Actual source code: bddcschurs.c

      1: #include <../src/ksp/pc/impls/bddc/bddc.h>
      2: #include <../src/ksp/pc/impls/bddc/bddcprivate.h>
      3: #include <../src/mat/impls/dense/seq/dense.h>
      4: #include <petscblaslapack.h>

      6: static inline PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt*,PetscInt,PetscBT,PetscInt*,PetscInt*,PetscInt*);
      7: static PetscErrorCode PCBDDCComputeExplicitSchur(Mat,PetscBool,MatReuse,Mat*);
      8: static PetscErrorCode PCBDDCReuseSolvers_Interior(PC,Vec,Vec);
      9: static PetscErrorCode PCBDDCReuseSolvers_Correction(PC,Vec,Vec);

     11: /* if v2 is not present, correction is done in-place */
     12: PetscErrorCode PCBDDCReuseSolversBenignAdapt(PCBDDCReuseSolvers ctx, Vec v, Vec v2, PetscBool sol, PetscBool full)
     13: {
     14:   PetscScalar    *array;
     15:   PetscScalar    *array2;

     17:   if (!ctx->benign_n) return 0;
     18:   if (sol && full) {
     19:     PetscInt n_I,size_schur;

     21:     /* get sizes */
     22:     MatGetSize(ctx->benign_csAIB,&size_schur,NULL);
     23:     VecGetSize(v,&n_I);
     24:     n_I = n_I - size_schur;
     25:     /* get schur sol from array */
     26:     VecGetArray(v,&array);
     27:     VecPlaceArray(ctx->benign_dummy_schur_vec,array+n_I);
     28:     VecRestoreArray(v,&array);
     29:     /* apply interior sol correction */
     30:     MatMultTranspose(ctx->benign_csAIB,ctx->benign_dummy_schur_vec,ctx->benign_corr_work);
     31:     VecResetArray(ctx->benign_dummy_schur_vec);
     32:     MatMultAdd(ctx->benign_AIIm1ones,ctx->benign_corr_work,v,v);
     33:   }
     34:   if (v2) {
     35:     PetscInt nl;

     37:     VecGetArrayRead(v,(const PetscScalar**)&array);
     38:     VecGetLocalSize(v2,&nl);
     39:     VecGetArray(v2,&array2);
     40:     PetscArraycpy(array2,array,nl);
     41:   } else {
     42:     VecGetArray(v,&array);
     43:     array2 = array;
     44:   }
     45:   if (!sol) { /* change rhs */
     46:     PetscInt n;
     47:     for (n=0;n<ctx->benign_n;n++) {
     48:       PetscScalar    sum = 0.;
     49:       const PetscInt *cols;
     50:       PetscInt       nz,i;

     52:       ISGetLocalSize(ctx->benign_zerodiag_subs[n],&nz);
     53:       ISGetIndices(ctx->benign_zerodiag_subs[n],&cols);
     54:       for (i=0;i<nz-1;i++) sum += array[cols[i]];
     55: #if defined(PETSC_USE_COMPLEX)
     56:       sum = -(PetscRealPart(sum)/nz + PETSC_i*(PetscImaginaryPart(sum)/nz));
     57: #else
     58:       sum = -sum/nz;
     59: #endif
     60:       for (i=0;i<nz-1;i++) array2[cols[i]] += sum;
     61:       ctx->benign_save_vals[n] = array2[cols[nz-1]];
     62:       array2[cols[nz-1]] = sum;
     63:       ISRestoreIndices(ctx->benign_zerodiag_subs[n],&cols);
     64:     }
     65:   } else {
     66:     PetscInt n;
     67:     for (n=0;n<ctx->benign_n;n++) {
     68:       PetscScalar    sum = 0.;
     69:       const PetscInt *cols;
     70:       PetscInt       nz,i;
     71:       ISGetLocalSize(ctx->benign_zerodiag_subs[n],&nz);
     72:       ISGetIndices(ctx->benign_zerodiag_subs[n],&cols);
     73:       for (i=0;i<nz-1;i++) sum += array[cols[i]];
     74: #if defined(PETSC_USE_COMPLEX)
     75:       sum = -(PetscRealPart(sum)/nz + PETSC_i*(PetscImaginaryPart(sum)/nz));
     76: #else
     77:       sum = -sum/nz;
     78: #endif
     79:       for (i=0;i<nz-1;i++) array2[cols[i]] += sum;
     80:       array2[cols[nz-1]] = ctx->benign_save_vals[n];
     81:       ISRestoreIndices(ctx->benign_zerodiag_subs[n],&cols);
     82:     }
     83:   }
     84:   if (v2) {
     85:     VecRestoreArrayRead(v,(const PetscScalar**)&array);
     86:     VecRestoreArray(v2,&array2);
     87:   } else {
     88:     VecRestoreArray(v,&array);
     89:   }
     90:   if (!sol && full) {
     91:     Vec      usedv;
     92:     PetscInt n_I,size_schur;

     94:     /* get sizes */
     95:     MatGetSize(ctx->benign_csAIB,&size_schur,NULL);
     96:     VecGetSize(v,&n_I);
     97:     n_I = n_I - size_schur;
     98:     /* compute schur rhs correction */
     99:     if (v2) {
    100:       usedv = v2;
    101:     } else {
    102:       usedv = v;
    103:     }
    104:     /* apply schur rhs correction */
    105:     MatMultTranspose(ctx->benign_AIIm1ones,usedv,ctx->benign_corr_work);
    106:     VecGetArrayRead(usedv,(const PetscScalar**)&array);
    107:     VecPlaceArray(ctx->benign_dummy_schur_vec,array+n_I);
    108:     VecRestoreArrayRead(usedv,(const PetscScalar**)&array);
    109:     MatMultAdd(ctx->benign_csAIB,ctx->benign_corr_work,ctx->benign_dummy_schur_vec,ctx->benign_dummy_schur_vec);
    110:     VecResetArray(ctx->benign_dummy_schur_vec);
    111:   }
    112:   return 0;
    113: }

    115: static PetscErrorCode PCBDDCReuseSolvers_Solve_Private(PC pc, Vec rhs, Vec sol, PetscBool transpose, PetscBool full)
    116: {
    117:   PCBDDCReuseSolvers ctx;
    118:   PetscBool          copy = PETSC_FALSE;

    120:   PCShellGetContext(pc,&ctx);
    121:   if (full) {
    122: #if defined(PETSC_HAVE_MUMPS)
    123:     MatMumpsSetIcntl(ctx->F,26,-1);
    124: #endif
    125: #if defined(PETSC_HAVE_MKL_PARDISO)
    126:     MatMkl_PardisoSetCntl(ctx->F,70,0);
    127: #endif
    128:     copy = ctx->has_vertices;
    129:   } else { /* interior solver */
    130: #if defined(PETSC_HAVE_MUMPS)
    131:     MatMumpsSetIcntl(ctx->F,26,0);
    132: #endif
    133: #if defined(PETSC_HAVE_MKL_PARDISO)
    134:     MatMkl_PardisoSetCntl(ctx->F,70,1);
    135: #endif
    136:     copy = PETSC_TRUE;
    137:   }
    138:   /* copy rhs into factored matrix workspace */
    139:   if (copy) {
    140:     PetscInt    n;
    141:     PetscScalar *array,*array_solver;

    143:     VecGetLocalSize(rhs,&n);
    144:     VecGetArrayRead(rhs,(const PetscScalar**)&array);
    145:     VecGetArray(ctx->rhs,&array_solver);
    146:     PetscArraycpy(array_solver,array,n);
    147:     VecRestoreArray(ctx->rhs,&array_solver);
    148:     VecRestoreArrayRead(rhs,(const PetscScalar**)&array);

    150:     PCBDDCReuseSolversBenignAdapt(ctx,ctx->rhs,NULL,PETSC_FALSE,full);
    151:     if (transpose) {
    152:       MatSolveTranspose(ctx->F,ctx->rhs,ctx->sol);
    153:     } else {
    154:       MatSolve(ctx->F,ctx->rhs,ctx->sol);
    155:     }
    156:     PCBDDCReuseSolversBenignAdapt(ctx,ctx->sol,NULL,PETSC_TRUE,full);

    158:     /* get back data to caller worskpace */
    159:     VecGetArrayRead(ctx->sol,(const PetscScalar**)&array_solver);
    160:     VecGetArray(sol,&array);
    161:     PetscArraycpy(array,array_solver,n);
    162:     VecRestoreArray(sol,&array);
    163:     VecRestoreArrayRead(ctx->sol,(const PetscScalar**)&array_solver);
    164:   } else {
    165:     if (ctx->benign_n) {
    166:       PCBDDCReuseSolversBenignAdapt(ctx,rhs,ctx->rhs,PETSC_FALSE,full);
    167:       if (transpose) {
    168:         MatSolveTranspose(ctx->F,ctx->rhs,sol);
    169:       } else {
    170:         MatSolve(ctx->F,ctx->rhs,sol);
    171:       }
    172:       PCBDDCReuseSolversBenignAdapt(ctx,sol,NULL,PETSC_TRUE,full);
    173:     } else {
    174:       if (transpose) {
    175:         MatSolveTranspose(ctx->F,rhs,sol);
    176:       } else {
    177:         MatSolve(ctx->F,rhs,sol);
    178:       }
    179:     }
    180:   }
    181:   /* restore defaults */
    182: #if defined(PETSC_HAVE_MUMPS)
    183:   MatMumpsSetIcntl(ctx->F,26,-1);
    184: #endif
    185: #if defined(PETSC_HAVE_MKL_PARDISO)
    186:   MatMkl_PardisoSetCntl(ctx->F,70,0);
    187: #endif
    188:   return 0;
    189: }

    191: static PetscErrorCode PCBDDCReuseSolvers_Correction(PC pc, Vec rhs, Vec sol)
    192: {
    193:   PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_FALSE,PETSC_TRUE);
    194:   return 0;
    195: }

    197: static PetscErrorCode PCBDDCReuseSolvers_CorrectionTranspose(PC pc, Vec rhs, Vec sol)
    198: {
    199:   PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_TRUE,PETSC_TRUE);
    200:   return 0;
    201: }

    203: static PetscErrorCode PCBDDCReuseSolvers_Interior(PC pc, Vec rhs, Vec sol)
    204: {
    205:   PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_FALSE,PETSC_FALSE);
    206:   return 0;
    207: }

    209: static PetscErrorCode PCBDDCReuseSolvers_InteriorTranspose(PC pc, Vec rhs, Vec sol)
    210: {
    211:   PCBDDCReuseSolvers_Solve_Private(pc,rhs,sol,PETSC_TRUE,PETSC_FALSE);
    212:   return 0;
    213: }

    215: static PetscErrorCode PCBDDCReuseSolvers_View(PC pc, PetscViewer viewer)
    216: {
    217:   PCBDDCReuseSolvers ctx;
    218:   PetscBool          iascii;

    220:   PCShellGetContext(pc,&ctx);
    221:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    222:   if (iascii) {
    223:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO);
    224:   }
    225:   MatView(ctx->F,viewer);
    226:   if (iascii) {
    227:     PetscViewerPopFormat(viewer);
    228:   }
    229:   return 0;
    230: }

    232: static PetscErrorCode PCBDDCReuseSolversReset(PCBDDCReuseSolvers reuse)
    233: {
    234:   PetscInt       i;

    236:   MatDestroy(&reuse->F);
    237:   VecDestroy(&reuse->sol);
    238:   VecDestroy(&reuse->rhs);
    239:   PCDestroy(&reuse->interior_solver);
    240:   PCDestroy(&reuse->correction_solver);
    241:   ISDestroy(&reuse->is_R);
    242:   ISDestroy(&reuse->is_B);
    243:   VecScatterDestroy(&reuse->correction_scatter_B);
    244:   VecDestroy(&reuse->sol_B);
    245:   VecDestroy(&reuse->rhs_B);
    246:   for (i=0;i<reuse->benign_n;i++) {
    247:     ISDestroy(&reuse->benign_zerodiag_subs[i]);
    248:   }
    249:   PetscFree(reuse->benign_zerodiag_subs);
    250:   PetscFree(reuse->benign_save_vals);
    251:   MatDestroy(&reuse->benign_csAIB);
    252:   MatDestroy(&reuse->benign_AIIm1ones);
    253:   VecDestroy(&reuse->benign_corr_work);
    254:   VecDestroy(&reuse->benign_dummy_schur_vec);
    255:   return 0;
    256: }

    258: static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
    259: {
    260:   Mat            B, C, D, Bd, Cd, AinvBd;
    261:   KSP            ksp;
    262:   PC             pc;
    263:   PetscBool      isLU, isILU, isCHOL, Bdense, Cdense;
    264:   PetscReal      fill = 2.0;
    265:   PetscInt       n_I;
    266:   PetscMPIInt    size;

    268:   MPI_Comm_size(PetscObjectComm((PetscObject)M),&size);
    270:   if (reuse == MAT_REUSE_MATRIX) {
    271:     PetscBool Sdense;

    273:     PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense);
    275:   }
    276:   MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D);
    277:   MatSchurComplementGetKSP(M, &ksp);
    278:   KSPGetPC(ksp, &pc);
    279:   PetscObjectTypeCompare((PetscObject) pc, PCLU, &isLU);
    280:   PetscObjectTypeCompare((PetscObject) pc, PCILU, &isILU);
    281:   PetscObjectTypeCompare((PetscObject) pc, PCCHOLESKY, &isCHOL);
    282:   PetscObjectTypeCompare((PetscObject) B, MATSEQDENSE, &Bdense);
    283:   PetscObjectTypeCompare((PetscObject) C, MATSEQDENSE, &Cdense);
    284:   MatGetSize(B,&n_I,NULL);
    285:   if (n_I) {
    286:     if (!Bdense) {
    287:       MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd);
    288:     } else {
    289:       Bd = B;
    290:     }

    292:     if (isLU || isILU || isCHOL) {
    293:       Mat fact;
    294:       KSPSetUp(ksp);
    295:       PCFactorGetMatrix(pc, &fact);
    296:       MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);
    297:       MatMatSolve(fact, Bd, AinvBd);
    298:     } else {
    299:       PetscBool ex = PETSC_TRUE;

    301:       if (ex) {
    302:         Mat Ainvd;

    304:         PCComputeOperator(pc, MATDENSE, &Ainvd);
    305:         MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd);
    306:         MatDestroy(&Ainvd);
    307:       } else {
    308:         Vec         sol,rhs;
    309:         PetscScalar *arrayrhs,*arraysol;
    310:         PetscInt    i,nrhs,n;

    312:         MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd);
    313:         MatGetSize(Bd,&n,&nrhs);
    314:         MatDenseGetArray(Bd,&arrayrhs);
    315:         MatDenseGetArray(AinvBd,&arraysol);
    316:         KSPGetSolution(ksp,&sol);
    317:         KSPGetRhs(ksp,&rhs);
    318:         for (i=0;i<nrhs;i++) {
    319:           VecPlaceArray(rhs,arrayrhs+i*n);
    320:           VecPlaceArray(sol,arraysol+i*n);
    321:           KSPSolve(ksp,rhs,sol);
    322:           VecResetArray(rhs);
    323:           VecResetArray(sol);
    324:         }
    325:         MatDenseRestoreArray(Bd,&arrayrhs);
    326:         MatDenseRestoreArray(AinvBd,&arrayrhs);
    327:       }
    328:     }
    329:     if (!Bdense & !issym) {
    330:       MatDestroy(&Bd);
    331:     }

    333:     if (!issym) {
    334:       if (!Cdense) {
    335:         MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd);
    336:       } else {
    337:         Cd = C;
    338:       }
    339:       MatMatMult(Cd, AinvBd, reuse, fill, S);
    340:       if (!Cdense) {
    341:         MatDestroy(&Cd);
    342:       }
    343:     } else {
    344:       MatTransposeMatMult(Bd, AinvBd, reuse, fill, S);
    345:       if (!Bdense) {
    346:         MatDestroy(&Bd);
    347:       }
    348:     }
    349:     MatDestroy(&AinvBd);
    350:   }

    352:   if (D) {
    353:     Mat       Dd;
    354:     PetscBool Ddense;

    356:     PetscObjectTypeCompare((PetscObject)D,MATSEQDENSE,&Ddense);
    357:     if (!Ddense) {
    358:       MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd);
    359:     } else {
    360:       Dd = D;
    361:     }
    362:     if (n_I) {
    363:       MatAYPX(*S,-1.0,Dd,SAME_NONZERO_PATTERN);
    364:     } else {
    365:       if (reuse == MAT_INITIAL_MATRIX) {
    366:         MatDuplicate(Dd,MAT_COPY_VALUES,S);
    367:       } else {
    368:         MatCopy(Dd,*S,SAME_NONZERO_PATTERN);
    369:       }
    370:     }
    371:     if (!Ddense) {
    372:       MatDestroy(&Dd);
    373:     }
    374:   } else {
    375:     MatScale(*S,-1.0);
    376:   }
    377:   return 0;
    378: }

    380: PetscErrorCode PCBDDCSubSchursSetUp(PCBDDCSubSchurs sub_schurs, Mat Ain, Mat Sin, PetscBool exact_schur, PetscInt xadj[], PetscInt adjncy[], PetscInt nlayers, Vec scaling, PetscBool compute_Stilda, PetscBool reuse_solvers, PetscBool benign_trick, PetscInt benign_n, PetscInt benign_p0_lidx[], IS benign_zerodiag_subs[], Mat change, IS change_primal)
    381: {
    382:   Mat                    F,A_II,A_IB,A_BI,A_BB,AE_II;
    383:   Mat                    S_all;
    384:   Vec                    gstash,lstash;
    385:   VecScatter             sstash;
    386:   IS                     is_I,is_I_layer;
    387:   IS                     all_subsets,all_subsets_mult,all_subsets_n;
    388:   PetscScalar            *stasharray,*Bwork;
    389:   PetscInt               *nnz,*all_local_idx_N;
    390:   PetscInt               *auxnum1,*auxnum2;
    391:   PetscInt               i,subset_size,max_subset_size;
    392:   PetscInt               n_B,extra,local_size,global_size;
    393:   PetscInt               local_stash_size;
    394:   PetscBLASInt           B_N,B_ierr,B_lwork,*pivots;
    395:   MPI_Comm               comm_n;
    396:   PetscBool              deluxe = PETSC_TRUE;
    397:   PetscBool              use_potr = PETSC_FALSE, use_sytr = PETSC_FALSE;
    398:   PetscViewer            matl_dbg_viewer = NULL;
    399:   PetscErrorCode         ierr;
    400:   PetscBool              flg;

    402:   MatDestroy(&sub_schurs->A);
    403:   MatDestroy(&sub_schurs->S);
    404:   if (Ain) {
    405:     PetscObjectReference((PetscObject)Ain);
    406:     sub_schurs->A = Ain;
    407:   }

    409:   PetscObjectReference((PetscObject)Sin);
    410:   sub_schurs->S = Sin;
    411:   if (sub_schurs->schur_explicit) {
    412:     sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);
    413:   }

    415:   /* preliminary checks */

    418:   if (benign_trick) sub_schurs->is_posdef = PETSC_FALSE;

    420:   /* debug (MATLAB) */
    421:   if (sub_schurs->debug) {
    422:     PetscMPIInt size,rank;
    423:     PetscInt    nr,*print_schurs_ranks,print_schurs = PETSC_FALSE;

    425:     MPI_Comm_size(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&size);
    426:     MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);
    427:     nr   = size;
    428:     PetscMalloc1(nr,&print_schurs_ranks);
    429:     PetscOptionsBegin(PetscObjectComm((PetscObject)sub_schurs->l2gmap),sub_schurs->prefix,"BDDC sub_schurs options","PC");
    430:     PetscOptionsIntArray("-sub_schurs_debug_ranks","Ranks to debug (all if the option is not used)",NULL,print_schurs_ranks,&nr,&flg);
    431:     if (!flg) print_schurs = PETSC_TRUE;
    432:     else {
    433:       print_schurs = PETSC_FALSE;
    434:       for (i=0;i<nr;i++) if (print_schurs_ranks[i] == (PetscInt)rank) { print_schurs = PETSC_TRUE; break; }
    435:     }
    436:     PetscOptionsEnd();
    437:     PetscFree(print_schurs_ranks);
    438:     if (print_schurs) {
    439:       char filename[256];

    441:       PetscSNPrintf(filename,sizeof(filename),"sub_schurs_Schur_r%d.m",PetscGlobalRank);
    442:       PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,&matl_dbg_viewer);
    443:       PetscViewerPushFormat(matl_dbg_viewer,PETSC_VIEWER_ASCII_MATLAB);
    444:     }
    445:   }

    447:   /* restrict work on active processes */
    448:   if (sub_schurs->restrict_comm) {
    449:     PetscSubcomm subcomm;
    450:     PetscMPIInt  color,rank;

    452:     color = 0;
    453:     if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
    454:     MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&rank);
    455:     PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&subcomm);
    456:     PetscSubcommSetNumber(subcomm,2);
    457:     PetscSubcommSetTypeGeneral(subcomm,color,rank);
    458:     PetscCommDuplicate(PetscSubcommChild(subcomm),&comm_n,NULL);
    459:     PetscSubcommDestroy(&subcomm);
    460:     if (!sub_schurs->n_subs) {
    461:       PetscCommDestroy(&comm_n);
    462:       return 0;
    463:     }
    464:   } else {
    465:     PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap),&comm_n,NULL);
    466:   }

    468:   /* get Schur complement matrices */
    469:   if (!sub_schurs->schur_explicit) {
    470:     Mat       tA_IB,tA_BI,tA_BB;
    471:     PetscBool isseqsbaij;
    472:     MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,&tA_IB,&tA_BI,&tA_BB);
    473:     PetscObjectTypeCompare((PetscObject)tA_BB,MATSEQSBAIJ,&isseqsbaij);
    474:     if (isseqsbaij) {
    475:       MatConvert(tA_BB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BB);
    476:       MatConvert(tA_IB,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_IB);
    477:       MatConvert(tA_BI,MATSEQAIJ,MAT_INITIAL_MATRIX,&A_BI);
    478:     } else {
    479:       PetscObjectReference((PetscObject)tA_BB);
    480:       A_BB = tA_BB;
    481:       PetscObjectReference((PetscObject)tA_IB);
    482:       A_IB = tA_IB;
    483:       PetscObjectReference((PetscObject)tA_BI);
    484:       A_BI = tA_BI;
    485:     }
    486:   } else {
    487:     A_II = NULL;
    488:     A_IB = NULL;
    489:     A_BI = NULL;
    490:     A_BB = NULL;
    491:   }
    492:   S_all = NULL;

    494:   /* determine interior problems */
    495:   ISGetLocalSize(sub_schurs->is_I,&i);
    496:   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
    497:     PetscBT                touched;
    498:     const PetscInt*        idx_B;
    499:     PetscInt               n_I,n_B,n_local_dofs,n_prev_added,j,layer,*local_numbering;

    502:     /* get sizes */
    503:     ISGetLocalSize(sub_schurs->is_I,&n_I);
    504:     ISGetLocalSize(sub_schurs->is_B,&n_B);

    506:     PetscMalloc1(n_I+n_B,&local_numbering);
    507:     PetscBTCreate(n_I+n_B,&touched);
    508:     PetscBTMemzero(n_I+n_B,touched);

    510:     /* all boundary dofs must be skipped when adding layers */
    511:     ISGetIndices(sub_schurs->is_B,&idx_B);
    512:     for (j=0;j<n_B;j++) {
    513:       PetscBTSet(touched,idx_B[j]);
    514:     }
    515:     PetscArraycpy(local_numbering,idx_B,n_B);
    516:     ISRestoreIndices(sub_schurs->is_B,&idx_B);

    518:     /* add prescribed number of layers of dofs */
    519:     n_local_dofs = n_B;
    520:     n_prev_added = n_B;
    521:     for (layer=0;layer<nlayers;layer++) {
    522:       PetscInt n_added = 0;
    523:       if (n_local_dofs == n_I+n_B) break;
    525:       PCBDDCAdjGetNextLayer_Private(local_numbering+n_local_dofs,n_prev_added,touched,xadj,adjncy,&n_added);
    526:       n_prev_added = n_added;
    527:       n_local_dofs += n_added;
    528:       if (!n_added) break;
    529:     }
    530:     PetscBTDestroy(&touched);

    532:     /* IS for I layer dofs in original numbering */
    533:     ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I),n_local_dofs-n_B,local_numbering+n_B,PETSC_COPY_VALUES,&is_I_layer);
    534:     PetscFree(local_numbering);
    535:     ISSort(is_I_layer);
    536:     /* IS for I layer dofs in I numbering */
    537:     if (!sub_schurs->schur_explicit) {
    538:       ISLocalToGlobalMapping ItoNmap;
    539:       ISLocalToGlobalMappingCreateIS(sub_schurs->is_I,&ItoNmap);
    540:       ISGlobalToLocalMappingApplyIS(ItoNmap,IS_GTOLM_DROP,is_I_layer,&is_I);
    541:       ISLocalToGlobalMappingDestroy(&ItoNmap);

    543:       /* II block */
    544:       MatCreateSubMatrix(A_II,is_I,is_I,MAT_INITIAL_MATRIX,&AE_II);
    545:     }
    546:   } else {
    547:     PetscInt n_I;

    549:     /* IS for I dofs in original numbering */
    550:     PetscObjectReference((PetscObject)sub_schurs->is_I);
    551:     is_I_layer = sub_schurs->is_I;

    553:     /* IS for I dofs in I numbering (strided 1) */
    554:     if (!sub_schurs->schur_explicit) {
    555:       ISGetSize(sub_schurs->is_I,&n_I);
    556:       ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I),n_I,0,1,&is_I);

    558:       /* II block is the same */
    559:       PetscObjectReference((PetscObject)A_II);
    560:       AE_II = A_II;
    561:     }
    562:   }

    564:   /* Get info on subset sizes and sum of all subsets sizes */
    565:   max_subset_size = 0;
    566:   local_size = 0;
    567:   for (i=0;i<sub_schurs->n_subs;i++) {
    568:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    569:     max_subset_size = PetscMax(subset_size,max_subset_size);
    570:     local_size += subset_size;
    571:   }

    573:   /* Work arrays for local indices */
    574:   extra = 0;
    575:   ISGetLocalSize(sub_schurs->is_B,&n_B);
    576:   if (sub_schurs->schur_explicit && is_I_layer) {
    577:     ISGetLocalSize(is_I_layer,&extra);
    578:   }
    579:   PetscMalloc1(n_B+extra,&all_local_idx_N);
    580:   if (extra) {
    581:     const PetscInt *idxs;
    582:     ISGetIndices(is_I_layer,&idxs);
    583:     PetscArraycpy(all_local_idx_N,idxs,extra);
    584:     ISRestoreIndices(is_I_layer,&idxs);
    585:   }
    586:   PetscMalloc1(sub_schurs->n_subs,&auxnum1);
    587:   PetscMalloc1(sub_schurs->n_subs,&auxnum2);

    589:   /* Get local indices in local numbering */
    590:   local_size = 0;
    591:   local_stash_size = 0;
    592:   for (i=0;i<sub_schurs->n_subs;i++) {
    593:     const PetscInt *idxs;

    595:     ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    596:     ISGetIndices(sub_schurs->is_subs[i],&idxs);
    597:     /* start (smallest in global ordering) and multiplicity */
    598:     auxnum1[i] = idxs[0];
    599:     auxnum2[i] = subset_size*subset_size;
    600:     /* subset indices in local numbering */
    601:     PetscArraycpy(all_local_idx_N+local_size+extra,idxs,subset_size);
    602:     ISRestoreIndices(sub_schurs->is_subs[i],&idxs);
    603:     local_size += subset_size;
    604:     local_stash_size += subset_size*subset_size;
    605:   }

    607:   /* allocate extra workspace needed only for GETRI or SYTRF */
    608:   use_potr = use_sytr = PETSC_FALSE;
    609:   if (benign_trick || (sub_schurs->is_hermitian && sub_schurs->is_posdef)) {
    610:     use_potr = PETSC_TRUE;
    611:   } else if (sub_schurs->is_symmetric) {
    612:     use_sytr = PETSC_TRUE;
    613:   }
    614:   if (local_size && !use_potr) {
    615:     PetscScalar  lwork,dummyscalar = 0.;
    616:     PetscBLASInt dummyint = 0;

    618:     B_lwork = -1;
    619:     PetscBLASIntCast(local_size,&B_N);
    620:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    621:     if (use_sytr) {
    622:       PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
    624:     } else {
    625:       PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,&dummyscalar,&B_N,&dummyint,&lwork,&B_lwork,&B_ierr));
    627:     }
    628:     PetscFPTrapPop();
    629:     PetscBLASIntCast((PetscInt)PetscRealPart(lwork),&B_lwork);
    630:     PetscMalloc2(B_lwork,&Bwork,B_N,&pivots);
    631:   } else {
    632:     Bwork = NULL;
    633:     pivots = NULL;
    634:   }

    636:   /* prepare data for summing up properly schurs on subsets */
    637:   ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum1,PETSC_OWN_POINTER,&all_subsets_n);
    638:   ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap,all_subsets_n,&all_subsets);
    639:   ISDestroy(&all_subsets_n);
    640:   ISCreateGeneral(comm_n,sub_schurs->n_subs,auxnum2,PETSC_OWN_POINTER,&all_subsets_mult);
    641:   ISRenumber(all_subsets,all_subsets_mult,&global_size,&all_subsets_n);
    642:   ISDestroy(&all_subsets);
    643:   ISDestroy(&all_subsets_mult);
    644:   ISGetLocalSize(all_subsets_n,&i);
    646:   VecCreateSeqWithArray(PETSC_COMM_SELF,1,local_stash_size,NULL,&lstash);
    647:   VecCreateMPI(comm_n,PETSC_DECIDE,global_size,&gstash);
    648:   VecScatterCreate(lstash,NULL,gstash,all_subsets_n,&sstash);
    649:   ISDestroy(&all_subsets_n);

    651:   /* subset indices in local boundary numbering */
    652:   if (!sub_schurs->is_Ej_all) {
    653:     PetscInt *all_local_idx_B;

    655:     PetscMalloc1(local_size,&all_local_idx_B);
    656:     ISGlobalToLocalMappingApply(sub_schurs->BtoNmap,IS_GTOLM_DROP,local_size,all_local_idx_N+extra,&subset_size,all_local_idx_B);
    658:     ISCreateGeneral(PETSC_COMM_SELF,local_size,all_local_idx_B,PETSC_OWN_POINTER,&sub_schurs->is_Ej_all);
    659:   }

    661:   if (change) {
    662:     ISLocalToGlobalMapping BtoS;
    663:     IS                     change_primal_B;
    664:     IS                     change_primal_all;

    668:     PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change_primal_sub);
    669:     for (i=0;i<sub_schurs->n_subs;i++) {
    670:       ISLocalToGlobalMapping NtoS;
    671:       ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i],&NtoS);
    672:       ISGlobalToLocalMappingApplyIS(NtoS,IS_GTOLM_DROP,change_primal,&sub_schurs->change_primal_sub[i]);
    673:       ISLocalToGlobalMappingDestroy(&NtoS);
    674:     }
    675:     ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,change_primal,&change_primal_B);
    676:     ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all,&BtoS);
    677:     ISGlobalToLocalMappingApplyIS(BtoS,IS_GTOLM_DROP,change_primal_B,&change_primal_all);
    678:     ISLocalToGlobalMappingDestroy(&BtoS);
    679:     ISDestroy(&change_primal_B);
    680:     PetscMalloc1(sub_schurs->n_subs,&sub_schurs->change);
    681:     for (i=0;i<sub_schurs->n_subs;i++) {
    682:       Mat change_sub;

    684:       ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    685:       KSPCreate(PETSC_COMM_SELF,&sub_schurs->change[i]);
    686:       KSPSetType(sub_schurs->change[i],KSPPREONLY);
    687:       if (!sub_schurs->change_with_qr) {
    688:         MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_sub);
    689:       } else {
    690:         Mat change_subt;
    691:         MatCreateSubMatrix(change,sub_schurs->is_subs[i],sub_schurs->is_subs[i],MAT_INITIAL_MATRIX,&change_subt);
    692:         MatConvert(change_subt,MATSEQDENSE,MAT_INITIAL_MATRIX,&change_sub);
    693:         MatDestroy(&change_subt);
    694:       }
    695:       KSPSetOperators(sub_schurs->change[i],change_sub,change_sub);
    696:       MatDestroy(&change_sub);
    697:       KSPSetOptionsPrefix(sub_schurs->change[i],sub_schurs->prefix);
    698:       KSPAppendOptionsPrefix(sub_schurs->change[i],"sub_schurs_change_");
    699:     }
    700:     ISDestroy(&change_primal_all);
    701:   }

    703:   /* Local matrix of all local Schur on subsets (transposed) */
    704:   if (!sub_schurs->S_Ej_all) {
    705:     Mat         T;
    706:     PetscScalar *v;
    707:     PetscInt    *ii,*jj;
    708:     PetscInt    cum,i,j,k;

    710:     /* MatSeqAIJSetPreallocation + MatSetValues is slow for these kind of matrices (may have large blocks)
    711:        Allocate properly a representative matrix and duplicate */
    712:     PetscMalloc3(local_size+1,&ii,local_stash_size,&jj,local_stash_size,&v);
    713:     ii[0] = 0;
    714:     cum   = 0;
    715:     for (i=0;i<sub_schurs->n_subs;i++) {
    716:       ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    717:       for (j=0;j<subset_size;j++) {
    718:         const PetscInt row = cum+j;
    719:         PetscInt col = cum;

    721:         ii[row+1] = ii[row] + subset_size;
    722:         for (k=ii[row];k<ii[row+1];k++) {
    723:           jj[k] = col;
    724:           col++;
    725:         }
    726:       }
    727:       cum += subset_size;
    728:     }
    729:     MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,local_size,local_size,ii,jj,v,&T);
    730:     MatDuplicate(T,MAT_DO_NOT_COPY_VALUES,&sub_schurs->S_Ej_all);
    731:     MatDestroy(&T);
    732:     PetscFree3(ii,jj,v);
    733:   }
    734:   /* matrices for deluxe scaling and adaptive selection */
    735:   if (compute_Stilda) {
    736:     if (!sub_schurs->sum_S_Ej_tilda_all) {
    737:       MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_tilda_all);
    738:     }
    739:     if (!sub_schurs->sum_S_Ej_inv_all && deluxe) {
    740:       MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_inv_all);
    741:     }
    742:   }

    744:   /* Compute Schur complements explicitly */
    745:   F = NULL;
    746:   if (!sub_schurs->schur_explicit) {
    747:     /* this code branch is used when MatFactor with Schur complement support is not present or when explicitly requested;
    748:        it is not efficient, unless the economic version of the scaling is used */
    749:     Mat         S_Ej_expl;
    750:     PetscScalar *work;
    751:     PetscInt    j,*dummy_idx;
    752:     PetscBool   Sdense;

    754:     PetscMalloc2(max_subset_size,&dummy_idx,max_subset_size*max_subset_size,&work);
    755:     local_size = 0;
    756:     for (i=0;i<sub_schurs->n_subs;i++) {
    757:       IS  is_subset_B;
    758:       Mat AE_EE,AE_IE,AE_EI,S_Ej;

    760:       /* subsets in original and boundary numbering */
    761:       ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,sub_schurs->is_subs[i],&is_subset_B);
    762:       /* EE block */
    763:       MatCreateSubMatrix(A_BB,is_subset_B,is_subset_B,MAT_INITIAL_MATRIX,&AE_EE);
    764:       /* IE block */
    765:       MatCreateSubMatrix(A_IB,is_I,is_subset_B,MAT_INITIAL_MATRIX,&AE_IE);
    766:       /* EI block */
    767:       if (sub_schurs->is_symmetric) {
    768:         MatCreateTranspose(AE_IE,&AE_EI);
    769:       } else if (sub_schurs->is_hermitian) {
    770:         MatCreateHermitianTranspose(AE_IE,&AE_EI);
    771:       } else {
    772:         MatCreateSubMatrix(A_BI,is_subset_B,is_I,MAT_INITIAL_MATRIX,&AE_EI);
    773:       }
    774:       ISDestroy(&is_subset_B);
    775:       MatCreateSchurComplement(AE_II,AE_II,AE_IE,AE_EI,AE_EE,&S_Ej);
    776:       MatDestroy(&AE_EE);
    777:       MatDestroy(&AE_IE);
    778:       MatDestroy(&AE_EI);
    779:       if (AE_II == A_II) { /* we can reuse the same ksp */
    780:         KSP ksp;
    781:         MatSchurComplementGetKSP(sub_schurs->S,&ksp);
    782:         MatSchurComplementSetKSP(S_Ej,ksp);
    783:       } else { /* build new ksp object which inherits ksp and pc types from the original one */
    784:         KSP       origksp,schurksp;
    785:         PC        origpc,schurpc;
    786:         KSPType   ksp_type;
    787:         PetscInt  n_internal;
    788:         PetscBool ispcnone;

    790:         MatSchurComplementGetKSP(sub_schurs->S,&origksp);
    791:         MatSchurComplementGetKSP(S_Ej,&schurksp);
    792:         KSPGetType(origksp,&ksp_type);
    793:         KSPSetType(schurksp,ksp_type);
    794:         KSPGetPC(schurksp,&schurpc);
    795:         KSPGetPC(origksp,&origpc);
    796:         PetscObjectTypeCompare((PetscObject)origpc,PCNONE,&ispcnone);
    797:         if (!ispcnone) {
    798:           PCType pc_type;
    799:           PCGetType(origpc,&pc_type);
    800:           PCSetType(schurpc,pc_type);
    801:         } else {
    802:           PCSetType(schurpc,PCLU);
    803:         }
    804:         ISGetSize(is_I,&n_internal);
    805:         if (!n_internal) { /* UMFPACK gives error with 0 sized problems */
    806:           MatSolverType solver = NULL;
    807:           PCFactorGetMatSolverType(origpc,(MatSolverType*)&solver);
    808:           if (solver) {
    809:             PCFactorSetMatSolverType(schurpc,solver);
    810:           }
    811:         }
    812:         KSPSetUp(schurksp);
    813:       }
    814:       ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    815:       MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&S_Ej_expl);
    816:       PCBDDCComputeExplicitSchur(S_Ej,sub_schurs->is_symmetric,MAT_REUSE_MATRIX,&S_Ej_expl);
    817:       PetscObjectTypeCompare((PetscObject)S_Ej_expl,MATSEQDENSE,&Sdense);
    818:       if (Sdense) {
    819:         for (j=0;j<subset_size;j++) {
    820:           dummy_idx[j]=local_size+j;
    821:         }
    822:         MatSetValues(sub_schurs->S_Ej_all,subset_size,dummy_idx,subset_size,dummy_idx,work,INSERT_VALUES);
    823:       } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not yet implemented for sparse matrices");
    824:       MatDestroy(&S_Ej);
    825:       MatDestroy(&S_Ej_expl);
    826:       local_size += subset_size;
    827:     }
    828:     PetscFree2(dummy_idx,work);
    829:     /* free */
    830:     ISDestroy(&is_I);
    831:     MatDestroy(&AE_II);
    832:     PetscFree(all_local_idx_N);
    833:   } else {
    834:     Mat               A,cs_AIB_mat = NULL,benign_AIIm1_ones_mat = NULL;
    835:     Vec               Dall = NULL;
    836:     IS                is_A_all,*is_p_r = NULL;
    837:     MatType           Stype;
    838:     PetscScalar       *work,*S_data,*schur_factor,infty = PETSC_MAX_REAL;
    839:     PetscScalar       *SEj_arr = NULL,*SEjinv_arr = NULL;
    840:     const PetscScalar *rS_data;
    841:     PetscInt          n,n_I,size_schur,size_active_schur,cum,cum2;
    842:     PetscBool         economic,solver_S,S_lower_triangular = PETSC_FALSE;
    843:     PetscBool         schur_has_vertices,factor_workaround;
    844:     PetscBool         use_cholesky;
    845: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    846:     PetscBool         oldpin;
    847: #endif

    849:     /* get sizes */
    850:     n_I = 0;
    851:     if (is_I_layer) {
    852:       ISGetLocalSize(is_I_layer,&n_I);
    853:     }
    854:     economic = PETSC_FALSE;
    855:     ISGetLocalSize(sub_schurs->is_I,&cum);
    856:     if (cum != n_I) economic = PETSC_TRUE;
    857:     MatGetLocalSize(sub_schurs->A,&n,NULL);
    858:     size_active_schur = local_size;

    860:     /* import scaling vector (wrong formulation if we have 3D edges) */
    861:     if (scaling && compute_Stilda) {
    862:       const PetscScalar *array;
    863:       PetscScalar       *array2;
    864:       const PetscInt    *idxs;
    865:       PetscInt          i;

    867:       ISGetIndices(sub_schurs->is_Ej_all,&idxs);
    868:       VecCreateSeq(PETSC_COMM_SELF,size_active_schur,&Dall);
    869:       VecGetArrayRead(scaling,&array);
    870:       VecGetArray(Dall,&array2);
    871:       for (i=0;i<size_active_schur;i++) array2[i] = array[idxs[i]];
    872:       VecRestoreArray(Dall,&array2);
    873:       VecRestoreArrayRead(scaling,&array);
    874:       ISRestoreIndices(sub_schurs->is_Ej_all,&idxs);
    875:       deluxe = PETSC_FALSE;
    876:     }

    878:     /* size active schurs does not count any dirichlet or vertex dof on the interface */
    879:     factor_workaround = PETSC_FALSE;
    880:     schur_has_vertices = PETSC_FALSE;
    881:     cum = n_I+size_active_schur;
    882:     if (sub_schurs->is_dir) {
    883:       const PetscInt* idxs;
    884:       PetscInt        n_dir;

    886:       ISGetLocalSize(sub_schurs->is_dir,&n_dir);
    887:       ISGetIndices(sub_schurs->is_dir,&idxs);
    888:       PetscArraycpy(all_local_idx_N+cum,idxs,n_dir);
    889:       ISRestoreIndices(sub_schurs->is_dir,&idxs);
    890:       cum += n_dir;
    891:       factor_workaround = PETSC_TRUE;
    892:     }
    893:     /* include the primal vertices in the Schur complement */
    894:     if (exact_schur && sub_schurs->is_vertices && (compute_Stilda || benign_n)) {
    895:       PetscInt n_v;

    897:       ISGetLocalSize(sub_schurs->is_vertices,&n_v);
    898:       if (n_v) {
    899:         const PetscInt* idxs;

    901:         ISGetIndices(sub_schurs->is_vertices,&idxs);
    902:         PetscArraycpy(all_local_idx_N+cum,idxs,n_v);
    903:         ISRestoreIndices(sub_schurs->is_vertices,&idxs);
    904:         cum += n_v;
    905:         factor_workaround = PETSC_TRUE;
    906:         schur_has_vertices = PETSC_TRUE;
    907:       }
    908:     }
    909:     size_schur = cum - n_I;
    910:     ISCreateGeneral(PETSC_COMM_SELF,cum,all_local_idx_N,PETSC_OWN_POINTER,&is_A_all);
    911: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    912:     oldpin = sub_schurs->A->boundtocpu;
    913:     MatBindToCPU(sub_schurs->A,PETSC_TRUE);
    914: #endif
    915:     if (cum == n) {
    916:       ISSetPermutation(is_A_all);
    917:       MatPermute(sub_schurs->A,is_A_all,is_A_all,&A);
    918:     } else {
    919:       MatCreateSubMatrix(sub_schurs->A,is_A_all,is_A_all,MAT_INITIAL_MATRIX,&A);
    920:     }
    921: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    922:     MatBindToCPU(sub_schurs->A,oldpin);
    923: #endif
    924:     MatSetOptionsPrefix(A,sub_schurs->prefix);
    925:     MatAppendOptionsPrefix(A,"sub_schurs_");

    927:     /* if we actually change the basis for the pressures, LDL^T factors will use a lot of memory
    928:        this is a workaround */
    929:     if (benign_n) {
    930:       Vec                    v,benign_AIIm1_ones;
    931:       ISLocalToGlobalMapping N_to_reor;
    932:       IS                     is_p0,is_p0_p;
    933:       PetscScalar            *cs_AIB,*AIIm1_data;
    934:       PetscInt               sizeA;

    936:       ISLocalToGlobalMappingCreateIS(is_A_all,&N_to_reor);
    937:       ISCreateGeneral(PETSC_COMM_SELF,benign_n,benign_p0_lidx,PETSC_COPY_VALUES,&is_p0);
    938:       ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,is_p0,&is_p0_p);
    939:       ISDestroy(&is_p0);
    940:       MatCreateVecs(A,&v,&benign_AIIm1_ones);
    941:       VecGetSize(v,&sizeA);
    942:       MatCreateSeqDense(PETSC_COMM_SELF,sizeA,benign_n,NULL,&benign_AIIm1_ones_mat);
    943:       MatCreateSeqDense(PETSC_COMM_SELF,size_schur,benign_n,NULL,&cs_AIB_mat);
    944:       MatDenseGetArray(cs_AIB_mat,&cs_AIB);
    945:       MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);
    946:       PetscMalloc1(benign_n,&is_p_r);
    947:       /* compute colsum of A_IB restricted to pressures */
    948:       for (i=0;i<benign_n;i++) {
    949:         const PetscScalar *array;
    950:         const PetscInt    *idxs;
    951:         PetscInt          j,nz;

    953:         ISGlobalToLocalMappingApplyIS(N_to_reor,IS_GTOLM_DROP,benign_zerodiag_subs[i],&is_p_r[i]);
    954:         ISGetLocalSize(is_p_r[i],&nz);
    955:         ISGetIndices(is_p_r[i],&idxs);
    956:         for (j=0;j<nz;j++) AIIm1_data[idxs[j]+sizeA*i] = 1.;
    957:         ISRestoreIndices(is_p_r[i],&idxs);
    958:         VecPlaceArray(benign_AIIm1_ones,AIIm1_data+sizeA*i);
    959:         MatMult(A,benign_AIIm1_ones,v);
    960:         VecResetArray(benign_AIIm1_ones);
    961:         VecGetArrayRead(v,&array);
    962:         for (j=0;j<size_schur;j++) {
    963: #if defined(PETSC_USE_COMPLEX)
    964:           cs_AIB[i*size_schur + j] = (PetscRealPart(array[j+n_I])/nz + PETSC_i*(PetscImaginaryPart(array[j+n_I])/nz));
    965: #else
    966:           cs_AIB[i*size_schur + j] = array[j+n_I]/nz;
    967: #endif
    968:         }
    969:         VecRestoreArrayRead(v,&array);
    970:       }
    971:       MatDenseRestoreArray(cs_AIB_mat,&cs_AIB);
    972:       MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);
    973:       VecDestroy(&v);
    974:       VecDestroy(&benign_AIIm1_ones);
    975:       MatSetOption(A,MAT_KEEP_NONZERO_PATTERN,PETSC_FALSE);
    976:       MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
    977:       MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
    978:       MatZeroRowsColumnsIS(A,is_p0_p,1.0,NULL,NULL);
    979:       ISDestroy(&is_p0_p);
    980:       ISLocalToGlobalMappingDestroy(&N_to_reor);
    981:     }
    982:     MatSetOption(A,MAT_SYMMETRIC,sub_schurs->is_symmetric);
    983:     MatSetOption(A,MAT_HERMITIAN,sub_schurs->is_hermitian);
    984:     MatSetOption(A,MAT_SPD,sub_schurs->is_posdef);

    986:     /* for complexes, symmetric and hermitian at the same time implies null imaginary part */
    987:     use_cholesky = (PetscBool)((use_potr || use_sytr) && sub_schurs->is_hermitian && sub_schurs->is_symmetric);

    989:     /* when using the benign subspace trick, the local Schur complements are SPD */
    990:     /* MKL_PARDISO does not handle well the computation of a Schur complement from a symmetric indefinite factorization
    991:        Use LU and adapt pivoting perturbation (still, solution is not as accurate as with using MUMPS) */
    992:     if (benign_trick) {
    993:       sub_schurs->is_posdef = PETSC_TRUE;
    994:       PetscStrcmp(sub_schurs->mat_solver_type,MATSOLVERMKL_PARDISO,&flg);
    995:       if (flg) use_cholesky = PETSC_FALSE;
    996:     }

    998:     if (n_I) {
    999:       IS        is_schur;
    1000:       char      stype[64];
    1001:       PetscBool gpu = PETSC_FALSE;

    1003:       if (use_cholesky) {
    1004:         MatGetFactor(A,sub_schurs->mat_solver_type,MAT_FACTOR_CHOLESKY,&F);
    1005:       } else {
    1006:         MatGetFactor(A,sub_schurs->mat_solver_type,MAT_FACTOR_LU,&F);
    1007:       }
    1008:       MatSetErrorIfFailure(A,PETSC_TRUE);
    1009: #if defined(PETSC_HAVE_MKL_PARDISO)
    1010:       if (benign_trick) MatMkl_PardisoSetCntl(F,10,10);
    1011: #endif
    1012:       /* subsets ordered last */
    1013:       ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is_schur);
    1014:       MatFactorSetSchurIS(F,is_schur);
    1015:       ISDestroy(&is_schur);

    1017:       /* factorization step */
    1018:       if (use_cholesky) {
    1019:         MatCholeskyFactorSymbolic(F,A,NULL,NULL);
    1020: #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
    1021:         MatMumpsSetIcntl(F,19,2);
    1022: #endif
    1023:         MatCholeskyFactorNumeric(F,A,NULL);
    1024:         S_lower_triangular = PETSC_TRUE;
    1025:       } else {
    1026:         MatLUFactorSymbolic(F,A,NULL,NULL,NULL);
    1027: #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
    1028:         MatMumpsSetIcntl(F,19,3);
    1029: #endif
    1030:         MatLUFactorNumeric(F,A,NULL);
    1031:       }
    1032:       MatViewFromOptions(F,(PetscObject)A,"-mat_factor_view");

    1034:       if (matl_dbg_viewer) {
    1035:         Mat S;
    1036:         IS  is;

    1038:         PetscObjectSetName((PetscObject)A,"A");
    1039:         MatView(A,matl_dbg_viewer);
    1040:         MatFactorCreateSchurComplement(F,&S,NULL);
    1041:         PetscObjectSetName((PetscObject)S,"S");
    1042:         MatView(S,matl_dbg_viewer);
    1043:         MatDestroy(&S);
    1044:         ISCreateStride(PETSC_COMM_SELF,n_I,0,1,&is);
    1045:         PetscObjectSetName((PetscObject)is,"I");
    1046:         ISView(is,matl_dbg_viewer);
    1047:         ISDestroy(&is);
    1048:         ISCreateStride(PETSC_COMM_SELF,size_schur,n_I,1,&is);
    1049:         PetscObjectSetName((PetscObject)is,"B");
    1050:         ISView(is,matl_dbg_viewer);
    1051:         ISDestroy(&is);
    1052:         PetscObjectSetName((PetscObject)is_A_all,"IA");
    1053:         ISView(is_A_all,matl_dbg_viewer);
    1054:       }

    1056:       /* get explicit Schur Complement computed during numeric factorization */
    1057:       MatFactorGetSchurComplement(F,&S_all,NULL);
    1058:       PetscStrncpy(stype,MATSEQDENSE,sizeof(stype));
    1059: #if defined(PETSC_HAVE_CUDA)
    1060:       PetscObjectTypeCompareAny((PetscObject)A,&gpu,MATSEQAIJVIENNACL,MATSEQAIJCUSPARSE,"");
    1061: #endif
    1062:       if (gpu) {
    1063:         PetscStrncpy(stype,MATSEQDENSECUDA,sizeof(stype));
    1064:       }
    1065:       PetscOptionsGetString(NULL,sub_schurs->prefix,"-sub_schurs_schur_mat_type",stype,sizeof(stype),NULL);
    1066:       MatConvert(S_all,stype,MAT_INPLACE_MATRIX,&S_all);
    1067:       MatSetOption(S_all,MAT_SPD,sub_schurs->is_posdef);
    1068:       MatSetOption(S_all,MAT_HERMITIAN,sub_schurs->is_hermitian);
    1069:       MatGetType(S_all,&Stype);

    1071:       /* we can reuse the solvers if we are not using the economic version */
    1072:       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
    1073:       factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
    1074:       if (!sub_schurs->is_posdef && factor_workaround && compute_Stilda && size_active_schur)
    1075:         reuse_solvers = factor_workaround = PETSC_FALSE;

    1077:       solver_S = PETSC_TRUE;

    1079:       /* update the Schur complement with the change of basis on the pressures */
    1080:       if (benign_n) {
    1081:         const PetscScalar *cs_AIB;
    1082:         PetscScalar       *S_data,*AIIm1_data;
    1083:         Mat               S2 = NULL,S3 = NULL; /* dbg */
    1084:         PetscScalar       *S2_data,*S3_data; /* dbg */
    1085:         Vec               v,benign_AIIm1_ones;
    1086:         PetscInt          sizeA;

    1088:         MatDenseGetArray(S_all,&S_data);
    1089:         MatCreateVecs(A,&v,&benign_AIIm1_ones);
    1090:         VecGetSize(v,&sizeA);
    1091: #if defined(PETSC_HAVE_MUMPS)
    1092:         MatMumpsSetIcntl(F,26,0);
    1093: #endif
    1094: #if defined(PETSC_HAVE_MKL_PARDISO)
    1095:         MatMkl_PardisoSetCntl(F,70,1);
    1096: #endif
    1097:         MatDenseGetArrayRead(cs_AIB_mat,&cs_AIB);
    1098:         MatDenseGetArray(benign_AIIm1_ones_mat,&AIIm1_data);
    1099:         if (matl_dbg_viewer) {
    1100:           MatDuplicate(S_all,MAT_DO_NOT_COPY_VALUES,&S2);
    1101:           MatDuplicate(S_all,MAT_DO_NOT_COPY_VALUES,&S3);
    1102:           MatDenseGetArray(S2,&S2_data);
    1103:           MatDenseGetArray(S3,&S3_data);
    1104:         }
    1105:         for (i=0;i<benign_n;i++) {
    1106:           PetscScalar    *array,sum = 0.,one = 1.,*sums;
    1107:           const PetscInt *idxs;
    1108:           PetscInt       k,j,nz;
    1109:           PetscBLASInt   B_k,B_n;

    1111:           PetscCalloc1(benign_n,&sums);
    1112:           VecPlaceArray(benign_AIIm1_ones,AIIm1_data+sizeA*i);
    1113:           VecCopy(benign_AIIm1_ones,v);
    1114:           MatSolve(F,v,benign_AIIm1_ones);
    1115:           MatMult(A,benign_AIIm1_ones,v);
    1116:           VecResetArray(benign_AIIm1_ones);
    1117:           /* p0 dofs (eliminated) are excluded from the sums */
    1118:           for (k=0;k<benign_n;k++) {
    1119:             ISGetLocalSize(is_p_r[k],&nz);
    1120:             ISGetIndices(is_p_r[k],&idxs);
    1121:             for (j=0;j<nz-1;j++) sums[k] -= AIIm1_data[idxs[j]+sizeA*i];
    1122:             ISRestoreIndices(is_p_r[k],&idxs);
    1123:           }
    1124:           VecGetArrayRead(v,(const PetscScalar**)&array);
    1125:           if (matl_dbg_viewer) {
    1126:             Vec  vv;
    1127:             char name[16];

    1129:             VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array+n_I,&vv);
    1130:             PetscSNPrintf(name,sizeof(name),"Pvs%D",i);
    1131:             PetscObjectSetName((PetscObject)vv,name);
    1132:             VecView(vv,matl_dbg_viewer);
    1133:           }
    1134:           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
    1135:           /* cs_AIB already scaled by 1./nz */
    1136:           B_k = 1;
    1137:           for (k=0;k<benign_n;k++) {
    1138:             sum  = sums[k];
    1139:             PetscBLASIntCast(size_schur,&B_n);

    1141:             if (PetscAbsScalar(sum) == 0.0) continue;
    1142:             if (k == i) {
    1143:               PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
    1144:               if (matl_dbg_viewer) {
    1145:                 PetscStackCallBLAS("BLASsyrk",BLASsyrk_("L","N",&B_n,&B_k,&sum,cs_AIB+i*size_schur,&B_n,&one,S3_data,&B_n));
    1146:               }
    1147:             } else { /* XXX Is it correct to use symmetric rank-2 update with half of the sum? */
    1148:               sum /= 2.0;
    1149:               PetscStackCallBLAS("BLASsyr2k",BLASsyr2k_("L","N",&B_n,&B_k,&sum,cs_AIB+k*size_schur,&B_n,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
    1150:               if (matl_dbg_viewer) {
    1151:                 PetscStackCallBLAS("BLASsyr2k",BLASsyr2k_("L","N",&B_n,&B_k,&sum,cs_AIB+k*size_schur,&B_n,cs_AIB+i*size_schur,&B_n,&one,S3_data,&B_n));
    1152:               }
    1153:             }
    1154:           }
    1155:           sum  = 1.;
    1156:           PetscStackCallBLAS("BLASsyr2k",BLASsyr2k_("L","N",&B_n,&B_k,&sum,array+n_I,&B_n,cs_AIB+i*size_schur,&B_n,&one,S_data,&B_n));
    1157:           if (matl_dbg_viewer) {
    1158:             PetscStackCallBLAS("BLASsyr2k",BLASsyr2k_("L","N",&B_n,&B_k,&sum,array+n_I,&B_n,cs_AIB+i*size_schur,&B_n,&one,S2_data,&B_n));
    1159:           }
    1160:           VecRestoreArrayRead(v,(const PetscScalar**)&array);
    1161:           /* set p0 entry of AIIm1_ones to zero */
    1162:           ISGetLocalSize(is_p_r[i],&nz);
    1163:           ISGetIndices(is_p_r[i],&idxs);
    1164:           for (j=0;j<benign_n;j++) AIIm1_data[idxs[nz-1]+sizeA*j] = 0.;
    1165:           ISRestoreIndices(is_p_r[i],&idxs);
    1166:           PetscFree(sums);
    1167:         }
    1168:         VecDestroy(&benign_AIIm1_ones);
    1169:         if (matl_dbg_viewer) {
    1170:           MatDenseRestoreArray(S2,&S2_data);
    1171:           MatDenseRestoreArray(S3,&S3_data);
    1172:         }
    1173:         if (!S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
    1174:           PetscInt k,j;
    1175:           for (k=0;k<size_schur;k++) {
    1176:             for (j=k;j<size_schur;j++) {
    1177:               S_data[j*size_schur+k] = PetscConj(S_data[k*size_schur+j]);
    1178:             }
    1179:           }
    1180:         }

    1182:         /* restore defaults */
    1183: #if defined(PETSC_HAVE_MUMPS)
    1184:         MatMumpsSetIcntl(F,26,-1);
    1185: #endif
    1186: #if defined(PETSC_HAVE_MKL_PARDISO)
    1187:         MatMkl_PardisoSetCntl(F,70,0);
    1188: #endif
    1189:         MatDenseRestoreArrayRead(cs_AIB_mat,&cs_AIB);
    1190:         MatDenseRestoreArray(benign_AIIm1_ones_mat,&AIIm1_data);
    1191:         VecDestroy(&v);
    1192:         MatDenseRestoreArray(S_all,&S_data);
    1193:         if (matl_dbg_viewer) {
    1194:           Mat S;

    1196:           MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);
    1197:           MatFactorCreateSchurComplement(F,&S,NULL);
    1198:           PetscObjectSetName((PetscObject)S,"Sb");
    1199:           MatView(S,matl_dbg_viewer);
    1200:           MatDestroy(&S);
    1201:           PetscObjectSetName((PetscObject)S2,"S2P");
    1202:           MatView(S2,matl_dbg_viewer);
    1203:           PetscObjectSetName((PetscObject)S3,"S3P");
    1204:           MatView(S3,matl_dbg_viewer);
    1205:           PetscObjectSetName((PetscObject)cs_AIB_mat,"cs");
    1206:           MatView(cs_AIB_mat,matl_dbg_viewer);
    1207:           MatFactorGetSchurComplement(F,&S_all,NULL);
    1208:         }
    1209:         MatDestroy(&S2);
    1210:         MatDestroy(&S3);
    1211:       }
    1212:       if (!reuse_solvers) {
    1213:         for (i=0;i<benign_n;i++) {
    1214:           ISDestroy(&is_p_r[i]);
    1215:         }
    1216:         PetscFree(is_p_r);
    1217:         MatDestroy(&cs_AIB_mat);
    1218:         MatDestroy(&benign_AIIm1_ones_mat);
    1219:       }
    1220:     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
    1221:       MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&S_all);
    1222:       MatGetType(S_all,&Stype);
    1223:       reuse_solvers = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
    1224:       factor_workaround = PETSC_FALSE;
    1225:       solver_S = PETSC_FALSE;
    1226:     }

    1228:     if (reuse_solvers) {
    1229:       Mat                A_II,Afake;
    1230:       Vec                vec1_B;
    1231:       PCBDDCReuseSolvers msolv_ctx;
    1232:       PetscInt           n_R;

    1234:       if (sub_schurs->reuse_solver) {
    1235:         PCBDDCReuseSolversReset(sub_schurs->reuse_solver);
    1236:       } else {
    1237:         PetscNew(&sub_schurs->reuse_solver);
    1238:       }
    1239:       msolv_ctx = sub_schurs->reuse_solver;
    1240:       MatSchurComplementGetSubMatrices(sub_schurs->S,&A_II,NULL,NULL,NULL,NULL);
    1241:       PetscObjectReference((PetscObject)F);
    1242:       msolv_ctx->F = F;
    1243:       MatCreateVecs(F,&msolv_ctx->sol,NULL);
    1244:       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
    1245:       {
    1246:         PetscScalar *array;
    1247:         PetscInt    n;

    1249:         VecGetLocalSize(msolv_ctx->sol,&n);
    1250:         VecGetArray(msolv_ctx->sol,&array);
    1251:         VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol),1,n,array,&msolv_ctx->rhs);
    1252:         VecRestoreArray(msolv_ctx->sol,&array);
    1253:       }
    1254:       msolv_ctx->has_vertices = schur_has_vertices;

    1256:       /* interior solver */
    1257:       PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->interior_solver);
    1258:       PCSetOperators(msolv_ctx->interior_solver,A_II,A_II);
    1259:       PCSetType(msolv_ctx->interior_solver,PCSHELL);
    1260:       PCShellSetName(msolv_ctx->interior_solver,"Interior solver (w/o Schur factorization)");
    1261:       PCShellSetContext(msolv_ctx->interior_solver,msolv_ctx);
    1262:       PCShellSetView(msolv_ctx->interior_solver,PCBDDCReuseSolvers_View);
    1263:       PCShellSetApply(msolv_ctx->interior_solver,PCBDDCReuseSolvers_Interior);
    1264:       PCShellSetApplyTranspose(msolv_ctx->interior_solver,PCBDDCReuseSolvers_InteriorTranspose);

    1266:       /* correction solver */
    1267:       PCCreate(PetscObjectComm((PetscObject)A_II),&msolv_ctx->correction_solver);
    1268:       PCSetType(msolv_ctx->correction_solver,PCSHELL);
    1269:       PCShellSetName(msolv_ctx->correction_solver,"Correction solver (with Schur factorization)");
    1270:       PCShellSetContext(msolv_ctx->correction_solver,msolv_ctx);
    1271:       PCShellSetView(msolv_ctx->interior_solver,PCBDDCReuseSolvers_View);
    1272:       PCShellSetApply(msolv_ctx->correction_solver,PCBDDCReuseSolvers_Correction);
    1273:       PCShellSetApplyTranspose(msolv_ctx->correction_solver,PCBDDCReuseSolvers_CorrectionTranspose);

    1275:       /* scatter and vecs for Schur complement solver */
    1276:       MatCreateVecs(S_all,&msolv_ctx->sol_B,&msolv_ctx->rhs_B);
    1277:       MatCreateVecs(sub_schurs->S,&vec1_B,NULL);
    1278:       if (!schur_has_vertices) {
    1279:         ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_A_all,&msolv_ctx->is_B);
    1280:         VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,NULL,&msolv_ctx->correction_scatter_B);
    1281:         PetscObjectReference((PetscObject)is_A_all);
    1282:         msolv_ctx->is_R = is_A_all;
    1283:       } else {
    1284:         IS              is_B_all;
    1285:         const PetscInt* idxs;
    1286:         PetscInt        dual,n_v,n;

    1288:         ISGetLocalSize(sub_schurs->is_vertices,&n_v);
    1289:         dual = size_schur - n_v;
    1290:         ISGetLocalSize(is_A_all,&n);
    1291:         ISGetIndices(is_A_all,&idxs);
    1292:         ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),dual,idxs+n_I,PETSC_COPY_VALUES,&is_B_all);
    1293:         ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap,IS_GTOLM_DROP,is_B_all,&msolv_ctx->is_B);
    1294:         ISDestroy(&is_B_all);
    1295:         ISCreateStride(PetscObjectComm((PetscObject)is_A_all),dual,0,1,&is_B_all);
    1296:         VecScatterCreate(vec1_B,msolv_ctx->is_B,msolv_ctx->sol_B,is_B_all,&msolv_ctx->correction_scatter_B);
    1297:         ISDestroy(&is_B_all);
    1298:         ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all),n-n_v,idxs,PETSC_COPY_VALUES,&msolv_ctx->is_R);
    1299:         ISRestoreIndices(is_A_all,&idxs);
    1300:       }
    1301:       ISGetLocalSize(msolv_ctx->is_R,&n_R);
    1302:       MatCreateSeqAIJ(PETSC_COMM_SELF,n_R,n_R,0,NULL,&Afake);
    1303:       MatAssemblyBegin(Afake,MAT_FINAL_ASSEMBLY);
    1304:       MatAssemblyEnd(Afake,MAT_FINAL_ASSEMBLY);
    1305:       PCSetOperators(msolv_ctx->correction_solver,Afake,Afake);
    1306:       MatDestroy(&Afake);
    1307:       VecDestroy(&vec1_B);

    1309:       /* communicate benign info to solver context */
    1310:       if (benign_n) {
    1311:         PetscScalar *array;

    1313:         msolv_ctx->benign_n = benign_n;
    1314:         msolv_ctx->benign_zerodiag_subs = is_p_r;
    1315:         PetscMalloc1(benign_n,&msolv_ctx->benign_save_vals);
    1316:         msolv_ctx->benign_csAIB = cs_AIB_mat;
    1317:         MatCreateVecs(cs_AIB_mat,&msolv_ctx->benign_corr_work,NULL);
    1318:         VecGetArray(msolv_ctx->benign_corr_work,&array);
    1319:         VecCreateSeqWithArray(PETSC_COMM_SELF,1,size_schur,array,&msolv_ctx->benign_dummy_schur_vec);
    1320:         VecRestoreArray(msolv_ctx->benign_corr_work,&array);
    1321:         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
    1322:       }
    1323:     } else {
    1324:       if (sub_schurs->reuse_solver) {
    1325:         PCBDDCReuseSolversReset(sub_schurs->reuse_solver);
    1326:       }
    1327:       PetscFree(sub_schurs->reuse_solver);
    1328:     }
    1329:     MatDestroy(&A);
    1330:     ISDestroy(&is_A_all);

    1332:     /* Work arrays */
    1333:     PetscMalloc1(max_subset_size*max_subset_size,&work);

    1335:     /* S_Ej_all */
    1336:     cum = cum2 = 0;
    1337:     MatDenseGetArrayRead(S_all,&rS_data);
    1338:     MatSeqAIJGetArray(sub_schurs->S_Ej_all,&SEj_arr);
    1339:     if (compute_Stilda) {
    1340:       MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&SEjinv_arr);
    1341:     }
    1342:     for (i=0;i<sub_schurs->n_subs;i++) {
    1343:       PetscInt j;

    1345:       /* get S_E */
    1346:       ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    1347:       if (S_lower_triangular) { /* I need to expand the upper triangular data (column oriented) */
    1348:         PetscInt k;
    1349:         for (k=0;k<subset_size;k++) {
    1350:           for (j=k;j<subset_size;j++) {
    1351:             work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
    1352:             work[j*subset_size+k] = PetscConj(rS_data[cum2+k*size_schur+j]);
    1353:           }
    1354:         }
    1355:       } else { /* just copy to workspace */
    1356:         PetscInt k;
    1357:         for (k=0;k<subset_size;k++) {
    1358:           for (j=0;j<subset_size;j++) {
    1359:             work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
    1360:           }
    1361:         }
    1362:       }
    1363:       /* insert S_E values */
    1364:       if (sub_schurs->change) {
    1365:         Mat change_sub,SEj,T;

    1367:         /* change basis */
    1368:         KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);
    1369:         MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);
    1370:         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
    1371:           Mat T2;
    1372:           MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);
    1373:           MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);
    1374:           MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);
    1375:           MatDestroy(&T2);
    1376:         } else {
    1377:           MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);
    1378:         }
    1379:         MatCopy(T,SEj,SAME_NONZERO_PATTERN);
    1380:         MatDestroy(&T);
    1381:         MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1.0,NULL,NULL);
    1382:         MatDestroy(&SEj);
    1383:       }
    1384:       if (deluxe) {
    1385:         PetscArraycpy(SEj_arr,work,subset_size*subset_size);
    1386:         /* if adaptivity is requested, invert S_E blocks */
    1387:         if (compute_Stilda) {
    1388:           Mat               M;
    1389:           const PetscScalar *vals;
    1390:           PetscBool         isdense,isdensecuda;

    1392:           MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&M);
    1393:           MatSetOption(M,MAT_SPD,sub_schurs->is_posdef);
    1394:           MatSetOption(M,MAT_HERMITIAN,sub_schurs->is_hermitian);
    1395:           if (!PetscBTLookup(sub_schurs->is_edge,i)) {
    1396:             MatSetType(M,Stype);
    1397:           }
    1398:           PetscObjectTypeCompare((PetscObject)M,MATSEQDENSE,&isdense);
    1399:           PetscObjectTypeCompare((PetscObject)M,MATSEQDENSECUDA,&isdensecuda);
    1400:           if (use_cholesky) {
    1401:             MatCholeskyFactor(M,NULL,NULL);
    1402:           } else {
    1403:             MatLUFactor(M,NULL,NULL,NULL);
    1404:           }
    1405:           if (isdense) {
    1406:             MatSeqDenseInvertFactors_Private(M);
    1407: #if defined(PETSC_HAVE_CUDA)
    1408:           } else if (isdensecuda) {
    1409:             MatSeqDenseCUDAInvertFactors_Private(M);
    1410: #endif
    1411:           } else SETERRQ(PetscObjectComm((PetscObject)M),PETSC_ERR_SUP,"Not implemented for type %s",Stype);
    1412:           MatDenseGetArrayRead(M,&vals);
    1413:           PetscArraycpy(SEjinv_arr,vals,subset_size*subset_size);
    1414:           MatDenseRestoreArrayRead(M,&vals);
    1415:           MatDestroy(&M);
    1416:         }
    1417:       } else if (compute_Stilda) { /* not using deluxe */
    1418:         Mat         SEj;
    1419:         Vec         D;
    1420:         PetscScalar *array;

    1422:         MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);
    1423:         VecGetArray(Dall,&array);
    1424:         VecCreateSeqWithArray(PETSC_COMM_SELF,1,subset_size,array+cum,&D);
    1425:         VecRestoreArray(Dall,&array);
    1426:         VecShift(D,-1.);
    1427:         MatDiagonalScale(SEj,D,D);
    1428:         MatDestroy(&SEj);
    1429:         VecDestroy(&D);
    1430:         PetscArraycpy(SEj_arr,work,subset_size*subset_size);
    1431:       }
    1432:       cum += subset_size;
    1433:       cum2 += subset_size*(size_schur + 1);
    1434:       SEj_arr += subset_size*subset_size;
    1435:       if (SEjinv_arr) SEjinv_arr += subset_size*subset_size;
    1436:     }
    1437:     MatDenseRestoreArrayRead(S_all,&rS_data);
    1438:     MatSeqAIJRestoreArray(sub_schurs->S_Ej_all,&SEj_arr);
    1439:     if (compute_Stilda) {
    1440:       MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&SEjinv_arr);
    1441:     }
    1442:     if (solver_S) {
    1443:       MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);
    1444:     }

    1446:     /* may prevent from unneeded copies, since MUMPS or MKL_Pardiso always use CPU memory
    1447:        however, preliminary tests indicate using GPUs is still faster in the solve phase */
    1448: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    1449:     if (reuse_solvers) {
    1450:       Mat                  St;
    1451:       MatFactorSchurStatus st;

    1453:       flg  = PETSC_FALSE;
    1454:       PetscOptionsGetBool(NULL,sub_schurs->prefix,"-sub_schurs_schur_pin_to_cpu",&flg,NULL);
    1455:       MatFactorGetSchurComplement(F,&St,&st);
    1456:       MatBindToCPU(St,flg);
    1457:       MatFactorRestoreSchurComplement(F,&St,st);
    1458:     }
    1459: #endif

    1461:     schur_factor = NULL;
    1462:     if (compute_Stilda && size_active_schur) {

    1464:       MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&SEjinv_arr);
    1465:       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
    1466:         PetscArraycpy(SEjinv_arr,work,size_schur*size_schur);
    1467:       } else {
    1468:         Mat S_all_inv=NULL;

    1470:         if (solver_S) {
    1471:           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
    1472:              The latter is not the principal subminor for S^-1. However, the factors can be reused since S_\Delta\Delta is the leading principal submatrix of S */
    1473:           if (factor_workaround) {/* invert without calling MatFactorInvertSchurComplement, since we are hacking */
    1474:             PetscScalar *data;
    1475:             PetscInt     nd = 0;

    1477:             if (!use_potr) {
    1478:               SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
    1479:             }
    1480:             MatFactorGetSchurComplement(F,&S_all_inv,NULL);
    1481:             MatDenseGetArray(S_all_inv,&data);
    1482:             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
    1483:               ISGetLocalSize(sub_schurs->is_dir,&nd);
    1484:             }

    1486:             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
    1487:             if (schur_has_vertices) {
    1488:               Mat          M;
    1489:               PetscScalar *tdata;
    1490:               PetscInt     nv = 0, news;

    1492:               ISGetLocalSize(sub_schurs->is_vertices,&nv);
    1493:               news = size_active_schur + nv;
    1494:               PetscCalloc1(news*news,&tdata);
    1495:               for (i=0;i<size_active_schur;i++) {
    1496:                 PetscArraycpy(tdata+i*(news+1),data+i*(size_schur+1),size_active_schur-i);
    1497:                 PetscArraycpy(tdata+i*(news+1)+size_active_schur-i,data+i*size_schur+size_active_schur+nd,nv);
    1498:               }
    1499:               for (i=0;i<nv;i++) {
    1500:                 PetscInt k = i+size_active_schur;
    1501:                 PetscArraycpy(tdata+k*(news+1),data+(k+nd)*(size_schur+1),nv-i);
    1502:               }

    1504:               MatCreateSeqDense(PETSC_COMM_SELF,news,news,tdata,&M);
    1505:               MatSetOption(M,MAT_SPD,PETSC_TRUE);
    1506:               MatCholeskyFactor(M,NULL,NULL);
    1507:               /* save the factors */
    1508:               cum = 0;
    1509:               PetscMalloc1((size_active_schur*(size_active_schur +1))/2+nd,&schur_factor);
    1510:               for (i=0;i<size_active_schur;i++) {
    1511:                 PetscArraycpy(schur_factor+cum,tdata+i*(news+1),size_active_schur-i);
    1512:                 cum += size_active_schur - i;
    1513:               }
    1514:               for (i=0;i<nd;i++) schur_factor[cum+i] = PetscSqrtReal(PetscRealPart(data[(i+size_active_schur)*(size_schur+1)]));
    1515:               MatSeqDenseInvertFactors_Private(M);
    1516:               /* move back just the active dofs to the Schur complement */
    1517:               for (i=0;i<size_active_schur;i++) {
    1518:                 PetscArraycpy(data+i*size_schur,tdata+i*news,size_active_schur);
    1519:               }
    1520:               PetscFree(tdata);
    1521:               MatDestroy(&M);
    1522:             } else { /* we can factorize and invert just the activedofs */
    1523:               Mat         M;
    1524:               PetscScalar *aux;

    1526:               PetscMalloc1(nd,&aux);
    1527:               for (i=0;i<nd;i++) aux[i] = 1.0/data[(i+size_active_schur)*(size_schur+1)];
    1528:               MatCreateSeqDense(PETSC_COMM_SELF,size_active_schur,size_active_schur,data,&M);
    1529:               MatDenseSetLDA(M,size_schur);
    1530:               MatSetOption(M,MAT_SPD,PETSC_TRUE);
    1531:               MatCholeskyFactor(M,NULL,NULL);
    1532:               MatSeqDenseInvertFactors_Private(M);
    1533:               MatDestroy(&M);
    1534:               MatCreateSeqDense(PETSC_COMM_SELF,size_schur,nd,data+size_active_schur*size_schur,&M);
    1535:               MatZeroEntries(M);
    1536:               MatDestroy(&M);
    1537:               MatCreateSeqDense(PETSC_COMM_SELF,nd,size_schur,data+size_active_schur,&M);
    1538:               MatDenseSetLDA(M,size_schur);
    1539:               MatZeroEntries(M);
    1540:               MatDestroy(&M);
    1541:               for (i=0;i<nd;i++) data[(i+size_active_schur)*(size_schur+1)] = aux[i];
    1542:               PetscFree(aux);
    1543:             }
    1544:             MatDenseRestoreArray(S_all_inv,&data);
    1545:           } else { /* use MatFactor calls to invert S */
    1546:             MatFactorInvertSchurComplement(F);
    1547:             MatFactorGetSchurComplement(F,&S_all_inv,NULL);
    1548:           }
    1549:         } else { /* we need to invert explicitly since we are not using MatFactor for S */
    1550:           PetscObjectReference((PetscObject)S_all);
    1551:           S_all_inv = S_all;
    1552:           MatDenseGetArray(S_all_inv,&S_data);
    1553:           PetscBLASIntCast(size_schur,&B_N);
    1554:           PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    1555:           if (use_potr) {
    1556:             PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,S_data,&B_N,&B_ierr));
    1558:             PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,S_data,&B_N,&B_ierr));
    1560:           } else if (use_sytr) {
    1561:             PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
    1563:             PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&B_N,S_data,&B_N,pivots,Bwork,&B_ierr));
    1565:           } else {
    1566:             PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,S_data,&B_N,pivots,&B_ierr));
    1568:             PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,S_data,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
    1570:           }
    1571:           PetscLogFlops(1.0*size_schur*size_schur*size_schur);
    1572:           PetscFPTrapPop();
    1573:           MatDenseRestoreArray(S_all_inv,&S_data);
    1574:         }
    1575:         /* S_Ej_tilda_all */
    1576:         cum = cum2 = 0;
    1577:         MatDenseGetArrayRead(S_all_inv,&rS_data);
    1578:         for (i=0;i<sub_schurs->n_subs;i++) {
    1579:           PetscInt j;

    1581:           ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    1582:           /* get (St^-1)_E */
    1583:           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
    1584:              will be properly accessed later during adaptive selection */
    1585:           if (S_lower_triangular) {
    1586:             PetscInt k;
    1587:             if (sub_schurs->change) {
    1588:               for (k=0;k<subset_size;k++) {
    1589:                 for (j=k;j<subset_size;j++) {
    1590:                   work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
    1591:                   work[j*subset_size+k] = work[k*subset_size+j];
    1592:                 }
    1593:               }
    1594:             } else {
    1595:               for (k=0;k<subset_size;k++) {
    1596:                 for (j=k;j<subset_size;j++) {
    1597:                   work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
    1598:                 }
    1599:               }
    1600:             }
    1601:           } else {
    1602:             PetscInt k;
    1603:             for (k=0;k<subset_size;k++) {
    1604:               for (j=0;j<subset_size;j++) {
    1605:                 work[k*subset_size+j] = rS_data[cum2+k*size_schur+j];
    1606:               }
    1607:             }
    1608:           }
    1609:           if (sub_schurs->change) {
    1610:             Mat change_sub,SEj,T;

    1612:             /* change basis */
    1613:             KSPGetOperators(sub_schurs->change[i],&change_sub,NULL);
    1614:             MatCreateSeqDense(PETSC_COMM_SELF,subset_size,subset_size,work,&SEj);
    1615:             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
    1616:               Mat T2;
    1617:               MatTransposeMatMult(change_sub,SEj,MAT_INITIAL_MATRIX,1.0,&T2);
    1618:               MatMatMult(T2,change_sub,MAT_INITIAL_MATRIX,1.0,&T);
    1619:               MatDestroy(&T2);
    1620:               MatConvert(T,MATSEQDENSE,MAT_INPLACE_MATRIX,&T);
    1621:             } else {
    1622:               MatPtAP(SEj,change_sub,MAT_INITIAL_MATRIX,1.0,&T);
    1623:             }
    1624:             MatCopy(T,SEj,SAME_NONZERO_PATTERN);
    1625:             MatDestroy(&T);
    1626:             /* set diagonal entry to a very large value to pick the basis we are eliminating as the first eigenvectors with adaptive selection */
    1627:             MatZeroRowsColumnsIS(SEj,sub_schurs->change_primal_sub[i],1./PETSC_SMALL,NULL,NULL);
    1628:             MatDestroy(&SEj);
    1629:           }
    1630:           PetscArraycpy(SEjinv_arr,work,subset_size*subset_size);
    1631:           cum += subset_size;
    1632:           cum2 += subset_size*(size_schur + 1);
    1633:           SEjinv_arr += subset_size*subset_size;
    1634:         }
    1635:         MatDenseRestoreArrayRead(S_all_inv,&rS_data);
    1636:         if (solver_S) {
    1637:           if (schur_has_vertices) {
    1638:             MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_FACTORED);
    1639:           } else {
    1640:             MatFactorRestoreSchurComplement(F,&S_all_inv,MAT_FACTOR_SCHUR_INVERTED);
    1641:           }
    1642:         }
    1643:         MatDestroy(&S_all_inv);
    1644:       }
    1645:       MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&SEjinv_arr);

    1647:       /* move back factors if needed */
    1648:       if (schur_has_vertices) {
    1649:         Mat      S_tmp;
    1650:         PetscInt nd = 0;

    1653:         MatFactorGetSchurComplement(F,&S_tmp,NULL);
    1654:         if (use_potr) {
    1655:           PetscScalar *data;

    1657:           MatDenseGetArray(S_tmp,&data);
    1658:           PetscArrayzero(data,size_schur*size_schur);

    1660:           if (S_lower_triangular) {
    1661:             cum = 0;
    1662:             for (i=0;i<size_active_schur;i++) {
    1663:               PetscArraycpy(data+i*(size_schur+1),schur_factor+cum,size_active_schur-i);
    1664:               cum += size_active_schur-i;
    1665:             }
    1666:           } else {
    1667:             PetscArraycpy(data,schur_factor,size_schur*size_schur);
    1668:           }
    1669:           if (sub_schurs->is_dir) {
    1670:             ISGetLocalSize(sub_schurs->is_dir,&nd);
    1671:             for (i=0;i<nd;i++) {
    1672:               data[(i+size_active_schur)*(size_schur+1)] = schur_factor[cum+i];
    1673:             }
    1674:           }
    1675:           /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
    1676:              set the diagonal entry of the Schur factor to a very large value */
    1677:           for (i=size_active_schur+nd;i<size_schur;i++) {
    1678:             data[i*(size_schur+1)] = infty;
    1679:           }
    1680:           MatDenseRestoreArray(S_tmp,&data);
    1681:         } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor update not yet implemented for non SPD matrices");
    1682:         MatFactorRestoreSchurComplement(F,&S_tmp,MAT_FACTOR_SCHUR_FACTORED);
    1683:       }
    1684:     } else if (factor_workaround) { /* we need to eliminate any unneeded coupling */
    1685:       PetscScalar *data;
    1686:       PetscInt    nd = 0;

    1688:       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
    1689:         ISGetLocalSize(sub_schurs->is_dir,&nd);
    1690:       }
    1691:       MatFactorGetSchurComplement(F,&S_all,NULL);
    1692:       MatDenseGetArray(S_all,&data);
    1693:       for (i=0;i<size_active_schur;i++) {
    1694:         PetscArrayzero(data+i*size_schur+size_active_schur,size_schur-size_active_schur);
    1695:       }
    1696:       for (i=size_active_schur+nd;i<size_schur;i++) {
    1697:         PetscArrayzero(data+i*size_schur+size_active_schur,size_schur-size_active_schur);
    1698:         data[i*(size_schur+1)] = infty;
    1699:       }
    1700:       MatDenseRestoreArray(S_all,&data);
    1701:       MatFactorRestoreSchurComplement(F,&S_all,MAT_FACTOR_SCHUR_UNFACTORED);
    1702:     }
    1703:     PetscFree(work);
    1704:     PetscFree(schur_factor);
    1705:     VecDestroy(&Dall);
    1706:   }
    1707:   ISDestroy(&is_I_layer);
    1708:   MatDestroy(&S_all);
    1709:   MatDestroy(&A_BB);
    1710:   MatDestroy(&A_IB);
    1711:   MatDestroy(&A_BI);
    1712:   MatDestroy(&F);

    1714:   PetscMalloc1(sub_schurs->n_subs,&nnz);
    1715:   for (i=0;i<sub_schurs->n_subs;i++) {
    1716:     ISGetLocalSize(sub_schurs->is_subs[i],&nnz[i]);
    1717:   }
    1718:   ISCreateGeneral(PETSC_COMM_SELF,sub_schurs->n_subs,nnz,PETSC_OWN_POINTER,&is_I_layer);
    1719:   MatSetVariableBlockSizes(sub_schurs->S_Ej_all,sub_schurs->n_subs,nnz);
    1720:   MatAssemblyBegin(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);
    1721:   MatAssemblyEnd(sub_schurs->S_Ej_all,MAT_FINAL_ASSEMBLY);
    1722:   if (compute_Stilda) {
    1723:     MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_tilda_all,sub_schurs->n_subs,nnz);
    1724:     MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);
    1725:     MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all,MAT_FINAL_ASSEMBLY);
    1726:     if (deluxe) {
    1727:       MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_inv_all,sub_schurs->n_subs,nnz);
    1728:       MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);
    1729:       MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all,MAT_FINAL_ASSEMBLY);
    1730:     }
    1731:   }
    1732:   ISDestroy(&is_I_layer);

    1734:   /* Get local part of (\sum_j S_Ej) */
    1735:   if (!sub_schurs->sum_S_Ej_all) {
    1736:     MatDuplicate(sub_schurs->S_Ej_all,MAT_DO_NOT_COPY_VALUES,&sub_schurs->sum_S_Ej_all);
    1737:   }
    1738:   VecSet(gstash,0.0);
    1739:   MatSeqAIJGetArray(sub_schurs->S_Ej_all,&stasharray);
    1740:   VecPlaceArray(lstash,stasharray);
    1741:   VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);
    1742:   VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);
    1743:   MatSeqAIJRestoreArray(sub_schurs->S_Ej_all,&stasharray);
    1744:   VecResetArray(lstash);
    1745:   MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all,&stasharray);
    1746:   VecPlaceArray(lstash,stasharray);
    1747:   VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);
    1748:   VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);
    1749:   MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all,&stasharray);
    1750:   VecResetArray(lstash);

    1752:   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
    1753:   if (compute_Stilda) {
    1754:     VecSet(gstash,0.0);
    1755:     MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&stasharray);
    1756:     VecPlaceArray(lstash,stasharray);
    1757:     VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);
    1758:     VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);
    1759:     VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);
    1760:     VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);
    1761:     MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&stasharray);
    1762:     VecResetArray(lstash);
    1763:     if (deluxe) {
    1764:       VecSet(gstash,0.0);
    1765:       MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all,&stasharray);
    1766:       VecPlaceArray(lstash,stasharray);
    1767:       VecScatterBegin(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);
    1768:       VecScatterEnd(sstash,lstash,gstash,ADD_VALUES,SCATTER_FORWARD);
    1769:       VecScatterBegin(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);
    1770:       VecScatterEnd(sstash,gstash,lstash,INSERT_VALUES,SCATTER_REVERSE);
    1771:       MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all,&stasharray);
    1772:       VecResetArray(lstash);
    1773:     } else {
    1774:       PetscScalar *array;
    1775:       PetscInt    cum;

    1777:       MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all,&array);
    1778:       cum = 0;
    1779:       for (i=0;i<sub_schurs->n_subs;i++) {
    1780:         ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    1781:         PetscBLASIntCast(subset_size,&B_N);
    1782:         PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    1783:         if (use_potr) {
    1784:           PetscStackCallBLAS("LAPACKpotrf",LAPACKpotrf_("L",&B_N,array+cum,&B_N,&B_ierr));
    1786:           PetscStackCallBLAS("LAPACKpotri",LAPACKpotri_("L",&B_N,array+cum,&B_N,&B_ierr));
    1788:         } else if (use_sytr) {
    1789:           PetscStackCallBLAS("LAPACKsytrf",LAPACKsytrf_("L",&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
    1791:           PetscStackCallBLAS("LAPACKsytri",LAPACKsytri_("L",&B_N,array+cum,&B_N,pivots,Bwork,&B_ierr));
    1793:         } else {
    1794:           PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&B_N,&B_N,array+cum,&B_N,pivots,&B_ierr));
    1796:           PetscStackCallBLAS("LAPACKgetri",LAPACKgetri_(&B_N,array+cum,&B_N,pivots,Bwork,&B_lwork,&B_ierr));
    1798:         }
    1799:         PetscLogFlops(1.0*subset_size*subset_size*subset_size);
    1800:         PetscFPTrapPop();
    1801:         cum += subset_size*subset_size;
    1802:       }
    1803:       MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all,&array);
    1804:       PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all);
    1805:       MatDestroy(&sub_schurs->sum_S_Ej_inv_all);
    1806:       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
    1807:     }
    1808:   }
    1809:   VecDestroy(&lstash);
    1810:   VecDestroy(&gstash);
    1811:   VecScatterDestroy(&sstash);

    1813:   if (matl_dbg_viewer) {
    1814:     PetscInt cum;

    1816:     if (sub_schurs->S_Ej_all) {
    1817:       PetscObjectSetName((PetscObject)sub_schurs->S_Ej_all,"SE");
    1818:       MatView(sub_schurs->S_Ej_all,matl_dbg_viewer);
    1819:     }
    1820:     if (sub_schurs->sum_S_Ej_all) {
    1821:       PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_all,"SSE");
    1822:       MatView(sub_schurs->sum_S_Ej_all,matl_dbg_viewer);
    1823:     }
    1824:     if (sub_schurs->sum_S_Ej_inv_all) {
    1825:       PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_inv_all,"SSEm");
    1826:       MatView(sub_schurs->sum_S_Ej_inv_all,matl_dbg_viewer);
    1827:     }
    1828:     if (sub_schurs->sum_S_Ej_tilda_all) {
    1829:       PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_tilda_all,"SSEt");
    1830:       MatView(sub_schurs->sum_S_Ej_tilda_all,matl_dbg_viewer);
    1831:     }
    1832:     for (i=0,cum=0;i<sub_schurs->n_subs;i++) {
    1833:       IS   is;
    1834:       char name[16];

    1836:       PetscSNPrintf(name,sizeof(name),"IE%D",i);
    1837:       ISGetLocalSize(sub_schurs->is_subs[i],&subset_size);
    1838:       ISCreateStride(PETSC_COMM_SELF,subset_size,cum,1,&is);
    1839:       PetscObjectSetName((PetscObject)is,name);
    1840:       ISView(is,matl_dbg_viewer);
    1841:       ISDestroy(&is);
    1842:       cum += subset_size;
    1843:     }
    1844:   }

    1846:   /* free workspace */
    1847:   if (matl_dbg_viewer) PetscViewerFlush(matl_dbg_viewer);
    1848:   if (sub_schurs->debug) MPI_Barrier(comm_n);
    1849:   PetscViewerDestroy(&matl_dbg_viewer);
    1850:   PetscFree2(Bwork,pivots);
    1851:   PetscCommDestroy(&comm_n);
    1852:   return 0;
    1853: }

    1855: PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, const char* prefix, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc)
    1856: {
    1857:   IS              *faces,*edges,*all_cc,vertices;
    1858:   PetscInt        i,n_faces,n_edges,n_all_cc;
    1859:   PetscBool       is_sorted,ispardiso,ismumps;
    1860:   PetscErrorCode  ierr;

    1862:   ISSorted(is_I,&is_sorted);
    1864:   ISSorted(is_B,&is_sorted);

    1867:   /* reset any previous data */
    1868:   PCBDDCSubSchursReset(sub_schurs);

    1870:   /* get index sets for faces and edges (already sorted by global ordering) */
    1871:   PCBDDCGraphGetCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);
    1872:   n_all_cc = n_faces+n_edges;
    1873:   PetscBTCreate(n_all_cc,&sub_schurs->is_edge);
    1874:   PetscMalloc1(n_all_cc,&all_cc);
    1875:   for (i=0;i<n_faces;i++) {
    1876:     if (copycc) {
    1877:       ISDuplicate(faces[i],&all_cc[i]);
    1878:     } else {
    1879:       PetscObjectReference((PetscObject)faces[i]);
    1880:       all_cc[i] = faces[i];
    1881:     }
    1882:   }
    1883:   for (i=0;i<n_edges;i++) {
    1884:     if (copycc) {
    1885:       ISDuplicate(edges[i],&all_cc[n_faces+i]);
    1886:     } else {
    1887:       PetscObjectReference((PetscObject)edges[i]);
    1888:       all_cc[n_faces+i] = edges[i];
    1889:     }
    1890:     PetscBTSet(sub_schurs->is_edge,n_faces+i);
    1891:   }
    1892:   PetscObjectReference((PetscObject)vertices);
    1893:   sub_schurs->is_vertices = vertices;
    1894:   PCBDDCGraphRestoreCandidatesIS(graph,&n_faces,&faces,&n_edges,&edges,&vertices);
    1895:   sub_schurs->is_dir = NULL;
    1896:   PCBDDCGraphGetDirichletDofsB(graph,&sub_schurs->is_dir);

    1898:   /* Determine if MatFactor can be used */
    1899:   PetscStrallocpy(prefix,&sub_schurs->prefix);
    1900: #if defined(PETSC_HAVE_MUMPS)
    1901:   PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERMUMPS,sizeof(sub_schurs->mat_solver_type));
    1902: #elif defined(PETSC_HAVE_MKL_PARDISO)
    1903:   PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERMKL_PARDISO,sizeof(sub_schurs->mat_solver_type));
    1904: #else
    1905:   PetscStrncpy(sub_schurs->mat_solver_type,MATSOLVERPETSC,sizeof(sub_schurs->mat_solver_type));
    1906: #endif
    1907: #if defined(PETSC_USE_COMPLEX)
    1908:   sub_schurs->is_hermitian  = PETSC_FALSE; /* Hermitian Cholesky is not supported by PETSc and external packages */
    1909: #else
    1910:   sub_schurs->is_hermitian  = PETSC_TRUE;
    1911: #endif
    1912:   sub_schurs->is_posdef     = PETSC_TRUE;
    1913:   sub_schurs->is_symmetric  = PETSC_TRUE;
    1914:   sub_schurs->debug         = PETSC_FALSE;
    1915:   sub_schurs->restrict_comm = PETSC_FALSE;
    1916:   PetscOptionsBegin(PetscObjectComm((PetscObject)graph->l2gmap),sub_schurs->prefix,"BDDC sub_schurs options","PC");
    1917:   PetscOptionsString("-sub_schurs_mat_solver_type","Specific direct solver to use",NULL,sub_schurs->mat_solver_type,sub_schurs->mat_solver_type,sizeof(sub_schurs->mat_solver_type),NULL);
    1918:   PetscOptionsBool("-sub_schurs_symmetric","Symmetric problem",NULL,sub_schurs->is_symmetric,&sub_schurs->is_symmetric,NULL);
    1919:   PetscOptionsBool("-sub_schurs_hermitian","Hermitian problem",NULL,sub_schurs->is_hermitian,&sub_schurs->is_hermitian,NULL);
    1920:   PetscOptionsBool("-sub_schurs_posdef","Positive definite problem",NULL,sub_schurs->is_posdef,&sub_schurs->is_posdef,NULL);
    1921:   PetscOptionsBool("-sub_schurs_restrictcomm","Restrict communicator on active processes only",NULL,sub_schurs->restrict_comm,&sub_schurs->restrict_comm,NULL);
    1922:   PetscOptionsBool("-sub_schurs_debug","Debug output",NULL,sub_schurs->debug,&sub_schurs->debug,NULL);
    1923:   PetscOptionsEnd();
    1924:   PetscStrcmp(sub_schurs->mat_solver_type,MATSOLVERMUMPS,&ismumps);
    1925:   PetscStrcmp(sub_schurs->mat_solver_type,MATSOLVERMKL_PARDISO,&ispardiso);
    1926:   sub_schurs->schur_explicit = (PetscBool)(ispardiso || ismumps);

    1928:   /* for reals, symmetric and hermitian are synonims */
    1929: #if !defined(PETSC_USE_COMPLEX)
    1930:   sub_schurs->is_symmetric = (PetscBool)(sub_schurs->is_symmetric && sub_schurs->is_hermitian);
    1931:   sub_schurs->is_hermitian = sub_schurs->is_symmetric;
    1932: #endif

    1934:   PetscObjectReference((PetscObject)is_I);
    1935:   sub_schurs->is_I = is_I;
    1936:   PetscObjectReference((PetscObject)is_B);
    1937:   sub_schurs->is_B = is_B;
    1938:   PetscObjectReference((PetscObject)graph->l2gmap);
    1939:   sub_schurs->l2gmap = graph->l2gmap;
    1940:   PetscObjectReference((PetscObject)BtoNmap);
    1941:   sub_schurs->BtoNmap = BtoNmap;
    1942:   sub_schurs->n_subs = n_all_cc;
    1943:   sub_schurs->is_subs = all_cc;
    1944:   sub_schurs->S_Ej_all = NULL;
    1945:   sub_schurs->sum_S_Ej_all = NULL;
    1946:   sub_schurs->sum_S_Ej_inv_all = NULL;
    1947:   sub_schurs->sum_S_Ej_tilda_all = NULL;
    1948:   sub_schurs->is_Ej_all = NULL;
    1949:   return 0;
    1950: }

    1952: PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
    1953: {
    1954:   PCBDDCSubSchurs schurs_ctx;

    1956:   PetscNew(&schurs_ctx);
    1957:   schurs_ctx->n_subs = 0;
    1958:   *sub_schurs = schurs_ctx;
    1959:   return 0;
    1960: }

    1962: PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
    1963: {
    1964:   PetscInt       i;

    1966:   if (!sub_schurs) return 0;
    1967:   PetscFree(sub_schurs->prefix);
    1968:   MatDestroy(&sub_schurs->A);
    1969:   MatDestroy(&sub_schurs->S);
    1970:   ISDestroy(&sub_schurs->is_I);
    1971:   ISDestroy(&sub_schurs->is_B);
    1972:   ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap);
    1973:   ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap);
    1974:   MatDestroy(&sub_schurs->S_Ej_all);
    1975:   MatDestroy(&sub_schurs->sum_S_Ej_all);
    1976:   MatDestroy(&sub_schurs->sum_S_Ej_inv_all);
    1977:   MatDestroy(&sub_schurs->sum_S_Ej_tilda_all);
    1978:   ISDestroy(&sub_schurs->is_Ej_all);
    1979:   ISDestroy(&sub_schurs->is_vertices);
    1980:   ISDestroy(&sub_schurs->is_dir);
    1981:   PetscBTDestroy(&sub_schurs->is_edge);
    1982:   for (i=0;i<sub_schurs->n_subs;i++) {
    1983:     ISDestroy(&sub_schurs->is_subs[i]);
    1984:   }
    1985:   if (sub_schurs->n_subs) {
    1986:     PetscFree(sub_schurs->is_subs);
    1987:   }
    1988:   if (sub_schurs->reuse_solver) {
    1989:     PCBDDCReuseSolversReset(sub_schurs->reuse_solver);
    1990:   }
    1991:   PetscFree(sub_schurs->reuse_solver);
    1992:   if (sub_schurs->change) {
    1993:     for (i=0;i<sub_schurs->n_subs;i++) {
    1994:       KSPDestroy(&sub_schurs->change[i]);
    1995:       ISDestroy(&sub_schurs->change_primal_sub[i]);
    1996:     }
    1997:   }
    1998:   PetscFree(sub_schurs->change);
    1999:   PetscFree(sub_schurs->change_primal_sub);
    2000:   sub_schurs->n_subs = 0;
    2001:   return 0;
    2002: }

    2004: PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs* sub_schurs)
    2005: {
    2006:   PCBDDCSubSchursReset(*sub_schurs);
    2007:   PetscFree(*sub_schurs);
    2008:   return 0;
    2009: }

    2011: static inline PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt* queue_tip,PetscInt n_prev,PetscBT touched,PetscInt* xadj,PetscInt* adjncy,PetscInt* n_added)
    2012: {
    2013:   PetscInt       i,j,n;

    2015:   n = 0;
    2016:   for (i=-n_prev;i<0;i++) {
    2017:     PetscInt start_dof = queue_tip[i];
    2018:     for (j=xadj[start_dof];j<xadj[start_dof+1];j++) {
    2019:       PetscInt dof = adjncy[j];
    2020:       if (!PetscBTLookup(touched,dof)) {
    2021:         PetscBTSet(touched,dof);
    2022:         queue_tip[n] = dof;
    2023:         n++;
    2024:       }
    2025:     }
    2026:   }
    2027:   *n_added = n;
    2028:   return 0;
    2029: }