PetscViewerFlush(pcbddc->dbg_viewer);
    1258:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change on N: %1.6e\n",error);
    1259:     VecDestroy(&x);
    1260:     VecDestroy(&x_change);
    1261:   }

    1263:   /* TODO: HOW TO WORK WITH BAIJ and SBAIJ and SEQDENSE? */
    1264:   PetscObjectTypeCompare((PetscObject)matis->A,MATSEQAIJ,&isseqaij);
    1265:   if (isseqaij) {
    1266:     MatPtAP(matis->A,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);
    1267:   } else {
    1268:     Mat work_mat;
    1269:     MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&work_mat);
    1270:     MatPtAP(work_mat,new_mat,MAT_INITIAL_MATRIX,2.0,&pcbddc->local_mat);
    1271:     MatDestroy(&work_mat);
    1272:   }
    1273:   if (matis->A->symmetric_set) {
    1274:     MatSetOption(pcbddc->local_mat,MAT_SYMMETRIC,matis->A->symmetric);
    1275: #if !defined(PETSC_USE_COMPLEX)
    1276:     MatSetOption(pcbddc->local_mat,MAT_HERMITIAN,matis->A->symmetric);
    1277: #endif
    1278:   }
    1279:   MatDestroy(&new_mat);
    1280:   return(0);
    1281: }

    1285: PetscErrorCode PCBDDCSetUpLocalScatters(PC pc)
    1286: {
    1287:   PC_IS*          pcis = (PC_IS*)(pc->data);
    1288:   PC_BDDC*        pcbddc = (PC_BDDC*)pc->data;
    1289:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    1290:   PetscInt        *idx_R_local=NULL;
    1291:   PetscInt        n_vertices,i,j,n_R,n_D,n_B;
    1292:   PetscInt        vbs,bs;
    1293:   PetscBT         bitmask=NULL;
    1294:   PetscErrorCode  ierr;

    1297:   /*
    1298:     No need to setup local scatters if
    1299:       - primal space is unchanged
    1300:         AND
    1301:       - we actually have locally some primal dofs (could not be true in multilevel or for isolated subdomains)
    1302:         AND
    1303:       - we are not in debugging mode (this is needed since there are Synchronized prints at the end of the subroutine
    1304:   */
    1305:   if (!pcbddc->new_primal_space_local && pcbddc->local_primal_size && !pcbddc->dbg_flag) {
    1306:     return(0);
    1307:   }
    1308:   /* destroy old objects */
    1309:   ISDestroy(&pcbddc->is_R_local);
    1310:   VecScatterDestroy(&pcbddc->R_to_B);
    1311:   VecScatterDestroy(&pcbddc->R_to_D);
    1312:   /* Set Non-overlapping dimensions */
    1313:   n_B = pcis->n_B;
    1314:   n_D = pcis->n - n_B;
    1315:   n_vertices = pcbddc->n_vertices;

    1317:   /* Dohrmann's notation: dofs splitted in R (Remaining: all dofs but the vertices) and V (Vertices) */

    1319:   /* create auxiliary bitmask and allocate workspace */
    1320:   if (!sub_schurs->reuse_mumps) {
    1321:     PetscMalloc1(pcis->n-n_vertices,&idx_R_local);
    1322:     PetscBTCreate(pcis->n,&bitmask);
    1323:     for (i=0;i<n_vertices;i++) {
    1324:       PetscBTSet(bitmask,pcbddc->local_primal_ref_node[i]);
    1325:     }

    1327:     for (i=0, n_R=0; i<pcis->n; i++) {
    1328:       if (!PetscBTLookup(bitmask,i)) {
    1329:         idx_R_local[n_R++] = i;
    1330:       }
    1331:     }
    1332:   } else { /* A different ordering (already computed) is present if we are reusing MUMPS Schur solver */
    1333:     PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;

    1335:     ISGetIndices(reuse_mumps->is_R,(const PetscInt**)&idx_R_local);
    1336:     ISGetLocalSize(reuse_mumps->is_R,&n_R);
    1337:   }

    1339:   /* Block code */
    1340:   vbs = 1;
    1341:   MatGetBlockSize(pcbddc->local_mat,&bs);
    1342:   if (bs>1 && !(n_vertices%bs)) {
    1343:     PetscBool is_blocked = PETSC_TRUE;
    1344:     PetscInt  *vary;
    1345:     if (!sub_schurs->reuse_mumps) {
    1346:       PetscMalloc1(pcis->n/bs,&vary);
    1347:       PetscMemzero(vary,pcis->n/bs*sizeof(PetscInt));
    1348:       /* Verify that the vertex indices correspond to each element in a block (code taken from sbaij2.c) */
    1349:       /* 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 */
    1350:       for (i=0; i<n_vertices; i++) vary[pcbddc->local_primal_ref_node[i]/bs]++;
    1351:       for (i=0; i<pcis->n/bs; i++) {
    1352:         if (vary[i]!=0 && vary[i]!=bs) {
    1353:           is_blocked = PETSC_FALSE;
    1354:           break;
    1355:         }
    1356:       }
    1357:       PetscFree(vary);
    1358:     } else {
    1359:       /* Verify directly the R set */
    1360:       for (i=0; i<n_R/bs; i++) {
    1361:         PetscInt j,node=idx_R_local[bs*i];
    1362:         for (j=1; j<bs; j++) {
    1363:           if (node != idx_R_local[bs*i+j]-j) {
    1364:             is_blocked = PETSC_FALSE;
    1365:             break;
    1366:           }
    1367:         }
    1368:       }
    1369:     }
    1370:     if (is_blocked) { /* build compressed IS for R nodes (complement of vertices) */
    1371:       vbs = bs;
    1372:       for (i=0;i<n_R/vbs;i++) {
    1373:         idx_R_local[i] = idx_R_local[vbs*i]/vbs;
    1374:       }
    1375:     }
    1376:   }
    1377:   ISCreateBlock(PETSC_COMM_SELF,vbs,n_R/vbs,idx_R_local,PETSC_COPY_VALUES,&pcbddc->is_R_local);
    1378:   if (sub_schurs->reuse_mumps) {
    1379:     PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;

    1381:     ISRestoreIndices(reuse_mumps->is_R,(const PetscInt**)&idx_R_local);
    1382:     ISDestroy(&reuse_mumps->is_R);
    1383:     PetscObjectReference((PetscObject)pcbddc->is_R_local);
    1384:     reuse_mumps->is_R = pcbddc->is_R_local;
    1385:   } else {
    1386:     PetscFree(idx_R_local);
    1387:   }

    1389:   /* print some info if requested */
    1390:   if (pcbddc->dbg_flag) {
    1391:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    1392:     PetscViewerFlush(pcbddc->dbg_viewer);
    1393:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    1394:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d local dimensions\n",PetscGlobalRank);
    1395:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"local_size = %d, dirichlet_size = %d, boundary_size = %d\n",pcis->n,n_D,n_B);
    1396:     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->local_primal_size);
    1397:     PetscViewerFlush(pcbddc->dbg_viewer);
    1398:   }

    1400:   /* VecScatters pcbddc->R_to_B and (optionally) pcbddc->R_to_D */
    1401:   if (!sub_schurs->reuse_mumps) {
    1402:     IS       is_aux1,is_aux2;
    1403:     PetscInt *aux_array1,*aux_array2,*is_indices,*idx_R_local;

    1405:     ISGetIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);
    1406:     PetscMalloc1(pcis->n_B-n_vertices,&aux_array1);
    1407:     PetscMalloc1(pcis->n_B-n_vertices,&aux_array2);
    1408:     ISGetIndices(pcis->is_I_local,(const PetscInt**)&is_indices);
    1409:     for (i=0; i<n_D; i++) {
    1410:       PetscBTSet(bitmask,is_indices[i]);
    1411:     }
    1412:     ISRestoreIndices(pcis->is_I_local,(const PetscInt**)&is_indices);
    1413:     for (i=0, j=0; i<n_R; i++) {
    1414:       if (!PetscBTLookup(bitmask,idx_R_local[i])) {
    1415:         aux_array1[j++] = i;
    1416:       }
    1417:     }
    1418:     ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);
    1419:     ISGetIndices(pcis->is_B_local,(const PetscInt**)&is_indices);
    1420:     for (i=0, j=0; i<n_B; i++) {
    1421:       if (!PetscBTLookup(bitmask,is_indices[i])) {
    1422:         aux_array2[j++] = i;
    1423:       }
    1424:     }
    1425:     ISRestoreIndices(pcis->is_B_local,(const PetscInt**)&is_indices);
    1426:     ISCreateGeneral(PETSC_COMM_SELF,j,aux_array2,PETSC_OWN_POINTER,&is_aux2);
    1427:     VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_B,is_aux2,&pcbddc->R_to_B);
    1428:     ISDestroy(&is_aux1);
    1429:     ISDestroy(&is_aux2);

    1431:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
    1432:       PetscMalloc1(n_D,&aux_array1);
    1433:       for (i=0, j=0; i<n_R; i++) {
    1434:         if (PetscBTLookup(bitmask,idx_R_local[i])) {
    1435:           aux_array1[j++] = i;
    1436:         }
    1437:       }
    1438:       ISCreateGeneral(PETSC_COMM_SELF,j,aux_array1,PETSC_OWN_POINTER,&is_aux1);
    1439:       VecScatterCreate(pcbddc->vec1_R,is_aux1,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);
    1440:       ISDestroy(&is_aux1);
    1441:     }
    1442:     PetscBTDestroy(&bitmask);
    1443:     ISRestoreIndices(pcbddc->is_R_local,(const PetscInt**)&idx_R_local);
    1444:   } else {
    1445:     PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;
    1446:     IS               tis;
    1447:     PetscInt         schur_size;

    1449:     ISGetLocalSize(reuse_mumps->is_B,&schur_size);
    1450:     ISCreateStride(PETSC_COMM_SELF,schur_size,n_D,1,&tis);
    1451:     VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_B,reuse_mumps->is_B,&pcbddc->R_to_B);
    1452:     ISDestroy(&tis);
    1453:     if (pcbddc->switch_static || pcbddc->dbg_flag) {
    1454:       ISCreateStride(PETSC_COMM_SELF,n_D,0,1,&tis);
    1455:       VecScatterCreate(pcbddc->vec1_R,tis,pcis->vec1_D,(IS)0,&pcbddc->R_to_D);
    1456:       ISDestroy(&tis);
    1457:     }
    1458:   }
    1459:   return(0);
    1460: }

    1465: PetscErrorCode PCBDDCSetUpLocalSolvers(PC pc, PetscBool dirichlet, PetscBool neumann)
    1466: {
    1467:   PC_BDDC        *pcbddc = (PC_BDDC*)pc->data;
    1468:   PC_IS          *pcis = (PC_IS*)pc->data;
    1469:   PC             pc_temp;
    1470:   Mat            A_RR;
    1471:   MatReuse       reuse;
    1472:   PetscScalar    m_one = -1.0;
    1473:   PetscReal      value;
    1474:   PetscInt       n_D,n_R;
    1475:   PetscBool      use_exact,use_exact_reduced,issbaij;
    1477:   /* prefixes stuff */
    1478:   char           dir_prefix[256],neu_prefix[256],str_level[16];
    1479:   size_t         len;

    1483:   /* compute prefixes */
    1484:   PetscStrcpy(dir_prefix,"");
    1485:   PetscStrcpy(neu_prefix,"");
    1486:   if (!pcbddc->current_level) {
    1487:     PetscStrcpy(dir_prefix,((PetscObject)pc)->prefix);
    1488:     PetscStrcpy(neu_prefix,((PetscObject)pc)->prefix);
    1489:     PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");
    1490:     PetscStrcat(neu_prefix,"pc_bddc_neumann_");
    1491:   } else {
    1492:     PetscStrcpy(str_level,"");
    1493:     sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
    1494:     PetscStrlen(((PetscObject)pc)->prefix,&len);
    1495:     len -= 15; /* remove "pc_bddc_coarse_" */
    1496:     if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
    1497:     if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
    1498:     PetscStrncpy(dir_prefix,((PetscObject)pc)->prefix,len+1);
    1499:     PetscStrncpy(neu_prefix,((PetscObject)pc)->prefix,len+1);
    1500:     PetscStrcat(dir_prefix,"pc_bddc_dirichlet_");
    1501:     PetscStrcat(neu_prefix,"pc_bddc_neumann_");
    1502:     PetscStrcat(dir_prefix,str_level);
    1503:     PetscStrcat(neu_prefix,str_level);
    1504:   }

    1506:   /* DIRICHLET PROBLEM */
    1507:   if (dirichlet) {
    1508:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    1509:     if (pcbddc->local_mat->symmetric_set) {
    1510:       MatSetOption(pcis->A_II,MAT_SYMMETRIC,pcbddc->local_mat->symmetric_set);
    1511:     }
    1512:     /* Matrix for Dirichlet problem is pcis->A_II */
    1513:     n_D = pcis->n - pcis->n_B;
    1514:     if (!pcbddc->ksp_D) { /* create object if not yet build */
    1515:       KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_D);
    1516:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_D,(PetscObject)pc,1);
    1517:       /* default */
    1518:       KSPSetType(pcbddc->ksp_D,KSPPREONLY);
    1519:       KSPSetOptionsPrefix(pcbddc->ksp_D,dir_prefix);
    1520:       PetscObjectTypeCompare((PetscObject)pcis->A_II,MATSEQSBAIJ,&issbaij);
    1521:       KSPGetPC(pcbddc->ksp_D,&pc_temp);
    1522:       if (issbaij) {
    1523:         PCSetType(pc_temp,PCCHOLESKY);
    1524:       } else {
    1525:         PCSetType(pc_temp,PCLU);
    1526:       }
    1527:       /* Allow user's customization */
    1528:       KSPSetFromOptions(pcbddc->ksp_D);
    1529:       PCFactorSetReuseFill(pc_temp,PETSC_TRUE);
    1530:     }
    1531:     KSPSetOperators(pcbddc->ksp_D,pcis->A_II,pcis->A_II);
    1532:     if (sub_schurs->reuse_mumps) {
    1533:       PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;

    1535:       KSPSetPC(pcbddc->ksp_D,reuse_mumps->interior_solver);
    1536:     }
    1537:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
    1538:     if (!n_D) {
    1539:       KSPGetPC(pcbddc->ksp_D,&pc_temp);
    1540:       PCSetType(pc_temp,PCNONE);
    1541:     }
    1542:     /* Set Up KSP for Dirichlet problem of BDDC */
    1543:     KSPSetUp(pcbddc->ksp_D);
    1544:     /* set ksp_D into pcis data */
    1545:     KSPDestroy(&pcis->ksp_D);
    1546:     PetscObjectReference((PetscObject)pcbddc->ksp_D);
    1547:     pcis->ksp_D = pcbddc->ksp_D;
    1548:   }

    1550:   /* NEUMANN PROBLEM */
    1551:   A_RR = 0;
    1552:   if (neumann) {
    1553:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
    1554:     PetscInt        ibs,mbs;
    1555:     PetscBool       issbaij;
    1556:     Mat_IS*         matis = (Mat_IS*)pc->pmat->data;
    1557:     /* Matrix for Neumann problem is A_RR -> we need to create/reuse it at this point */
    1558:     ISGetSize(pcbddc->is_R_local,&n_R);
    1559:     if (pcbddc->ksp_R) { /* already created ksp */
    1560:       PetscInt nn_R;
    1561:       KSPGetOperators(pcbddc->ksp_R,NULL,&A_RR);
    1562:       PetscObjectReference((PetscObject)A_RR);
    1563:       MatGetSize(A_RR,&nn_R,NULL);
    1564:       if (nn_R != n_R) { /* old ksp is not reusable, so reset it */
    1565:         KSPReset(pcbddc->ksp_R);
    1566:         MatDestroy(&A_RR);
    1567:         reuse = MAT_INITIAL_MATRIX;
    1568:       } else { /* same sizes, but nonzero pattern depend on primal vertices so it can be changed */
    1569:         if (pcbddc->new_primal_space_local) { /* we are not sure the matrix will have the same nonzero pattern */
    1570:           MatDestroy(&A_RR);
    1571:           reuse = MAT_INITIAL_MATRIX;
    1572:         } else { /* safe to reuse the matrix */
    1573:           reuse = MAT_REUSE_MATRIX;
    1574:         }
    1575:       }
    1576:       /* last check */
    1577:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
    1578:         MatDestroy(&A_RR);
    1579:         reuse = MAT_INITIAL_MATRIX;
    1580:       }
    1581:     } else { /* first time, so we need to create the matrix */
    1582:       reuse = MAT_INITIAL_MATRIX;
    1583:     }
    1584:     /* extract A_RR */
    1585:     MatGetBlockSize(pcbddc->local_mat,&mbs);
    1586:     ISGetBlockSize(pcbddc->is_R_local,&ibs);
    1587:     PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQSBAIJ,&issbaij);
    1588:     if (ibs != mbs) { /* need to convert to SEQAIJ to extract any submatrix with is_R_local */
    1589:       if (matis->A == pcbddc->local_mat) {
    1590:         MatDestroy(&pcbddc->local_mat);
    1591:         MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
    1592:       } else {
    1593:         MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
    1594:       }
    1595:     } else if (issbaij) { /* need to convert to BAIJ to get offdiagonal blocks */
    1596:       if (matis->A == pcbddc->local_mat) {
    1597:         MatDestroy(&pcbddc->local_mat);
    1598:         MatConvert(matis->A,MATSEQBAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
    1599:       } else {
    1600:         MatConvert(pcbddc->local_mat,MATSEQBAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
    1601:       }
    1602:     }
    1603:     if (!sub_schurs->reuse_mumps) {
    1604:       MatGetSubMatrix(pcbddc->local_mat,pcbddc->is_R_local,pcbddc->is_R_local,reuse,&A_RR);
    1605:       if (pcbddc->local_mat->symmetric_set) {
    1606:         MatSetOption(A_RR,MAT_SYMMETRIC,pcbddc->local_mat->symmetric_set);
    1607:       }
    1608:     } else {
    1609:       PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;

    1611:       MatDestroy(&A_RR);
    1612:       PCGetOperators(reuse_mumps->correction_solver,&A_RR,NULL);
    1613:       PetscObjectReference((PetscObject)A_RR);
    1614:     }
    1615:     if (!pcbddc->ksp_R) { /* create object if not present */
    1616:       KSPCreate(PETSC_COMM_SELF,&pcbddc->ksp_R);
    1617:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->ksp_R,(PetscObject)pc,1);
    1618:       /* default */
    1619:       KSPSetType(pcbddc->ksp_R,KSPPREONLY);
    1620:       KSPSetOptionsPrefix(pcbddc->ksp_R,neu_prefix);
    1621:       KSPGetPC(pcbddc->ksp_R,&pc_temp);
    1622:       PetscObjectTypeCompare((PetscObject)A_RR,MATSEQSBAIJ,&issbaij);
    1623:       if (issbaij) {
    1624:         PCSetType(pc_temp,PCCHOLESKY);
    1625:       } else {
    1626:         PCSetType(pc_temp,PCLU);
    1627:       }
    1628:       /* Allow user's customization */
    1629:       KSPSetFromOptions(pcbddc->ksp_R);
    1630:       PCFactorSetReuseFill(pc_temp,PETSC_TRUE);
    1631:     }
    1632:     KSPSetOperators(pcbddc->ksp_R,A_RR,A_RR);
    1633:     /* umfpack interface has a bug when matrix dimension is zero. TODO solve from umfpack interface */
    1634:     if (!n_R) {
    1635:       KSPGetPC(pcbddc->ksp_R,&pc_temp);
    1636:       PCSetType(pc_temp,PCNONE);
    1637:     }
    1638:     /* Reuse MUMPS solver if it is present */
    1639:     if (sub_schurs->reuse_mumps) {
    1640:       PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;

    1642:       KSPSetPC(pcbddc->ksp_R,reuse_mumps->correction_solver);
    1643:     }
    1644:     /* Set Up KSP for Neumann problem of BDDC */
    1645:     KSPSetUp(pcbddc->ksp_R);
    1646:   }
    1647:   /* free Neumann problem's matrix */
    1648:   MatDestroy(&A_RR);

    1650:   /* check Dirichlet and Neumann solvers and adapt them if a nullspace correction is needed */
    1651:   if (pcbddc->NullSpace || pcbddc->dbg_flag) {
    1652:     if (pcbddc->dbg_flag) {
    1653:       PetscViewerFlush(pcbddc->dbg_viewer);
    1654:       PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    1655:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    1656:     }
    1657:     if (dirichlet) { /* Dirichlet */
    1658:       VecSetRandom(pcis->vec1_D,NULL);
    1659:       MatMult(pcis->A_II,pcis->vec1_D,pcis->vec2_D);
    1660:       KSPSolve(pcbddc->ksp_D,pcis->vec2_D,pcis->vec2_D);
    1661:       VecAXPY(pcis->vec1_D,m_one,pcis->vec2_D);
    1662:       VecNorm(pcis->vec1_D,NORM_INFINITY,&value);
    1663:       /* need to be adapted? */
    1664:       use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
    1665:       MPIU_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));
    1666:       PCBDDCSetUseExactDirichlet(pc,use_exact_reduced);
    1667:       /* print info */
    1668:       if (pcbddc->dbg_flag) {
    1669:         PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Dirichlet solve (%s) = % 1.14e \n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_D))->prefix,value);
    1670:         PetscViewerFlush(pcbddc->dbg_viewer);
    1671:       }
    1672:       if (pcbddc->NullSpace && !use_exact_reduced && !pcbddc->switch_static) {
    1673:         PCBDDCNullSpaceAssembleCorrection(pc,PETSC_TRUE,pcis->is_I_local);
    1674:       }
    1675:     }
    1676:     if (neumann) { /* Neumann */
    1677:       KSPGetOperators(pcbddc->ksp_R,&A_RR,NULL);
    1678:       VecSetRandom(pcbddc->vec1_R,NULL);
    1679:       MatMult(A_RR,pcbddc->vec1_R,pcbddc->vec2_R);
    1680:       KSPSolve(pcbddc->ksp_R,pcbddc->vec2_R,pcbddc->vec2_R);
    1681:       VecAXPY(pcbddc->vec1_R,m_one,pcbddc->vec2_R);
    1682:       VecNorm(pcbddc->vec1_R,NORM_INFINITY,&value);
    1683:       /* need to be adapted? */
    1684:       use_exact = (PetscAbsReal(value) > 1.e-4 ? PETSC_FALSE : PETSC_TRUE);
    1685:       MPIU_Allreduce(&use_exact,&use_exact_reduced,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)pc));
    1686:       /* print info */
    1687:       if (pcbddc->dbg_flag) {
    1688:         PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d infinity error for Neumann solve (%s) = % 1.14e\n",PetscGlobalRank,((PetscObject)(pcbddc->ksp_R))->prefix,value);
    1689:         PetscViewerFlush(pcbddc->dbg_viewer);
    1690:       }
    1691:       if (pcbddc->NullSpace && !use_exact_reduced) { /* is it the right logic? */
    1692:         PCBDDCNullSpaceAssembleCorrection(pc,PETSC_FALSE,pcbddc->is_R_local);
    1693:       }
    1694:     }
    1695:   }
    1696:   return(0);
    1697: }

    1701: static PetscErrorCode  PCBDDCSolveSubstructureCorrection(PC pc, Vec inout_B, Vec inout_D, PetscBool applytranspose)
    1702: {
    1703:   PetscErrorCode  ierr;
    1704:   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
    1705:   PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

    1708:   if (!sub_schurs->reuse_mumps) {
    1709:     VecSet(pcbddc->vec1_R,0.);
    1710:   }
    1711:   if (!pcbddc->switch_static) {
    1712:     if (applytranspose && pcbddc->local_auxmat1) {
    1713:       MatMultTranspose(pcbddc->local_auxmat2,inout_B,pcbddc->vec1_C);
    1714:       MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);
    1715:     }
    1716:     if (!sub_schurs->reuse_mumps) {
    1717:       VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    1718:       VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    1719:     } else {
    1720:       PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;

    1722:       VecScatterBegin(reuse_mumps->correction_scatter_B,inout_B,reuse_mumps->rhs_B,INSERT_VALUES,SCATTER_FORWARD);
    1723:       VecScatterEnd(reuse_mumps->correction_scatter_B,inout_B,reuse_mumps->rhs_B,INSERT_VALUES,SCATTER_FORWARD);
    1724:     }
    1725:   } else {
    1726:     VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    1727:     VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    1728:     VecScatterBegin(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    1729:     VecScatterEnd(pcbddc->R_to_D,inout_D,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    1730:     if (applytranspose && pcbddc->local_auxmat1) {
    1731:       MatMultTranspose(pcbddc->local_auxmat2,pcbddc->vec1_R,pcbddc->vec1_C);
    1732:       MatMultTransposeAdd(pcbddc->local_auxmat1,pcbddc->vec1_C,inout_B,inout_B);
    1733:       VecScatterBegin(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    1734:       VecScatterEnd(pcbddc->R_to_B,inout_B,pcbddc->vec1_R,INSERT_VALUES,SCATTER_REVERSE);
    1735:     }
    1736:   }
    1737:   if (!sub_schurs->reuse_mumps) {
    1738:     if (applytranspose) {
    1739:       KSPSolveTranspose(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);
    1740:     } else {
    1741:       KSPSolve(pcbddc->ksp_R,pcbddc->vec1_R,pcbddc->vec1_R);
    1742:     }
    1743:   } else {
    1744:     PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;

    1746:     if (applytranspose) {
    1747:       MatFactorSolveSchurComplementTranspose(reuse_mumps->F,reuse_mumps->rhs_B,reuse_mumps->sol_B);
    1748:     } else {
    1749:       MatFactorSolveSchurComplement(reuse_mumps->F,reuse_mumps->rhs_B,reuse_mumps->sol_B);
    1750:     }
    1751:   }
    1752:   VecSet(inout_B,0.);
    1753:   if (!pcbddc->switch_static) {
    1754:     if (!sub_schurs->reuse_mumps) {
    1755:       VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    1756:       VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    1757:     } else {
    1758:       PCBDDCReuseMumps reuse_mumps = sub_schurs->reuse_mumps;

    1760:       VecScatterBegin(reuse_mumps->correction_scatter_B,reuse_mumps->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);
    1761:       VecScatterEnd(reuse_mumps->correction_scatter_B,reuse_mumps->sol_B,inout_B,INSERT_VALUES,SCATTER_REVERSE);
    1762:     }
    1763:     if (!applytranspose && pcbddc->local_auxmat1) {
    1764:       MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);
    1765:       MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,inout_B,inout_B);
    1766:     }
    1767:   } else {
    1768:     VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    1769:     VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    1770:     VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
    1771:     VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
    1772:     if (!applytranspose && pcbddc->local_auxmat1) {
    1773:       MatMult(pcbddc->local_auxmat1,inout_B,pcbddc->vec1_C);
    1774:       MatMultAdd(pcbddc->local_auxmat2,pcbddc->vec1_C,pcbddc->vec1_R,pcbddc->vec1_R);
    1775:     }
    1776:     VecScatterBegin(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    1777:     VecScatterEnd(pcbddc->R_to_B,pcbddc->vec1_R,inout_B,INSERT_VALUES,SCATTER_FORWARD);
    1778:     VecScatterBegin(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
    1779:     VecScatterEnd(pcbddc->R_to_D,pcbddc->vec1_R,inout_D,INSERT_VALUES,SCATTER_FORWARD);
    1780:   }
    1781:   return(0);
    1782: }

    1784: /* parameter apply transpose determines if the interface preconditioner should be applied transposed or not */
    1787: PetscErrorCode  PCBDDCApplyInterfacePreconditioner(PC pc, PetscBool applytranspose)
    1788: {
    1790:   PC_BDDC*        pcbddc = (PC_BDDC*)(pc->data);
    1791:   PC_IS*            pcis = (PC_IS*)  (pc->data);
    1792:   const PetscScalar zero = 0.0;

    1795:   /* Application of PSI^T or PHI^T (depending on applytranspose, see comment above) */
    1796:   if (applytranspose) {
    1797:     MatMultTranspose(pcbddc->coarse_phi_B,pcis->vec1_B,pcbddc->vec1_P);
    1798:     if (pcbddc->switch_static) { MatMultTransposeAdd(pcbddc->coarse_phi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P); }
    1799:   } else {
    1800:     MatMultTranspose(pcbddc->coarse_psi_B,pcis->vec1_B,pcbddc->vec1_P);
    1801:     if (pcbddc->switch_static) { MatMultTransposeAdd(pcbddc->coarse_psi_D,pcis->vec1_D,pcbddc->vec1_P,pcbddc->vec1_P); }
    1802:   }
    1803:   /* start communications from local primal nodes to rhs of coarse solver */
    1804:   VecSet(pcbddc->coarse_vec,zero);
    1805:   PCBDDCScatterCoarseDataBegin(pc,ADD_VALUES,SCATTER_FORWARD);
    1806:   PCBDDCScatterCoarseDataEnd(pc,ADD_VALUES,SCATTER_FORWARD);

    1808:   /* Coarse solution -> rhs and sol updated inside PCBDDCScattarCoarseDataBegin/End */
    1809:   /* TODO remove null space when doing multilevel */
    1810:   if (pcbddc->coarse_ksp) {
    1811:     Vec rhs,sol;

    1813:     KSPGetRhs(pcbddc->coarse_ksp,&rhs);
    1814:     KSPGetSolution(pcbddc->coarse_ksp,&sol);
    1815:     if (applytranspose) {
    1816:       KSPSolveTranspose(pcbddc->coarse_ksp,rhs,sol);
    1817:     } else {
    1818:       KSPSolve(pcbddc->coarse_ksp,rhs,sol);
    1819:     }
    1820:   }

    1822:   /* Local solution on R nodes */
    1823:   if (pcis->n) { /* in/out pcbddc->vec1_B,pcbddc->vec1_D */
    1824:     PCBDDCSolveSubstructureCorrection(pc,pcis->vec1_B,pcis->vec1_D,applytranspose);
    1825:   }

    1827:   /* communications from coarse sol to local primal nodes */
    1828:   PCBDDCScatterCoarseDataBegin(pc,INSERT_VALUES,SCATTER_REVERSE);
    1829:   PCBDDCScatterCoarseDataEnd(pc,INSERT_VALUES,SCATTER_REVERSE);

    1831:   /* Sum contributions from two levels */
    1832:   if (applytranspose) {
    1833:     MatMultAdd(pcbddc->coarse_psi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);
    1834:     if (pcbddc->switch_static) { MatMultAdd(pcbddc->coarse_psi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D); }
    1835:   } else {
    1836:     MatMultAdd(pcbddc->coarse_phi_B,pcbddc->vec1_P,pcis->vec1_B,pcis->vec1_B);
    1837:     if (pcbddc->switch_static) { MatMultAdd(pcbddc->coarse_phi_D,pcbddc->vec1_P,pcis->vec1_D,pcis->vec1_D); }
    1838:   }
    1839:   return(0);
    1840: }

    1844: PetscErrorCode PCBDDCScatterCoarseDataBegin(PC pc,InsertMode imode, ScatterMode smode)
    1845: {
    1847:   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
    1848:   PetscScalar    *array;
    1849:   Vec            from,to;

    1852:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
    1853:     from = pcbddc->coarse_vec;
    1854:     to = pcbddc->vec1_P;
    1855:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
    1856:       Vec tvec;

    1858:       KSPGetRhs(pcbddc->coarse_ksp,&tvec);
    1859:       VecResetArray(tvec);
    1860:       KSPGetSolution(pcbddc->coarse_ksp,&tvec);
    1861:       VecGetArray(tvec,&array);
    1862:       VecPlaceArray(from,array);
    1863:       VecRestoreArray(tvec,&array);
    1864:     }
    1865:   } else { /* from local to global -> put data in coarse right hand side */
    1866:     from = pcbddc->vec1_P;
    1867:     to = pcbddc->coarse_vec;
    1868:   }
    1869:   VecScatterBegin(pcbddc->coarse_loc_to_glob,from,to,imode,smode);
    1870:   return(0);
    1871: }

    1875: PetscErrorCode PCBDDCScatterCoarseDataEnd(PC pc, InsertMode imode, ScatterMode smode)
    1876: {
    1878:   PC_BDDC*       pcbddc = (PC_BDDC*)(pc->data);
    1879:   PetscScalar    *array;
    1880:   Vec            from,to;

    1883:   if (smode == SCATTER_REVERSE) { /* from global to local -> get data from coarse solution */
    1884:     from = pcbddc->coarse_vec;
    1885:     to = pcbddc->vec1_P;
    1886:   } else { /* from local to global -> put data in coarse right hand side */
    1887:     from = pcbddc->vec1_P;
    1888:     to = pcbddc->coarse_vec;
    1889:   }
    1890:   VecScatterEnd(pcbddc->coarse_loc_to_glob,from,to,imode,smode);
    1891:   if (smode == SCATTER_FORWARD) {
    1892:     if (pcbddc->coarse_ksp) { /* get array from coarse processes */
    1893:       Vec tvec;

    1895:       KSPGetRhs(pcbddc->coarse_ksp,&tvec);
    1896:       VecGetArray(to,&array);
    1897:       VecPlaceArray(tvec,array);
    1898:       VecRestoreArray(to,&array);
    1899:     }
    1900:   } else {
    1901:     if (pcbddc->coarse_ksp) { /* restore array of pcbddc->coarse_vec */
    1902:      VecResetArray(from);
    1903:     }
    1904:   }
    1905:   return(0);
    1906: }

    1908: /* uncomment for testing purposes */
    1909: /* #define PETSC_MISSING_LAPACK_GESVD 1 */
    1912: PetscErrorCode PCBDDCConstraintsSetUp(PC pc)
    1913: {
    1914:   PetscErrorCode    ierr;
    1915:   PC_IS*            pcis = (PC_IS*)(pc->data);
    1916:   PC_BDDC*          pcbddc = (PC_BDDC*)pc->data;
    1917:   Mat_IS*           matis = (Mat_IS*)pc->pmat->data;
    1918:   /* one and zero */
    1919:   PetscScalar       one=1.0,zero=0.0;
    1920:   /* space to store constraints and their local indices */
    1921:   PetscScalar       *constraints_data;
    1922:   PetscInt          *constraints_idxs,*constraints_idxs_B;
    1923:   PetscInt          *constraints_idxs_ptr,*constraints_data_ptr;
    1924:   PetscInt          *constraints_n;
    1925:   /* iterators */
    1926:   PetscInt          i,j,k,total_counts,total_counts_cc,cum;
    1927:   /* BLAS integers */
    1928:   PetscBLASInt      lwork,lierr;
    1929:   PetscBLASInt      Blas_N,Blas_M,Blas_K,Blas_one=1;
    1930:   PetscBLASInt      Blas_LDA,Blas_LDB,Blas_LDC;
    1931:   /* reuse */
    1932:   PetscInt          olocal_primal_size,olocal_primal_size_cc;
    1933:   PetscInt          *olocal_primal_ref_node,*olocal_primal_ref_mult;
    1934:   /* change of basis */
    1935:   PetscBool         qr_needed;
    1936:   PetscBT           change_basis,qr_needed_idx;
    1937:   /* auxiliary stuff */
    1938:   PetscInt          *nnz,*is_indices;
    1939:   PetscInt          ncc;
    1940:   /* some quantities */
    1941:   PetscInt          n_vertices,total_primal_vertices,valid_constraints;
    1942:   PetscInt          size_of_constraint,max_size_of_constraint=0,max_constraints,temp_constraints;

    1945:   /* Destroy Mat objects computed previously */
    1946:   MatDestroy(&pcbddc->ChangeOfBasisMatrix);
    1947:   MatDestroy(&pcbddc->ConstraintMatrix);
    1948:   /* save info on constraints from previous setup (if any) */
    1949:   olocal_primal_size = pcbddc->local_primal_size;
    1950:   olocal_primal_size_cc = pcbddc->local_primal_size_cc;
    1951:   PetscMalloc2(olocal_primal_size_cc,&olocal_primal_ref_node,olocal_primal_size_cc,&olocal_primal_ref_mult);
    1952:   PetscMemcpy(olocal_primal_ref_node,pcbddc->local_primal_ref_node,olocal_primal_size_cc*sizeof(PetscInt));
    1953:   PetscMemcpy(olocal_primal_ref_mult,pcbddc->local_primal_ref_mult,olocal_primal_size_cc*sizeof(PetscInt));
    1954:   PetscFree2(pcbddc->local_primal_ref_node,pcbddc->local_primal_ref_mult);
    1955:   PetscFree(pcbddc->primal_indices_local_idxs);

    1957:   /* print some info */
    1958:   if (pcbddc->dbg_flag) {
    1959:     IS       vertices;
    1960:     PetscInt nv,nedges,nfaces;
    1961:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&nfaces,NULL,&nedges,NULL,&vertices);
    1962:     ISGetSize(vertices,&nv);
    1963:     ISDestroy(&vertices);
    1964:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    1965:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
    1966:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate vertices (%d)\n",PetscGlobalRank,nv,pcbddc->use_vertices);
    1967:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate edges    (%d)\n",PetscGlobalRank,nedges,pcbddc->use_edges);
    1968:     PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d got %02d local candidate faces    (%d)\n",PetscGlobalRank,nfaces,pcbddc->use_faces);
    1969:     PetscViewerFlush(pcbddc->dbg_viewer);
    1970:     PetscViewerASCIIPopSynchronized(pcbddc->dbg_viewer);
    1971:   }

    1973:   if (!pcbddc->adaptive_selection) {
    1974:     IS           ISForVertices,*ISForFaces,*ISForEdges;
    1975:     MatNullSpace nearnullsp;
    1976:     const Vec    *nearnullvecs;
    1977:     Vec          *localnearnullsp;
    1978:     PetscScalar  *array;
    1979:     PetscInt     n_ISForFaces,n_ISForEdges,nnsp_size;
    1980:     PetscBool    nnsp_has_cnst;
    1981:     /* LAPACK working arrays for SVD or POD */
    1982:     PetscBool    skip_lapack,boolforchange;
    1983:     PetscScalar  *work;
    1984:     PetscReal    *singular_vals;
    1985: #if defined(PETSC_USE_COMPLEX)
    1986:     PetscReal    *rwork;
    1987: #endif
    1988: #if defined(PETSC_MISSING_LAPACK_GESVD)
    1989:     PetscScalar  *temp_basis,*correlation_mat;
    1990: #else
    1991:     PetscBLASInt dummy_int=1;
    1992:     PetscScalar  dummy_scalar=1.;
    1993: #endif

    1995:     /* Get index sets for faces, edges and vertices from graph */
    1996:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,&n_ISForFaces,&ISForFaces,&n_ISForEdges,&ISForEdges,&ISForVertices);
    1997:     /* free unneeded index sets */
    1998:     if (!pcbddc->use_vertices) {
    1999:       ISDestroy(&ISForVertices);
    2000:     }
    2001:     if (!pcbddc->use_edges) {
    2002:       for (i=0;i<n_ISForEdges;i++) {
    2003:         ISDestroy(&ISForEdges[i]);
    2004:       }
    2005:       PetscFree(ISForEdges);
    2006:       n_ISForEdges = 0;
    2007:     }
    2008:     if (!pcbddc->use_faces) {
    2009:       for (i=0;i<n_ISForFaces;i++) {
    2010:         ISDestroy(&ISForFaces[i]);
    2011:       }
    2012:       PetscFree(ISForFaces);
    2013:       n_ISForFaces = 0;
    2014:     }

    2016: #if defined(PETSC_USE_DEBUG)
    2017:     /* HACK: when solving singular problems not using vertices, a change of basis is mandatory.
    2018:        Also use_change_of_basis should be consistent among processors */
    2019:     if (pcbddc->NullSpace) {
    2020:       PetscBool tbool[2],gbool[2];

    2022:       if (!ISForVertices && !pcbddc->user_ChangeOfBasisMatrix) {
    2023:         pcbddc->use_change_of_basis = PETSC_TRUE;
    2024:         if (!ISForEdges) {
    2025:           pcbddc->use_change_on_faces = PETSC_TRUE;
    2026:         }
    2027:       }
    2028:       tbool[0] = pcbddc->use_change_of_basis;
    2029:       tbool[1] = pcbddc->use_change_on_faces;
    2030:       MPIU_Allreduce(tbool,gbool,2,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
    2031:       pcbddc->use_change_of_basis = gbool[0];
    2032:       pcbddc->use_change_on_faces = gbool[1];
    2033:     }
    2034: #endif

    2036:     /* check if near null space is attached to global mat */
    2037:     MatGetNearNullSpace(pc->pmat,&nearnullsp);
    2038:     if (nearnullsp) {
    2039:       MatNullSpaceGetVecs(nearnullsp,&nnsp_has_cnst,&nnsp_size,&nearnullvecs);
    2040:       /* remove any stored info */
    2041:       MatNullSpaceDestroy(&pcbddc->onearnullspace);
    2042:       PetscFree(pcbddc->onearnullvecs_state);
    2043:       /* store information for BDDC solver reuse */
    2044:       PetscObjectReference((PetscObject)nearnullsp);
    2045:       pcbddc->onearnullspace = nearnullsp;
    2046:       PetscMalloc1(nnsp_size,&pcbddc->onearnullvecs_state);
    2047:       for (i=0;i<nnsp_size;i++) {
    2048:         PetscObjectStateGet((PetscObject)nearnullvecs[i],&pcbddc->onearnullvecs_state[i]);
    2049:       }
    2050:     } else { /* if near null space is not provided BDDC uses constants by default */
    2051:       nnsp_size = 0;
    2052:       nnsp_has_cnst = PETSC_TRUE;
    2053:     }
    2054:     /* get max number of constraints on a single cc */
    2055:     max_constraints = nnsp_size;
    2056:     if (nnsp_has_cnst) max_constraints++;

    2058:     /*
    2059:          Evaluate maximum storage size needed by the procedure
    2060:          - Indices for connected component i stored at "constraints_idxs + constraints_idxs_ptr[i]"
    2061:          - Values for constraints on connected component i stored at "constraints_data + constraints_data_ptr[i]"
    2062:          There can be multiple constraints per connected component
    2063:                                                                                                                                                            */
    2064:     n_vertices = 0;
    2065:     if (ISForVertices) {
    2066:       ISGetSize(ISForVertices,&n_vertices);
    2067:     }
    2068:     ncc = n_vertices+n_ISForFaces+n_ISForEdges;
    2069:     PetscMalloc3(ncc+1,&constraints_idxs_ptr,ncc+1,&constraints_data_ptr,ncc,&constraints_n);

    2071:     total_counts = n_ISForFaces+n_ISForEdges;
    2072:     total_counts *= max_constraints;
    2073:     total_counts += n_vertices;
    2074:     PetscBTCreate(total_counts,&change_basis);

    2076:     total_counts = 0;
    2077:     max_size_of_constraint = 0;
    2078:     for (i=0;i<n_ISForEdges+n_ISForFaces;i++) {
    2079:       IS used_is;
    2080:       if (i<n_ISForEdges) {
    2081:         used_is = ISForEdges[i];
    2082:       } else {
    2083:         used_is = ISForFaces[i-n_ISForEdges];
    2084:       }
    2085:       ISGetSize(used_is,&j);
    2086:       total_counts += j;
    2087:       max_size_of_constraint = PetscMax(j,max_size_of_constraint);
    2088:     }
    2089:     PetscMalloc3(total_counts*max_constraints+n_vertices,&constraints_data,total_counts+n_vertices,&constraints_idxs,total_counts+n_vertices,&constraints_idxs_B);

    2091:     /* get local part of global near null space vectors */
    2092:     PetscMalloc1(nnsp_size,&localnearnullsp);
    2093:     for (k=0;k<nnsp_size;k++) {
    2094:       VecDuplicate(pcis->vec1_N,&localnearnullsp[k]);
    2095:       VecScatterBegin(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);
    2096:       VecScatterEnd(matis->rctx,nearnullvecs[k],localnearnullsp[k],INSERT_VALUES,SCATTER_FORWARD);
    2097:     }

    2099:     /* whether or not to skip lapack calls */
    2100:     skip_lapack = PETSC_TRUE;
    2101:     if (n_ISForFaces+n_ISForEdges && max_constraints > 1 && !pcbddc->use_nnsp_true) skip_lapack = PETSC_FALSE;

    2103:     /* First we issue queries to allocate optimal workspace for LAPACKgesvd (or LAPACKsyev if SVD is missing) */
    2104:     if (!skip_lapack) {
    2105:       PetscScalar temp_work;

    2107: #if defined(PETSC_MISSING_LAPACK_GESVD)
    2108:       /* Proper Orthogonal Decomposition (POD) using the snapshot method */
    2109:       PetscMalloc1(max_constraints*max_constraints,&correlation_mat);
    2110:       PetscMalloc1(max_constraints,&singular_vals);
    2111:       PetscMalloc1(max_size_of_constraint*max_constraints,&temp_basis);
    2112: #if defined(PETSC_USE_COMPLEX)
    2113:       PetscMalloc1(3*max_constraints,&rwork);
    2114: #endif
    2115:       /* now we evaluate the optimal workspace using query with lwork=-1 */
    2116:       PetscBLASIntCast(max_constraints,&Blas_N);
    2117:       PetscBLASIntCast(max_constraints,&Blas_LDA);
    2118:       lwork = -1;
    2119:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2120: #if !defined(PETSC_USE_COMPLEX)
    2121:       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,&lierr));
    2122: #else
    2123:       PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,&temp_work,&lwork,rwork,&lierr));
    2124: #endif
    2125:       PetscFPTrapPop();
    2126:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to SYEV Lapack routine %d",(int)lierr);
    2127: #else /* on missing GESVD */
    2128:       /* SVD */
    2129:       PetscInt max_n,min_n;
    2130:       max_n = max_size_of_constraint;
    2131:       min_n = max_constraints;
    2132:       if (max_size_of_constraint < max_constraints) {
    2133:         min_n = max_size_of_constraint;
    2134:         max_n = max_constraints;
    2135:       }
    2136:       PetscMalloc1(min_n,&singular_vals);
    2137: #if defined(PETSC_USE_COMPLEX)
    2138:       PetscMalloc1(5*min_n,&rwork);
    2139: #endif
    2140:       /* now we evaluate the optimal workspace using query with lwork=-1 */
    2141:       lwork = -1;
    2142:       PetscBLASIntCast(max_n,&Blas_M);
    2143:       PetscBLASIntCast(min_n,&Blas_N);
    2144:       PetscBLASIntCast(max_n,&Blas_LDA);
    2145:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2146: #if !defined(PETSC_USE_COMPLEX)
    2147:       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));
    2148: #else
    2149:       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));
    2150: #endif
    2151:       PetscFPTrapPop();
    2152:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GESVD Lapack routine %d",(int)lierr);
    2153: #endif /* on missing GESVD */
    2154:       /* Allocate optimal workspace */
    2155:       PetscBLASIntCast((PetscInt)PetscRealPart(temp_work),&lwork);
    2156:       PetscMalloc1(lwork,&work);
    2157:     }
    2158:     /* Now we can loop on constraining sets */
    2159:     total_counts = 0;
    2160:     constraints_idxs_ptr[0] = 0;
    2161:     constraints_data_ptr[0] = 0;
    2162:     /* vertices */
    2163:     if (n_vertices) {
    2164:       ISGetIndices(ISForVertices,(const PetscInt**)&is_indices);
    2165:       if (nnsp_has_cnst) { /* it considers all possible vertices */
    2166:         PetscMemcpy(constraints_idxs,is_indices,n_vertices*sizeof(PetscInt));
    2167:         for (i=0;i<n_vertices;i++) {
    2168:           constraints_n[total_counts] = 1;
    2169:           constraints_data[total_counts] = 1.0;
    2170:           constraints_idxs_ptr[total_counts+1] = constraints_idxs_ptr[total_counts]+1;
    2171:           constraints_data_ptr[total_counts+1] = constraints_data_ptr[total_counts]+1;
    2172:           total_counts++;
    2173:         }
    2174:       } else { /* consider vertices for which exist at least a localnearnullsp which is not null there */
    2175:         PetscBool used_vertex;
    2176:         for (i=0;i<n_vertices;i++) {
    2177:           used_vertex = PETSC_FALSE;
    2178:           k = 0;
    2179:           while (!used_vertex && k<nnsp_size) {
    2180:             VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
    2181:             if (PetscAbsScalar(array[is_indices[i]])>0.0) {
    2182:               constraints_n[total_counts] = 1;
    2183:               constraints_idxs[total_counts] = is_indices[i];
    2184:               constraints_data[total_counts] = 1.0;
    2185:               constraints_idxs_ptr[total_counts+1] = constraints_idxs_ptr[total_counts]+1;
    2186:               constraints_data_ptr[total_counts+1] = constraints_data_ptr[total_counts]+1;
    2187:               total_counts++;
    2188:               used_vertex = PETSC_TRUE;
    2189:             }
    2190:             VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
    2191:             k++;
    2192:           }
    2193:         }
    2194:       }
    2195:       ISRestoreIndices(ISForVertices,(const PetscInt**)&is_indices);
    2196:       n_vertices = total_counts;
    2197:     }

    2199:     /* edges and faces */
    2200:     total_counts_cc = total_counts;
    2201:     for (ncc=0;ncc<n_ISForEdges+n_ISForFaces;ncc++) {
    2202:       IS        used_is;
    2203:       PetscBool idxs_copied = PETSC_FALSE;

    2205:       if (ncc<n_ISForEdges) {
    2206:         used_is = ISForEdges[ncc];
    2207:         boolforchange = pcbddc->use_change_of_basis; /* change or not the basis on the edge */
    2208:       } else {
    2209:         used_is = ISForFaces[ncc-n_ISForEdges];
    2210:         boolforchange = (PetscBool)(pcbddc->use_change_of_basis && pcbddc->use_change_on_faces); /* change or not the basis on the face */
    2211:       }
    2212:       temp_constraints = 0;          /* zero the number of constraints I have on this conn comp */

    2214:       ISGetSize(used_is,&size_of_constraint);
    2215:       ISGetIndices(used_is,(const PetscInt**)&is_indices);
    2216:       /* change of basis should not be performed on local periodic nodes */
    2217:       if (pcbddc->mat_graph->mirrors && pcbddc->mat_graph->mirrors[is_indices[0]]) boolforchange = PETSC_FALSE;
    2218:       if (nnsp_has_cnst) {
    2219:         PetscScalar quad_value;

    2221:         PetscMemcpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint*sizeof(PetscInt));
    2222:         idxs_copied = PETSC_TRUE;

    2224:         if (!pcbddc->use_nnsp_true) {
    2225:           quad_value = (PetscScalar)(1.0/PetscSqrtReal((PetscReal)size_of_constraint));
    2226:         } else {
    2227:           quad_value = 1.0;
    2228:         }
    2229:         for (j=0;j<size_of_constraint;j++) {
    2230:           constraints_data[constraints_data_ptr[total_counts_cc]+j] = quad_value;
    2231:         }
    2232:         temp_constraints++;
    2233:         total_counts++;
    2234:       }
    2235:       for (k=0;k<nnsp_size;k++) {
    2236:         PetscReal real_value;
    2237:         PetscScalar *ptr_to_data;

    2239:         VecGetArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
    2240:         ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]+temp_constraints*size_of_constraint];
    2241:         for (j=0;j<size_of_constraint;j++) {
    2242:           ptr_to_data[j] = array[is_indices[j]];
    2243:         }
    2244:         VecRestoreArrayRead(localnearnullsp[k],(const PetscScalar**)&array);
    2245:         /* check if array is null on the connected component */
    2246:         PetscBLASIntCast(size_of_constraint,&Blas_N);
    2247:         PetscStackCallBLAS("BLASasum",real_value = BLASasum_(&Blas_N,ptr_to_data,&Blas_one));
    2248:         if (real_value > 0.0) { /* keep indices and values */
    2249:           temp_constraints++;
    2250:           total_counts++;
    2251:           if (!idxs_copied) {
    2252:             PetscMemcpy(constraints_idxs + constraints_idxs_ptr[total_counts_cc],is_indices,size_of_constraint*sizeof(PetscInt));
    2253:             idxs_copied = PETSC_TRUE;
    2254:           }
    2255:         }
    2256:       }
    2257:       ISRestoreIndices(used_is,(const PetscInt**)&is_indices);
    2258:       valid_constraints = temp_constraints;
    2259:       if (!pcbddc->use_nnsp_true && temp_constraints) {
    2260:         if (temp_constraints == 1) { /* just normalize the constraint */
    2261:           PetscScalar norm,*ptr_to_data;

    2263:           ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];
    2264:           PetscBLASIntCast(size_of_constraint,&Blas_N);
    2265:           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,ptr_to_data,&Blas_one,ptr_to_data,&Blas_one));
    2266:           norm = 1.0/PetscSqrtReal(PetscRealPart(norm));
    2267:           PetscStackCallBLAS("BLASscal",BLASscal_(&Blas_N,&norm,ptr_to_data,&Blas_one));
    2268:         } else { /* perform SVD */
    2269:           PetscReal   tol = 1.0e-8; /* tolerance for retaining eigenmodes */
    2270:           PetscScalar *ptr_to_data = &constraints_data[constraints_data_ptr[total_counts_cc]];

    2272: #if defined(PETSC_MISSING_LAPACK_GESVD)
    2273:           /* SVD: Y = U*S*V^H                -> U (eigenvectors of Y*Y^H) = Y*V*(S)^\dag
    2274:              POD: Y^H*Y = V*D*V^H, D = S^H*S -> U = Y*V*D^(-1/2)
    2275:              -> When PETSC_USE_COMPLEX and PETSC_MISSING_LAPACK_GESVD are defined
    2276:                 the constraints basis will differ (by a complex factor with absolute value equal to 1)
    2277:                 from that computed using LAPACKgesvd
    2278:              -> This is due to a different computation of eigenvectors in LAPACKheev
    2279:              -> The quality of the POD-computed basis will be the same */
    2280:           PetscMemzero(correlation_mat,temp_constraints*temp_constraints*sizeof(PetscScalar));
    2281:           /* Store upper triangular part of correlation matrix */
    2282:           PetscBLASIntCast(size_of_constraint,&Blas_N);
    2283:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2284:           for (j=0;j<temp_constraints;j++) {
    2285:             for (k=0;k<j+1;k++) {
    2286:               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));
    2287:             }
    2288:           }
    2289:           /* compute eigenvalues and eigenvectors of correlation matrix */
    2290:           PetscBLASIntCast(temp_constraints,&Blas_N);
    2291:           PetscBLASIntCast(temp_constraints,&Blas_LDA);
    2292: #if !defined(PETSC_USE_COMPLEX)
    2293:           PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,&lierr));
    2294: #else
    2295:           PetscStackCallBLAS("LAPACKsyev",LAPACKsyev_("V","U",&Blas_N,correlation_mat,&Blas_LDA,singular_vals,work,&lwork,rwork,&lierr));
    2296: #endif
    2297:           PetscFPTrapPop();
    2298:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SYEV Lapack routine %d",(int)lierr);
    2299:           /* retain eigenvalues greater than tol: note that LAPACKsyev gives eigs in ascending order */
    2300:           j = 0;
    2301:           while (j < temp_constraints && singular_vals[j] < tol) j++;
    2302:           total_counts = total_counts-j;
    2303:           valid_constraints = temp_constraints-j;
    2304:           /* scale and copy POD basis into used quadrature memory */
    2305:           PetscBLASIntCast(size_of_constraint,&Blas_M);
    2306:           PetscBLASIntCast(temp_constraints,&Blas_N);
    2307:           PetscBLASIntCast(temp_constraints,&Blas_K);
    2308:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    2309:           PetscBLASIntCast(temp_constraints,&Blas_LDB);
    2310:           PetscBLASIntCast(size_of_constraint,&Blas_LDC);
    2311:           if (j<temp_constraints) {
    2312:             PetscInt ii;
    2313:             for (k=j;k<temp_constraints;k++) singular_vals[k] = 1.0/PetscSqrtReal(singular_vals[k]);
    2314:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2315:             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));
    2316:             PetscFPTrapPop();
    2317:             for (k=0;k<temp_constraints-j;k++) {
    2318:               for (ii=0;ii<size_of_constraint;ii++) {
    2319:                 ptr_to_data[k*size_of_constraint+ii] = singular_vals[temp_constraints-1-k]*temp_basis[(temp_constraints-1-k)*size_of_constraint+ii];
    2320:               }
    2321:             }
    2322:           }
    2323: #else  /* on missing GESVD */
    2324:           PetscBLASIntCast(size_of_constraint,&Blas_M);
    2325:           PetscBLASIntCast(temp_constraints,&Blas_N);
    2326:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    2327:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2328: #if !defined(PETSC_USE_COMPLEX)
    2329:           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));
    2330: #else
    2331:           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));
    2332: #endif
    2333:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GESVD Lapack routine %d",(int)lierr);
    2334:           PetscFPTrapPop();
    2335:           /* retain eigenvalues greater than tol: note that LAPACKgesvd gives eigs in descending order */
    2336:           k = temp_constraints;
    2337:           if (k > size_of_constraint) k = size_of_constraint;
    2338:           j = 0;
    2339:           while (j < k && singular_vals[k-j-1] < tol) j++;
    2340:           valid_constraints = k-j;
    2341:           total_counts = total_counts-temp_constraints+valid_constraints;
    2342: #endif /* on missing GESVD */
    2343:         }
    2344:       }
    2345:       /* update pointers information */
    2346:       if (valid_constraints) {
    2347:         constraints_n[total_counts_cc] = valid_constraints;
    2348:         constraints_idxs_ptr[total_counts_cc+1] = constraints_idxs_ptr[total_counts_cc]+size_of_constraint;
    2349:         constraints_data_ptr[total_counts_cc+1] = constraints_data_ptr[total_counts_cc]+size_of_constraint*valid_constraints;
    2350:         /* set change_of_basis flag */
    2351:         if (boolforchange) {
    2352:           PetscBTSet(change_basis,total_counts_cc);
    2353:         }
    2354:         total_counts_cc++;
    2355:       }
    2356:     }
    2357:     /* free workspace */
    2358:     if (!skip_lapack) {
    2359:       PetscFree(work);
    2360: #if defined(PETSC_USE_COMPLEX)
    2361:       PetscFree(rwork);
    2362: #endif
    2363:       PetscFree(singular_vals);
    2364: #if defined(PETSC_MISSING_LAPACK_GESVD)
    2365:       PetscFree(correlation_mat);
    2366:       PetscFree(temp_basis);
    2367: #endif
    2368:     }
    2369:     for (k=0;k<nnsp_size;k++) {
    2370:       VecDestroy(&localnearnullsp[k]);
    2371:     }
    2372:     PetscFree(localnearnullsp);
    2373:     /* free index sets of faces, edges and vertices */
    2374:     for (i=0;i<n_ISForFaces;i++) {
    2375:       ISDestroy(&ISForFaces[i]);
    2376:     }
    2377:     if (n_ISForFaces) {
    2378:       PetscFree(ISForFaces);
    2379:     }
    2380:     for (i=0;i<n_ISForEdges;i++) {
    2381:       ISDestroy(&ISForEdges[i]);
    2382:     }
    2383:     if (n_ISForEdges) {
    2384:       PetscFree(ISForEdges);
    2385:     }
    2386:     ISDestroy(&ISForVertices);
    2387:   } else {
    2388:     PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;

    2390:     total_counts = 0;
    2391:     n_vertices = 0;
    2392:     if (sub_schurs->is_vertices && pcbddc->use_vertices) {
    2393:       ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);
    2394:     }
    2395:     max_constraints = 0;
    2396:     total_counts_cc = 0;
    2397:     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
    2398:       total_counts += pcbddc->adaptive_constraints_n[i];
    2399:       if (pcbddc->adaptive_constraints_n[i]) total_counts_cc++;
    2400:       max_constraints = PetscMax(max_constraints,pcbddc->adaptive_constraints_n[i]);
    2401:     }
    2402:     constraints_idxs_ptr = pcbddc->adaptive_constraints_idxs_ptr;
    2403:     constraints_data_ptr = pcbddc->adaptive_constraints_data_ptr;
    2404:     constraints_idxs = pcbddc->adaptive_constraints_idxs;
    2405:     constraints_data = pcbddc->adaptive_constraints_data;
    2406:     /* constraints_n differs from pcbddc->adaptive_constraints_n */
    2407:     PetscMalloc1(total_counts_cc,&constraints_n);
    2408:     total_counts_cc = 0;
    2409:     for (i=0;i<sub_schurs->n_subs+n_vertices;i++) {
    2410:       if (pcbddc->adaptive_constraints_n[i]) {
    2411:         constraints_n[total_counts_cc++] = pcbddc->adaptive_constraints_n[i];
    2412:       }
    2413:     }
    2414: #if 0
    2415:     printf("Found %d totals (%d)\n",total_counts_cc,total_counts);
    2416:     for (i=0;i<total_counts_cc;i++) {
    2417:       printf("const %d, start %d",i,constraints_idxs_ptr[i]);
    2418:       printf(" end %d:\n",constraints_idxs_ptr[i+1]);
    2419:       for (j=constraints_idxs_ptr[i];j<constraints_idxs_ptr[i+1];j++) {
    2420:         printf(" %d",constraints_idxs[j]);
    2421:       }
    2422:       printf("\n");
    2423:       printf("number of cc: %d\n",constraints_n[i]);
    2424:     }
    2425:     for (i=0;i<n_vertices;i++) {
    2426:       PetscPrintf(PETSC_COMM_SELF,"[%d] vertex %d, n %d\n",PetscGlobalRank,i,pcbddc->adaptive_constraints_n[i]);
    2427:     }
    2428:     for (i=0;i<sub_schurs->n_subs;i++) {
    2429:       PetscPrintf(PETSC_COMM_SELF,"[%d] sub %d, edge %d, n %d\n",PetscGlobalRank,i,(PetscBool)PetscBTLookup(sub_schurs->is_edge,i),pcbddc->adaptive_constraints_n[i+n_vertices]);
    2430:     }
    2431: #endif

    2433:     max_size_of_constraint = 0;
    2434:     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]);
    2435:     PetscMalloc1(constraints_idxs_ptr[total_counts_cc],&constraints_idxs_B);
    2436:     /* Change of basis */
    2437:     PetscBTCreate(total_counts_cc,&change_basis);
    2438:     if (pcbddc->use_change_of_basis) {
    2439:       for (i=0;i<sub_schurs->n_subs;i++) {
    2440:         if (PetscBTLookup(sub_schurs->is_edge,i) || pcbddc->use_change_on_faces) {
    2441:           PetscBTSet(change_basis,i+n_vertices);
    2442:         }
    2443:       }
    2444:     }
    2445:   }
    2446:   pcbddc->local_primal_size = total_counts;
    2447:   PetscMalloc1(pcbddc->local_primal_size,&pcbddc->primal_indices_local_idxs);

    2449:   /* map constraints_idxs in boundary numbering */
    2450:   ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,constraints_idxs_ptr[total_counts_cc],constraints_idxs,&i,constraints_idxs_B);
    2451:   if (i != constraints_idxs_ptr[total_counts_cc]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for constraints indices %D != %D\n",constraints_idxs_ptr[total_counts_cc],i);

    2453:   /* Create constraint matrix */
    2454:   MatCreate(PETSC_COMM_SELF,&pcbddc->ConstraintMatrix);
    2455:   MatSetType(pcbddc->ConstraintMatrix,MATAIJ);
    2456:   MatSetSizes(pcbddc->ConstraintMatrix,pcbddc->local_primal_size,pcis->n,pcbddc->local_primal_size,pcis->n);

    2458:   /* find primal_dofs: subdomain corners plus dofs selected as primal after change of basis */
    2459:   /* determine if a QR strategy is needed for change of basis */
    2460:   qr_needed = PETSC_FALSE;
    2461:   PetscBTCreate(total_counts_cc,&qr_needed_idx);
    2462:   total_primal_vertices=0;
    2463:   pcbddc->local_primal_size_cc = 0;
    2464:   for (i=0;i<total_counts_cc;i++) {
    2465:     size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    2466:     if (size_of_constraint == 1) {
    2467:       pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]];
    2468:       pcbddc->local_primal_size_cc += 1;
    2469:     } else if (PetscBTLookup(change_basis,i)) {
    2470:       for (k=0;k<constraints_n[i];k++) {
    2471:         pcbddc->primal_indices_local_idxs[total_primal_vertices++] = constraints_idxs[constraints_idxs_ptr[i]+k];
    2472:       }
    2473:       pcbddc->local_primal_size_cc += constraints_n[i];
    2474:       if (constraints_n[i] > 1 || pcbddc->use_qr_single || pcbddc->faster_deluxe) {
    2475:         PetscBTSet(qr_needed_idx,i);
    2476:         qr_needed = PETSC_TRUE;
    2477:       }
    2478:     } else {
    2479:       pcbddc->local_primal_size_cc += 1;
    2480:     }
    2481:   }
    2482:   /* note that the local variable n_vertices used below stores the number of pointwise constraints */
    2483:   pcbddc->n_vertices = total_primal_vertices;
    2484:   /* permute indices in order to have a sorted set of vertices */
    2485:   PetscSortInt(total_primal_vertices,pcbddc->primal_indices_local_idxs);

    2487:   PetscMalloc2(pcbddc->local_primal_size_cc,&pcbddc->local_primal_ref_node,pcbddc->local_primal_size_cc,&pcbddc->local_primal_ref_mult);
    2488:   PetscMemcpy(pcbddc->local_primal_ref_node,pcbddc->primal_indices_local_idxs,total_primal_vertices*sizeof(PetscInt));
    2489:   for (i=0;i<total_primal_vertices;i++) pcbddc->local_primal_ref_mult[i] = 1;

    2491:   /* nonzero structure of constraint matrix */
    2492:   /* and get reference dof for local constraints */
    2493:   PetscMalloc1(pcbddc->local_primal_size,&nnz);
    2494:   for (i=0;i<total_primal_vertices;i++) nnz[i] = 1;

    2496:   j = total_primal_vertices;
    2497:   total_counts = total_primal_vertices;
    2498:   cum = total_primal_vertices;
    2499:   for (i=n_vertices;i<total_counts_cc;i++) {
    2500:     if (!PetscBTLookup(change_basis,i)) {
    2501:       pcbddc->local_primal_ref_node[cum] = constraints_idxs[constraints_idxs_ptr[i]];
    2502:       pcbddc->local_primal_ref_mult[cum] = constraints_n[i];
    2503:       cum++;
    2504:       size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    2505:       for (k=0;k<constraints_n[i];k++) {
    2506:         pcbddc->primal_indices_local_idxs[total_counts++] = constraints_idxs[constraints_idxs_ptr[i]+k];
    2507:         nnz[j+k] = size_of_constraint;
    2508:       }
    2509:       j += constraints_n[i];
    2510:     }
    2511:   }
    2512:   MatSeqAIJSetPreallocation(pcbddc->ConstraintMatrix,0,nnz);
    2513:   PetscFree(nnz);

    2515:   /* set values in constraint matrix */
    2516:   for (i=0;i<total_primal_vertices;i++) {
    2517:     MatSetValue(pcbddc->ConstraintMatrix,i,pcbddc->local_primal_ref_node[i],1.0,INSERT_VALUES);
    2518:   }
    2519:   total_counts = total_primal_vertices;
    2520:   for (i=n_vertices;i<total_counts_cc;i++) {
    2521:     if (!PetscBTLookup(change_basis,i)) {
    2522:       PetscInt *cols;

    2524:       size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    2525:       cols = constraints_idxs+constraints_idxs_ptr[i];
    2526:       for (k=0;k<constraints_n[i];k++) {
    2527:         PetscInt    row = total_counts+k;
    2528:         PetscScalar *vals;

    2530:         vals = constraints_data+constraints_data_ptr[i]+k*size_of_constraint;
    2531:         MatSetValues(pcbddc->ConstraintMatrix,1,&row,size_of_constraint,cols,vals,INSERT_VALUES);
    2532:       }
    2533:       total_counts += constraints_n[i];
    2534:     }
    2535:   }
    2536:   /* assembling */
    2537:   MatAssemblyBegin(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);
    2538:   MatAssemblyEnd(pcbddc->ConstraintMatrix,MAT_FINAL_ASSEMBLY);

    2540:   /*
    2541:   PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF,PETSC_VIEWER_ASCII_MATLAB);
    2542:   MatView(pcbddc->ConstraintMatrix,(PetscViewer)0);
    2543:   PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF);
    2544:   */
    2545:   /* Create matrix for change of basis. We don't need it in case pcbddc->use_change_of_basis is FALSE */
    2546:   if (pcbddc->use_change_of_basis) {
    2547:     /* dual and primal dofs on a single cc */
    2548:     PetscInt     dual_dofs,primal_dofs;
    2549:     /* working stuff for GEQRF */
    2550:     PetscScalar  *qr_basis,*qr_tau = NULL,*qr_work,lqr_work_t;
    2551:     PetscBLASInt lqr_work;
    2552:     /* working stuff for UNGQR */
    2553:     PetscScalar  *gqr_work,lgqr_work_t;
    2554:     PetscBLASInt lgqr_work;
    2555:     /* working stuff for TRTRS */
    2556:     PetscScalar  *trs_rhs;
    2557:     PetscBLASInt Blas_NRHS;
    2558:     /* pointers for values insertion into change of basis matrix */
    2559:     PetscInt     *start_rows,*start_cols;
    2560:     PetscScalar  *start_vals;
    2561:     /* working stuff for values insertion */
    2562:     PetscBT      is_primal;
    2563:     PetscInt     *aux_primal_numbering_B;
    2564:     /* matrix sizes */
    2565:     PetscInt     global_size,local_size;
    2566:     /* temporary change of basis */
    2567:     Mat          localChangeOfBasisMatrix;
    2568:     /* extra space for debugging */
    2569:     PetscScalar  *dbg_work;

    2571:     /* local temporary change of basis acts on local interfaces -> dimension is n_B x n_B */
    2572:     MatCreate(PETSC_COMM_SELF,&localChangeOfBasisMatrix);
    2573:     MatSetType(localChangeOfBasisMatrix,MATAIJ);
    2574:     MatSetSizes(localChangeOfBasisMatrix,pcis->n,pcis->n,pcis->n,pcis->n);
    2575:     /* nonzeros for local mat */
    2576:     PetscMalloc1(pcis->n,&nnz);
    2577:     for (i=0;i<pcis->n;i++) nnz[i]=1;
    2578:     for (i=n_vertices;i<total_counts_cc;i++) {
    2579:       if (PetscBTLookup(change_basis,i)) {
    2580:         size_of_constraint = constraints_idxs_ptr[i+1]-constraints_idxs_ptr[i];
    2581:         if (PetscBTLookup(qr_needed_idx,i)) {
    2582:           for (j=0;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = size_of_constraint;
    2583:         } else {
    2584:           nnz[constraints_idxs[constraints_idxs_ptr[i]]] = size_of_constraint;
    2585:           for (j=1;j<size_of_constraint;j++) nnz[constraints_idxs[constraints_idxs_ptr[i]+j]] = 2;
    2586:         }
    2587:       }
    2588:     }
    2589:     MatSeqAIJSetPreallocation(localChangeOfBasisMatrix,0,nnz);
    2590:     PetscFree(nnz);
    2591:     /* Set initial identity in the matrix */
    2592:     for (i=0;i<pcis->n;i++) {
    2593:       MatSetValue(localChangeOfBasisMatrix,i,i,1.0,INSERT_VALUES);
    2594:     }

    2596:     if (pcbddc->dbg_flag) {
    2597:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"--------------------------------------------------------------\n");
    2598:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Checking change of basis computation for subdomain %04d\n",PetscGlobalRank);
    2599:     }

    2602:     /* Now we loop on the constraints which need a change of basis */
    2603:     /*
    2604:        Change of basis matrix is evaluated similarly to the FIRST APPROACH in
    2605:        Klawonn and Widlund, Dual-primal FETI-DP methods for linear elasticity, (see Sect 6.2.1)

    2607:        Basic blocks of change of basis matrix T computed by

    2609:           - Using the following block transformation if there is only a primal dof on the cc (and -pc_bddc_use_qr_single is not specified)

    2611:             | 1        0   ...        0         s_1/S |
    2612:             | 0        1   ...        0         s_2/S |
    2613:             |              ...                        |
    2614:             | 0        ...            1     s_{n-1}/S |
    2615:             | -s_1/s_n ...    -s_{n-1}/s_n      s_n/S |

    2617:             with S = \sum_{i=1}^n s_i^2
    2618:             NOTE: in the above example, the primal dof is the last one of the edge in LOCAL ordering
    2619:                   in the current implementation, the primal dof is the first one of the edge in GLOBAL ordering

    2621:           - QR decomposition of constraints otherwise
    2622:     */
    2623:     if (qr_needed) {
    2624:       /* space to store Q */
    2625:       PetscMalloc1(max_size_of_constraint*max_size_of_constraint,&qr_basis);
    2626:       /* first we issue queries for optimal work */
    2627:       PetscBLASIntCast(max_size_of_constraint,&Blas_M);
    2628:       PetscBLASIntCast(max_constraints,&Blas_N);
    2629:       PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);
    2630:       lqr_work = -1;
    2631:       PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,&lqr_work_t,&lqr_work,&lierr));
    2632:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to GEQRF Lapack routine %d",(int)lierr);
    2633:       PetscBLASIntCast((PetscInt)PetscRealPart(lqr_work_t),&lqr_work);
    2634:       PetscMalloc1((PetscInt)PetscRealPart(lqr_work_t),&qr_work);
    2635:       lgqr_work = -1;
    2636:       PetscBLASIntCast(max_size_of_constraint,&Blas_M);
    2637:       PetscBLASIntCast(max_size_of_constraint,&Blas_N);
    2638:       PetscBLASIntCast(max_constraints,&Blas_K);
    2639:       PetscBLASIntCast(max_size_of_constraint,&Blas_LDA);
    2640:       if (Blas_K>Blas_M) Blas_K=Blas_M; /* adjust just for computing optimal work */
    2641:       PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,&lgqr_work_t,&lgqr_work,&lierr));
    2642:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in query to UNGQR Lapack routine %d",(int)lierr);
    2643:       PetscBLASIntCast((PetscInt)PetscRealPart(lgqr_work_t),&lgqr_work);
    2644:       PetscMalloc1((PetscInt)PetscRealPart(lgqr_work_t),&gqr_work);
    2645:       /* array to store scaling factors for reflectors */
    2646:       PetscMalloc1(max_constraints,&qr_tau);
    2647:       /* array to store rhs and solution of triangular solver */
    2648:       PetscMalloc1(max_constraints*max_constraints,&trs_rhs);
    2649:       /* allocating workspace for check */
    2650:       if (pcbddc->dbg_flag) {
    2651:         PetscMalloc1(max_size_of_constraint*(max_constraints+max_size_of_constraint),&dbg_work);
    2652:       }
    2653:     }
    2654:     /* array to store whether a node is primal or not */
    2655:     PetscBTCreate(pcis->n_B,&is_primal);
    2656:     PetscMalloc1(total_primal_vertices,&aux_primal_numbering_B);
    2657:     ISGlobalToLocalMappingApply(pcis->BtoNmap,IS_GTOLM_DROP,total_primal_vertices,pcbddc->local_primal_ref_node,&i,aux_primal_numbering_B);
    2658:     if (i != total_primal_vertices) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Error in boundary numbering for BDDC vertices! %D != %D\n",total_primal_vertices,i);
    2659:     for (i=0;i<total_primal_vertices;i++) {
    2660:       PetscBTSet(is_primal,aux_primal_numbering_B[i]);
    2661:     }
    2662:     PetscFree(aux_primal_numbering_B);

    2664:     /* loop on constraints and see whether or not they need a change of basis and compute it */
    2665:     for (total_counts=n_vertices;total_counts<total_counts_cc;total_counts++) {
    2666:       size_of_constraint = constraints_idxs_ptr[total_counts+1]-constraints_idxs_ptr[total_counts];
    2667:       if (PetscBTLookup(change_basis,total_counts)) {
    2668:         /* get constraint info */
    2669:         primal_dofs = constraints_n[total_counts];
    2670:         dual_dofs = size_of_constraint-primal_dofs;

    2672:         if (pcbddc->dbg_flag) {
    2673:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraints %d: %d need a change of basis (size %d)\n",total_counts,primal_dofs,size_of_constraint);
    2674:         }

    2676:         if (PetscBTLookup(qr_needed_idx,total_counts)) { /* QR */

    2678:           /* copy quadrature constraints for change of basis check */
    2679:           if (pcbddc->dbg_flag) {
    2680:             PetscMemcpy(dbg_work,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));
    2681:           }
    2682:           /* copy temporary constraints into larger work vector (in order to store all columns of Q) */
    2683:           PetscMemcpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));

    2685:           /* compute QR decomposition of constraints */
    2686:           PetscBLASIntCast(size_of_constraint,&Blas_M);
    2687:           PetscBLASIntCast(primal_dofs,&Blas_N);
    2688:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    2689:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2690:           PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&Blas_M,&Blas_N,qr_basis,&Blas_LDA,qr_tau,qr_work,&lqr_work,&lierr));
    2691:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in GEQRF Lapack routine %d",(int)lierr);
    2692:           PetscFPTrapPop();

    2694:           /* explictly compute R^-T */
    2695:           PetscMemzero(trs_rhs,primal_dofs*primal_dofs*sizeof(*trs_rhs));
    2696:           for (j=0;j<primal_dofs;j++) trs_rhs[j*(primal_dofs+1)] = 1.0;
    2697:           PetscBLASIntCast(primal_dofs,&Blas_N);
    2698:           PetscBLASIntCast(primal_dofs,&Blas_NRHS);
    2699:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    2700:           PetscBLASIntCast(primal_dofs,&Blas_LDB);
    2701:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2702:           PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U","T","N",&Blas_N,&Blas_NRHS,qr_basis,&Blas_LDA,trs_rhs,&Blas_LDB,&lierr));
    2703:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TRTRS Lapack routine %d",(int)lierr);
    2704:           PetscFPTrapPop();

    2706:           /* explicitly compute all columns of Q (Q = [Q1 | Q2] ) overwriting QR factorization in qr_basis */
    2707:           PetscBLASIntCast(size_of_constraint,&Blas_M);
    2708:           PetscBLASIntCast(size_of_constraint,&Blas_N);
    2709:           PetscBLASIntCast(primal_dofs,&Blas_K);
    2710:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    2711:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2712:           PetscStackCallBLAS("LAPACKungqr",LAPACKungqr_(&Blas_M,&Blas_N,&Blas_K,qr_basis,&Blas_LDA,qr_tau,gqr_work,&lgqr_work,&lierr));
    2713:           if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in UNGQR Lapack routine %d",(int)lierr);
    2714:           PetscFPTrapPop();

    2716:           /* first primal_dofs columns of Q need to be re-scaled in order to be unitary w.r.t constraints
    2717:              i.e. C_{pxn}*Q_{nxn} should be equal to [I_pxp | 0_pxd] (see check below)
    2718:              where n=size_of_constraint, p=primal_dofs, d=dual_dofs (n=p+d), I and 0 identity and null matrix resp. */
    2719:           PetscBLASIntCast(size_of_constraint,&Blas_M);
    2720:           PetscBLASIntCast(primal_dofs,&Blas_N);
    2721:           PetscBLASIntCast(primal_dofs,&Blas_K);
    2722:           PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    2723:           PetscBLASIntCast(primal_dofs,&Blas_LDB);
    2724:           PetscBLASIntCast(size_of_constraint,&Blas_LDC);
    2725:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2726:           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));
    2727:           PetscFPTrapPop();
    2728:           PetscMemcpy(qr_basis,&constraints_data[constraints_data_ptr[total_counts]],size_of_constraint*primal_dofs*sizeof(PetscScalar));

    2730:           /* insert values in change of basis matrix respecting global ordering of new primal dofs */
    2731:           start_rows = &constraints_idxs[constraints_idxs_ptr[total_counts]];
    2732:           /* insert cols for primal dofs */
    2733:           for (j=0;j<primal_dofs;j++) {
    2734:             start_vals = &qr_basis[j*size_of_constraint];
    2735:             start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+j];
    2736:             MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);
    2737:           }
    2738:           /* insert cols for dual dofs */
    2739:           for (j=0,k=0;j<dual_dofs;k++) {
    2740:             if (!PetscBTLookup(is_primal,constraints_idxs_B[constraints_idxs_ptr[total_counts]+k])) {
    2741:               start_vals = &qr_basis[(primal_dofs+j)*size_of_constraint];
    2742:               start_cols = &constraints_idxs[constraints_idxs_ptr[total_counts]+k];
    2743:               MatSetValues(localChangeOfBasisMatrix,size_of_constraint,start_rows,1,start_cols,start_vals,INSERT_VALUES);
    2744:               j++;
    2745:             }
    2746:           }

    2748:           /* check change of basis */
    2749:           if (pcbddc->dbg_flag) {
    2750:             PetscInt   ii,jj;
    2751:             PetscBool valid_qr=PETSC_TRUE;
    2752:             PetscBLASIntCast(primal_dofs,&Blas_M);
    2753:             PetscBLASIntCast(size_of_constraint,&Blas_N);
    2754:             PetscBLASIntCast(size_of_constraint,&Blas_K);
    2755:             PetscBLASIntCast(size_of_constraint,&Blas_LDA);
    2756:             PetscBLASIntCast(size_of_constraint,&Blas_LDB);
    2757:             PetscBLASIntCast(primal_dofs,&Blas_LDC);
    2758:             PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    2759:             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));
    2760:             PetscFPTrapPop();
    2761:             for (jj=0;jj<size_of_constraint;jj++) {
    2762:               for (ii=0;ii<primal_dofs;ii++) {
    2763:                 if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) valid_qr = PETSC_FALSE;
    2764:                 if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) valid_qr = PETSC_FALSE;
    2765:               }
    2766:             }
    2767:             if (!valid_qr) {
    2768:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> wrong change of basis!\n");
    2769:               for (jj=0;jj<size_of_constraint;jj++) {
    2770:                 for (ii=0;ii<primal_dofs;ii++) {
    2771:                   if (ii != jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]) > 1.e-12) {
    2772:                     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]));
    2773:                   }
    2774:                   if (ii == jj && PetscAbsScalar(dbg_work[size_of_constraint*primal_dofs+jj*primal_dofs+ii]-1.0) > 1.e-12) {
    2775:                     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]));
    2776:                   }
    2777:                 }
    2778:               }
    2779:             } else {
    2780:               PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> right change of basis!\n");
    2781:             }
    2782:           }
    2783:         } else { /* simple transformation block */
    2784:           PetscInt    row,col;
    2785:           PetscScalar val,norm;

    2787:           PetscBLASIntCast(size_of_constraint,&Blas_N);
    2788:           PetscStackCallBLAS("BLASdot",norm = BLASdot_(&Blas_N,constraints_data+constraints_data_ptr[total_counts],&Blas_one,constraints_data+constraints_data_ptr[total_counts],&Blas_one));
    2789:           for (j=0;j<size_of_constraint;j++) {
    2790:             PetscInt row_B = constraints_idxs_B[constraints_idxs_ptr[total_counts]+j];
    2791:             row = constraints_idxs[constraints_idxs_ptr[total_counts]+j];
    2792:             if (!PetscBTLookup(is_primal,row_B)) {
    2793:               col = constraints_idxs[constraints_idxs_ptr[total_counts]];
    2794:               MatSetValue(localChangeOfBasisMatrix,row,row,1.0,INSERT_VALUES);
    2795:               MatSetValue(localChangeOfBasisMatrix,row,col,constraints_data[constraints_data_ptr[total_counts]+j]/norm,INSERT_VALUES);
    2796:             } else {
    2797:               for (k=0;k<size_of_constraint;k++) {
    2798:                 col = constraints_idxs[constraints_idxs_ptr[total_counts]+k];
    2799:                 if (row != col) {
    2800:                   val = -constraints_data[constraints_data_ptr[total_counts]+k]/constraints_data[constraints_data_ptr[total_counts]];
    2801:                 } else {
    2802:                   val = constraints_data[constraints_data_ptr[total_counts]]/norm;
    2803:                 }
    2804:                 MatSetValue(localChangeOfBasisMatrix,row,col,val,INSERT_VALUES);
    2805:               }
    2806:             }
    2807:           }
    2808:           if (pcbddc->dbg_flag) {
    2809:             PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"\t-> using standard change of basis\n");
    2810:           }
    2811:         }
    2812:       } else {
    2813:         if (pcbddc->dbg_flag) {
    2814:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Constraint %d does not need a change of basis (size %d)\n",total_counts,size_of_constraint);
    2815:         }
    2816:       }
    2817:     }

    2819:     /* free workspace */
    2820:     if (qr_needed) {
    2821:       if (pcbddc->dbg_flag) {
    2822:         PetscFree(dbg_work);
    2823:       }
    2824:       PetscFree(trs_rhs);
    2825:       PetscFree(qr_tau);
    2826:       PetscFree(qr_work);
    2827:       PetscFree(gqr_work);
    2828:       PetscFree(qr_basis);
    2829:     }
    2830:     PetscBTDestroy(&is_primal);
    2831:     MatAssemblyBegin(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);
    2832:     MatAssemblyEnd(localChangeOfBasisMatrix,MAT_FINAL_ASSEMBLY);

    2834:     /* assembling of global change of variable */
    2835:     {
    2836:       Mat      tmat;
    2837:       PetscInt bs;

    2839:       VecGetSize(pcis->vec1_global,&global_size);
    2840:       VecGetLocalSize(pcis->vec1_global,&local_size);
    2841:       MatDuplicate(pc->pmat,MAT_DO_NOT_COPY_VALUES,&tmat);
    2842:       MatISSetLocalMat(tmat,localChangeOfBasisMatrix);
    2843:       MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->ChangeOfBasisMatrix);
    2844:       MatSetType(pcbddc->ChangeOfBasisMatrix,MATAIJ);
    2845:       MatGetBlockSize(pc->pmat,&bs);
    2846:       MatSetBlockSize(pcbddc->ChangeOfBasisMatrix,bs);
    2847:       MatSetSizes(pcbddc->ChangeOfBasisMatrix,local_size,local_size,global_size,global_size);
    2848:       MatISSetMPIXAIJPreallocation_Private(tmat,pcbddc->ChangeOfBasisMatrix,PETSC_TRUE);
    2849:       MatISGetMPIXAIJ(tmat,MAT_REUSE_MATRIX,&pcbddc->ChangeOfBasisMatrix);
    2850:       MatDestroy(&tmat);
    2851:       VecSet(pcis->vec1_global,0.0);
    2852:       VecSet(pcis->vec1_N,1.0);
    2853:       VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    2854:       VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    2855:       VecReciprocal(pcis->vec1_global);
    2856:       MatDiagonalScale(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,NULL);
    2857:     }
    2858:     /* check */
    2859:     if (pcbddc->dbg_flag) {
    2860:       PetscReal error;
    2861:       Vec       x,x_change;

    2863:       VecDuplicate(pcis->vec1_global,&x);
    2864:       VecDuplicate(pcis->vec1_global,&x_change);
    2865:       VecSetRandom(x,NULL);
    2866:       VecCopy(x,pcis->vec1_global);
    2867:       VecScatterBegin(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    2868:       VecScatterEnd(matis->rctx,x,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    2869:       MatMult(localChangeOfBasisMatrix,pcis->vec1_N,pcis->vec2_N);
    2870:       VecScatterBegin(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);
    2871:       VecScatterEnd(matis->rctx,pcis->vec2_N,x,INSERT_VALUES,SCATTER_REVERSE);
    2872:       MatMult(pcbddc->ChangeOfBasisMatrix,pcis->vec1_global,x_change);
    2873:       VecAXPY(x,-1.0,x_change);
    2874:       VecNorm(x,NORM_INFINITY,&error);
    2875:       PetscViewerFlush(pcbddc->dbg_viewer);
    2876:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Error global vs local change: %1.6e\n",error);
    2877:       VecDestroy(&x);
    2878:       VecDestroy(&x_change);
    2879:     }

    2881:     /* adapt sub_schurs computed (if any) */
    2882:     if (pcbddc->use_deluxe_scaling) {
    2883:       PCBDDCSubSchurs sub_schurs=pcbddc->sub_schurs;
    2884:       if (sub_schurs->S_Ej_all) {
    2885:         Mat S_new,tmat;
    2886:         IS is_all_N;

    2888:         ISLocalToGlobalMappingApplyIS(pcis->BtoNmap,sub_schurs->is_Ej_all,&is_all_N);
    2889:         MatGetSubMatrix(localChangeOfBasisMatrix,is_all_N,is_all_N,MAT_INITIAL_MATRIX,&tmat);
    2890:         ISDestroy(&is_all_N);
    2891:         MatPtAP(sub_schurs->S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);
    2892:         MatDestroy(&sub_schurs->S_Ej_all);
    2893:         PetscObjectReference((PetscObject)S_new);
    2894:         sub_schurs->S_Ej_all = S_new;
    2895:         MatDestroy(&S_new);
    2896:         if (sub_schurs->sum_S_Ej_all) {
    2897:           MatPtAP(sub_schurs->sum_S_Ej_all,tmat,MAT_INITIAL_MATRIX,1.0,&S_new);
    2898:           MatDestroy(&sub_schurs->sum_S_Ej_all);
    2899:           PetscObjectReference((PetscObject)S_new);
    2900:           sub_schurs->sum_S_Ej_all = S_new;
    2901:           MatDestroy(&S_new);
    2902:         }
    2903:         MatDestroy(&tmat);
    2904:       }
    2905:     }
    2906:     MatDestroy(&localChangeOfBasisMatrix);
    2907:   } else if (pcbddc->user_ChangeOfBasisMatrix) {
    2908:     PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);
    2909:     pcbddc->ChangeOfBasisMatrix = pcbddc->user_ChangeOfBasisMatrix;
    2910:   }

    2912:   /* set up change of basis context */
    2913:   if (pcbddc->ChangeOfBasisMatrix) {
    2914:     PCBDDCChange_ctx change_ctx;

    2916:     if (!pcbddc->new_global_mat) {
    2917:       PetscInt global_size,local_size;

    2919:       VecGetSize(pcis->vec1_global,&global_size);
    2920:       VecGetLocalSize(pcis->vec1_global,&local_size);
    2921:       MatCreate(PetscObjectComm((PetscObject)pc),&pcbddc->new_global_mat);
    2922:       MatSetSizes(pcbddc->new_global_mat,local_size,local_size,global_size,global_size);
    2923:       MatSetType(pcbddc->new_global_mat,MATSHELL);
    2924:       MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT,(void (*)(void))PCBDDCMatMult_Private);
    2925:       MatShellSetOperation(pcbddc->new_global_mat,MATOP_MULT_TRANSPOSE,(void (*)(void))PCBDDCMatMultTranspose_Private);
    2926:       PetscNew(&change_ctx);
    2927:       MatShellSetContext(pcbddc->new_global_mat,change_ctx);
    2928:     } else {
    2929:       MatShellGetContext(pcbddc->new_global_mat,&change_ctx);
    2930:       MatDestroy(&change_ctx->global_change);
    2931:       VecDestroyVecs(2,&change_ctx->work);
    2932:     }
    2933:     if (!pcbddc->user_ChangeOfBasisMatrix) {
    2934:       PetscObjectReference((PetscObject)pcbddc->ChangeOfBasisMatrix);
    2935:       change_ctx->global_change = pcbddc->ChangeOfBasisMatrix;
    2936:     } else {
    2937:       PetscObjectReference((PetscObject)pcbddc->user_ChangeOfBasisMatrix);
    2938:       change_ctx->global_change = pcbddc->user_ChangeOfBasisMatrix;
    2939:     }
    2940:     VecDuplicateVecs(pcis->vec1_global,2,&change_ctx->work);
    2941:     MatSetUp(pcbddc->new_global_mat);
    2942:     MatAssemblyBegin(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);
    2943:     MatAssemblyEnd(pcbddc->new_global_mat,MAT_FINAL_ASSEMBLY);
    2944:   }

    2946:   /* check if a new primal space has been introduced */
    2947:   pcbddc->new_primal_space_local = PETSC_TRUE;
    2948:   if (olocal_primal_size == pcbddc->local_primal_size) {
    2949:     PetscMemcmp(pcbddc->local_primal_ref_node,olocal_primal_ref_node,olocal_primal_size_cc*sizeof(PetscScalar),&pcbddc->new_primal_space_local);
    2950:     pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
    2951:     if (!pcbddc->new_primal_space_local) {
    2952:       PetscMemcmp(pcbddc->local_primal_ref_mult,olocal_primal_ref_mult,olocal_primal_size_cc*sizeof(PetscScalar),&pcbddc->new_primal_space_local);
    2953:       pcbddc->new_primal_space_local = (PetscBool)(!pcbddc->new_primal_space_local);
    2954:     }
    2955:   }
    2956:   PetscFree2(olocal_primal_ref_node,olocal_primal_ref_mult);
    2957:   /* new_primal_space will be used for numbering of coarse dofs, so it should be the same across all subdomains */
    2958:   MPIU_Allreduce(&pcbddc->new_primal_space_local,&pcbddc->new_primal_space,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));

    2960:   /* flush dbg viewer */
    2961:   if (pcbddc->dbg_flag) {
    2962:     PetscViewerFlush(pcbddc->dbg_viewer);
    2963:   }

    2965:   /* free workspace */
    2966:   PetscBTDestroy(&qr_needed_idx);
    2967:   PetscBTDestroy(&change_basis);
    2968:   if (!pcbddc->adaptive_selection) {
    2969:     PetscFree3(constraints_idxs_ptr,constraints_data_ptr,constraints_n);
    2970:     PetscFree3(constraints_data,constraints_idxs,constraints_idxs_B);
    2971:   } else {
    2972:     PetscFree5(pcbddc->adaptive_constraints_n,
    2973:                       pcbddc->adaptive_constraints_idxs_ptr,
    2974:                       pcbddc->adaptive_constraints_data_ptr,
    2975:                       pcbddc->adaptive_constraints_idxs,
    2976:                       pcbddc->adaptive_constraints_data);
    2977:     PetscFree(constraints_n);
    2978:     PetscFree(constraints_idxs_B);
    2979:   }
    2980:   return(0);
    2981: }

    2985: PetscErrorCode PCBDDCAnalyzeInterface(PC pc)
    2986: {
    2987:   PC_BDDC     *pcbddc = (PC_BDDC*)pc->data;
    2988:   PC_IS       *pcis = (PC_IS*)pc->data;
    2989:   Mat_IS      *matis  = (Mat_IS*)pc->pmat->data;
    2990:   PetscInt    ierr,i,vertex_size,N;
    2991:   PetscViewer viewer=pcbddc->dbg_viewer;

    2994:   /* Reset previously computed graph */
    2995:   PCBDDCGraphReset(pcbddc->mat_graph);
    2996:   /* Init local Graph struct */
    2997:   MatGetSize(pc->pmat,&N,NULL);
    2998:   PCBDDCGraphInit(pcbddc->mat_graph,pcis->mapping,N);

    3000:   /* Check validity of the csr graph passed in by the user */
    3001:   if (pcbddc->mat_graph->nvtxs_csr != pcbddc->mat_graph->nvtxs) {
    3002:     PCBDDCGraphResetCSR(pcbddc->mat_graph);
    3003:   }

    3005:   /* Set default CSR adjacency of local dofs if not provided by the user with PCBDDCSetLocalAdjacencyGraph */
    3006:   if (!pcbddc->mat_graph->xadj || !pcbddc->mat_graph->adjncy) {
    3007:     PetscInt  *xadj,*adjncy;
    3008:     PetscInt  nvtxs;
    3009:     PetscBool flg_row=PETSC_FALSE;

    3011:     if (pcbddc->use_local_adj) {

    3013:       MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
    3014:       if (flg_row) {
    3015:         PCBDDCSetLocalAdjacencyGraph(pc,nvtxs,xadj,adjncy,PETSC_COPY_VALUES);
    3016:         pcbddc->computed_rowadj = PETSC_TRUE;
    3017:       }
    3018:       MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
    3019:     } else if (pcbddc->current_level && pcis->n_B) { /* just compute subdomain's connected components for coarser levels when the local boundary is not empty */
    3020:       IS                     is_dummy;
    3021:       ISLocalToGlobalMapping l2gmap_dummy;
    3022:       PetscInt               j,sum;
    3023:       PetscInt               *cxadj,*cadjncy;
    3024:       const PetscInt         *idxs;
    3025:       PCBDDCGraph            graph;
    3026:       PetscBT                is_on_boundary;

    3028:       ISCreateStride(PETSC_COMM_SELF,pcis->n,0,1,&is_dummy);
    3029:       ISLocalToGlobalMappingCreateIS(is_dummy,&l2gmap_dummy);
    3030:       ISDestroy(&is_dummy);
    3031:       PCBDDCGraphCreate(&graph);
    3032:       PCBDDCGraphInit(graph,l2gmap_dummy,pcis->n);
    3033:       ISLocalToGlobalMappingDestroy(&l2gmap_dummy);
    3034:       MatGetRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);
    3035:       if (flg_row) {
    3036:         graph->xadj = xadj;
    3037:         graph->adjncy = adjncy;
    3038:       }
    3039:       PCBDDCGraphSetUp(graph,1,NULL,NULL,0,NULL,NULL);
    3040:       PCBDDCGraphComputeConnectedComponents(graph);
    3041:       MatRestoreRowIJ(matis->A,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,(const PetscInt**)&xadj,(const PetscInt**)&adjncy,&flg_row);

    3043:       if (pcbddc->dbg_flag) {
    3044:         PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"[%d] Found %d subdomains (local size %d)\n",PetscGlobalRank,graph->ncc,pcis->n);
    3045:         for (i=0;i<graph->ncc;i++) {
    3046:           PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"[%d] %d cc size %d\n",PetscGlobalRank,i,graph->cptr[i+1]-graph->cptr[i]);
    3047:         }
    3048:       }

    3050:       PetscBTCreate(pcis->n,&is_on_boundary);
    3051:       ISGetIndices(pcis->is_B_local,&idxs);
    3052:       for (i=0;i<pcis->n_B;i++) {
    3053:         PetscBTSet(is_on_boundary,idxs[i]);
    3054:       }
    3055:       ISRestoreIndices(pcis->is_B_local,&idxs);

    3057:       PetscCalloc1(pcis->n+1,&cxadj);
    3058:       sum = 0;
    3059:       for (i=0;i<graph->ncc;i++) {
    3060:         PetscInt sizecc = 0;
    3061:         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
    3062:           if (PetscBTLookup(is_on_boundary,graph->queue[j])) {
    3063:             sizecc++;
    3064:           }
    3065:         }
    3066:         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
    3067:           if (PetscBTLookup(is_on_boundary,graph->queue[j])) {
    3068:             cxadj[graph->queue[j]] = sizecc;
    3069:           }
    3070:         }
    3071:         sum += sizecc*sizecc;
    3072:       }
    3073:       PetscMalloc1(sum,&cadjncy);
    3074:       sum = 0;
    3075:       for (i=0;i<pcis->n;i++) {
    3076:         PetscInt temp = cxadj[i];
    3077:         cxadj[i] = sum;
    3078:         sum += temp;
    3079:       }
    3080:       cxadj[pcis->n] = sum;
    3081:       for (i=0;i<graph->ncc;i++) {
    3082:         for (j=graph->cptr[i];j<graph->cptr[i+1];j++) {
    3083:           if (PetscBTLookup(is_on_boundary,graph->queue[j])) {
    3084:             PetscInt k,sizecc = 0;
    3085:             for (k=graph->cptr[i];k<graph->cptr[i+1];k++) {
    3086:               if (PetscBTLookup(is_on_boundary,graph->queue[k])) {
    3087:                 cadjncy[cxadj[graph->queue[j]]+sizecc]=graph->queue[k];
    3088:                 sizecc++;
    3089:               }
    3090:             }
    3091:           }
    3092:         }
    3093:       }
    3094:       if (sum) {
    3095:         PCBDDCSetLocalAdjacencyGraph(pc,pcis->n,cxadj,cadjncy,PETSC_OWN_POINTER);
    3096:       } else {
    3097:         PetscFree(cxadj);
    3098:         PetscFree(cadjncy);
    3099:       }
    3100:       graph->xadj = 0;
    3101:       graph->adjncy = 0;
    3102:       PCBDDCGraphDestroy(&graph);
    3103:       PetscBTDestroy(&is_on_boundary);
    3104:     }
    3105:   }
    3106:   if (pcbddc->dbg_flag) {
    3107:     PetscViewerFlush(pcbddc->dbg_viewer);
    3108:   }

    3110:   /* Set default dofs' splitting if no information has been provided by the user with PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal */
    3111:   vertex_size = 1;
    3112:   if (pcbddc->user_provided_isfordofs) {
    3113:     if (pcbddc->n_ISForDofs) { /* need to convert from global to local and remove references to global dofs splitting */
    3114:       PetscMalloc1(pcbddc->n_ISForDofs,&pcbddc->ISForDofsLocal);
    3115:       for (i=0;i<pcbddc->n_ISForDofs;i++) {
    3116:         PCBDDCGlobalToLocal(matis->rctx,pcis->vec1_global,pcis->vec1_N,pcbddc->ISForDofs[i],&pcbddc->ISForDofsLocal[i]);
    3117:         ISDestroy(&pcbddc->ISForDofs[i]);
    3118:       }
    3119:       pcbddc->n_ISForDofsLocal = pcbddc->n_ISForDofs;
    3120:       pcbddc->n_ISForDofs = 0;
    3121:       PetscFree(pcbddc->ISForDofs);
    3122:     }
    3123:     /* mat block size as vertex size (used for elasticity with rigid body modes as nearnullspace) */
    3124:     MatGetBlockSize(matis->A,&vertex_size);
    3125:   } else {
    3126:     if (!pcbddc->n_ISForDofsLocal) { /* field split not present, create it in local ordering */
    3127:       MatGetBlockSize(pc->pmat,&pcbddc->n_ISForDofsLocal);
    3128:       PetscMalloc1(pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal);
    3129:       for (i=0;i<pcbddc->n_ISForDofsLocal;i++) {
    3130:         ISCreateStride(PetscObjectComm((PetscObject)pc),pcis->n/pcbddc->n_ISForDofsLocal,i,pcbddc->n_ISForDofsLocal,&pcbddc->ISForDofsLocal[i]);
    3131:       }
    3132:     }
    3133:   }

    3135:   /* Setup of Graph */
    3136:   if (!pcbddc->DirichletBoundariesLocal && pcbddc->DirichletBoundaries) { /* need to convert from global to local */
    3137:     PCBDDCGlobalToLocal(matis->rctx,pcis->vec1_global,pcis->vec1_N,pcbddc->DirichletBoundaries,&pcbddc->DirichletBoundariesLocal);
    3138:   }
    3139:   if (!pcbddc->NeumannBoundariesLocal && pcbddc->NeumannBoundaries) { /* need to convert from global to local */
    3140:     PCBDDCGlobalToLocal(matis->rctx,pcis->vec1_global,pcis->vec1_N,pcbddc->NeumannBoundaries,&pcbddc->NeumannBoundariesLocal);
    3141:   }
    3142:   PCBDDCGraphSetUp(pcbddc->mat_graph,vertex_size,pcbddc->NeumannBoundariesLocal,pcbddc->DirichletBoundariesLocal,pcbddc->n_ISForDofsLocal,pcbddc->ISForDofsLocal,pcbddc->user_primal_vertices);

    3144:   /* Graph's connected components analysis */
    3145:   PCBDDCGraphComputeConnectedComponents(pcbddc->mat_graph);

    3147:   /* print some info to stdout */
    3148:   if (pcbddc->dbg_flag) {
    3149:     PCBDDCGraphASCIIView(pcbddc->mat_graph,pcbddc->dbg_flag,viewer);
    3150:   }

    3152:   /* mark topography has done */
    3153:   pcbddc->recompute_topography = PETSC_FALSE;
    3154:   return(0);
    3155: }

    3157: /* given an index sets possibly with holes, renumbers the indexes removing the holes */
    3160: PetscErrorCode PCBDDCSubsetNumbering(IS subset, IS subset_mult, PetscInt *N_n, IS *subset_n)
    3161: {
    3162:   PetscSF        sf;
    3163:   PetscLayout    map;
    3164:   const PetscInt *idxs;
    3165:   PetscInt       *leaf_data,*root_data,*gidxs;
    3166:   PetscInt       N,n,i,lbounds[2],gbounds[2],Nl;
    3167:   PetscInt       n_n,nlocals,start,first_index;
    3168:   PetscMPIInt    commsize;
    3169:   PetscBool      first_found;

    3173:   ISGetLocalSize(subset,&n);
    3174:   if (subset_mult) {
    3176:     ISGetLocalSize(subset,&i);
    3177:     if (i != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Local subset and multiplicity sizes don't match! %d != %d",n,i);
    3178:   }
    3179:   /* create workspace layout for computing global indices of subset */
    3180:   ISGetIndices(subset,&idxs);
    3181:   lbounds[0] = lbounds[1] = 0;
    3182:   for (i=0;i<n;i++) {
    3183:     if (idxs[i] < lbounds[0]) lbounds[0] = idxs[i];
    3184:     else if (idxs[i] > lbounds[1]) lbounds[1] = idxs[i];
    3185:   }
    3186:   lbounds[0] = -lbounds[0];
    3187:   MPIU_Allreduce(lbounds,gbounds,2,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)subset));
    3188:   gbounds[0] = -gbounds[0];
    3189:   N = gbounds[1] - gbounds[0] + 1;
    3190:   PetscLayoutCreate(PetscObjectComm((PetscObject)subset),&map);
    3191:   PetscLayoutSetBlockSize(map,1);
    3192:   PetscLayoutSetSize(map,N);
    3193:   PetscLayoutSetUp(map);
    3194:   PetscLayoutGetLocalSize(map,&Nl);

    3196:   /* create sf : leaf_data == multiplicity of indexes, root data == global index in layout */
    3197:   PetscMalloc2(n,&leaf_data,Nl,&root_data);
    3198:   if (subset_mult) {
    3199:     const PetscInt* idxs_mult;

    3201:     ISGetIndices(subset_mult,&idxs_mult);
    3202:     PetscMemcpy(leaf_data,idxs_mult,n*sizeof(PetscInt));
    3203:     ISRestoreIndices(subset_mult,&idxs_mult);
    3204:   } else {
    3205:     for (i=0;i<n;i++) leaf_data[i] = 1;
    3206:   }
    3207:   /* local size of new subset */
    3208:   n_n = 0;
    3209:   for (i=0;i<n;i++) n_n += leaf_data[i];

    3211:   /* global indexes in layout */
    3212:   PetscMalloc1(n_n,&gidxs); /* allocating possibly extra space in gidxs which will be used later */
    3213:   for (i=0;i<n;i++) gidxs[i] = idxs[i] - gbounds[0];
    3214:   ISRestoreIndices(subset,&idxs);
    3215:   PetscSFCreate(PetscObjectComm((PetscObject)subset),&sf);
    3216:   PetscSFSetGraphLayout(sf,map,n,NULL,PETSC_COPY_VALUES,gidxs);
    3217:   PetscLayoutDestroy(&map);

    3219:   /* reduce from leaves to roots */
    3220:   PetscMemzero(root_data,Nl*sizeof(PetscInt));
    3221:   PetscSFReduceBegin(sf,MPIU_INT,leaf_data,root_data,MPI_MAX);
    3222:   PetscSFReduceEnd(sf,MPIU_INT,leaf_data,root_data,MPI_MAX);

    3224:   /* count indexes in local part of layout */
    3225:   nlocals = 0;
    3226:   first_index = -1;
    3227:   first_found = PETSC_FALSE;
    3228:   for (i=0;i<Nl;i++) {
    3229:     if (!first_found && root_data[i]) {
    3230:       first_found = PETSC_TRUE;
    3231:       first_index = i;
    3232:     }
    3233:     nlocals += root_data[i];
    3234:   }

    3236:   /* cumulative of number of indexes and size of subset without holes */
    3237: #if defined(PETSC_HAVE_MPI_EXSCAN)
    3238:   start = 0;
    3239:   MPI_Exscan(&nlocals,&start,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)subset));
    3240: #else
    3241:   MPI_Scan(&nlocals,&start,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)subset));
    3242:   start = start-nlocals;
    3243: #endif

    3245:   if (N_n) { /* compute total size of new subset if requested */
    3246:     *N_n = start + nlocals;
    3247:     MPI_Comm_size(PetscObjectComm((PetscObject)subset),&commsize);
    3248:     MPI_Bcast(N_n,1,MPIU_INT,commsize-1,PetscObjectComm((PetscObject)subset));
    3249:   }

    3251:   /* adapt root data with cumulative */
    3252:   if (first_found) {
    3253:     PetscInt old_index;

    3255:     root_data[first_index] += start;
    3256:     old_index = first_index;
    3257:     for (i=first_index+1;i<Nl;i++) {
    3258:       if (root_data[i]) {
    3259:         root_data[i] += root_data[old_index];
    3260:         old_index = i;
    3261:       }
    3262:     }
    3263:   }

    3265:   /* from roots to leaves */
    3266:   PetscSFBcastBegin(sf,MPIU_INT,root_data,leaf_data);
    3267:   PetscSFBcastEnd(sf,MPIU_INT,root_data,leaf_data);
    3268:   PetscSFDestroy(&sf);

    3270:   /* create new IS with global indexes without holes */
    3271:   if (subset_mult) {
    3272:     const PetscInt* idxs_mult;
    3273:     PetscInt        cum;

    3275:     cum = 0;
    3276:     ISGetIndices(subset_mult,&idxs_mult);
    3277:     for (i=0;i<n;i++) {
    3278:       PetscInt j;
    3279:       for (j=0;j<idxs_mult[i];j++) gidxs[cum++] = leaf_data[i] - idxs_mult[i] + j;
    3280:     }
    3281:     ISRestoreIndices(subset_mult,&idxs_mult);
    3282:   } else {
    3283:     for (i=0;i<n;i++) {
    3284:       gidxs[i] = leaf_data[i]-1;
    3285:     }
    3286:   }
    3287:   ISCreateGeneral(PetscObjectComm((PetscObject)subset),n_n,gidxs,PETSC_OWN_POINTER,subset_n);
    3288:   PetscFree2(leaf_data,root_data);
    3289:   return(0);
    3290: }

    3294: PetscErrorCode PCBDDCOrthonormalizeVecs(PetscInt n, Vec vecs[])
    3295: {
    3296:   PetscInt       i,j;
    3297:   PetscScalar    *alphas;

    3301:   /* this implements stabilized Gram-Schmidt */
    3302:   PetscMalloc1(n,&alphas);
    3303:   for (i=0;i<n;i++) {
    3304:     VecNormalize(vecs[i],NULL);
    3305:     if (i<n) { VecMDot(vecs[i],n-i-1,&vecs[i+1],&alphas[i+1]); }
    3306:     for (j=i+1;j<n;j++) { VecAXPY(vecs[j],PetscConj(-alphas[j]),vecs[i]); }
    3307:   }
    3308:   PetscFree(alphas);
    3309:   return(0);
    3310: }

    3314: PetscErrorCode MatISGetSubassemblingPattern(Mat mat, PetscInt n_subdomains, PetscInt redprocs, IS* is_sends)
    3315: {
    3316:   IS             ranks_send_to;
    3317:   PetscInt       n_neighs,*neighs,*n_shared,**shared;
    3318:   PetscMPIInt    size,rank,color;
    3319:   PetscInt       *xadj,*adjncy;
    3320:   PetscInt       *adjncy_wgt,*v_wgt,*ranks_send_to_idx;
    3321:   PetscInt       i,local_size,threshold=0;
    3322:   PetscBool      use_vwgt=PETSC_FALSE,use_square=PETSC_FALSE;
    3323:   PetscSubcomm   subcomm;

    3327:   PetscOptionsGetBool(NULL,NULL,"-matis_partitioning_use_square",&use_square,NULL);
    3328:   PetscOptionsGetBool(NULL,NULL,"-matis_partitioning_use_vwgt",&use_vwgt,NULL);
    3329:   PetscOptionsGetInt(NULL,NULL,"-matis_partitioning_threshold",&threshold,NULL);

    3331:   /* Get info on mapping */
    3332:   ISLocalToGlobalMappingGetSize(mat->rmap->mapping,&local_size);
    3333:   ISLocalToGlobalMappingGetInfo(mat->rmap->mapping,&n_neighs,&neighs,&n_shared,&shared);

    3335:   /* build local CSR graph of subdomains' connectivity */
    3336:   PetscMalloc1(2,&xadj);
    3337:   xadj[0] = 0;
    3338:   xadj[1] = PetscMax(n_neighs-1,0);
    3339:   PetscMalloc1(xadj[1],&adjncy);
    3340:   PetscMalloc1(xadj[1],&adjncy_wgt);

    3342:   if (threshold) {
    3343:     PetscInt xadj_count = 0;
    3344:     for (i=1;i<n_neighs;i++) {
    3345:       if (n_shared[i] > threshold) {
    3346:         adjncy[xadj_count] = neighs[i];
    3347:         adjncy_wgt[xadj_count] = n_shared[i];
    3348:         xadj_count++;
    3349:       }
    3350:     }
    3351:     xadj[1] = xadj_count;
    3352:   } else {
    3353:     if (xadj[1]) {
    3354:       PetscMemcpy(adjncy,&neighs[1],xadj[1]*sizeof(*adjncy));
    3355:       PetscMemcpy(adjncy_wgt,&n_shared[1],xadj[1]*sizeof(*adjncy_wgt));
    3356:     }
    3357:   }
    3358:   ISLocalToGlobalMappingRestoreInfo(mat->rmap->mapping,&n_neighs,&neighs,&n_shared,&shared);
    3359:   if (use_square) {
    3360:     for (i=0;i<xadj[1];i++) {
    3361:       adjncy_wgt[i] = adjncy_wgt[i]*adjncy_wgt[i];
    3362:     }
    3363:   }
    3364:   PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);

    3366:   PetscMalloc1(1,&ranks_send_to_idx);

    3368:   /*
    3369:     Restrict work on active processes only.
    3370:   */
    3371:   PetscSubcommCreate(PetscObjectComm((PetscObject)mat),&subcomm);
    3372:   PetscSubcommSetNumber(subcomm,2); /* 2 groups, active process and not active processes */
    3373:   MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);
    3374:   PetscMPIIntCast(!local_size,&color);
    3375:   PetscSubcommSetTypeGeneral(subcomm,color,rank);
    3376:   if (color) {
    3377:     PetscFree(xadj);
    3378:     PetscFree(adjncy);
    3379:     PetscFree(adjncy_wgt);
    3380:   } else {
    3381:     Mat             subdomain_adj;
    3382:     IS              new_ranks,new_ranks_contig;
    3383:     MatPartitioning partitioner;
    3384:     PetscInt        prank,rstart=0,rend=0;
    3385:     PetscInt        *is_indices,*oldranks;
    3386:     PetscBool       aggregate;

    3388:     MPI_Comm_size(PetscSubcommChild(subcomm),&size);
    3389:     PetscMalloc1(size,&oldranks);
    3390:     prank = rank;
    3391:     MPI_Allgather(&prank,1,MPIU_INT,oldranks,1,MPIU_INT,PetscSubcommChild(subcomm));
    3392:     /*
    3393:     for (i=0;i<size;i++) {
    3394:       PetscPrintf(subcomm->comm,"oldranks[%d] = %d\n",i,oldranks[i]);
    3395:     }
    3396:     */
    3397:     for (i=0;i<xadj[1];i++) {
    3398:       PetscFindInt(adjncy[i],size,oldranks,&adjncy[i]);
    3399:     }
    3400:     PetscSortIntWithArray(xadj[1],adjncy,adjncy_wgt);
    3401:     aggregate = ((redprocs > 0 && redprocs < size) ? PETSC_TRUE : PETSC_FALSE);
    3402:     if (aggregate) {
    3403:       PetscInt    lrows,row,ncols,*cols;
    3404:       PetscMPIInt nrank;
    3405:       PetscScalar *vals;

    3407:       MPI_Comm_rank(PetscSubcommChild(subcomm),&nrank);
    3408:       lrows = 0;
    3409:       if (nrank<redprocs) {
    3410:         lrows = size/redprocs;
    3411:         if (nrank<size%redprocs) lrows++;
    3412:       }
    3413:       MatCreateAIJ(PetscSubcommChild(subcomm),lrows,lrows,size,size,50,NULL,50,NULL,&subdomain_adj);
    3414:       MatGetOwnershipRange(subdomain_adj,&rstart,&rend);
    3415:       MatSetOption(subdomain_adj,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
    3416:       MatSetOption(subdomain_adj,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
    3417:       row = nrank;
    3418:       ncols = xadj[1]-xadj[0];
    3419:       cols = adjncy;
    3420:       PetscMalloc1(ncols,&vals);
    3421:       for (i=0;i<ncols;i++) vals[i] = adjncy_wgt[i];
    3422:       MatSetValues(subdomain_adj,1,&row,ncols,cols,vals,INSERT_VALUES);
    3423:       MatAssemblyBegin(subdomain_adj,MAT_FINAL_ASSEMBLY);
    3424:       MatAssemblyEnd(subdomain_adj,MAT_FINAL_ASSEMBLY);
    3425:       PetscFree(xadj);
    3426:       PetscFree(adjncy);
    3427:       PetscFree(adjncy_wgt);
    3428:       PetscFree(vals);
    3429:     } else {
    3430:       MatCreateMPIAdj(PetscSubcommChild(subcomm),1,(PetscInt)size,xadj,adjncy,adjncy_wgt,&subdomain_adj);
    3431:     }
    3432:     /* MatView(subdomain_adj,0); */

    3434:     /* Partition */
    3435:     MatPartitioningCreate(PetscSubcommChild(subcomm),&partitioner);
    3436:     MatPartitioningSetAdjacency(partitioner,subdomain_adj);
    3437:     if (use_vwgt) {
    3438:       PetscMalloc1(1,&v_wgt);
    3439:       v_wgt[0] = local_size;
    3440:       MatPartitioningSetVertexWeights(partitioner,v_wgt);
    3441:     }
    3442:     n_subdomains = PetscMin((PetscInt)size,n_subdomains);
    3443:     MatPartitioningSetNParts(partitioner,n_subdomains);
    3444:     MatPartitioningSetFromOptions(partitioner);
    3445:     MatPartitioningApply(partitioner,&new_ranks);
    3446:     /* MatPartitioningView(partitioner,0); */

    3448:     /* renumber new_ranks to avoid "holes" in new set of processors */
    3449:     PCBDDCSubsetNumbering(new_ranks,NULL,NULL,&new_ranks_contig);
    3450:     ISDestroy(&new_ranks);
    3451:     ISGetIndices(new_ranks_contig,(const PetscInt**)&is_indices);
    3452:     if (!redprocs) {
    3453:       ranks_send_to_idx[0] = oldranks[is_indices[0]];
    3454:     } else {
    3455:       PetscInt    idxs[1];
    3456:       PetscMPIInt tag;
    3457:       MPI_Request *reqs;

    3459:       PetscObjectGetNewTag((PetscObject)subdomain_adj,&tag);
    3460:       PetscMalloc1(rend-rstart,&reqs);
    3461:       for (i=rstart;i<rend;i++) {
    3462:         MPI_Isend(is_indices+i-rstart,1,MPIU_INT,i,tag,PetscSubcommChild(subcomm),&reqs[i-rstart]);
    3463:       }
    3464:       MPI_Recv(idxs,1,MPIU_INT,MPI_ANY_SOURCE,tag,PetscSubcommChild(subcomm),MPI_STATUS_IGNORE);
    3465:       MPI_Waitall(rend-rstart,reqs,MPI_STATUSES_IGNORE);
    3466:       PetscFree(reqs);
    3467:       ranks_send_to_idx[0] = oldranks[idxs[0]];
    3468:     }
    3469:     ISRestoreIndices(new_ranks_contig,(const PetscInt**)&is_indices);
    3470:     /* clean up */
    3471:     PetscFree(oldranks);
    3472:     ISDestroy(&new_ranks_contig);
    3473:     MatDestroy(&subdomain_adj);
    3474:     MatPartitioningDestroy(&partitioner);
    3475:   }
    3476:   PetscSubcommDestroy(&subcomm);

    3478:   /* assemble parallel IS for sends */
    3479:   i = 1;
    3480:   if (color) i=0;
    3481:   ISCreateGeneral(PetscObjectComm((PetscObject)mat),i,ranks_send_to_idx,PETSC_OWN_POINTER,&ranks_send_to);
    3482:   /* get back IS */
    3483:   *is_sends = ranks_send_to;
    3484:   return(0);
    3485: }

    3487: typedef enum {MATDENSE_PRIVATE=0,MATAIJ_PRIVATE,MATBAIJ_PRIVATE,MATSBAIJ_PRIVATE}MatTypePrivate;

    3491: PetscErrorCode MatISSubassemble(Mat mat, IS is_sends, PetscInt n_subdomains, PetscBool restrict_comm, PetscBool restrict_full, MatReuse reuse, Mat *mat_n, PetscInt nis, IS isarray[])
    3492: {
    3493:   Mat                    local_mat;
    3494:   IS                     is_sends_internal;
    3495:   PetscInt               rows,cols,new_local_rows;
    3496:   PetscInt               i,bs,buf_size_idxs,buf_size_idxs_is,buf_size_vals;
    3497:   PetscBool              ismatis,isdense,newisdense,destroy_mat;
    3498:   ISLocalToGlobalMapping l2gmap;
    3499:   PetscInt*              l2gmap_indices;
    3500:   const PetscInt*        is_indices;
    3501:   MatType                new_local_type;
    3502:   /* buffers */
    3503:   PetscInt               *ptr_idxs,*send_buffer_idxs,*recv_buffer_idxs;
    3504:   PetscInt               *ptr_idxs_is,*send_buffer_idxs_is,*recv_buffer_idxs_is;
    3505:   PetscInt               *recv_buffer_idxs_local;
    3506:   PetscScalar            *ptr_vals,*send_buffer_vals,*recv_buffer_vals;
    3507:   /* MPI */
    3508:   MPI_Comm               comm,comm_n;
    3509:   PetscSubcomm           subcomm;
    3510:   PetscMPIInt            n_sends,n_recvs,commsize;
    3511:   PetscMPIInt            *iflags,*ilengths_idxs,*ilengths_vals,*ilengths_idxs_is;
    3512:   PetscMPIInt            *onodes,*onodes_is,*olengths_idxs,*olengths_idxs_is,*olengths_vals;
    3513:   PetscMPIInt            len,tag_idxs,tag_idxs_is,tag_vals,source_dest;
    3514:   MPI_Request            *send_req_idxs,*send_req_idxs_is,*send_req_vals;
    3515:   MPI_Request            *recv_req_idxs,*recv_req_idxs_is,*recv_req_vals;
    3516:   PetscErrorCode         ierr;

    3519:   /* TODO: add missing checks */
    3524:   PetscObjectTypeCompare((PetscObject)mat,MATIS,&ismatis);
    3525:   if (!ismatis) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot use %s on a matrix object which is not of type MATIS",__FUNCT__);
    3526:   MatISGetLocalMat(mat,&local_mat);
    3527:   PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&isdense);
    3528:   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Currently cannot subassemble MATIS when local matrix type is not of type SEQDENSE");
    3529:   MatGetSize(local_mat,&rows,&cols);
    3530:   if (rows != cols) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Local MATIS matrices should be square");
    3531:   if (reuse == MAT_REUSE_MATRIX && *mat_n) {
    3532:     PetscInt mrows,mcols,mnrows,mncols;
    3533:     PetscObjectTypeCompare((PetscObject)*mat_n,MATIS,&ismatis);
    3534:     if (!ismatis) SETERRQ(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_SUP,"Cannot reuse a matrix which is not of type MATIS");
    3535:     MatGetSize(mat,&mrows,&mcols);
    3536:     MatGetSize(*mat_n,&mnrows,&mncols);
    3537:     if (mrows != mnrows) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of rows %D != %D",mrows,mnrows);
    3538:     if (mcols != mncols) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot reuse matrix! Wrong number of cols %D != %D",mcols,mncols);
    3539:   }
    3540:   MatGetBlockSize(local_mat,&bs);
    3542:   /* prepare IS for sending if not provided */
    3543:   if (!is_sends) {
    3544:     if (!n_subdomains) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"You should specify either an IS or a target number of subdomains");
    3545:     MatISGetSubassemblingPattern(mat,n_subdomains,0,&is_sends_internal);
    3546:   } else {
    3547:     PetscObjectReference((PetscObject)is_sends);
    3548:     is_sends_internal = is_sends;
    3549:   }

    3551:   /* get comm */
    3552:   PetscObjectGetComm((PetscObject)mat,&comm);

    3554:   /* compute number of sends */
    3555:   ISGetLocalSize(is_sends_internal,&i);
    3556:   PetscMPIIntCast(i,&n_sends);

    3558:   /* compute number of receives */
    3559:   MPI_Comm_size(comm,&commsize);
    3560:   PetscMalloc1(commsize,&iflags);
    3561:   PetscMemzero(iflags,commsize*sizeof(*iflags));
    3562:   ISGetIndices(is_sends_internal,&is_indices);
    3563:   for (i=0;i<n_sends;i++) iflags[is_indices[i]] = 1;
    3564:   PetscGatherNumberOfMessages(comm,iflags,NULL,&n_recvs);
    3565:   PetscFree(iflags);

    3567:   /* restrict comm if requested */
    3568:   subcomm = 0;
    3569:   destroy_mat = PETSC_FALSE;
    3570:   if (restrict_comm) {
    3571:     PetscMPIInt color,subcommsize;

    3573:     color = 0;
    3574:     if (restrict_full) {
    3575:       if (!n_recvs) color = 1; /* processes not receiving anything will not partecipate in new comm (full restriction) */
    3576:     } else {
    3577:       if (!n_recvs && n_sends) color = 1; /* just those processes that are sending but not receiving anything will not partecipate in new comm */
    3578:     }
    3579:     MPIU_Allreduce(&color,&subcommsize,1,MPI_INT,MPI_SUM,comm);
    3580:     subcommsize = commsize - subcommsize;
    3581:     /* check if reuse has been requested */
    3582:     if (reuse == MAT_REUSE_MATRIX) {
    3583:       if (*mat_n) {
    3584:         PetscMPIInt subcommsize2;
    3585:         MPI_Comm_size(PetscObjectComm((PetscObject)*mat_n),&subcommsize2);
    3586:         if (subcommsize != subcommsize2) SETERRQ2(PetscObjectComm((PetscObject)*mat_n),PETSC_ERR_PLIB,"Cannot reuse matrix! wrong subcomm size %d != %d",subcommsize,subcommsize2);
    3587:         comm_n = PetscObjectComm((PetscObject)*mat_n);
    3588:       } else {
    3589:         comm_n = PETSC_COMM_SELF;
    3590:       }
    3591:     } else { /* MAT_INITIAL_MATRIX */
    3592:       PetscMPIInt rank;

    3594:       MPI_Comm_rank(comm,&rank);
    3595:       PetscSubcommCreate(comm,&subcomm);
    3596:       PetscSubcommSetNumber(subcomm,2);
    3597:       PetscSubcommSetTypeGeneral(subcomm,color,rank);
    3598:       comm_n = PetscSubcommChild(subcomm);
    3599:     }
    3600:     /* flag to destroy *mat_n if not significative */
    3601:     if (color) destroy_mat = PETSC_TRUE;
    3602:   } else {
    3603:     comm_n = comm;
    3604:   }

    3606:   /* prepare send/receive buffers */
    3607:   PetscMalloc1(commsize,&ilengths_idxs);
    3608:   PetscMemzero(ilengths_idxs,commsize*sizeof(*ilengths_idxs));
    3609:   PetscMalloc1(commsize,&ilengths_vals);
    3610:   PetscMemzero(ilengths_vals,commsize*sizeof(*ilengths_vals));
    3611:   if (nis) {
    3612:     PetscCalloc1(commsize,&ilengths_idxs_is);
    3613:   }

    3615:   /* Get data from local matrices */
    3616:   if (!isdense) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Subassembling of AIJ local matrices not yet implemented");
    3617:     /* TODO: See below some guidelines on how to prepare the local buffers */
    3618:     /*
    3619:        send_buffer_vals should contain the raw values of the local matrix
    3620:        send_buffer_idxs should contain:
    3621:        - MatType_PRIVATE type
    3622:        - PetscInt        size_of_l2gmap
    3623:        - PetscInt        global_row_indices[size_of_l2gmap]
    3624:        - PetscInt        all_other_info_which_is_needed_to_compute_preallocation_and_set_values
    3625:     */
    3626:   else {
    3627:     MatDenseGetArray(local_mat,&send_buffer_vals);
    3628:     ISLocalToGlobalMappingGetSize(mat->rmap->mapping,&i);
    3629:     PetscMalloc1(i+2,&send_buffer_idxs);
    3630:     send_buffer_idxs[0] = (PetscInt)MATDENSE_PRIVATE;
    3631:     send_buffer_idxs[1] = i;
    3632:     ISLocalToGlobalMappingGetIndices(mat->rmap->mapping,(const PetscInt**)&ptr_idxs);
    3633:     PetscMemcpy(&send_buffer_idxs[2],ptr_idxs,i*sizeof(PetscInt));
    3634:     ISLocalToGlobalMappingRestoreIndices(mat->rmap->mapping,(const PetscInt**)&ptr_idxs);
    3635:     PetscMPIIntCast(i,&len);
    3636:     for (i=0;i<n_sends;i++) {
    3637:       ilengths_vals[is_indices[i]] = len*len;
    3638:       ilengths_idxs[is_indices[i]] = len+2;
    3639:     }
    3640:   }
    3641:   PetscGatherMessageLengths2(comm,n_sends,n_recvs,ilengths_idxs,ilengths_vals,&onodes,&olengths_idxs,&olengths_vals);
    3642:   /* additional is (if any) */
    3643:   if (nis) {
    3644:     PetscMPIInt psum;
    3645:     PetscInt j;
    3646:     for (j=0,psum=0;j<nis;j++) {
    3647:       PetscInt plen;
    3648:       ISGetLocalSize(isarray[j],&plen);
    3649:       PetscMPIIntCast(plen,&len);
    3650:       psum += len+1; /* indices + lenght */
    3651:     }
    3652:     PetscMalloc1(psum,&send_buffer_idxs_is);
    3653:     for (j=0,psum=0;j<nis;j++) {
    3654:       PetscInt plen;
    3655:       const PetscInt *is_array_idxs;
    3656:       ISGetLocalSize(isarray[j],&plen);
    3657:       send_buffer_idxs_is[psum] = plen;
    3658:       ISGetIndices(isarray[j],&is_array_idxs);
    3659:       PetscMemcpy(&send_buffer_idxs_is[psum+1],is_array_idxs,plen*sizeof(PetscInt));
    3660:       ISRestoreIndices(isarray[j],&is_array_idxs);
    3661:       psum += plen+1; /* indices + lenght */
    3662:     }
    3663:     for (i=0;i<n_sends;i++) {
    3664:       ilengths_idxs_is[is_indices[i]] = psum;
    3665:     }
    3666:     PetscGatherMessageLengths(comm,n_sends,n_recvs,ilengths_idxs_is,&onodes_is,&olengths_idxs_is);
    3667:   }

    3669:   buf_size_idxs = 0;
    3670:   buf_size_vals = 0;
    3671:   buf_size_idxs_is = 0;
    3672:   for (i=0;i<n_recvs;i++) {
    3673:     buf_size_idxs += (PetscInt)olengths_idxs[i];
    3674:     buf_size_vals += (PetscInt)olengths_vals[i];
    3675:     if (nis) buf_size_idxs_is += (PetscInt)olengths_idxs_is[i];
    3676:   }
    3677:   PetscMalloc1(buf_size_idxs,&recv_buffer_idxs);
    3678:   PetscMalloc1(buf_size_vals,&recv_buffer_vals);
    3679:   PetscMalloc1(buf_size_idxs_is,&recv_buffer_idxs_is);

    3681:   /* get new tags for clean communications */
    3682:   PetscObjectGetNewTag((PetscObject)mat,&tag_idxs);
    3683:   PetscObjectGetNewTag((PetscObject)mat,&tag_vals);
    3684:   PetscObjectGetNewTag((PetscObject)mat,&tag_idxs_is);

    3686:   /* allocate for requests */
    3687:   PetscMalloc1(n_sends,&send_req_idxs);
    3688:   PetscMalloc1(n_sends,&send_req_vals);
    3689:   PetscMalloc1(n_sends,&send_req_idxs_is);
    3690:   PetscMalloc1(n_recvs,&recv_req_idxs);
    3691:   PetscMalloc1(n_recvs,&recv_req_vals);
    3692:   PetscMalloc1(n_recvs,&recv_req_idxs_is);

    3694:   /* communications */
    3695:   ptr_idxs = recv_buffer_idxs;
    3696:   ptr_vals = recv_buffer_vals;
    3697:   ptr_idxs_is = recv_buffer_idxs_is;
    3698:   for (i=0;i<n_recvs;i++) {
    3699:     source_dest = onodes[i];
    3700:     MPI_Irecv(ptr_idxs,olengths_idxs[i],MPIU_INT,source_dest,tag_idxs,comm,&recv_req_idxs[i]);
    3701:     MPI_Irecv(ptr_vals,olengths_vals[i],MPIU_SCALAR,source_dest,tag_vals,comm,&recv_req_vals[i]);
    3702:     ptr_idxs += olengths_idxs[i];
    3703:     ptr_vals += olengths_vals[i];
    3704:     if (nis) {
    3705:       MPI_Irecv(ptr_idxs_is,olengths_idxs_is[i],MPIU_INT,source_dest,tag_idxs_is,comm,&recv_req_idxs_is[i]);
    3706:       ptr_idxs_is += olengths_idxs_is[i];
    3707:     }
    3708:   }
    3709:   for (i=0;i<n_sends;i++) {
    3710:     PetscMPIIntCast(is_indices[i],&source_dest);
    3711:     MPI_Isend(send_buffer_idxs,ilengths_idxs[source_dest],MPIU_INT,source_dest,tag_idxs,comm,&send_req_idxs[i]);
    3712:     MPI_Isend(send_buffer_vals,ilengths_vals[source_dest],MPIU_SCALAR,source_dest,tag_vals,comm,&send_req_vals[i]);
    3713:     if (nis) {
    3714:       MPI_Isend(send_buffer_idxs_is,ilengths_idxs_is[source_dest],MPIU_INT,source_dest,tag_idxs_is,comm,&send_req_idxs_is[i]);
    3715:     }
    3716:   }
    3717:   ISRestoreIndices(is_sends_internal,&is_indices);
    3718:   ISDestroy(&is_sends_internal);

    3720:   /* assemble new l2g map */
    3721:   MPI_Waitall(n_recvs,recv_req_idxs,MPI_STATUSES_IGNORE);
    3722:   ptr_idxs = recv_buffer_idxs;
    3723:   new_local_rows = 0;
    3724:   for (i=0;i<n_recvs;i++) {
    3725:     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
    3726:     ptr_idxs += olengths_idxs[i];
    3727:   }
    3728:   PetscMalloc1(new_local_rows,&l2gmap_indices);
    3729:   ptr_idxs = recv_buffer_idxs;
    3730:   new_local_rows = 0;
    3731:   for (i=0;i<n_recvs;i++) {
    3732:     PetscMemcpy(&l2gmap_indices[new_local_rows],ptr_idxs+2,(*(ptr_idxs+1))*sizeof(PetscInt));
    3733:     new_local_rows += *(ptr_idxs+1); /* second element is the local size of the l2gmap */
    3734:     ptr_idxs += olengths_idxs[i];
    3735:   }
    3736:   PetscSortRemoveDupsInt(&new_local_rows,l2gmap_indices);
    3737:   ISLocalToGlobalMappingCreate(comm_n,1,new_local_rows,l2gmap_indices,PETSC_COPY_VALUES,&l2gmap);
    3738:   PetscFree(l2gmap_indices);

    3740:   /* infer new local matrix type from received local matrices type */
    3741:   /* currently if all local matrices are of type X, then the resulting matrix will be of type X, except for the dense case */
    3742:   /* 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) */
    3743:   if (n_recvs) {
    3744:     MatTypePrivate new_local_type_private = (MatTypePrivate)send_buffer_idxs[0];
    3745:     ptr_idxs = recv_buffer_idxs;
    3746:     for (i=0;i<n_recvs;i++) {
    3747:       if ((PetscInt)new_local_type_private != *ptr_idxs) {
    3748:         new_local_type_private = MATAIJ_PRIVATE;
    3749:         break;
    3750:       }
    3751:       ptr_idxs += olengths_idxs[i];
    3752:     }
    3753:     switch (new_local_type_private) {
    3754:       case MATDENSE_PRIVATE:
    3755:         if (n_recvs>1) { /* subassembling of dense matrices does not give a dense matrix! */
    3756:           new_local_type = MATSEQAIJ;
    3757:           bs = 1;
    3758:         } else { /* if I receive only 1 dense matrix */
    3759:           new_local_type = MATSEQDENSE;
    3760:           bs = 1;
    3761:         }
    3762:         break;
    3763:       case MATAIJ_PRIVATE:
    3764:         new_local_type = MATSEQAIJ;
    3765:         bs = 1;
    3766:         break;
    3767:       case MATBAIJ_PRIVATE:
    3768:         new_local_type = MATSEQBAIJ;
    3769:         break;
    3770:       case MATSBAIJ_PRIVATE:
    3771:         new_local_type = MATSEQSBAIJ;
    3772:         break;
    3773:       default:
    3774:         SETERRQ2(comm,PETSC_ERR_SUP,"Unsupported private type %d in %s",new_local_type_private,__FUNCT__);
    3775:         break;
    3776:     }
    3777:   } else { /* by default, new_local_type is seqdense */
    3778:     new_local_type = MATSEQDENSE;
    3779:     bs = 1;
    3780:   }

    3782:   /* create MATIS object if needed */
    3783:   if (reuse == MAT_INITIAL_MATRIX) {
    3784:     MatGetSize(mat,&rows,&cols);
    3785:     MatCreateIS(comm_n,bs,PETSC_DECIDE,PETSC_DECIDE,rows,cols,l2gmap,NULL,mat_n);
    3786:   } else {
    3787:     /* it also destroys the local matrices */
    3788:     MatSetLocalToGlobalMapping(*mat_n,l2gmap,l2gmap);
    3789:   }
    3790:   MatISGetLocalMat(*mat_n,&local_mat);
    3791:   MatSetType(local_mat,new_local_type);

    3793:   MPI_Waitall(n_recvs,recv_req_vals,MPI_STATUSES_IGNORE);

    3795:   /* Global to local map of received indices */
    3796:   PetscMalloc1(buf_size_idxs,&recv_buffer_idxs_local); /* needed for values insertion */
    3797:   ISGlobalToLocalMappingApply(l2gmap,IS_GTOLM_MASK,buf_size_idxs,recv_buffer_idxs,&i,recv_buffer_idxs_local);
    3798:   ISLocalToGlobalMappingDestroy(&l2gmap);

    3800:   /* restore attributes -> type of incoming data and its size */
    3801:   buf_size_idxs = 0;
    3802:   for (i=0;i<n_recvs;i++) {
    3803:     recv_buffer_idxs_local[buf_size_idxs] = recv_buffer_idxs[buf_size_idxs];
    3804:     recv_buffer_idxs_local[buf_size_idxs+1] = recv_buffer_idxs[buf_size_idxs+1];
    3805:     buf_size_idxs += (PetscInt)olengths_idxs[i];
    3806:   }
    3807:   PetscFree(recv_buffer_idxs);

    3809:   /* set preallocation */
    3810:   PetscObjectTypeCompare((PetscObject)local_mat,MATSEQDENSE,&newisdense);
    3811:   if (!newisdense) {
    3812:     PetscInt *new_local_nnz=0;

    3814:     ptr_idxs = recv_buffer_idxs_local;
    3815:     if (n_recvs) {
    3816:       PetscCalloc1(new_local_rows,&new_local_nnz);
    3817:     }
    3818:     for (i=0;i<n_recvs;i++) {
    3819:       PetscInt j;
    3820:       if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* preallocation provided for dense case only */
    3821:         for (j=0;j<*(ptr_idxs+1);j++) {
    3822:           new_local_nnz[*(ptr_idxs+2+j)] += *(ptr_idxs+1);
    3823:         }
    3824:       } else {
    3825:         /* TODO */
    3826:       }
    3827:       ptr_idxs += olengths_idxs[i];
    3828:     }
    3829:     if (new_local_nnz) {
    3830:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMin(new_local_nnz[i],new_local_rows);
    3831:       MatSeqAIJSetPreallocation(local_mat,0,new_local_nnz);
    3832:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] /= bs;
    3833:       MatSeqBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);
    3834:       for (i=0;i<new_local_rows;i++) new_local_nnz[i] = PetscMax(new_local_nnz[i]-i,0);
    3835:       MatSeqSBAIJSetPreallocation(local_mat,bs,0,new_local_nnz);
    3836:     } else {
    3837:       MatSetUp(local_mat);
    3838:     }
    3839:     PetscFree(new_local_nnz);
    3840:   } else {
    3841:     MatSetUp(local_mat);
    3842:   }

    3844:   /* set values */
    3845:   ptr_vals = recv_buffer_vals;
    3846:   ptr_idxs = recv_buffer_idxs_local;
    3847:   for (i=0;i<n_recvs;i++) {
    3848:     if (*ptr_idxs == (PetscInt)MATDENSE_PRIVATE) { /* values insertion provided for dense case only */
    3849:       MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_FALSE);
    3850:       MatSetValues(local_mat,*(ptr_idxs+1),ptr_idxs+2,*(ptr_idxs+1),ptr_idxs+2,ptr_vals,ADD_VALUES);
    3851:       MatAssemblyBegin(local_mat,MAT_FLUSH_ASSEMBLY);
    3852:       MatAssemblyEnd(local_mat,MAT_FLUSH_ASSEMBLY);
    3853:       MatSetOption(local_mat,MAT_ROW_ORIENTED,PETSC_TRUE);
    3854:     } else {
    3855:       /* TODO */
    3856:     }
    3857:     ptr_idxs += olengths_idxs[i];
    3858:     ptr_vals += olengths_vals[i];
    3859:   }
    3860:   MatAssemblyBegin(local_mat,MAT_FINAL_ASSEMBLY);
    3861:   MatAssemblyEnd(local_mat,MAT_FINAL_ASSEMBLY);
    3862:   MatAssemblyBegin(*mat_n,MAT_FINAL_ASSEMBLY);
    3863:   MatAssemblyEnd(*mat_n,MAT_FINAL_ASSEMBLY);
    3864:   PetscFree(recv_buffer_vals);
    3865:   PetscFree(recv_buffer_idxs_local);

    3867: #if 0
    3868:   if (!restrict_comm) { /* check */
    3869:     Vec       lvec,rvec;
    3870:     PetscReal infty_error;

    3872:     MatCreateVecs(mat,&rvec,&lvec);
    3873:     VecSetRandom(rvec,NULL);
    3874:     MatMult(mat,rvec,lvec);
    3875:     VecScale(lvec,-1.0);
    3876:     MatMultAdd(*mat_n,rvec,lvec,lvec);
    3877:     VecNorm(lvec,NORM_INFINITY,&infty_error);
    3878:     PetscPrintf(PetscObjectComm((PetscObject)mat),"Infinity error subassembling %1.6e\n",infty_error);
    3879:     VecDestroy(&rvec);
    3880:     VecDestroy(&lvec);
    3881:   }
    3882: #endif

    3884:   /* assemble new additional is (if any) */
    3885:   if (nis) {
    3886:     PetscInt **temp_idxs,*count_is,j,psum;

    3888:     MPI_Waitall(n_recvs,recv_req_idxs_is,MPI_STATUSES_IGNORE);
    3889:     PetscCalloc1(nis,&count_is);
    3890:     ptr_idxs = recv_buffer_idxs_is;
    3891:     psum = 0;
    3892:     for (i=0;i<n_recvs;i++) {
    3893:       for (j=0;j<nis;j++) {
    3894:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
    3895:         count_is[j] += plen; /* increment counting of buffer for j-th IS */
    3896:         psum += plen;
    3897:         ptr_idxs += plen+1; /* shift pointer to received data */
    3898:       }
    3899:     }
    3900:     PetscMalloc1(nis,&temp_idxs);
    3901:     PetscMalloc1(psum,&temp_idxs[0]);
    3902:     for (i=1;i<nis;i++) {
    3903:       temp_idxs[i] = temp_idxs[i-1]+count_is[i-1];
    3904:     }
    3905:     PetscMemzero(count_is,nis*sizeof(PetscInt));
    3906:     ptr_idxs = recv_buffer_idxs_is;
    3907:     for (i=0;i<n_recvs;i++) {
    3908:       for (j=0;j<nis;j++) {
    3909:         PetscInt plen = *(ptr_idxs); /* first element is the local size of IS's indices */
    3910:         PetscMemcpy(&temp_idxs[j][count_is[j]],ptr_idxs+1,plen*sizeof(PetscInt));
    3911:         count_is[j] += plen; /* increment starting point of buffer for j-th IS */
    3912:         ptr_idxs += plen+1; /* shift pointer to received data */
    3913:       }
    3914:     }
    3915:     for (i=0;i<nis;i++) {
    3916:       ISDestroy(&isarray[i]);
    3917:       PetscSortRemoveDupsInt(&count_is[i],temp_idxs[i]);
    3918:       ISCreateGeneral(comm_n,count_is[i],temp_idxs[i],PETSC_COPY_VALUES,&isarray[i]);
    3919:     }
    3920:     PetscFree(count_is);
    3921:     PetscFree(temp_idxs[0]);
    3922:     PetscFree(temp_idxs);
    3923:   }
    3924:   /* free workspace */
    3925:   PetscFree(recv_buffer_idxs_is);
    3926:   MPI_Waitall(n_sends,send_req_idxs,MPI_STATUSES_IGNORE);
    3927:   PetscFree(send_buffer_idxs);
    3928:   MPI_Waitall(n_sends,send_req_vals,MPI_STATUSES_IGNORE);
    3929:   if (isdense) {
    3930:     MatISGetLocalMat(mat,&local_mat);
    3931:     MatDenseRestoreArray(local_mat,&send_buffer_vals);
    3932:   } else {
    3933:     /* PetscFree(send_buffer_vals); */
    3934:   }
    3935:   if (nis) {
    3936:     MPI_Waitall(n_sends,send_req_idxs_is,MPI_STATUSES_IGNORE);
    3937:     PetscFree(send_buffer_idxs_is);
    3938:   }
    3939:   PetscFree(recv_req_idxs);
    3940:   PetscFree(recv_req_vals);
    3941:   PetscFree(recv_req_idxs_is);
    3942:   PetscFree(send_req_idxs);
    3943:   PetscFree(send_req_vals);
    3944:   PetscFree(send_req_idxs_is);
    3945:   PetscFree(ilengths_vals);
    3946:   PetscFree(ilengths_idxs);
    3947:   PetscFree(olengths_vals);
    3948:   PetscFree(olengths_idxs);
    3949:   PetscFree(onodes);
    3950:   if (nis) {
    3951:     PetscFree(ilengths_idxs_is);
    3952:     PetscFree(olengths_idxs_is);
    3953:     PetscFree(onodes_is);
    3954:   }
    3955:   PetscSubcommDestroy(&subcomm);
    3956:   if (destroy_mat) { /* destroy mat is true only if restrict comm is true and process will not partecipate */
    3957:     MatDestroy(mat_n);
    3958:     for (i=0;i<nis;i++) {
    3959:       ISDestroy(&isarray[i]);
    3960:     }
    3961:     *mat_n = NULL;
    3962:   }
    3963:   return(0);
    3964: }

    3966: /* temporary hack into ksp private data structure */
    3967: #include <petsc/private/kspimpl.h>

    3971: PetscErrorCode PCBDDCSetUpCoarseSolver(PC pc,PetscScalar* coarse_submat_vals)
    3972: {
    3973:   PC_BDDC                *pcbddc = (PC_BDDC*)pc->data;
    3974:   PC_IS                  *pcis = (PC_IS*)pc->data;
    3975:   Mat                    coarse_mat,coarse_mat_is,coarse_submat_dense;
    3976:   MatNullSpace           CoarseNullSpace=NULL;
    3977:   ISLocalToGlobalMapping coarse_islg;
    3978:   IS                     coarse_is,*isarray;
    3979:   PetscInt               i,im_active=-1,active_procs=-1;
    3980:   PetscInt               nis,nisdofs,nisneu;
    3981:   PC                     pc_temp;
    3982:   PCType                 coarse_pc_type;
    3983:   KSPType                coarse_ksp_type;
    3984:   PetscBool              multilevel_requested,multilevel_allowed;
    3985:   PetscBool              isredundant,isbddc,isnn,coarse_reuse;
    3986:   Mat                    t_coarse_mat_is;
    3987:   PetscInt               void_procs,ncoarse_ml,ncoarse_ds,ncoarse;
    3988:   PetscMPIInt            all_procs;
    3989:   PetscBool              csin_ml,csin_ds,csin,csin_type_simple,redist;
    3990:   PetscBool              compute_vecs = PETSC_FALSE;
    3991:   PetscScalar            *array;
    3992:   PetscErrorCode         ierr;

    3995:   /* Assign global numbering to coarse dofs */
    3996:   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 */
    3997:     PetscInt ocoarse_size;
    3998:     compute_vecs = PETSC_TRUE;
    3999:     ocoarse_size = pcbddc->coarse_size;
    4000:     PetscFree(pcbddc->global_primal_indices);
    4001:     PCBDDCComputePrimalNumbering(pc,&pcbddc->coarse_size,&pcbddc->global_primal_indices);
    4002:     /* see if we can avoid some work */
    4003:     if (pcbddc->coarse_ksp) { /* coarse ksp has already been created */
    4004:       /* if the coarse size is different or we are using adaptive selection, better to not reuse the coarse matrix */
    4005:       if (ocoarse_size != pcbddc->coarse_size || pcbddc->adaptive_selection) {
    4006:         PC        pc;
    4007:         PetscBool isbddc;

    4009:         /* temporary workaround since PCBDDC does not have a reset method so far */
    4010:         KSPGetPC(pcbddc->coarse_ksp,&pc);
    4011:         PetscObjectTypeCompare((PetscObject)pc,PCBDDC,&isbddc);
    4012:         if (isbddc) {
    4013:           PCDestroy(&pc);
    4014:         }
    4015:         KSPReset(pcbddc->coarse_ksp);
    4016:         coarse_reuse = PETSC_FALSE;
    4017:       } else { /* we can safely reuse already computed coarse matrix */
    4018:         coarse_reuse = PETSC_TRUE;
    4019:       }
    4020:     } else { /* there's no coarse ksp, so we need to create the coarse matrix too */
    4021:       coarse_reuse = PETSC_FALSE;
    4022:     }
    4023:     /* reset any subassembling information */
    4024:     ISDestroy(&pcbddc->coarse_subassembling);
    4025:     ISDestroy(&pcbddc->coarse_subassembling_init);
    4026:   } else { /* primal space is unchanged, so we can reuse coarse matrix */
    4027:     coarse_reuse = PETSC_TRUE;
    4028:   }

    4030:   /* count "active" (i.e. with positive local size) and "void" processes */
    4031:   im_active = !!(pcis->n);
    4032:   MPIU_Allreduce(&im_active,&active_procs,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
    4033:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&all_procs);
    4034:   void_procs = all_procs-active_procs;
    4035:   csin_type_simple = PETSC_TRUE;
    4036:   redist = PETSC_FALSE;
    4037:   if (pcbddc->current_level && void_procs) {
    4038:     csin_ml = PETSC_TRUE;
    4039:     ncoarse_ml = void_procs;
    4040:     /* it has no sense to redistribute on a set of processors larger than the number of active processes */
    4041:     if (pcbddc->redistribute_coarse > 0 && pcbddc->redistribute_coarse < active_procs) {
    4042:       csin_ds = PETSC_TRUE;
    4043:       ncoarse_ds = pcbddc->redistribute_coarse;
    4044:       redist = PETSC_TRUE;
    4045:     } else {
    4046:       csin_ds = PETSC_TRUE;
    4047:       ncoarse_ds = active_procs;
    4048:       redist = PETSC_TRUE;
    4049:     }
    4050:   } else {
    4051:     csin_ml = PETSC_FALSE;
    4052:     ncoarse_ml = all_procs;
    4053:     if (void_procs) {
    4054:       csin_ds = PETSC_TRUE;
    4055:       ncoarse_ds = void_procs;
    4056:       csin_type_simple = PETSC_FALSE;
    4057:     } else {
    4058:       if (pcbddc->redistribute_coarse > 0 && pcbddc->redistribute_coarse < all_procs) {
    4059:         csin_ds = PETSC_TRUE;
    4060:         ncoarse_ds = pcbddc->redistribute_coarse;
    4061:         redist = PETSC_TRUE;
    4062:       } else {
    4063:         csin_ds = PETSC_FALSE;
    4064:         ncoarse_ds = all_procs;
    4065:       }
    4066:     }
    4067:   }

    4069:   /*
    4070:     test if we can go multilevel: three conditions must be satisfied:
    4071:     - we have not exceeded the number of levels requested
    4072:     - we can actually subassemble the active processes
    4073:     - we can find a suitable number of MPI processes where we can place the subassembled problem
    4074:   */
    4075:   multilevel_allowed = PETSC_FALSE;
    4076:   multilevel_requested = PETSC_FALSE;
    4077:   if (pcbddc->current_level < pcbddc->max_levels) {
    4078:     multilevel_requested = PETSC_TRUE;
    4079:     if (active_procs/pcbddc->coarsening_ratio < 2 || ncoarse_ml/pcbddc->coarsening_ratio < 2) {
    4080:       multilevel_allowed = PETSC_FALSE;
    4081:     } else {
    4082:       multilevel_allowed = PETSC_TRUE;
    4083:     }
    4084:   }
    4085:   /* determine number of process partecipating to coarse solver */
    4086:   if (multilevel_allowed) {
    4087:     ncoarse = ncoarse_ml;
    4088:     csin = csin_ml;
    4089:     redist = PETSC_FALSE;
    4090:   } else {
    4091:     ncoarse = ncoarse_ds;
    4092:     csin = csin_ds;
    4093:   }

    4095:   /* creates temporary l2gmap and IS for coarse indexes */
    4096:   ISCreateGeneral(PetscObjectComm((PetscObject)pc),pcbddc->local_primal_size,pcbddc->global_primal_indices,PETSC_COPY_VALUES,&coarse_is);
    4097:   ISLocalToGlobalMappingCreateIS(coarse_is,&coarse_islg);

    4099:   /* creates temporary MATIS object for coarse matrix */
    4100:   MatCreateSeqDense(PETSC_COMM_SELF,pcbddc->local_primal_size,pcbddc->local_primal_size,NULL,&coarse_submat_dense);
    4101:   MatDenseGetArray(coarse_submat_dense,&array);
    4102:   PetscMemcpy(array,coarse_submat_vals,sizeof(*coarse_submat_vals)*pcbddc->local_primal_size*pcbddc->local_primal_size);
    4103:   MatDenseRestoreArray(coarse_submat_dense,&array);
    4104: #if 0
    4105:   {
    4106:     PetscViewer viewer;
    4107:     char filename[256];
    4108:     sprintf(filename,"local_coarse_mat%d.m",PetscGlobalRank);
    4109:     PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&viewer);
    4110:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    4111:     MatView(coarse_submat_dense,viewer);
    4112:     PetscViewerPopFormat(viewer);
    4113:     PetscViewerDestroy(&viewer);
    4114:   }
    4115: #endif
    4116:   MatCreateIS(PetscObjectComm((PetscObject)pc),1,PETSC_DECIDE,PETSC_DECIDE,pcbddc->coarse_size,pcbddc->coarse_size,coarse_islg,NULL,&t_coarse_mat_is);
    4117:   MatISSetLocalMat(t_coarse_mat_is,coarse_submat_dense);
    4118:   MatAssemblyBegin(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);
    4119:   MatAssemblyEnd(t_coarse_mat_is,MAT_FINAL_ASSEMBLY);
    4120:   MatDestroy(&coarse_submat_dense);

    4122:   /* compute dofs splitting and neumann boundaries for coarse dofs */
    4123:   if (multilevel_allowed && (pcbddc->n_ISForDofsLocal || pcbddc->NeumannBoundariesLocal) ) { /* protects from unneded computations */
    4124:     PetscInt               *tidxs,*tidxs2,nout,tsize,i;
    4125:     const PetscInt         *idxs;
    4126:     ISLocalToGlobalMapping tmap;

    4128:     /* create map between primal indices (in local representative ordering) and local primal numbering */
    4129:     ISLocalToGlobalMappingCreate(PETSC_COMM_SELF,1,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,PETSC_COPY_VALUES,&tmap);
    4130:     /* allocate space for temporary storage */
    4131:     PetscMalloc1(pcbddc->local_primal_size,&tidxs);
    4132:     PetscMalloc1(pcbddc->local_primal_size,&tidxs2);
    4133:     /* allocate for IS array */
    4134:     nisdofs = pcbddc->n_ISForDofsLocal;
    4135:     nisneu = !!pcbddc->NeumannBoundariesLocal;
    4136:     nis = nisdofs + nisneu;
    4137:     PetscMalloc1(nis,&isarray);
    4138:     /* dofs splitting */
    4139:     for (i=0;i<nisdofs;i++) {
    4140:       /* ISView(pcbddc->ISForDofsLocal[i],0); */
    4141:       ISGetLocalSize(pcbddc->ISForDofsLocal[i],&tsize);
    4142:       ISGetIndices(pcbddc->ISForDofsLocal[i],&idxs);
    4143:       ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
    4144:       ISRestoreIndices(pcbddc->ISForDofsLocal[i],&idxs);
    4145:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
    4146:       ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->ISForDofsLocal[i]),nout,tidxs2,PETSC_COPY_VALUES,&isarray[i]);
    4147:       /* ISView(isarray[i],0); */
    4148:     }
    4149:     /* neumann boundaries */
    4150:     if (pcbddc->NeumannBoundariesLocal) {
    4151:       /* ISView(pcbddc->NeumannBoundariesLocal,0); */
    4152:       ISGetLocalSize(pcbddc->NeumannBoundariesLocal,&tsize);
    4153:       ISGetIndices(pcbddc->NeumannBoundariesLocal,&idxs);
    4154:       ISGlobalToLocalMappingApply(tmap,IS_GTOLM_DROP,tsize,idxs,&nout,tidxs);
    4155:       ISRestoreIndices(pcbddc->NeumannBoundariesLocal,&idxs);
    4156:       ISLocalToGlobalMappingApply(coarse_islg,nout,tidxs,tidxs2);
    4157:       ISCreateGeneral(PetscObjectComm((PetscObject)pcbddc->NeumannBoundariesLocal),nout,tidxs2,PETSC_COPY_VALUES,&isarray[nisdofs]);
    4158:       /* ISView(isarray[nisdofs],0); */
    4159:     }
    4160:     /* free memory */
    4161:     PetscFree(tidxs);
    4162:     PetscFree(tidxs2);
    4163:     ISLocalToGlobalMappingDestroy(&tmap);
    4164:   } else {
    4165:     nis = 0;
    4166:     nisdofs = 0;
    4167:     nisneu = 0;
    4168:     isarray = NULL;
    4169:   }
    4170:   /* destroy no longer needed map */
    4171:   ISLocalToGlobalMappingDestroy(&coarse_islg);

    4173:   /* restrict on coarse candidates (if needed) */
    4174:   coarse_mat_is = NULL;
    4175:   if (csin) {
    4176:     if (!pcbddc->coarse_subassembling_init ) { /* creates subassembling init pattern if not present */
    4177:       if (redist) {
    4178:         PetscMPIInt rank;
    4179:         PetscInt    spc,n_spc_p1,dest[1],destsize;

    4181:         MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
    4182:         spc = active_procs/ncoarse;
    4183:         n_spc_p1 = active_procs%ncoarse;
    4184:         if (im_active) {
    4185:           destsize = 1;
    4186:           if (rank > n_spc_p1*(spc+1)-1) {
    4187:             dest[0] = n_spc_p1+(rank-(n_spc_p1*(spc+1)))/spc;
    4188:           } else {
    4189:             dest[0] = rank/(spc+1);
    4190:           }
    4191:         } else {
    4192:           destsize = 0;
    4193:         }
    4194:         ISCreateGeneral(PetscObjectComm((PetscObject)pc),destsize,dest,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);
    4195:       } else if (csin_type_simple) {
    4196:         PetscMPIInt rank;
    4197:         PetscInt    issize,isidx;

    4199:         MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
    4200:         if (im_active) {
    4201:           issize = 1;
    4202:           isidx = (PetscInt)rank;
    4203:         } else {
    4204:           issize = 0;
    4205:           isidx = -1;
    4206:         }
    4207:         ISCreateGeneral(PetscObjectComm((PetscObject)pc),issize,&isidx,PETSC_COPY_VALUES,&pcbddc->coarse_subassembling_init);
    4208:       } else { /* get a suitable subassembling pattern from MATIS code */
    4209:         MatISGetSubassemblingPattern(t_coarse_mat_is,ncoarse,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling_init);
    4210:       }

    4212:       /* we need to shift on coarse candidates either if we are not redistributing or we are redistributing and we have enough void processes */
    4213:       if (!redist || ncoarse <= void_procs) {
    4214:         PetscInt ncoarse_cand,tissize,*nisindices;
    4215:         PetscInt *coarse_candidates;
    4216:         const PetscInt* tisindices;

    4218:         /* get coarse candidates' ranks in pc communicator */
    4219:         PetscMalloc1(all_procs,&coarse_candidates);
    4220:         MPI_Allgather(&im_active,1,MPIU_INT,coarse_candidates,1,MPIU_INT,PetscObjectComm((PetscObject)pc));
    4221:         for (i=0,ncoarse_cand=0;i<all_procs;i++) {
    4222:           if (!coarse_candidates[i]) {
    4223:             coarse_candidates[ncoarse_cand++]=i;
    4224:           }
    4225:         }
    4226:         if (ncoarse_cand < ncoarse) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"This should not happen! %d < %d",ncoarse_cand,ncoarse);

    4229:         if (pcbddc->dbg_flag) {
    4230:           PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    4231:           PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init (before shift)\n");
    4232:           ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);
    4233:           PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse candidates\n");
    4234:           for (i=0;i<ncoarse_cand;i++) {
    4235:             PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"%d ",coarse_candidates[i]);
    4236:           }
    4237:           PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"\n");
    4238:           PetscViewerFlush(pcbddc->dbg_viewer);
    4239:         }
    4240:         /* shift the pattern on coarse candidates */
    4241:         ISGetLocalSize(pcbddc->coarse_subassembling_init,&tissize);
    4242:         ISGetIndices(pcbddc->coarse_subassembling_init,&tisindices);
    4243:         PetscMalloc1(tissize,&nisindices);
    4244:         for (i=0;i<tissize;i++) nisindices[i] = coarse_candidates[tisindices[i]];
    4245:         ISRestoreIndices(pcbddc->coarse_subassembling_init,&tisindices);
    4246:         ISGeneralSetIndices(pcbddc->coarse_subassembling_init,tissize,nisindices,PETSC_OWN_POINTER);
    4247:         PetscFree(coarse_candidates);
    4248:       }
    4249:       if (pcbddc->dbg_flag) {
    4250:         PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    4251:         PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init\n");
    4252:         ISView(pcbddc->coarse_subassembling_init,pcbddc->dbg_viewer);
    4253:         PetscViewerFlush(pcbddc->dbg_viewer);
    4254:       }
    4255:     }
    4256:     /* get temporary coarse mat in IS format restricted on coarse procs (plus additional index sets of isarray) */
    4257:     if (multilevel_allowed) { /* we need to keep tracking of void processes for future placements */
    4258:       MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,PETSC_FALSE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);
    4259:     } else { /* this is the last level, so use just receiving processes in subcomm */
    4260:       MatISSubassemble(t_coarse_mat_is,pcbddc->coarse_subassembling_init,0,PETSC_TRUE,PETSC_TRUE,MAT_INITIAL_MATRIX,&coarse_mat_is,nis,isarray);
    4261:     }
    4262:   } else {
    4263:     if (pcbddc->dbg_flag) {
    4264:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    4265:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Subassembling pattern init not needed\n");
    4266:       PetscViewerFlush(pcbddc->dbg_viewer);
    4267:     }
    4268:     PetscObjectReference((PetscObject)t_coarse_mat_is);
    4269:     coarse_mat_is = t_coarse_mat_is;
    4270:   }

    4272:   /* create local to global scatters for coarse problem */
    4273:   if (compute_vecs) {
    4274:     PetscInt lrows;
    4275:     VecDestroy(&pcbddc->coarse_vec);
    4276:     if (coarse_mat_is) {
    4277:       MatGetLocalSize(coarse_mat_is,&lrows,NULL);
    4278:     } else {
    4279:       lrows = 0;
    4280:     }
    4281:     VecCreate(PetscObjectComm((PetscObject)pc),&pcbddc->coarse_vec);
    4282:     VecSetSizes(pcbddc->coarse_vec,lrows,PETSC_DECIDE);
    4283:     VecSetType(pcbddc->coarse_vec,VECSTANDARD);
    4284:     VecScatterDestroy(&pcbddc->coarse_loc_to_glob);
    4285:     VecScatterCreate(pcbddc->vec1_P,NULL,pcbddc->coarse_vec,coarse_is,&pcbddc->coarse_loc_to_glob);
    4286:   }
    4287:   ISDestroy(&coarse_is);
    4288:   MatDestroy(&t_coarse_mat_is);

    4290:   /* set defaults for coarse KSP and PC */
    4291:   if (multilevel_allowed) {
    4292:     coarse_ksp_type = KSPRICHARDSON;
    4293:     coarse_pc_type = PCBDDC;
    4294:   } else {
    4295:     coarse_ksp_type = KSPPREONLY;
    4296:     coarse_pc_type = PCREDUNDANT;
    4297:   }

    4299:   /* print some info if requested */
    4300:   if (pcbddc->dbg_flag) {
    4301:     if (!multilevel_allowed) {
    4302:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    4303:       if (multilevel_requested) {
    4304:         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);
    4305:       } else if (pcbddc->max_levels) {
    4306:         PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Maximum number of requested levels reached (%d)\n",pcbddc->max_levels);
    4307:       }
    4308:       PetscViewerFlush(pcbddc->dbg_viewer);
    4309:     }
    4310:   }

    4312:   /* create the coarse KSP object only once with defaults */
    4313:   if (coarse_mat_is) {
    4314:     MatReuse coarse_mat_reuse;
    4315:     PetscViewer dbg_viewer = NULL;
    4316:     if (pcbddc->dbg_flag) {
    4317:       dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)coarse_mat_is));
    4318:       PetscViewerASCIIAddTab(dbg_viewer,2*pcbddc->current_level);
    4319:     }
    4320:     if (!pcbddc->coarse_ksp) {
    4321:       char prefix[256],str_level[16];
    4322:       size_t len;
    4323:       KSPCreate(PetscObjectComm((PetscObject)coarse_mat_is),&pcbddc->coarse_ksp);
    4324:       KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,pc->erroriffailure);
    4325:       PetscObjectIncrementTabLevel((PetscObject)pcbddc->coarse_ksp,(PetscObject)pc,1);
    4326:       KSPSetTolerances(pcbddc->coarse_ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1);
    4327:       KSPSetOperators(pcbddc->coarse_ksp,coarse_mat_is,coarse_mat_is);
    4328:       KSPSetType(pcbddc->coarse_ksp,coarse_ksp_type);
    4329:       KSPSetNormType(pcbddc->coarse_ksp,KSP_NORM_NONE);
    4330:       KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
    4331:       PCSetType(pc_temp,coarse_pc_type);
    4332:       /* prefix */
    4333:       PetscStrcpy(prefix,"");
    4334:       PetscStrcpy(str_level,"");
    4335:       if (!pcbddc->current_level) {
    4336:         PetscStrcpy(prefix,((PetscObject)pc)->prefix);
    4337:         PetscStrcat(prefix,"pc_bddc_coarse_");
    4338:       } else {
    4339:         PetscStrlen(((PetscObject)pc)->prefix,&len);
    4340:         if (pcbddc->current_level>1) len -= 3; /* remove "lX_" with X level number */
    4341:         if (pcbddc->current_level>10) len -= 1; /* remove another char from level number */
    4342:         PetscStrncpy(prefix,((PetscObject)pc)->prefix,len+1);
    4343:         sprintf(str_level,"l%d_",(int)(pcbddc->current_level));
    4344:         PetscStrcat(prefix,str_level);
    4345:       }
    4346:       KSPSetOptionsPrefix(pcbddc->coarse_ksp,prefix);
    4347:       /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
    4348:       PCBDDCSetLevel(pc_temp,pcbddc->current_level+1);
    4349:       PCBDDCSetCoarseningRatio(pc_temp,pcbddc->coarsening_ratio);
    4350:       PCBDDCSetLevels(pc_temp,pcbddc->max_levels);
    4351:       /* allow user customization */
    4352:       KSPSetFromOptions(pcbddc->coarse_ksp);
    4353:     }
    4354:     /* propagate BDDC info to the next level (these are dummy calls if pc_temp is not of type PCBDDC) */
    4355:     KSPGetPC(pcbddc->coarse_ksp,&pc_temp);
    4356:     if (nisdofs) {
    4357:       PCBDDCSetDofsSplitting(pc_temp,nisdofs,isarray);
    4358:       for (i=0;i<nisdofs;i++) {
    4359:         ISDestroy(&isarray[i]);
    4360:       }
    4361:     }
    4362:     if (nisneu) {
    4363:       PCBDDCSetNeumannBoundaries(pc_temp,isarray[nisdofs]);
    4364:       ISDestroy(&isarray[nisdofs]);
    4365:     }

    4367:     /* get some info after set from options */
    4368:     PetscObjectTypeCompare((PetscObject)pc_temp,PCNN,&isnn);
    4369:     PetscObjectTypeCompare((PetscObject)pc_temp,PCBDDC,&isbddc);
    4370:     PetscObjectTypeCompare((PetscObject)pc_temp,PCREDUNDANT,&isredundant);
    4371:     if (isbddc && !multilevel_allowed) { /* multilevel can only be requested via pc_bddc_set_levels */
    4372:       PCSetType(pc_temp,coarse_pc_type);
    4373:       isbddc = PETSC_FALSE;
    4374:     }
    4375:     PCFactorSetReuseFill(pc_temp,PETSC_TRUE);
    4376:     if (isredundant) {
    4377:       KSP inner_ksp;
    4378:       PC  inner_pc;
    4379:       PCRedundantGetKSP(pc_temp,&inner_ksp);
    4380:       KSPGetPC(inner_ksp,&inner_pc);
    4381:       PCFactorSetReuseFill(inner_pc,PETSC_TRUE);
    4382:     }

    4384:     /* assemble coarse matrix */
    4385:     if (coarse_reuse) {
    4386:       KSPGetOperators(pcbddc->coarse_ksp,&coarse_mat,NULL);
    4387:       PetscObjectReference((PetscObject)coarse_mat);
    4388:       coarse_mat_reuse = MAT_REUSE_MATRIX;
    4389:     } else {
    4390:       coarse_mat_reuse = MAT_INITIAL_MATRIX;
    4391:     }
    4392:     if (isbddc || isnn) {
    4393:       if (pcbddc->coarsening_ratio > 1) {
    4394:         if (!pcbddc->coarse_subassembling) { /* subassembling info is not present */
    4395:           MatISGetSubassemblingPattern(coarse_mat_is,active_procs/pcbddc->coarsening_ratio,pcbddc->coarse_adj_red,&pcbddc->coarse_subassembling);
    4396:           if (pcbddc->dbg_flag) {
    4397:             PetscViewerASCIIPrintf(dbg_viewer,"--------------------------------------------------\n");
    4398:             PetscViewerASCIIPrintf(dbg_viewer,"Subassembling pattern\n");
    4399:             ISView(pcbddc->coarse_subassembling,dbg_viewer);
    4400:             PetscViewerFlush(dbg_viewer);
    4401:           }
    4402:         }
    4403:         MatISSubassemble(coarse_mat_is,pcbddc->coarse_subassembling,0,PETSC_FALSE,PETSC_FALSE,coarse_mat_reuse,&coarse_mat,0,NULL);
    4404:       } else {
    4405:         PetscObjectReference((PetscObject)coarse_mat_is);
    4406:         coarse_mat = coarse_mat_is;
    4407:       }
    4408:     } else {
    4409:       MatISGetMPIXAIJ(coarse_mat_is,coarse_mat_reuse,&coarse_mat);
    4410:     }
    4411:     MatDestroy(&coarse_mat_is);

    4413:     /* propagate symmetry info of coarse matrix */
    4414:     MatSetOption(coarse_mat,MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);
    4415:     if (pc->pmat->symmetric_set) {
    4416:       MatSetOption(coarse_mat,MAT_SYMMETRIC,pc->pmat->symmetric);
    4417:     }
    4418:     if (pc->pmat->hermitian_set) {
    4419:       MatSetOption(coarse_mat,MAT_HERMITIAN,pc->pmat->hermitian);
    4420:     }
    4421:     if (pc->pmat->spd_set) {
    4422:       MatSetOption(coarse_mat,MAT_SPD,pc->pmat->spd);
    4423:     }
    4424:     /* set operators */
    4425:     KSPSetOperators(pcbddc->coarse_ksp,coarse_mat,coarse_mat);
    4426:     if (pcbddc->dbg_flag) {
    4427:       PetscViewerASCIISubtractTab(dbg_viewer,2*pcbddc->current_level);
    4428:     }
    4429:   } else { /* processes non partecipating to coarse solver (if any) */
    4430:     coarse_mat = 0;
    4431:   }
    4432:   PetscFree(isarray);
    4433: #if 0
    4434:   {
    4435:     PetscViewer viewer;
    4436:     char filename[256];
    4437:     sprintf(filename,"coarse_mat.m");
    4438:     PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,&viewer);
    4439:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    4440:     MatView(coarse_mat,viewer);
    4441:     PetscViewerPopFormat(viewer);
    4442:     PetscViewerDestroy(&viewer);
    4443:   }
    4444: #endif

    4446:   /* Compute coarse null space (special handling by BDDC only) */
    4447: #if 0
    4448:   if (pcbddc->NullSpace) {
    4449:     PCBDDCNullSpaceAssembleCoarse(pc,coarse_mat,&CoarseNullSpace);
    4450:   }
    4451: #endif

    4453:   if (pcbddc->coarse_ksp) {
    4454:     Vec crhs,csol;
    4455:     PetscBool ispreonly;

    4457:     if (CoarseNullSpace) {
    4458:       if (isbddc) {
    4459:         PCBDDCSetNullSpace(pc_temp,CoarseNullSpace);
    4460:       } else {
    4461:         MatSetNullSpace(coarse_mat,CoarseNullSpace);
    4462:       }
    4463:     }
    4464:     /* setup coarse ksp */
    4465:     KSPSetUp(pcbddc->coarse_ksp);
    4466:     KSPGetSolution(pcbddc->coarse_ksp,&csol);
    4467:     KSPGetRhs(pcbddc->coarse_ksp,&crhs);
    4468:     /* hack */
    4469:     if (!csol) {
    4470:       MatCreateVecs(coarse_mat,&((pcbddc->coarse_ksp)->vec_sol),NULL);
    4471:     }
    4472:     if (!crhs) {
    4473:       MatCreateVecs(coarse_mat,NULL,&((pcbddc->coarse_ksp)->vec_rhs));
    4474:     }
    4475:     /* Check coarse problem if in debug mode or if solving with an iterative method */
    4476:     PetscObjectTypeCompare((PetscObject)pcbddc->coarse_ksp,KSPPREONLY,&ispreonly);
    4477:     if (pcbddc->dbg_flag || (!ispreonly && pcbddc->use_coarse_estimates) ) {
    4478:       KSP       check_ksp;
    4479:       KSPType   check_ksp_type;
    4480:       PC        check_pc;
    4481:       Vec       check_vec,coarse_vec;
    4482:       PetscReal abs_infty_error,infty_error,lambda_min=1.0,lambda_max=1.0;
    4483:       PetscInt  its;
    4484:       PetscBool compute_eigs;
    4485:       PetscReal *eigs_r,*eigs_c;
    4486:       PetscInt  neigs;
    4487:       const char *prefix;

    4489:       /* Create ksp object suitable for estimation of extreme eigenvalues */
    4490:       KSPCreate(PetscObjectComm((PetscObject)pcbddc->coarse_ksp),&check_ksp);
    4491:       KSPSetErrorIfNotConverged(pcbddc->coarse_ksp,pc->erroriffailure);
    4492:       KSPSetOperators(check_ksp,coarse_mat,coarse_mat);
    4493:       KSPSetTolerances(check_ksp,1.e-12,1.e-12,PETSC_DEFAULT,pcbddc->coarse_size);
    4494:       if (ispreonly) {
    4495:         check_ksp_type = KSPPREONLY;
    4496:         compute_eigs = PETSC_FALSE;
    4497:       } else {
    4498:         check_ksp_type = KSPGMRES;
    4499:         compute_eigs = PETSC_TRUE;
    4500:       }
    4501:       KSPSetType(check_ksp,check_ksp_type);
    4502:       KSPSetComputeSingularValues(check_ksp,compute_eigs);
    4503:       KSPSetComputeEigenvalues(check_ksp,compute_eigs);
    4504:       KSPGMRESSetRestart(check_ksp,pcbddc->coarse_size+1);
    4505:       KSPGetOptionsPrefix(pcbddc->coarse_ksp,&prefix);
    4506:       KSPSetOptionsPrefix(check_ksp,prefix);
    4507:       KSPAppendOptionsPrefix(check_ksp,"check_");
    4508:       KSPSetFromOptions(check_ksp);
    4509:       KSPSetUp(check_ksp);
    4510:       KSPGetPC(pcbddc->coarse_ksp,&check_pc);
    4511:       KSPSetPC(check_ksp,check_pc);
    4512:       /* create random vec */
    4513:       KSPGetSolution(pcbddc->coarse_ksp,&coarse_vec);
    4514:       VecDuplicate(coarse_vec,&check_vec);
    4515:       VecSetRandom(check_vec,NULL);
    4516:       if (CoarseNullSpace) {
    4517:         MatNullSpaceRemove(CoarseNullSpace,check_vec);
    4518:       }
    4519:       MatMult(coarse_mat,check_vec,coarse_vec);
    4520:       /* solve coarse problem */
    4521:       KSPSolve(check_ksp,coarse_vec,coarse_vec);
    4522:       if (CoarseNullSpace) {
    4523:         MatNullSpaceRemove(CoarseNullSpace,coarse_vec);
    4524:       }
    4525:       /* set eigenvalue estimation if preonly has not been requested */
    4526:       if (compute_eigs) {
    4527:         PetscMalloc1(pcbddc->coarse_size+1,&eigs_r);
    4528:         PetscMalloc1(pcbddc->coarse_size+1,&eigs_c);
    4529:         KSPComputeEigenvalues(check_ksp,pcbddc->coarse_size+1,eigs_r,eigs_c,&neigs);
    4530:         lambda_max = eigs_r[neigs-1];
    4531:         lambda_min = eigs_r[0];
    4532:         if (pcbddc->use_coarse_estimates) {
    4533:           if (lambda_max>lambda_min) {
    4534:             KSPChebyshevSetEigenvalues(pcbddc->coarse_ksp,lambda_max,lambda_min);
    4535:             KSPRichardsonSetScale(pcbddc->coarse_ksp,2.0/(lambda_max+lambda_min));
    4536:           }
    4537:         }
    4538:       }

    4540:       /* check coarse problem residual error */
    4541:       if (pcbddc->dbg_flag) {
    4542:         PetscViewer dbg_viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)pcbddc->coarse_ksp));
    4543:         PetscViewerASCIIAddTab(dbg_viewer,2*(pcbddc->current_level+1));
    4544:         VecAXPY(check_vec,-1.0,coarse_vec);
    4545:         VecNorm(check_vec,NORM_INFINITY,&infty_error);
    4546:         MatMult(coarse_mat,check_vec,coarse_vec);
    4547:         VecNorm(coarse_vec,NORM_INFINITY,&abs_infty_error);
    4548:         VecDestroy(&check_vec);
    4549:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem details (use estimates %d)\n",pcbddc->use_coarse_estimates);
    4550:         PetscObjectPrintClassNamePrefixType((PetscObject)(pcbddc->coarse_ksp),dbg_viewer);
    4551:         PetscObjectPrintClassNamePrefixType((PetscObject)(check_pc),dbg_viewer);
    4552:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem exact infty_error   : %1.6e\n",infty_error);
    4553:         PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem residual infty_error: %1.6e\n",abs_infty_error);
    4554:         if (compute_eigs) {
    4555:           PetscReal lambda_max_s,lambda_min_s;
    4556:           KSPGetType(check_ksp,&check_ksp_type);
    4557:           KSPGetIterationNumber(check_ksp,&its);
    4558:           KSPComputeExtremeSingularValues(check_ksp,&lambda_max_s,&lambda_min_s);
    4559:           PetscViewerASCIIPrintf(dbg_viewer,"Coarse problem eigenvalues (estimated with %d iterations of %s): %1.6e %1.6e (%1.6e %1.6e)\n",its,check_ksp_type,lambda_min,lambda_max,lambda_min_s,lambda_max_s);
    4560:           for (i=0;i<neigs;i++) {
    4561:             PetscViewerASCIIPrintf(dbg_viewer,"%1.6e %1.6ei\n",eigs_r[i],eigs_c[i]);
    4562:           }
    4563:         }
    4564:         PetscViewerFlush(dbg_viewer);
    4565:         PetscViewerASCIISubtractTab(dbg_viewer,2*(pcbddc->current_level+1));
    4566:       }
    4567:       KSPDestroy(&check_ksp);
    4568:       if (compute_eigs) {
    4569:         PetscFree(eigs_r);
    4570:         PetscFree(eigs_c);
    4571:       }
    4572:     }
    4573:   }
    4574:   /* print additional info */
    4575:   if (pcbddc->dbg_flag) {
    4576:     /* waits until all processes reaches this point */
    4577:     PetscBarrier((PetscObject)pc);
    4578:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Coarse solver setup completed at level %d\n",pcbddc->current_level);
    4579:     PetscViewerFlush(pcbddc->dbg_viewer);
    4580:   }

    4582:   /* free memory */
    4583:   MatNullSpaceDestroy(&CoarseNullSpace);
    4584:   MatDestroy(&coarse_mat);
    4585:   return(0);
    4586: }

    4590: PetscErrorCode PCBDDCComputePrimalNumbering(PC pc,PetscInt* coarse_size_n,PetscInt** local_primal_indices_n)
    4591: {
    4592:   PC_BDDC*       pcbddc = (PC_BDDC*)pc->data;
    4593:   PC_IS*         pcis = (PC_IS*)pc->data;
    4594:   Mat_IS*        matis = (Mat_IS*)pc->pmat->data;
    4595:   IS             subset,subset_mult,subset_n;
    4596:   PetscInt       local_size,coarse_size=0;
    4597:   PetscInt       *local_primal_indices=NULL;
    4598:   const PetscInt *t_local_primal_indices;

    4602:   /* Compute global number of coarse dofs */
    4603:   if (pcbddc->local_primal_size && !pcbddc->local_primal_ref_node) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"BDDC ConstraintsSetUp should be called first");
    4604:   ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_node,PETSC_COPY_VALUES,&subset_n);
    4605:   ISLocalToGlobalMappingApplyIS(pcis->mapping,subset_n,&subset);
    4606:   ISDestroy(&subset_n);
    4607:   ISCreateGeneral(PetscObjectComm((PetscObject)(pc->pmat)),pcbddc->local_primal_size_cc,pcbddc->local_primal_ref_mult,PETSC_COPY_VALUES,&subset_mult);
    4608:   PCBDDCSubsetNumbering(subset,subset_mult,&coarse_size,&subset_n);
    4609:   ISDestroy(&subset);
    4610:   ISDestroy(&subset_mult);
    4611:   ISGetLocalSize(subset_n,&local_size);
    4612:   if (local_size != pcbddc->local_primal_size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid number of local primal indices computed %D != %D",local_size,pcbddc->local_primal_size);
    4613:   PetscMalloc1(local_size,&local_primal_indices);
    4614:   ISGetIndices(subset_n,&t_local_primal_indices);
    4615:   PetscMemcpy(local_primal_indices,t_local_primal_indices,local_size*sizeof(PetscInt));
    4616:   ISRestoreIndices(subset_n,&t_local_primal_indices);
    4617:   ISDestroy(&subset_n);

    4619:   /* check numbering */
    4620:   if (pcbddc->dbg_flag) {
    4621:     PetscScalar coarsesum,*array;
    4622:     PetscInt    i;
    4623:     PetscBool   set_error = PETSC_FALSE,set_error_reduced = PETSC_FALSE;

    4625:     PetscViewerFlush(pcbddc->dbg_viewer);
    4626:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"--------------------------------------------------\n");
    4627:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Check coarse indices\n");
    4628:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    4629:     VecSet(pcis->vec1_N,0.0);
    4630:     for (i=0;i<pcbddc->local_primal_size;i++) {
    4631:       VecSetValue(pcis->vec1_N,pcbddc->primal_indices_local_idxs[i],1.0,INSERT_VALUES);
    4632:     }
    4633:     VecAssemblyBegin(pcis->vec1_N);
    4634:     VecAssemblyEnd(pcis->vec1_N);
    4635:     VecSet(pcis->vec1_global,0.0);
    4636:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    4637:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    4638:     VecScatterBegin(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    4639:     VecScatterEnd(matis->rctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    4640:     VecGetArray(pcis->vec1_N,&array);
    4641:     for (i=0;i<pcis->n;i++) {
    4642:       if (array[i] == 1.0) {
    4643:         set_error = PETSC_TRUE;
    4644:         PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d: local index %d owned by a single process!\n",PetscGlobalRank,i);
    4645:       }
    4646:     }
    4647:     MPIU_Allreduce(&set_error,&set_error_reduced,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)pc));
    4648:     PetscViewerFlush(pcbddc->dbg_viewer);
    4649:     for (i=0;i<pcis->n;i++) {
    4650:       if (PetscRealPart(array[i]) > 0.0) array[i] = 1.0/PetscRealPart(array[i]);
    4651:     }
    4652:     VecRestoreArray(pcis->vec1_N,&array);
    4653:     VecSet(pcis->vec1_global,0.0);
    4654:     VecScatterBegin(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    4655:     VecScatterEnd(matis->rctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    4656:     VecSum(pcis->vec1_global,&coarsesum);
    4657:     PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Size of coarse problem is %d (%lf)\n",coarse_size,PetscRealPart(coarsesum));
    4658:     if (pcbddc->dbg_flag > 1 || set_error_reduced) {
    4659:       PetscInt *gidxs;

    4661:       PetscMalloc1(pcbddc->local_primal_size,&gidxs);
    4662:       ISLocalToGlobalMappingApply(pcis->mapping,pcbddc->local_primal_size,pcbddc->primal_indices_local_idxs,gidxs);
    4663:       PetscViewerASCIIPrintf(pcbddc->dbg_viewer,"Distribution of local primal indices\n");
    4664:       PetscViewerFlush(pcbddc->dbg_viewer);
    4665:       PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d\n",PetscGlobalRank);
    4666:       for (i=0;i<pcbddc->local_primal_size;i++) {
    4667:         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]);
    4668:       }
    4669:       PetscViewerFlush(pcbddc->dbg_viewer);
    4670:       PetscFree(gidxs);
    4671:     }
    4672:     PetscViewerFlush(pcbddc->dbg_viewer);
    4673:     PetscViewerASCIIPushSynchronized(pcbddc->dbg_viewer);
    4674:     if (set_error_reduced) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"BDDC Numbering of coarse dofs failed");
    4675:   }
    4676:   /* PetscPrintf(PetscObjectComm((PetscObject)pc),"Size of coarse problem is %d\n",coarse_size); */
    4677:   /* get back data */
    4678:   *coarse_size_n = coarse_size;
    4679:   *local_primal_indices_n = local_primal_indices;
    4680:   return(0);
    4681: }

    4685: PetscErrorCode PCBDDCGlobalToLocal(VecScatter g2l_ctx,Vec gwork, Vec lwork, IS globalis, IS* localis)
    4686: {
    4687:   IS             localis_t;
    4688:   PetscInt       i,lsize,*idxs,n;
    4689:   PetscScalar    *vals;

    4693:   /* get indices in local ordering exploiting local to global map */
    4694:   ISGetLocalSize(globalis,&lsize);
    4695:   PetscMalloc1(lsize,&vals);
    4696:   for (i=0;i<lsize;i++) vals[i] = 1.0;
    4697:   ISGetIndices(globalis,(const PetscInt**)&idxs);
    4698:   VecSet(gwork,0.0);
    4699:   VecSet(lwork,0.0);
    4700:   if (idxs) { /* multilevel guard */
    4701:     VecSetValues(gwork,lsize,idxs,vals,INSERT_VALUES);
    4702:   }
    4703:   VecAssemblyBegin(gwork);
    4704:   ISRestoreIndices(globalis,(const PetscInt**)&idxs);
    4705:   PetscFree(vals);
    4706:   VecAssemblyEnd(gwork);
    4707:   /* now compute set in local ordering */
    4708:   VecScatterBegin(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);
    4709:   VecScatterEnd(g2l_ctx,gwork,lwork,INSERT_VALUES,SCATTER_FORWARD);
    4710:   VecGetArrayRead(lwork,(const PetscScalar**)&vals);
    4711:   VecGetSize(lwork,&n);
    4712:   for (i=0,lsize=0;i<n;i++) {
    4713:     if (PetscRealPart(vals[i]) > 0.5) {
    4714:       lsize++;
    4715:     }
    4716:   }
    4717:   PetscMalloc1(lsize,&idxs);
    4718:   for (i=0,lsize=0;i<n;i++) {
    4719:     if (PetscRealPart(vals[i]) > 0.5) {
    4720:       idxs[lsize++] = i;
    4721:     }
    4722:   }
    4723:   VecRestoreArrayRead(lwork,(const PetscScalar**)&vals);
    4724:   ISCreateGeneral(PetscObjectComm((PetscObject)gwork),lsize,idxs,PETSC_OWN_POINTER,&localis_t);
    4725:   *localis = localis_t;
    4726:   return(0);
    4727: }

    4729: /* the next two functions will be called in KSPMatMult if a change of basis has been requested */
    4732: static PetscErrorCode PCBDDCMatMult_Private(Mat A, Vec x, Vec y)
    4733: {
    4734:   PCBDDCChange_ctx change_ctx;
    4735:   PetscErrorCode   ierr;

    4738:   MatShellGetContext(A,&change_ctx);
    4739:   MatMult(change_ctx->global_change,x,change_ctx->work[0]);
    4740:   MatMult(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);
    4741:   MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);
    4742:   return(0);
    4743: }

    4747: static PetscErrorCode PCBDDCMatMultTranspose_Private(Mat A, Vec x, Vec y)
    4748: {
    4749:   PCBDDCChange_ctx change_ctx;
    4750:   PetscErrorCode   ierr;

    4753:   MatShellGetContext(A,&change_ctx);
    4754:   MatMult(change_ctx->global_change,x,change_ctx->work[0]);
    4755:   MatMultTranspose(change_ctx->original_mat,change_ctx->work[0],change_ctx->work[1]);
    4756:   MatMultTranspose(change_ctx->global_change,change_ctx->work[1],y);
    4757:   return(0);
    4758: }

    4762: PetscErrorCode PCBDDCSetUpSubSchurs(PC pc)
    4763: {
    4764:   PC_IS               *pcis=(PC_IS*)pc->data;
    4765:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
    4766:   PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
    4767:   Mat                 S_j;
    4768:   PetscInt            *used_xadj,*used_adjncy;
    4769:   PetscBool           free_used_adj;
    4770:   PetscErrorCode      ierr;

    4773:   /* decide the adjacency to be used for determining internal problems for local schur on subsets */
    4774:   free_used_adj = PETSC_FALSE;
    4775:   if (pcbddc->sub_schurs_layers == -1) {
    4776:     used_xadj = NULL;
    4777:     used_adjncy = NULL;
    4778:   } else {
    4779:     if (pcbddc->sub_schurs_use_useradj && pcbddc->mat_graph->xadj) {
    4780:       used_xadj = pcbddc->mat_graph->xadj;
    4781:       used_adjncy = pcbddc->mat_graph->adjncy;
    4782:     } else if (pcbddc->computed_rowadj) {
    4783:       used_xadj = pcbddc->mat_graph->xadj;
    4784:       used_adjncy = pcbddc->mat_graph->adjncy;
    4785:     } else {
    4786:       PetscBool      flg_row=PETSC_FALSE;
    4787:       const PetscInt *xadj,*adjncy;
    4788:       PetscInt       nvtxs;

    4790:       MatGetRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);
    4791:       if (flg_row) {
    4792:         PetscMalloc2(nvtxs+1,&used_xadj,xadj[nvtxs],&used_adjncy);
    4793:         PetscMemcpy(used_xadj,xadj,(nvtxs+1)*sizeof(*xadj));
    4794:         PetscMemcpy(used_adjncy,adjncy,(xadj[nvtxs])*sizeof(*adjncy));
    4795:         free_used_adj = PETSC_TRUE;
    4796:       } else {
    4797:         pcbddc->sub_schurs_layers = -1;
    4798:         used_xadj = NULL;
    4799:         used_adjncy = NULL;
    4800:       }
    4801:       MatRestoreRowIJ(pcbddc->local_mat,0,PETSC_TRUE,PETSC_FALSE,&nvtxs,&xadj,&adjncy,&flg_row);
    4802:     }
    4803:   }

    4805:   /* setup sub_schurs data */
    4806:   MatCreateSchurComplement(pcis->A_II,pcis->A_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&S_j);
    4807:   if (!sub_schurs->use_mumps) {
    4808:     /* pcbddc->ksp_D up to date only if not using MUMPS */
    4809:     MatSchurComplementSetKSP(S_j,pcbddc->ksp_D);
    4810:     PCBDDCSubSchursSetUp(sub_schurs,NULL,S_j,used_xadj,used_adjncy,pcbddc->sub_schurs_layers,pcbddc->faster_deluxe,pcbddc->adaptive_selection,PETSC_FALSE);
    4811:   } else {
    4812:     PetscBool reuse_solvers = (PetscBool)!pcbddc->use_change_of_basis;
    4813:     PetscBool isseqaij;
    4814:     if (!pcbddc->use_vertices && reuse_solvers) {
    4815:       PetscInt n_vertices;

    4817:       ISGetLocalSize(sub_schurs->is_vertices,&n_vertices);
    4818:       reuse_solvers = (PetscBool)!n_vertices;
    4819:     }
    4820:     PetscObjectTypeCompare((PetscObject)pcbddc->local_mat,MATSEQAIJ,&isseqaij);
    4821:     if (!isseqaij) {
    4822:       Mat_IS* matis = (Mat_IS*)pc->pmat->data;
    4823:       if (matis->A == pcbddc->local_mat) {
    4824:         MatDestroy(&pcbddc->local_mat);
    4825:         MatConvert(matis->A,MATSEQAIJ,MAT_INITIAL_MATRIX,&pcbddc->local_mat);
    4826:       } else {
    4827:         MatConvert(pcbddc->local_mat,MATSEQAIJ,MAT_INPLACE_MATRIX,&pcbddc->local_mat);
    4828:       }
    4829:     }
    4830:     PCBDDCSubSchursSetUp(sub_schurs,pcbddc->local_mat,S_j,used_xadj,used_adjncy,pcbddc->sub_schurs_layers,pcbddc->faster_deluxe,pcbddc->adaptive_selection,reuse_solvers);
    4831:   }
    4832:   MatDestroy(&S_j);

    4834:   /* free adjacency */
    4835:   if (free_used_adj) {
    4836:     PetscFree2(used_xadj,used_adjncy);
    4837:   }
    4838:   return(0);
    4839: }

    4843: PetscErrorCode PCBDDCInitSubSchurs(PC pc)
    4844: {
    4845:   PC_IS               *pcis=(PC_IS*)pc->data;
    4846:   PC_BDDC             *pcbddc=(PC_BDDC*)pc->data;
    4847:   PCBDDCSubSchurs     sub_schurs=pcbddc->sub_schurs;
    4848:   PCBDDCGraph         graph;
    4849:   PetscErrorCode      ierr;

    4852:   /* attach interface graph for determining subsets */
    4853:   if (pcbddc->sub_schurs_rebuild) { /* in case rebuild has been requested, it uses a graph generated only by the neighbouring information */
    4854:     IS       verticesIS,verticescomm;
    4855:     PetscInt vsize,*idxs;

    4857:     PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph,NULL,NULL,NULL,NULL,&verticesIS);
    4858:     ISGetSize(verticesIS,&vsize);
    4859:     ISGetIndices(verticesIS,(const PetscInt**)&idxs);
    4860:     ISCreateGeneral(PetscObjectComm((PetscObject)pc),vsize,idxs,PETSC_COPY_VALUES,&verticescomm);
    4861:     ISRestoreIndices(verticesIS,(const PetscInt**)&idxs);
    4862:     ISDestroy(&verticesIS);
    4863:     PCBDDCGraphCreate(&graph);
    4864:     PCBDDCGraphInit(graph,pcbddc->mat_graph->l2gmap,pcbddc->mat_graph->nvtxs_global);
    4865:     PCBDDCGraphSetUp(graph,0,NULL,pcbddc->DirichletBoundariesLocal,0,NULL,verticescomm);
    4866:     ISDestroy(&verticescomm);
    4867:     PCBDDCGraphComputeConnectedComponents(graph);
    4868: /*
    4869:     if (pcbddc->dbg_flag) {
    4870:       PCBDDCGraphASCIIView(graph,pcbddc->dbg_flag,pcbddc->dbg_viewer);
    4871:     }
    4872: */
    4873:   } else {
    4874:     graph = pcbddc->mat_graph;
    4875:   }

    4877:   /* sub_schurs init */
    4878:   PCBDDCSubSchursInit(sub_schurs,pcis->is_I_local,pcis->is_B_local,graph,pcis->BtoNmap);

    4880:   /* free graph struct */
    4881:   if (pcbddc->sub_schurs_rebuild) {
    4882:     PCBDDCGraphDestroy(&graph);
    4883:   }
    4884:   return(0);
    4885: }