Date: 2025-03-29T05:58:29+00:00

Actual source code: bddcschurs.c

      1: #include <petsc/private/pcbddcimpl.h>
      2: #include <petsc/private/pcbddcprivateimpl.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:   PetscFunctionBegin;
     18:   if (!ctx->benign_n) PetscFunctionReturn(PETSC_SUCCESS);
     19:   if (sol && full) {
     20:     PetscInt n_I, size_schur;

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

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

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

     95:     /* get sizes */
     96:     PetscCall(MatGetSize(ctx->benign_csAIB, &size_schur, NULL));
     97:     PetscCall(VecGetSize(v, &n_I));
     98:     n_I = n_I - size_schur;
     99:     /* compute schur rhs correction */
    100:     if (v2) {
    101:       usedv = v2;
    102:     } else {
    103:       usedv = v;
    104:     }
    105:     /* apply schur rhs correction */
    106:     PetscCall(MatMultTranspose(ctx->benign_AIIm1ones, usedv, ctx->benign_corr_work));
    107:     PetscCall(VecGetArrayRead(usedv, (const PetscScalar **)&array));
    108:     PetscCall(VecPlaceArray(ctx->benign_dummy_schur_vec, array + n_I));
    109:     PetscCall(VecRestoreArrayRead(usedv, (const PetscScalar **)&array));
    110:     PetscCall(MatMultAdd(ctx->benign_csAIB, ctx->benign_corr_work, ctx->benign_dummy_schur_vec, ctx->benign_dummy_schur_vec));
    111:     PetscCall(VecResetArray(ctx->benign_dummy_schur_vec));
    112:   }
    113:   PetscFunctionReturn(PETSC_SUCCESS);
    114: }

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

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

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

    152:     PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, ctx->rhs, NULL, PETSC_FALSE, full));
    153:     if (transpose) {
    154:       PetscCall(MatSolveTranspose(ctx->F, ctx->rhs, ctx->sol));
    155:     } else {
    156:       PetscCall(MatSolve(ctx->F, ctx->rhs, ctx->sol));
    157:     }
    158:     PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, ctx->sol, NULL, PETSC_TRUE, full));

    160:     /* get back data to caller worskpace */
    161:     PetscCall(VecGetArrayRead(ctx->sol, (const PetscScalar **)&array_solver));
    162:     PetscCall(VecGetArray(sol, &array));
    163:     PetscCall(PetscArraycpy(array, array_solver, n));
    164:     PetscCall(VecRestoreArray(sol, &array));
    165:     PetscCall(VecRestoreArrayRead(ctx->sol, (const PetscScalar **)&array_solver));
    166:   } else {
    167:     if (ctx->benign_n) {
    168:       PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, rhs, ctx->rhs, PETSC_FALSE, full));
    169:       if (transpose) {
    170:         PetscCall(MatSolveTranspose(ctx->F, ctx->rhs, sol));
    171:       } else {
    172:         PetscCall(MatSolve(ctx->F, ctx->rhs, sol));
    173:       }
    174:       PetscCall(PCBDDCReuseSolversBenignAdapt(ctx, sol, NULL, PETSC_TRUE, full));
    175:     } else {
    176:       if (transpose) {
    177:         PetscCall(MatSolveTranspose(ctx->F, rhs, sol));
    178:       } else {
    179:         PetscCall(MatSolve(ctx->F, rhs, sol));
    180:       }
    181:     }
    182:   }
    183:   /* restore defaults */
    184: #if defined(PETSC_HAVE_MUMPS)
    185:   PetscCall(MatMumpsSetIcntl(ctx->F, 26, -1));
    186: #endif
    187: #if defined(PETSC_HAVE_MKL_PARDISO)
    188:   PetscCall(MatMkl_PardisoSetCntl(ctx->F, 70, 0));
    189: #endif
    190:   PetscFunctionReturn(PETSC_SUCCESS);
    191: }

    193: static PetscErrorCode PCBDDCReuseSolvers_Correction(PC pc, Vec rhs, Vec sol)
    194: {
    195:   PetscFunctionBegin;
    196:   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_FALSE, PETSC_TRUE));
    197:   PetscFunctionReturn(PETSC_SUCCESS);
    198: }

    200: static PetscErrorCode PCBDDCReuseSolvers_CorrectionTranspose(PC pc, Vec rhs, Vec sol)
    201: {
    202:   PetscFunctionBegin;
    203:   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_TRUE, PETSC_TRUE));
    204:   PetscFunctionReturn(PETSC_SUCCESS);
    205: }

    207: static PetscErrorCode PCBDDCReuseSolvers_Interior(PC pc, Vec rhs, Vec sol)
    208: {
    209:   PetscFunctionBegin;
    210:   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_FALSE, PETSC_FALSE));
    211:   PetscFunctionReturn(PETSC_SUCCESS);
    212: }

    214: static PetscErrorCode PCBDDCReuseSolvers_InteriorTranspose(PC pc, Vec rhs, Vec sol)
    215: {
    216:   PetscFunctionBegin;
    217:   PetscCall(PCBDDCReuseSolvers_Solve_Private(pc, rhs, sol, PETSC_TRUE, PETSC_FALSE));
    218:   PetscFunctionReturn(PETSC_SUCCESS);
    219: }

    221: static PetscErrorCode PCBDDCReuseSolvers_View(PC pc, PetscViewer viewer)
    222: {
    223:   PCBDDCReuseSolvers ctx;
    224:   PetscBool          iascii;

    226:   PetscFunctionBegin;
    227:   PetscCall(PCShellGetContext(pc, &ctx));
    228:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    229:   if (iascii) PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_INFO));
    230:   PetscCall(MatView(ctx->F, viewer));
    231:   if (iascii) PetscCall(PetscViewerPopFormat(viewer));
    232:   PetscFunctionReturn(PETSC_SUCCESS);
    233: }

    235: static PetscErrorCode PCBDDCReuseSolversReset(PCBDDCReuseSolvers reuse)
    236: {
    237:   PetscInt i;

    239:   PetscFunctionBegin;
    240:   PetscCall(MatDestroy(&reuse->F));
    241:   PetscCall(VecDestroy(&reuse->sol));
    242:   PetscCall(VecDestroy(&reuse->rhs));
    243:   PetscCall(PCDestroy(&reuse->interior_solver));
    244:   PetscCall(PCDestroy(&reuse->correction_solver));
    245:   PetscCall(ISDestroy(&reuse->is_R));
    246:   PetscCall(ISDestroy(&reuse->is_B));
    247:   PetscCall(VecScatterDestroy(&reuse->correction_scatter_B));
    248:   PetscCall(VecDestroy(&reuse->sol_B));
    249:   PetscCall(VecDestroy(&reuse->rhs_B));
    250:   for (i = 0; i < reuse->benign_n; i++) PetscCall(ISDestroy(&reuse->benign_zerodiag_subs[i]));
    251:   PetscCall(PetscFree(reuse->benign_zerodiag_subs));
    252:   PetscCall(PetscFree(reuse->benign_save_vals));
    253:   PetscCall(MatDestroy(&reuse->benign_csAIB));
    254:   PetscCall(MatDestroy(&reuse->benign_AIIm1ones));
    255:   PetscCall(VecDestroy(&reuse->benign_corr_work));
    256:   PetscCall(VecDestroy(&reuse->benign_dummy_schur_vec));
    257:   PetscFunctionReturn(PETSC_SUCCESS);
    258: }

    260: static PetscErrorCode PCBDDCReuseSolvers_Destroy(PC pc)
    261: {
    262:   PCBDDCReuseSolvers ctx;

    264:   PetscFunctionBegin;
    265:   PetscCall(PCShellGetContext(pc, &ctx));
    266:   PetscCall(PCBDDCReuseSolversReset(ctx));
    267:   PetscCall(PetscFree(ctx));
    268:   PetscCall(PCShellSetContext(pc, NULL));
    269:   PetscFunctionReturn(PETSC_SUCCESS);
    270: }

    272: static PetscErrorCode PCBDDCComputeExplicitSchur(Mat M, PetscBool issym, MatReuse reuse, Mat *S)
    273: {
    274:   Mat         B, C, D, Bd, Cd, AinvBd;
    275:   KSP         ksp;
    276:   PC          pc;
    277:   PetscBool   isLU, isILU, isCHOL, Bdense, Cdense;
    278:   PetscReal   fill = 2.0;
    279:   PetscInt    n_I;
    280:   PetscMPIInt size;

    282:   PetscFunctionBegin;
    283:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)M), &size));
    284:   PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not for parallel matrices");
    285:   if (reuse == MAT_REUSE_MATRIX) {
    286:     PetscBool Sdense;

    288:     PetscCall(PetscObjectTypeCompare((PetscObject)*S, MATSEQDENSE, &Sdense));
    289:     PetscCheck(Sdense, PetscObjectComm((PetscObject)M), PETSC_ERR_SUP, "S should dense");
    290:   }
    291:   PetscCall(MatSchurComplementGetSubMatrices(M, NULL, NULL, &B, &C, &D));
    292:   PetscCall(MatSchurComplementGetKSP(M, &ksp));
    293:   PetscCall(KSPGetPC(ksp, &pc));
    294:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCLU, &isLU));
    295:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCILU, &isILU));
    296:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCCHOLESKY, &isCHOL));
    297:   PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQDENSE, &Bdense));
    298:   PetscCall(PetscObjectTypeCompare((PetscObject)C, MATSEQDENSE, &Cdense));
    299:   PetscCall(MatGetSize(B, &n_I, NULL));
    300:   if (n_I) {
    301:     if (!Bdense) {
    302:       PetscCall(MatConvert(B, MATSEQDENSE, MAT_INITIAL_MATRIX, &Bd));
    303:     } else {
    304:       Bd = B;
    305:     }

    307:     if (isLU || isILU || isCHOL) {
    308:       Mat fact;
    309:       PetscCall(KSPSetUp(ksp));
    310:       PetscCall(PCFactorGetMatrix(pc, &fact));
    311:       PetscCall(MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd));
    312:       PetscCall(MatMatSolve(fact, Bd, AinvBd));
    313:     } else {
    314:       PetscBool ex = PETSC_TRUE;

    316:       if (ex) {
    317:         Mat Ainvd;

    319:         PetscCall(PCComputeOperator(pc, MATDENSE, &Ainvd));
    320:         PetscCall(MatMatMult(Ainvd, Bd, MAT_INITIAL_MATRIX, fill, &AinvBd));
    321:         PetscCall(MatDestroy(&Ainvd));
    322:       } else {
    323:         Vec          sol, rhs;
    324:         PetscScalar *arrayrhs, *arraysol;
    325:         PetscInt     i, nrhs, n;

    327:         PetscCall(MatDuplicate(Bd, MAT_DO_NOT_COPY_VALUES, &AinvBd));
    328:         PetscCall(MatGetSize(Bd, &n, &nrhs));
    329:         PetscCall(MatDenseGetArray(Bd, &arrayrhs));
    330:         PetscCall(MatDenseGetArray(AinvBd, &arraysol));
    331:         PetscCall(KSPGetSolution(ksp, &sol));
    332:         PetscCall(KSPGetRhs(ksp, &rhs));
    333:         for (i = 0; i < nrhs; i++) {
    334:           PetscCall(VecPlaceArray(rhs, arrayrhs + i * n));
    335:           PetscCall(VecPlaceArray(sol, arraysol + i * n));
    336:           PetscCall(KSPSolve(ksp, rhs, sol));
    337:           PetscCall(VecResetArray(rhs));
    338:           PetscCall(VecResetArray(sol));
    339:         }
    340:         PetscCall(MatDenseRestoreArray(Bd, &arrayrhs));
    341:         PetscCall(MatDenseRestoreArray(AinvBd, &arrayrhs));
    342:       }
    343:     }
    344:     if (!Bdense & !issym) PetscCall(MatDestroy(&Bd));

    346:     if (!issym) {
    347:       if (!Cdense) {
    348:         PetscCall(MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cd));
    349:       } else {
    350:         Cd = C;
    351:       }
    352:       PetscCall(MatMatMult(Cd, AinvBd, reuse, fill, S));
    353:       if (!Cdense) PetscCall(MatDestroy(&Cd));
    354:     } else {
    355:       PetscCall(MatTransposeMatMult(Bd, AinvBd, reuse, fill, S));
    356:       if (!Bdense) PetscCall(MatDestroy(&Bd));
    357:     }
    358:     PetscCall(MatDestroy(&AinvBd));
    359:   }

    361:   if (D) {
    362:     Mat       Dd;
    363:     PetscBool Ddense;

    365:     PetscCall(PetscObjectTypeCompare((PetscObject)D, MATSEQDENSE, &Ddense));
    366:     if (!Ddense) {
    367:       PetscCall(MatConvert(D, MATSEQDENSE, MAT_INITIAL_MATRIX, &Dd));
    368:     } else {
    369:       Dd = D;
    370:     }
    371:     if (n_I) {
    372:       PetscCall(MatAYPX(*S, -1.0, Dd, SAME_NONZERO_PATTERN));
    373:     } else {
    374:       if (reuse == MAT_INITIAL_MATRIX) {
    375:         PetscCall(MatDuplicate(Dd, MAT_COPY_VALUES, S));
    376:       } else {
    377:         PetscCall(MatCopy(Dd, *S, SAME_NONZERO_PATTERN));
    378:       }
    379:     }
    380:     if (!Ddense) PetscCall(MatDestroy(&Dd));
    381:   } else {
    382:     PetscCall(MatScale(*S, -1.0));
    383:   }
    384:   PetscFunctionReturn(PETSC_SUCCESS);
    385: }

    387: 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)
    388: {
    389:   Mat          F, A_II, A_IB, A_BI, A_BB, AE_II;
    390:   Mat          S_all;
    391:   Vec          gstash, lstash;
    392:   VecScatter   sstash;
    393:   IS           is_I, is_I_layer;
    394:   IS           all_subsets, all_subsets_mult, all_subsets_n;
    395:   PetscScalar *stasharray, *Bwork;
    396:   PetscInt    *nnz, *all_local_idx_N;
    397:   PetscInt    *auxnum1, *auxnum2;
    398:   PetscInt     i, subset_size, max_subset_size;
    399:   PetscInt     n_B, extra, local_size, global_size;
    400:   PetscInt     local_stash_size;
    401:   PetscBLASInt B_N, B_ierr, B_lwork, *pivots;
    402:   MPI_Comm     comm_n;
    403:   PetscBool    deluxe   = PETSC_TRUE;
    404:   PetscBool    use_potr = PETSC_FALSE, use_sytr = PETSC_FALSE;
    405:   PetscViewer  matl_dbg_viewer = NULL;
    406:   PetscBool    flg;

    408:   PetscFunctionBegin;
    409:   PetscCall(MatDestroy(&sub_schurs->A));
    410:   PetscCall(MatDestroy(&sub_schurs->S));
    411:   if (Ain) {
    412:     PetscCall(PetscObjectReference((PetscObject)Ain));
    413:     sub_schurs->A = Ain;
    414:   }

    416:   PetscCall(PetscObjectReference((PetscObject)Sin));
    417:   sub_schurs->S = Sin;
    418:   if (sub_schurs->schur_explicit) sub_schurs->schur_explicit = (PetscBool)(!!sub_schurs->A);

    420:   /* preliminary checks */
    421:   PetscCheck(sub_schurs->schur_explicit || !compute_Stilda, PetscObjectComm((PetscObject)sub_schurs->l2gmap), PETSC_ERR_SUP, "Adaptive selection of constraints requires MUMPS and/or MKL_PARDISO");

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

    425:   /* debug (MATLAB) */
    426:   if (sub_schurs->debug) {
    427:     PetscMPIInt size, rank;
    428:     PetscInt    nr, *print_schurs_ranks, print_schurs = PETSC_FALSE;

    430:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &size));
    431:     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &rank));
    432:     nr = size;
    433:     PetscCall(PetscMalloc1(nr, &print_schurs_ranks));
    434:     PetscOptionsBegin(PetscObjectComm((PetscObject)sub_schurs->l2gmap), sub_schurs->prefix, "BDDC sub_schurs options", "PC");
    435:     PetscCall(PetscOptionsIntArray("-sub_schurs_debug_ranks", "Ranks to debug (all if the option is not used)", NULL, print_schurs_ranks, &nr, &flg));
    436:     if (!flg) print_schurs = PETSC_TRUE;
    437:     else {
    438:       print_schurs = PETSC_FALSE;
    439:       for (i = 0; i < nr; i++)
    440:         if (print_schurs_ranks[i] == rank) {
    441:           print_schurs = PETSC_TRUE;
    442:           break;
    443:         }
    444:     }
    445:     PetscOptionsEnd();
    446:     PetscCall(PetscFree(print_schurs_ranks));
    447:     if (print_schurs) {
    448:       char filename[256];

    450:       PetscCall(PetscSNPrintf(filename, sizeof(filename), "sub_schurs_Schur_r%d.m", PetscGlobalRank));
    451:       PetscCall(PetscViewerASCIIOpen(PETSC_COMM_SELF, filename, &matl_dbg_viewer));
    452:       PetscCall(PetscViewerPushFormat(matl_dbg_viewer, PETSC_VIEWER_ASCII_MATLAB));
    453:     }
    454:   }

    456:   /* restrict work on active processes */
    457:   if (sub_schurs->restrict_comm) {
    458:     PetscSubcomm subcomm;
    459:     PetscMPIInt  color, rank;

    461:     color = 0;
    462:     if (!sub_schurs->n_subs) color = 1; /* this can happen if we are in a multilevel case or if the subdomain is disconnected */
    463:     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &rank));
    464:     PetscCall(PetscSubcommCreate(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &subcomm));
    465:     PetscCall(PetscSubcommSetNumber(subcomm, 2));
    466:     PetscCall(PetscSubcommSetTypeGeneral(subcomm, color, rank));
    467:     PetscCall(PetscCommDuplicate(PetscSubcommChild(subcomm), &comm_n, NULL));
    468:     PetscCall(PetscSubcommDestroy(&subcomm));
    469:     if (!sub_schurs->n_subs) {
    470:       PetscCall(PetscCommDestroy(&comm_n));
    471:       PetscFunctionReturn(PETSC_SUCCESS);
    472:     }
    473:   } else {
    474:     PetscCall(PetscCommDuplicate(PetscObjectComm((PetscObject)sub_schurs->l2gmap), &comm_n, NULL));
    475:   }

    477:   /* get Schur complement matrices */
    478:   if (!sub_schurs->schur_explicit) {
    479:     Mat       tA_IB, tA_BI, tA_BB;
    480:     PetscBool isseqsbaij;
    481:     PetscCall(MatSchurComplementGetSubMatrices(sub_schurs->S, &A_II, NULL, &tA_IB, &tA_BI, &tA_BB));
    482:     PetscCall(PetscObjectTypeCompare((PetscObject)tA_BB, MATSEQSBAIJ, &isseqsbaij));
    483:     if (isseqsbaij) {
    484:       PetscCall(MatConvert(tA_BB, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_BB));
    485:       PetscCall(MatConvert(tA_IB, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_IB));
    486:       PetscCall(MatConvert(tA_BI, MATSEQAIJ, MAT_INITIAL_MATRIX, &A_BI));
    487:     } else {
    488:       PetscCall(PetscObjectReference((PetscObject)tA_BB));
    489:       A_BB = tA_BB;
    490:       PetscCall(PetscObjectReference((PetscObject)tA_IB));
    491:       A_IB = tA_IB;
    492:       PetscCall(PetscObjectReference((PetscObject)tA_BI));
    493:       A_BI = tA_BI;
    494:     }
    495:   } else {
    496:     A_II = NULL;
    497:     A_IB = NULL;
    498:     A_BI = NULL;
    499:     A_BB = NULL;
    500:   }
    501:   S_all = NULL;

    503:   /* determine interior problems */
    504:   PetscCall(ISGetLocalSize(sub_schurs->is_I, &i));
    505:   if (nlayers >= 0 && i) { /* Interior problems can be different from the original one */
    506:     PetscBT         touched;
    507:     const PetscInt *idx_B;
    508:     PetscInt        n_I, n_B, n_local_dofs, n_prev_added, j, layer, *local_numbering;

    510:     PetscCheck(xadj, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot request layering without adjacency");
    511:     /* get sizes */
    512:     PetscCall(ISGetLocalSize(sub_schurs->is_I, &n_I));
    513:     PetscCall(ISGetLocalSize(sub_schurs->is_B, &n_B));

    515:     PetscCall(PetscMalloc1(n_I + n_B, &local_numbering));
    516:     PetscCall(PetscBTCreate(n_I + n_B, &touched));
    517:     PetscCall(PetscBTMemzero(n_I + n_B, touched));

    519:     /* all boundary dofs must be skipped when adding layers */
    520:     PetscCall(ISGetIndices(sub_schurs->is_B, &idx_B));
    521:     for (j = 0; j < n_B; j++) PetscCall(PetscBTSet(touched, idx_B[j]));
    522:     PetscCall(PetscArraycpy(local_numbering, idx_B, n_B));
    523:     PetscCall(ISRestoreIndices(sub_schurs->is_B, &idx_B));

    525:     /* add prescribed number of layers of dofs */
    526:     n_local_dofs = n_B;
    527:     n_prev_added = n_B;
    528:     for (layer = 0; layer < nlayers; layer++) {
    529:       PetscInt n_added = 0;
    530:       if (n_local_dofs == n_I + n_B) break;
    531:       PetscCheck(n_local_dofs <= n_I + n_B, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error querying layer %" PetscInt_FMT ". Out of bound access (%" PetscInt_FMT " > %" PetscInt_FMT ")", layer, n_local_dofs, n_I + n_B);
    532:       PetscCall(PCBDDCAdjGetNextLayer_Private(local_numbering + n_local_dofs, n_prev_added, touched, xadj, adjncy, &n_added));
    533:       n_prev_added = n_added;
    534:       n_local_dofs += n_added;
    535:       if (!n_added) break;
    536:     }
    537:     PetscCall(PetscBTDestroy(&touched));

    539:     /* IS for I layer dofs in original numbering */
    540:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)sub_schurs->is_I), n_local_dofs - n_B, local_numbering + n_B, PETSC_COPY_VALUES, &is_I_layer));
    541:     PetscCall(PetscFree(local_numbering));
    542:     PetscCall(ISSort(is_I_layer));
    543:     /* IS for I layer dofs in I numbering */
    544:     if (!sub_schurs->schur_explicit) {
    545:       ISLocalToGlobalMapping ItoNmap;
    546:       PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_I, &ItoNmap));
    547:       PetscCall(ISGlobalToLocalMappingApplyIS(ItoNmap, IS_GTOLM_DROP, is_I_layer, &is_I));
    548:       PetscCall(ISLocalToGlobalMappingDestroy(&ItoNmap));

    550:       /* II block */
    551:       PetscCall(MatCreateSubMatrix(A_II, is_I, is_I, MAT_INITIAL_MATRIX, &AE_II));
    552:     }
    553:   } else {
    554:     PetscInt n_I;

    556:     /* IS for I dofs in original numbering */
    557:     PetscCall(PetscObjectReference((PetscObject)sub_schurs->is_I));
    558:     is_I_layer = sub_schurs->is_I;

    560:     /* IS for I dofs in I numbering (strided 1) */
    561:     if (!sub_schurs->schur_explicit) {
    562:       PetscCall(ISGetSize(sub_schurs->is_I, &n_I));
    563:       PetscCall(ISCreateStride(PetscObjectComm((PetscObject)sub_schurs->is_I), n_I, 0, 1, &is_I));

    565:       /* II block is the same */
    566:       PetscCall(PetscObjectReference((PetscObject)A_II));
    567:       AE_II = A_II;
    568:     }
    569:   }

    571:   /* Get info on subset sizes and sum of all subsets sizes */
    572:   max_subset_size = 0;
    573:   local_size      = 0;
    574:   for (i = 0; i < sub_schurs->n_subs; i++) {
    575:     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
    576:     max_subset_size = PetscMax(subset_size, max_subset_size);
    577:     local_size += subset_size;
    578:   }

    580:   /* Work arrays for local indices */
    581:   extra = 0;
    582:   PetscCall(ISGetLocalSize(sub_schurs->is_B, &n_B));
    583:   if (sub_schurs->schur_explicit && is_I_layer) PetscCall(ISGetLocalSize(is_I_layer, &extra));
    584:   PetscCall(PetscMalloc1(n_B + extra, &all_local_idx_N));
    585:   if (extra) {
    586:     const PetscInt *idxs;
    587:     PetscCall(ISGetIndices(is_I_layer, &idxs));
    588:     PetscCall(PetscArraycpy(all_local_idx_N, idxs, extra));
    589:     PetscCall(ISRestoreIndices(is_I_layer, &idxs));
    590:   }
    591:   PetscCall(PetscMalloc1(sub_schurs->n_subs, &auxnum1));
    592:   PetscCall(PetscMalloc1(sub_schurs->n_subs, &auxnum2));

    594:   /* Get local indices in local numbering */
    595:   local_size       = 0;
    596:   local_stash_size = 0;
    597:   for (i = 0; i < sub_schurs->n_subs; i++) {
    598:     const PetscInt *idxs;

    600:     PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
    601:     PetscCall(ISGetIndices(sub_schurs->is_subs[i], &idxs));
    602:     /* start (smallest in global ordering) and multiplicity */
    603:     auxnum1[i] = idxs[0];
    604:     auxnum2[i] = subset_size * subset_size;
    605:     /* subset indices in local numbering */
    606:     PetscCall(PetscArraycpy(all_local_idx_N + local_size + extra, idxs, subset_size));
    607:     PetscCall(ISRestoreIndices(sub_schurs->is_subs[i], &idxs));
    608:     local_size += subset_size;
    609:     local_stash_size += subset_size * subset_size;
    610:   }

    612:   /* allocate extra workspace needed only for GETRI or SYTRF */
    613:   use_potr = use_sytr = PETSC_FALSE;
    614:   if (benign_trick || (sub_schurs->is_hermitian && sub_schurs->is_posdef)) {
    615:     use_potr = PETSC_TRUE;
    616:   } else if (sub_schurs->is_symmetric) {
    617:     use_sytr = PETSC_TRUE;
    618:   }
    619:   if (local_size && !use_potr) {
    620:     PetscScalar  lwork, dummyscalar = 0.;
    621:     PetscBLASInt dummyint = 0;

    623:     B_lwork = -1;
    624:     PetscCall(PetscBLASIntCast(local_size, &B_N));
    625:     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    626:     if (use_sytr) {
    627:       PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, &dummyscalar, &B_N, &dummyint, &lwork, &B_lwork, &B_ierr));
    628:       PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
    629:     } else {
    630:       PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, &dummyscalar, &B_N, &dummyint, &lwork, &B_lwork, &B_ierr));
    631:       PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
    632:     }
    633:     PetscCall(PetscFPTrapPop());
    634:     PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(lwork), &B_lwork));
    635:     PetscCall(PetscMalloc2(B_lwork, &Bwork, B_N, &pivots));
    636:   } else {
    637:     Bwork  = NULL;
    638:     pivots = NULL;
    639:   }

    641:   /* prepare data for summing up properly schurs on subsets */
    642:   PetscCall(ISCreateGeneral(comm_n, sub_schurs->n_subs, auxnum1, PETSC_OWN_POINTER, &all_subsets_n));
    643:   PetscCall(ISLocalToGlobalMappingApplyIS(sub_schurs->l2gmap, all_subsets_n, &all_subsets));
    644:   PetscCall(ISDestroy(&all_subsets_n));
    645:   PetscCall(ISCreateGeneral(comm_n, sub_schurs->n_subs, auxnum2, PETSC_OWN_POINTER, &all_subsets_mult));
    646:   PetscCall(ISRenumber(all_subsets, all_subsets_mult, &global_size, &all_subsets_n));
    647:   PetscCall(ISDestroy(&all_subsets));
    648:   PetscCall(ISDestroy(&all_subsets_mult));
    649:   PetscCall(ISGetLocalSize(all_subsets_n, &i));
    650:   PetscCheck(i == local_stash_size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid size of new subset! %" PetscInt_FMT " != %" PetscInt_FMT, i, local_stash_size);
    651:   PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, local_stash_size, NULL, &lstash));
    652:   PetscCall(VecCreateMPI(comm_n, PETSC_DECIDE, global_size, &gstash));
    653:   PetscCall(VecScatterCreate(lstash, NULL, gstash, all_subsets_n, &sstash));
    654:   PetscCall(ISDestroy(&all_subsets_n));

    656:   /* subset indices in local boundary numbering */
    657:   if (!sub_schurs->is_Ej_all) {
    658:     PetscInt *all_local_idx_B;

    660:     PetscCall(PetscMalloc1(local_size, &all_local_idx_B));
    661:     PetscCall(ISGlobalToLocalMappingApply(sub_schurs->BtoNmap, IS_GTOLM_DROP, local_size, all_local_idx_N + extra, &subset_size, all_local_idx_B));
    662:     PetscCheck(subset_size == local_size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error in sub_schurs serial (BtoNmap)! %" PetscInt_FMT " != %" PetscInt_FMT, subset_size, local_size);
    663:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, local_size, all_local_idx_B, PETSC_OWN_POINTER, &sub_schurs->is_Ej_all));
    664:   }

    666:   if (change) {
    667:     ISLocalToGlobalMapping BtoS;
    668:     IS                     change_primal_B;
    669:     IS                     change_primal_all;

    671:     PetscCheck(!sub_schurs->change_primal_sub, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
    672:     PetscCheck(!sub_schurs->change, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
    673:     PetscCall(PetscMalloc1(sub_schurs->n_subs, &sub_schurs->change_primal_sub));
    674:     for (i = 0; i < sub_schurs->n_subs; i++) {
    675:       ISLocalToGlobalMapping NtoS;
    676:       PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_subs[i], &NtoS));
    677:       PetscCall(ISGlobalToLocalMappingApplyIS(NtoS, IS_GTOLM_DROP, change_primal, &sub_schurs->change_primal_sub[i]));
    678:       PetscCall(ISLocalToGlobalMappingDestroy(&NtoS));
    679:     }
    680:     PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, change_primal, &change_primal_B));
    681:     PetscCall(ISLocalToGlobalMappingCreateIS(sub_schurs->is_Ej_all, &BtoS));
    682:     PetscCall(ISGlobalToLocalMappingApplyIS(BtoS, IS_GTOLM_DROP, change_primal_B, &change_primal_all));
    683:     PetscCall(ISLocalToGlobalMappingDestroy(&BtoS));
    684:     PetscCall(ISDestroy(&change_primal_B));
    685:     PetscCall(PetscMalloc1(sub_schurs->n_subs, &sub_schurs->change));
    686:     for (i = 0; i < sub_schurs->n_subs; i++) {
    687:       Mat change_sub;

    689:       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
    690:       PetscCall(KSPCreate(PETSC_COMM_SELF, &sub_schurs->change[i]));
    691:       PetscCall(KSPSetNestLevel(sub_schurs->change[i], 1)); /* do not seem to have direct access to a PC from which to get the level of nests */
    692:       PetscCall(KSPSetType(sub_schurs->change[i], KSPPREONLY));
    693:       if (!sub_schurs->change_with_qr) {
    694:         PetscCall(MatCreateSubMatrix(change, sub_schurs->is_subs[i], sub_schurs->is_subs[i], MAT_INITIAL_MATRIX, &change_sub));
    695:       } else {
    696:         Mat change_subt;
    697:         PetscCall(MatCreateSubMatrix(change, sub_schurs->is_subs[i], sub_schurs->is_subs[i], MAT_INITIAL_MATRIX, &change_subt));
    698:         PetscCall(MatConvert(change_subt, MATSEQDENSE, MAT_INITIAL_MATRIX, &change_sub));
    699:         PetscCall(MatDestroy(&change_subt));
    700:       }
    701:       PetscCall(KSPSetOperators(sub_schurs->change[i], change_sub, change_sub));
    702:       PetscCall(MatDestroy(&change_sub));
    703:       PetscCall(KSPSetOptionsPrefix(sub_schurs->change[i], sub_schurs->prefix));
    704:       PetscCall(KSPAppendOptionsPrefix(sub_schurs->change[i], "sub_schurs_change_"));
    705:     }
    706:     PetscCall(ISDestroy(&change_primal_all));
    707:   }

    709:   /* Local matrix of all local Schur on subsets (transposed) */
    710:   if (!sub_schurs->S_Ej_all) {
    711:     Mat          T;
    712:     PetscScalar *v;
    713:     PetscInt    *ii, *jj;
    714:     PetscInt     cum, i, j, k;

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

    727:         ii[row + 1] = ii[row] + subset_size;
    728:         for (k = ii[row]; k < ii[row + 1]; k++) {
    729:           jj[k] = col;
    730:           col++;
    731:         }
    732:       }
    733:       cum += subset_size;
    734:     }
    735:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, local_size, local_size, ii, jj, v, &T));
    736:     PetscCall(MatDuplicate(T, MAT_DO_NOT_COPY_VALUES, &sub_schurs->S_Ej_all));
    737:     PetscCall(MatDestroy(&T));
    738:     PetscCall(PetscFree3(ii, jj, v));
    739:   }
    740:   /* matrices for deluxe scaling and adaptive selection */
    741:   if (compute_Stilda) {
    742:     if (!sub_schurs->sum_S_Ej_tilda_all) PetscCall(MatDuplicate(sub_schurs->S_Ej_all, MAT_DO_NOT_COPY_VALUES, &sub_schurs->sum_S_Ej_tilda_all));
    743:     if (!sub_schurs->sum_S_Ej_inv_all && deluxe) PetscCall(MatDuplicate(sub_schurs->S_Ej_all, MAT_DO_NOT_COPY_VALUES, &sub_schurs->sum_S_Ej_inv_all));
    744:   }

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

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

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

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

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

    856:     /* import scaling vector (wrong formulation if we have 3D edges) */
    857:     if (scaling && compute_Stilda) {
    858:       const PetscScalar *array;
    859:       PetscScalar       *array2;
    860:       const PetscInt    *idxs;
    861:       PetscInt           i;

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

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

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

    893:       PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &n_v));
    894:       if (n_v) {
    895:         const PetscInt *idxs;

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

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

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

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

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

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

    994:     if (n_I) {
    995:       IS        is_schur;
    996:       char      stype[64];
    997:       PetscBool gpu = PETSC_FALSE;

    999:       if (use_cholesky) {
    1000:         PetscCall(MatGetFactor(A, sub_schurs->mat_solver_type, MAT_FACTOR_CHOLESKY, &F));
    1001:       } else {
    1002:         PetscCall(MatGetFactor(A, sub_schurs->mat_solver_type, MAT_FACTOR_LU, &F));
    1003:       }
    1004:       PetscCheck(F, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MatGetFactor not supported by matrix instance of type %s. Rerun with \"-info :mat | grep MatGetFactor_\" for additional information", ((PetscObject)A)->type_name);
    1005:       PetscCall(MatSetErrorIfFailure(A, PETSC_TRUE));
    1006: #if defined(PETSC_HAVE_MKL_PARDISO)
    1007:       if (benign_trick) PetscCall(MatMkl_PardisoSetCntl(F, 10, 10));
    1008: #endif
    1009:       /* subsets ordered last */
    1010:       PetscCall(ISCreateStride(PETSC_COMM_SELF, size_schur, n_I, 1, &is_schur));
    1011:       PetscCall(MatFactorSetSchurIS(F, is_schur));
    1012:       PetscCall(ISDestroy(&is_schur));

    1014:       /* factorization step */
    1015:       if (use_cholesky) {
    1016:         PetscCall(MatCholeskyFactorSymbolic(F, A, NULL, NULL));
    1017: #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
    1018:         PetscCall(MatMumpsSetIcntl(F, 19, 2));
    1019: #endif
    1020:         PetscCall(MatCholeskyFactorNumeric(F, A, NULL));
    1021:         S_lower_triangular = PETSC_TRUE;
    1022:       } else {
    1023:         PetscCall(MatLUFactorSymbolic(F, A, NULL, NULL, NULL));
    1024: #if defined(PETSC_HAVE_MUMPS) /* be sure that icntl 19 is not set by command line */
    1025:         PetscCall(MatMumpsSetIcntl(F, 19, 3));
    1026: #endif
    1027:         PetscCall(MatLUFactorNumeric(F, A, NULL));
    1028:       }
    1029:       PetscCall(MatViewFromOptions(F, (PetscObject)A, "-mat_factor_view"));

    1031:       if (matl_dbg_viewer) {
    1032:         Mat S;
    1033:         IS  is;

    1035:         PetscCall(PetscObjectSetName((PetscObject)A, "A"));
    1036:         PetscCall(MatView(A, matl_dbg_viewer));
    1037:         PetscCall(MatFactorCreateSchurComplement(F, &S, NULL));
    1038:         PetscCall(PetscObjectSetName((PetscObject)S, "S"));
    1039:         PetscCall(MatView(S, matl_dbg_viewer));
    1040:         PetscCall(MatDestroy(&S));
    1041:         PetscCall(ISCreateStride(PETSC_COMM_SELF, n_I, 0, 1, &is));
    1042:         PetscCall(PetscObjectSetName((PetscObject)is, "I"));
    1043:         PetscCall(ISView(is, matl_dbg_viewer));
    1044:         PetscCall(ISDestroy(&is));
    1045:         PetscCall(ISCreateStride(PETSC_COMM_SELF, size_schur, n_I, 1, &is));
    1046:         PetscCall(PetscObjectSetName((PetscObject)is, "B"));
    1047:         PetscCall(ISView(is, matl_dbg_viewer));
    1048:         PetscCall(ISDestroy(&is));
    1049:         PetscCall(PetscObjectSetName((PetscObject)is_A_all, "IA"));
    1050:         PetscCall(ISView(is_A_all, matl_dbg_viewer));
    1051:         for (i = 0, cum = 0; i < sub_schurs->n_subs; i++) {
    1052:           IS   is;
    1053:           char name[16];

    1055:           PetscCall(PetscSNPrintf(name, sizeof(name), "IE%" PetscInt_FMT, i));
    1056:           PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
    1057:           PetscCall(ISCreateStride(PETSC_COMM_SELF, subset_size, cum, 1, &is));
    1058:           PetscCall(PetscObjectSetName((PetscObject)is, name));
    1059:           PetscCall(ISView(is, matl_dbg_viewer));
    1060:           PetscCall(ISDestroy(&is));
    1061:           if (sub_schurs->change) {
    1062:             Mat T;

    1064:             PetscCall(PetscSNPrintf(name, sizeof(name), "TE%" PetscInt_FMT, i));
    1065:             PetscCall(KSPGetOperators(sub_schurs->change[i], &T, NULL));
    1066:             PetscCall(PetscObjectSetName((PetscObject)T, name));
    1067:             PetscCall(MatView(T, matl_dbg_viewer));
    1068:             PetscCall(PetscSNPrintf(name, sizeof(name), "ITE%" PetscInt_FMT, i));
    1069:             PetscCall(PetscObjectSetName((PetscObject)sub_schurs->change_primal_sub[i], name));
    1070:             PetscCall(ISView(sub_schurs->change_primal_sub[i], matl_dbg_viewer));
    1071:           }
    1072:           cum += subset_size;
    1073:         }
    1074:         PetscCall(PetscViewerFlush(matl_dbg_viewer));
    1075:       }

    1077:       /* get explicit Schur Complement computed during numeric factorization */
    1078:       PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
    1079:       PetscCall(PetscStrncpy(stype, MATSEQDENSE, sizeof(stype)));
    1080: #if defined(PETSC_HAVE_CUDA)
    1081:       PetscCall(PetscObjectTypeCompareAny((PetscObject)A, &gpu, MATSEQAIJVIENNACL, MATSEQAIJCUSPARSE, ""));
    1082: #endif
    1083:       if (gpu) PetscCall(PetscStrncpy(stype, MATSEQDENSECUDA, sizeof(stype)));
    1084:       PetscCall(PetscOptionsGetString(NULL, sub_schurs->prefix, "-sub_schurs_schur_mat_type", stype, sizeof(stype), NULL));
    1085:       PetscCall(MatConvert(S_all, stype, MAT_INPLACE_MATRIX, &S_all));
    1086:       PetscCall(MatSetOption(S_all, MAT_SPD, sub_schurs->is_posdef));
    1087:       PetscCall(MatSetOption(S_all, MAT_HERMITIAN, sub_schurs->is_hermitian));
    1088:       PetscCall(MatGetType(S_all, &Stype));

    1090:       /* we can reuse the solvers if we are not using the economic version */
    1091:       reuse_solvers = (PetscBool)(reuse_solvers && !economic);
    1092:       if (!sub_schurs->gdsw) {
    1093:         factor_workaround = (PetscBool)(reuse_solvers && factor_workaround);
    1094:         if (!sub_schurs->is_posdef && factor_workaround && compute_Stilda && size_active_schur) reuse_solvers = factor_workaround = PETSC_FALSE;
    1095:       }
    1096:       solver_S = PETSC_TRUE;

    1098:       /* update the Schur complement with the change of basis on the pressures */
    1099:       if (benign_n) {
    1100:         const PetscScalar *cs_AIB;
    1101:         PetscScalar       *S_data, *AIIm1_data;
    1102:         Mat                S2 = NULL, S3 = NULL; /* dbg */
    1103:         PetscScalar       *S2_data, *S3_data;    /* dbg */
    1104:         Vec                v, benign_AIIm1_ones;
    1105:         PetscInt           sizeA;

    1107:         PetscCall(MatDenseGetArray(S_all, &S_data));
    1108:         PetscCall(MatCreateVecs(A, &v, &benign_AIIm1_ones));
    1109:         PetscCall(VecGetSize(v, &sizeA));
    1110: #if defined(PETSC_HAVE_MUMPS)
    1111:         PetscCall(MatMumpsSetIcntl(F, 26, 0));
    1112: #endif
    1113: #if defined(PETSC_HAVE_MKL_PARDISO)
    1114:         PetscCall(MatMkl_PardisoSetCntl(F, 70, 1));
    1115: #endif
    1116:         PetscCall(MatDenseGetArrayRead(cs_AIB_mat, &cs_AIB));
    1117:         PetscCall(MatDenseGetArray(benign_AIIm1_ones_mat, &AIIm1_data));
    1118:         if (matl_dbg_viewer) {
    1119:           PetscCall(MatDuplicate(S_all, MAT_DO_NOT_COPY_VALUES, &S2));
    1120:           PetscCall(MatDuplicate(S_all, MAT_DO_NOT_COPY_VALUES, &S3));
    1121:           PetscCall(MatDenseGetArray(S2, &S2_data));
    1122:           PetscCall(MatDenseGetArray(S3, &S3_data));
    1123:         }
    1124:         for (i = 0; i < benign_n; i++) {
    1125:           PetscScalar    *array, sum = 0., one = 1., *sums;
    1126:           const PetscInt *idxs;
    1127:           PetscInt        k, j, nz;
    1128:           PetscBLASInt    B_k, B_n;

    1130:           PetscCall(PetscCalloc1(benign_n, &sums));
    1131:           PetscCall(VecPlaceArray(benign_AIIm1_ones, AIIm1_data + sizeA * i));
    1132:           PetscCall(VecCopy(benign_AIIm1_ones, v));
    1133:           PetscCall(MatSolve(F, v, benign_AIIm1_ones));
    1134:           PetscCall(MatMult(A, benign_AIIm1_ones, v));
    1135:           PetscCall(VecResetArray(benign_AIIm1_ones));
    1136:           /* p0 dofs (eliminated) are excluded from the sums */
    1137:           for (k = 0; k < benign_n; k++) {
    1138:             PetscCall(ISGetLocalSize(is_p_r[k], &nz));
    1139:             PetscCall(ISGetIndices(is_p_r[k], &idxs));
    1140:             for (j = 0; j < nz - 1; j++) sums[k] -= AIIm1_data[idxs[j] + sizeA * i];
    1141:             PetscCall(ISRestoreIndices(is_p_r[k], &idxs));
    1142:           }
    1143:           PetscCall(VecGetArrayRead(v, (const PetscScalar **)&array));
    1144:           if (matl_dbg_viewer) {
    1145:             Vec  vv;
    1146:             char name[16];

    1148:             PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, size_schur, array + n_I, &vv));
    1149:             PetscCall(PetscSNPrintf(name, sizeof(name), "Pvs%" PetscInt_FMT, i));
    1150:             PetscCall(PetscObjectSetName((PetscObject)vv, name));
    1151:             PetscCall(VecView(vv, matl_dbg_viewer));
    1152:           }
    1153:           /* perform sparse rank updates on symmetric Schur (TODO: move outside of the loop?) */
    1154:           /* cs_AIB already scaled by 1./nz */
    1155:           B_k = 1;
    1156:           PetscCall(PetscBLASIntCast(size_schur, &B_n));
    1157:           for (k = 0; k < benign_n; k++) {
    1158:             sum = sums[k];

    1160:             if (PetscAbsScalar(sum) == 0.0) continue;
    1161:             if (k == i) {
    1162:               if (B_n) PetscCallBLAS("BLASsyrk", BLASsyrk_("L", "N", &B_n, &B_k, &sum, cs_AIB + i * size_schur, &B_n, &one, S_data, &B_n));
    1163:               if (matl_dbg_viewer && B_n) PetscCallBLAS("BLASsyrk", BLASsyrk_("L", "N", &B_n, &B_k, &sum, cs_AIB + i * size_schur, &B_n, &one, S3_data, &B_n));
    1164:             } else { /* XXX Is it correct to use symmetric rank-2 update with half of the sum? */
    1165:               sum /= 2.0;
    1166:               if (B_n) PetscCallBLAS("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));
    1167:               if (matl_dbg_viewer && B_n) PetscCallBLAS("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));
    1168:             }
    1169:           }
    1170:           sum = 1.;
    1171:           if (B_n) PetscCallBLAS("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));
    1172:           if (matl_dbg_viewer && B_n) PetscCallBLAS("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));
    1173:           PetscCall(VecRestoreArrayRead(v, (const PetscScalar **)&array));
    1174:           /* set p0 entry of AIIm1_ones to zero */
    1175:           PetscCall(ISGetLocalSize(is_p_r[i], &nz));
    1176:           PetscCall(ISGetIndices(is_p_r[i], &idxs));
    1177:           for (j = 0; j < benign_n; j++) AIIm1_data[idxs[nz - 1] + sizeA * j] = 0.;
    1178:           PetscCall(ISRestoreIndices(is_p_r[i], &idxs));
    1179:           PetscCall(PetscFree(sums));
    1180:         }
    1181:         PetscCall(VecDestroy(&benign_AIIm1_ones));
    1182:         if (matl_dbg_viewer) {
    1183:           PetscCall(MatDenseRestoreArray(S2, &S2_data));
    1184:           PetscCall(MatDenseRestoreArray(S3, &S3_data));
    1185:         }
    1186:         if (!S_lower_triangular) { /* I need to expand the upper triangular data (column-oriented) */
    1187:           PetscInt k, j;
    1188:           for (k = 0; k < size_schur; k++) {
    1189:             for (j = k; j < size_schur; j++) S_data[j * size_schur + k] = PetscConj(S_data[k * size_schur + j]);
    1190:           }
    1191:         }

    1193:         /* restore defaults */
    1194: #if defined(PETSC_HAVE_MUMPS)
    1195:         PetscCall(MatMumpsSetIcntl(F, 26, -1));
    1196: #endif
    1197: #if defined(PETSC_HAVE_MKL_PARDISO)
    1198:         PetscCall(MatMkl_PardisoSetCntl(F, 70, 0));
    1199: #endif
    1200:         PetscCall(MatDenseRestoreArrayRead(cs_AIB_mat, &cs_AIB));
    1201:         PetscCall(MatDenseRestoreArray(benign_AIIm1_ones_mat, &AIIm1_data));
    1202:         PetscCall(VecDestroy(&v));
    1203:         PetscCall(MatDenseRestoreArray(S_all, &S_data));
    1204:         if (matl_dbg_viewer) {
    1205:           Mat S;

    1207:           PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));
    1208:           PetscCall(MatFactorCreateSchurComplement(F, &S, NULL));
    1209:           PetscCall(PetscObjectSetName((PetscObject)S, "Sb"));
    1210:           PetscCall(MatView(S, matl_dbg_viewer));
    1211:           PetscCall(MatDestroy(&S));
    1212:           PetscCall(PetscObjectSetName((PetscObject)S2, "S2P"));
    1213:           PetscCall(MatView(S2, matl_dbg_viewer));
    1214:           PetscCall(PetscObjectSetName((PetscObject)S3, "S3P"));
    1215:           PetscCall(MatView(S3, matl_dbg_viewer));
    1216:           PetscCall(PetscObjectSetName((PetscObject)cs_AIB_mat, "cs"));
    1217:           PetscCall(MatView(cs_AIB_mat, matl_dbg_viewer));
    1218:           PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
    1219:         }
    1220:         PetscCall(MatDestroy(&S2));
    1221:         PetscCall(MatDestroy(&S3));
    1222:       }
    1223:       if (!reuse_solvers) {
    1224:         for (i = 0; i < benign_n; i++) PetscCall(ISDestroy(&is_p_r[i]));
    1225:         PetscCall(PetscFree(is_p_r));
    1226:         PetscCall(MatDestroy(&cs_AIB_mat));
    1227:         PetscCall(MatDestroy(&benign_AIIm1_ones_mat));
    1228:       }
    1229:     } else { /* we can't use MatFactor when size_schur == size_of_the_problem */
    1230:       PetscCall(MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &S_all));
    1231:       PetscCall(MatGetType(S_all, &Stype));
    1232:       reuse_solvers     = PETSC_FALSE; /* TODO: why we can't reuse the solvers here? */
    1233:       factor_workaround = PETSC_FALSE;
    1234:       solver_S          = PETSC_FALSE;
    1235:     }

    1237:     if (reuse_solvers) {
    1238:       Mat                A_II, pA_II, Afake;
    1239:       Vec                vec1_B;
    1240:       PCBDDCReuseSolvers msolv_ctx;
    1241:       PetscInt           n_R;

    1243:       if (sub_schurs->reuse_solver) {
    1244:         PetscCall(PCBDDCReuseSolversReset(sub_schurs->reuse_solver));
    1245:       } else {
    1246:         PetscCall(PetscNew(&sub_schurs->reuse_solver));
    1247:       }
    1248:       msolv_ctx = sub_schurs->reuse_solver;
    1249:       PetscCall(MatSchurComplementGetSubMatrices(sub_schurs->S, &A_II, &pA_II, NULL, NULL, NULL));
    1250:       PetscCall(PetscObjectReference((PetscObject)F));
    1251:       msolv_ctx->F = F;
    1252:       PetscCall(MatCreateVecs(F, &msolv_ctx->sol, NULL));
    1253:       /* currently PETSc has no support for MatSolve(F,x,x), so cheat and let rhs and sol share the same memory */
    1254:       {
    1255:         PetscScalar *array;
    1256:         PetscInt     n;

    1258:         PetscCall(VecGetLocalSize(msolv_ctx->sol, &n));
    1259:         PetscCall(VecGetArray(msolv_ctx->sol, &array));
    1260:         PetscCall(VecCreateSeqWithArray(PetscObjectComm((PetscObject)msolv_ctx->sol), 1, n, array, &msolv_ctx->rhs));
    1261:         PetscCall(VecRestoreArray(msolv_ctx->sol, &array));
    1262:       }
    1263:       msolv_ctx->has_vertices = schur_has_vertices;

    1265:       /* interior solver */
    1266:       PetscCall(PCCreate(PetscObjectComm((PetscObject)A_II), &msolv_ctx->interior_solver));
    1267:       PetscCall(PCSetOperators(msolv_ctx->interior_solver, A_II, pA_II));
    1268:       PetscCall(PCSetType(msolv_ctx->interior_solver, PCSHELL));
    1269:       PetscCall(PCShellSetName(msolv_ctx->interior_solver, "Interior solver (w/o Schur factorization)"));
    1270:       PetscCall(PCShellSetContext(msolv_ctx->interior_solver, msolv_ctx));
    1271:       PetscCall(PCShellSetView(msolv_ctx->interior_solver, PCBDDCReuseSolvers_View));
    1272:       PetscCall(PCShellSetApply(msolv_ctx->interior_solver, PCBDDCReuseSolvers_Interior));
    1273:       PetscCall(PCShellSetApplyTranspose(msolv_ctx->interior_solver, PCBDDCReuseSolvers_InteriorTranspose));
    1274:       if (sub_schurs->gdsw) PetscCall(PCShellSetDestroy(msolv_ctx->interior_solver, PCBDDCReuseSolvers_Destroy));

    1276:       /* correction solver */
    1277:       if (!sub_schurs->gdsw) {
    1278:         PetscCall(PCCreate(PetscObjectComm((PetscObject)A_II), &msolv_ctx->correction_solver));
    1279:         PetscCall(PCSetType(msolv_ctx->correction_solver, PCSHELL));
    1280:         PetscCall(PCShellSetName(msolv_ctx->correction_solver, "Correction solver (with Schur factorization)"));
    1281:         PetscCall(PCShellSetContext(msolv_ctx->correction_solver, msolv_ctx));
    1282:         PetscCall(PCShellSetView(msolv_ctx->interior_solver, PCBDDCReuseSolvers_View));
    1283:         PetscCall(PCShellSetApply(msolv_ctx->correction_solver, PCBDDCReuseSolvers_Correction));
    1284:         PetscCall(PCShellSetApplyTranspose(msolv_ctx->correction_solver, PCBDDCReuseSolvers_CorrectionTranspose));

    1286:         /* scatter and vecs for Schur complement solver */
    1287:         PetscCall(MatCreateVecs(S_all, &msolv_ctx->sol_B, &msolv_ctx->rhs_B));
    1288:         PetscCall(MatCreateVecs(sub_schurs->S, &vec1_B, NULL));
    1289:         if (!schur_has_vertices) {
    1290:           PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, is_A_all, &msolv_ctx->is_B));
    1291:           PetscCall(VecScatterCreate(vec1_B, msolv_ctx->is_B, msolv_ctx->sol_B, NULL, &msolv_ctx->correction_scatter_B));
    1292:           PetscCall(PetscObjectReference((PetscObject)is_A_all));
    1293:           msolv_ctx->is_R = is_A_all;
    1294:         } else {
    1295:           IS              is_B_all;
    1296:           const PetscInt *idxs;
    1297:           PetscInt        dual, n_v, n;

    1299:           PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &n_v));
    1300:           dual = size_schur - n_v;
    1301:           PetscCall(ISGetLocalSize(is_A_all, &n));
    1302:           PetscCall(ISGetIndices(is_A_all, &idxs));
    1303:           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all), dual, idxs + n_I, PETSC_COPY_VALUES, &is_B_all));
    1304:           PetscCall(ISGlobalToLocalMappingApplyIS(sub_schurs->BtoNmap, IS_GTOLM_DROP, is_B_all, &msolv_ctx->is_B));
    1305:           PetscCall(ISDestroy(&is_B_all));
    1306:           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)is_A_all), dual, 0, 1, &is_B_all));
    1307:           PetscCall(VecScatterCreate(vec1_B, msolv_ctx->is_B, msolv_ctx->sol_B, is_B_all, &msolv_ctx->correction_scatter_B));
    1308:           PetscCall(ISDestroy(&is_B_all));
    1309:           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)is_A_all), n - n_v, idxs, PETSC_COPY_VALUES, &msolv_ctx->is_R));
    1310:           PetscCall(ISRestoreIndices(is_A_all, &idxs));
    1311:         }
    1312:         PetscCall(ISGetLocalSize(msolv_ctx->is_R, &n_R));
    1313:         PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, n_R, n_R, 0, NULL, &Afake));
    1314:         PetscCall(MatAssemblyBegin(Afake, MAT_FINAL_ASSEMBLY));
    1315:         PetscCall(MatAssemblyEnd(Afake, MAT_FINAL_ASSEMBLY));
    1316:         PetscCall(PCSetOperators(msolv_ctx->correction_solver, Afake, Afake));
    1317:         PetscCall(MatDestroy(&Afake));
    1318:         PetscCall(VecDestroy(&vec1_B));
    1319:       }
    1320:       /* communicate benign info to solver context */
    1321:       if (benign_n) {
    1322:         PetscScalar *array;

    1324:         msolv_ctx->benign_n             = benign_n;
    1325:         msolv_ctx->benign_zerodiag_subs = is_p_r;
    1326:         PetscCall(PetscMalloc1(benign_n, &msolv_ctx->benign_save_vals));
    1327:         msolv_ctx->benign_csAIB = cs_AIB_mat;
    1328:         PetscCall(MatCreateVecs(cs_AIB_mat, &msolv_ctx->benign_corr_work, NULL));
    1329:         PetscCall(VecGetArray(msolv_ctx->benign_corr_work, &array));
    1330:         PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, size_schur, array, &msolv_ctx->benign_dummy_schur_vec));
    1331:         PetscCall(VecRestoreArray(msolv_ctx->benign_corr_work, &array));
    1332:         msolv_ctx->benign_AIIm1ones = benign_AIIm1_ones_mat;
    1333:       }
    1334:     } else {
    1335:       if (sub_schurs->reuse_solver) PetscCall(PCBDDCReuseSolversReset(sub_schurs->reuse_solver));
    1336:       PetscCall(PetscFree(sub_schurs->reuse_solver));
    1337:     }
    1338:     PetscCall(MatDestroy(&A));
    1339:     PetscCall(ISDestroy(&is_A_all));

    1341:     /* Work arrays */
    1342:     PetscCall(PetscMalloc1(max_subset_size * max_subset_size, &work));

    1344:     /* S_Ej_all */
    1345:     cum = cum2 = 0;
    1346:     PetscCall(MatDenseGetArrayRead(S_all, &rS_data));
    1347:     PetscCall(MatSeqAIJGetArray(sub_schurs->S_Ej_all, &SEj_arr));
    1348:     if (sub_schurs->sum_S_Ej_inv_all) PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all, &SEjinv_arr));
    1349:     if (sub_schurs->gdsw) PetscCall(MatCreateSubMatrices(sub_schurs->A, sub_schurs->n_subs, sub_schurs->is_subs, sub_schurs->is_subs, MAT_INITIAL_MATRIX, &gdswA));
    1350:     for (i = 0; i < sub_schurs->n_subs; i++) {
    1351:       PetscInt j;

    1353:       /* get S_E (or K^i_EE for GDSW) */
    1354:       PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
    1355:       if (sub_schurs->gdsw) {
    1356:         Mat T;

    1358:         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &T));
    1359:         PetscCall(MatConvert(gdswA[i], MATDENSE, MAT_REUSE_MATRIX, &T));
    1360:         PetscCall(MatDestroy(&T));
    1361:       } else {
    1362:         if (S_lower_triangular) { /* I need to expand the upper triangular data (column-oriented) */
    1363:           PetscInt k;
    1364:           for (k = 0; k < subset_size; k++) {
    1365:             for (j = k; j < subset_size; j++) {
    1366:               work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
    1367:               work[j * subset_size + k] = PetscConj(rS_data[cum2 + k * size_schur + j]);
    1368:             }
    1369:           }
    1370:         } else { /* just copy to workspace */
    1371:           PetscInt k;
    1372:           for (k = 0; k < subset_size; k++) {
    1373:             for (j = 0; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
    1374:           }
    1375:         }
    1376:       }
    1377:       /* insert S_E values */
    1378:       if (sub_schurs->change) {
    1379:         Mat change_sub, SEj, T;

    1381:         /* change basis */
    1382:         PetscCall(KSPGetOperators(sub_schurs->change[i], &change_sub, NULL));
    1383:         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &SEj));
    1384:         if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
    1385:           Mat T2;
    1386:           PetscCall(MatTransposeMatMult(change_sub, SEj, MAT_INITIAL_MATRIX, 1.0, &T2));
    1387:           PetscCall(MatMatMult(T2, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
    1388:           PetscCall(MatConvert(T, MATSEQDENSE, MAT_INPLACE_MATRIX, &T));
    1389:           PetscCall(MatDestroy(&T2));
    1390:         } else {
    1391:           PetscCall(MatPtAP(SEj, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
    1392:         }
    1393:         PetscCall(MatCopy(T, SEj, SAME_NONZERO_PATTERN));
    1394:         PetscCall(MatDestroy(&T));
    1395:         PetscCall(MatZeroRowsColumnsIS(SEj, sub_schurs->change_primal_sub[i], 1.0, NULL, NULL));
    1396:         PetscCall(MatDestroy(&SEj));
    1397:       }
    1398:       PetscCall(PetscArraycpy(SEj_arr, work, subset_size * subset_size));
    1399:       if (compute_Stilda) {
    1400:         if (deluxe) { /* if adaptivity is requested, invert S_E blocks */
    1401:           Mat                M;
    1402:           const PetscScalar *vals;
    1403:           PetscBool          isdense, isdensecuda;

    1405:           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &M));
    1406:           PetscCall(MatSetOption(M, MAT_SPD, sub_schurs->is_posdef));
    1407:           PetscCall(MatSetOption(M, MAT_HERMITIAN, sub_schurs->is_hermitian));
    1408:           if (!PetscBTLookup(sub_schurs->is_edge, i)) PetscCall(MatSetType(M, Stype));
    1409:           PetscCall(PetscObjectTypeCompare((PetscObject)M, MATSEQDENSE, &isdense));
    1410:           PetscCall(PetscObjectTypeCompare((PetscObject)M, MATSEQDENSECUDA, &isdensecuda));
    1411:           if (use_cholesky) {
    1412:             PetscCall(MatCholeskyFactor(M, NULL, NULL));
    1413:           } else {
    1414:             PetscCall(MatLUFactor(M, NULL, NULL, NULL));
    1415:           }
    1416:           if (isdense) {
    1417:             PetscCall(MatSeqDenseInvertFactors_Private(M));
    1418: #if defined(PETSC_HAVE_CUDA)
    1419:           } else if (isdensecuda) {
    1420:             PetscCall(MatSeqDenseCUDAInvertFactors_Internal(M));
    1421: #endif
    1422:           } else SETERRQ(PetscObjectComm((PetscObject)M), PETSC_ERR_SUP, "Not implemented for type %s", Stype);
    1423:           PetscCall(MatDenseGetArrayRead(M, &vals));
    1424:           PetscCall(PetscArraycpy(SEjinv_arr, vals, subset_size * subset_size));
    1425:           PetscCall(MatDenseRestoreArrayRead(M, &vals));
    1426:           PetscCall(MatDestroy(&M));
    1427:         } else if (scaling) { /* not using deluxe */
    1428:           Mat          SEj;
    1429:           Vec          D;
    1430:           PetscScalar *array;

    1432:           PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, work, &SEj));
    1433:           PetscCall(VecGetArray(Dall, &array));
    1434:           PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, subset_size, array + cum, &D));
    1435:           PetscCall(VecRestoreArray(Dall, &array));
    1436:           PetscCall(VecShift(D, -1.));
    1437:           PetscCall(MatDiagonalScale(SEj, D, D));
    1438:           PetscCall(MatDestroy(&SEj));
    1439:           PetscCall(VecDestroy(&D));
    1440:           PetscCall(PetscArraycpy(SEj_arr, work, subset_size * subset_size));
    1441:         }
    1442:       }
    1443:       cum += subset_size;
    1444:       cum2 += subset_size * (size_schur + 1);
    1445:       SEj_arr += subset_size * subset_size;
    1446:       if (SEjinv_arr) SEjinv_arr += subset_size * subset_size;
    1447:     }
    1448:     if (sub_schurs->gdsw) PetscCall(MatDestroySubMatrices(sub_schurs->n_subs, &gdswA));
    1449:     PetscCall(MatDenseRestoreArrayRead(S_all, &rS_data));
    1450:     PetscCall(MatSeqAIJRestoreArray(sub_schurs->S_Ej_all, &SEj_arr));
    1451:     if (sub_schurs->sum_S_Ej_inv_all) PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all, &SEjinv_arr));
    1452:     if (solver_S) PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));

    1454:     /* may prevent from unneeded copies, since MUMPS or MKL_Pardiso always use CPU memory
    1455:        however, preliminary tests indicate using GPUs is still faster in the solve phase */
    1456: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA)
    1457:     if (reuse_solvers) {
    1458:       Mat                  St;
    1459:       MatFactorSchurStatus st;

    1461:       flg = PETSC_FALSE;
    1462:       PetscCall(PetscOptionsGetBool(NULL, sub_schurs->prefix, "-sub_schurs_schur_pin_to_cpu", &flg, NULL));
    1463:       PetscCall(MatFactorGetSchurComplement(F, &St, &st));
    1464:       PetscCall(MatBindToCPU(St, flg));
    1465:       PetscCall(MatFactorRestoreSchurComplement(F, &St, st));
    1466:     }
    1467: #endif

    1469:     schur_factor = NULL;
    1470:     if (compute_Stilda && size_active_schur) {
    1471:       if (sub_schurs->n_subs == 1 && size_schur == size_active_schur && deluxe) { /* we already computed the inverse */
    1472:         PetscCall(MatSeqAIJGetArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
    1473:         PetscCall(PetscArraycpy(SEjinv_arr, work, size_schur * size_schur));
    1474:         PetscCall(MatSeqAIJRestoreArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
    1475:       } else {
    1476:         Mat S_all_inv = NULL;

    1478:         if (solver_S && !sub_schurs->gdsw) {
    1479:           /* for adaptive selection we need S^-1; for solver reusage we need S_\Delta\Delta^-1.
    1480:              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 */
    1481:           if (factor_workaround) { /* invert without calling MatFactorInvertSchurComplement, since we are hacking */
    1482:             PetscScalar *data;
    1483:             PetscInt     nd = 0;

    1485:             PetscCheck(use_potr, PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor update not yet implemented for non SPD matrices");
    1486:             PetscCall(MatFactorGetSchurComplement(F, &S_all_inv, NULL));
    1487:             PetscCall(MatDenseGetArray(S_all_inv, &data));
    1488:             if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
    1489:               PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
    1490:             }

    1492:             /* factor and invert activedofs and vertices (dirichlet dofs does not contribute) */
    1493:             if (schur_has_vertices) {
    1494:               Mat          M;
    1495:               PetscScalar *tdata;
    1496:               PetscInt     nv = 0, news;

    1498:               PetscCall(ISGetLocalSize(sub_schurs->is_vertices, &nv));
    1499:               news = size_active_schur + nv;
    1500:               PetscCall(PetscCalloc1(news * news, &tdata));
    1501:               for (i = 0; i < size_active_schur; i++) {
    1502:                 PetscCall(PetscArraycpy(tdata + i * (news + 1), data + i * (size_schur + 1), size_active_schur - i));
    1503:                 PetscCall(PetscArraycpy(tdata + i * (news + 1) + size_active_schur - i, data + i * size_schur + size_active_schur + nd, nv));
    1504:               }
    1505:               for (i = 0; i < nv; i++) {
    1506:                 PetscInt k = i + size_active_schur;
    1507:                 PetscCall(PetscArraycpy(tdata + k * (news + 1), data + (k + nd) * (size_schur + 1), nv - i));
    1508:               }

    1510:               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, news, news, tdata, &M));
    1511:               PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE));
    1512:               PetscCall(MatCholeskyFactor(M, NULL, NULL));
    1513:               /* save the factors */
    1514:               cum = 0;
    1515:               PetscCall(PetscMalloc1((size_active_schur * (size_active_schur + 1)) / 2 + nd, &schur_factor));
    1516:               for (i = 0; i < size_active_schur; i++) {
    1517:                 PetscCall(PetscArraycpy(schur_factor + cum, tdata + i * (news + 1), size_active_schur - i));
    1518:                 cum += size_active_schur - i;
    1519:               }
    1520:               for (i = 0; i < nd; i++) schur_factor[cum + i] = PetscSqrtReal(PetscRealPart(data[(i + size_active_schur) * (size_schur + 1)]));
    1521:               PetscCall(MatSeqDenseInvertFactors_Private(M));
    1522:               /* move back just the active dofs to the Schur complement */
    1523:               for (i = 0; i < size_active_schur; i++) PetscCall(PetscArraycpy(data + i * size_schur, tdata + i * news, size_active_schur));
    1524:               PetscCall(PetscFree(tdata));
    1525:               PetscCall(MatDestroy(&M));
    1526:             } else { /* we can factorize and invert just the activedofs */
    1527:               Mat          M;
    1528:               PetscScalar *aux;

    1530:               PetscCall(PetscMalloc1(nd, &aux));
    1531:               for (i = 0; i < nd; i++) aux[i] = 1.0 / data[(i + size_active_schur) * (size_schur + 1)];
    1532:               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size_active_schur, size_active_schur, data, &M));
    1533:               PetscCall(MatDenseSetLDA(M, size_schur));
    1534:               PetscCall(MatSetOption(M, MAT_SPD, PETSC_TRUE));
    1535:               PetscCall(MatCholeskyFactor(M, NULL, NULL));
    1536:               PetscCall(MatSeqDenseInvertFactors_Private(M));
    1537:               PetscCall(MatDestroy(&M));
    1538:               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, size_schur, nd, data + size_active_schur * size_schur, &M));
    1539:               PetscCall(MatZeroEntries(M));
    1540:               PetscCall(MatDestroy(&M));
    1541:               PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nd, size_schur, data + size_active_schur, &M));
    1542:               PetscCall(MatDenseSetLDA(M, size_schur));
    1543:               PetscCall(MatZeroEntries(M));
    1544:               PetscCall(MatDestroy(&M));
    1545:               for (i = 0; i < nd; i++) data[(i + size_active_schur) * (size_schur + 1)] = aux[i];
    1546:               PetscCall(PetscFree(aux));
    1547:             }
    1548:             PetscCall(MatDenseRestoreArray(S_all_inv, &data));
    1549:           } else { /* use MatFactor calls to invert S */
    1550:             PetscCall(MatFactorInvertSchurComplement(F));
    1551:             PetscCall(MatFactorGetSchurComplement(F, &S_all_inv, NULL));
    1552:           }
    1553:         } else if (!sub_schurs->gdsw) { /* we need to invert explicitly since we are not using MatFactor for S */
    1554:           PetscCall(PetscObjectReference((PetscObject)S_all));
    1555:           S_all_inv = S_all;
    1556:           PetscCall(MatDenseGetArray(S_all_inv, &S_data));
    1557:           PetscCall(PetscBLASIntCast(size_schur, &B_N));
    1558:           PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    1559:           if (use_potr) {
    1560:             PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("L", &B_N, S_data, &B_N, &B_ierr));
    1561:             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1562:             PetscCallBLAS("LAPACKpotri", LAPACKpotri_("L", &B_N, S_data, &B_N, &B_ierr));
    1563:             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1564:           } else if (use_sytr) {
    1565:             PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, S_data, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
    1566:             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1567:             PetscCallBLAS("LAPACKsytri", LAPACKsytri_("L", &B_N, S_data, &B_N, pivots, Bwork, &B_ierr));
    1568:             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1569:           } else {
    1570:             PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&B_N, &B_N, S_data, &B_N, pivots, &B_ierr));
    1571:             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1572:             PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, S_data, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
    1573:             PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1574:           }
    1575:           PetscCall(PetscLogFlops(1.0 * size_schur * size_schur * size_schur));
    1576:           PetscCall(PetscFPTrapPop());
    1577:           PetscCall(MatDenseRestoreArray(S_all_inv, &S_data));
    1578:         } else if (sub_schurs->gdsw) {
    1579:           Mat      tS, tX, SEj, S_II, S_IE, S_EE;
    1580:           KSP      pS_II;
    1581:           PC       pS_II_pc;
    1582:           IS       EE, II;
    1583:           PetscInt nS;

    1585:           PetscCall(MatFactorCreateSchurComplement(F, &tS, NULL));
    1586:           PetscCall(MatGetSize(tS, &nS, NULL));
    1587:           PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
    1588:           for (i = 0, cum = 0; i < sub_schurs->n_subs; i++) { /* naive implementation */
    1589:             PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
    1590:             PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, SEjinv_arr, &SEj));

    1592:             PetscCall(ISCreateStride(PETSC_COMM_SELF, subset_size, cum, 1, &EE));
    1593:             PetscCall(ISComplement(EE, 0, nS, &II));
    1594:             PetscCall(MatCreateSubMatrix(tS, II, II, MAT_INITIAL_MATRIX, &S_II));
    1595:             PetscCall(MatCreateSubMatrix(tS, II, EE, MAT_INITIAL_MATRIX, &S_IE));
    1596:             PetscCall(MatCreateSubMatrix(tS, EE, EE, MAT_INITIAL_MATRIX, &S_EE));
    1597:             PetscCall(ISDestroy(&II));
    1598:             PetscCall(ISDestroy(&EE));

    1600:             PetscCall(KSPCreate(PETSC_COMM_SELF, &pS_II));
    1601:             PetscCall(KSPSetNestLevel(pS_II, 1)); /* do not have direct access to a PC to provide the level of nesting of the KSP */
    1602:             PetscCall(KSPSetType(pS_II, KSPPREONLY));
    1603:             PetscCall(KSPGetPC(pS_II, &pS_II_pc));
    1604:             PetscCall(PCSetType(pS_II_pc, PCSVD));
    1605:             PetscCall(KSPSetOptionsPrefix(pS_II, sub_schurs->prefix));
    1606:             PetscCall(KSPAppendOptionsPrefix(pS_II, "pseudo_"));
    1607:             PetscCall(KSPSetOperators(pS_II, S_II, S_II));
    1608:             PetscCall(MatDestroy(&S_II));
    1609:             PetscCall(KSPSetFromOptions(pS_II));
    1610:             PetscCall(KSPSetUp(pS_II));
    1611:             PetscCall(MatDuplicate(S_IE, MAT_DO_NOT_COPY_VALUES, &tX));
    1612:             PetscCall(KSPMatSolve(pS_II, S_IE, tX));
    1613:             PetscCall(KSPDestroy(&pS_II));

    1615:             PetscCall(MatTransposeMatMult(S_IE, tX, MAT_REUSE_MATRIX, PETSC_DETERMINE, &SEj));
    1616:             PetscCall(MatDestroy(&S_IE));
    1617:             PetscCall(MatDestroy(&tX));
    1618:             PetscCall(MatAYPX(SEj, -1, S_EE, SAME_NONZERO_PATTERN));
    1619:             PetscCall(MatDestroy(&S_EE));

    1621:             PetscCall(MatDestroy(&SEj));
    1622:             cum += subset_size;
    1623:             SEjinv_arr += subset_size * subset_size;
    1624:           }
    1625:           PetscCall(MatDestroy(&tS));
    1626:           PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
    1627:         }
    1628:         /* S_Ej_tilda_all */
    1629:         cum = cum2 = 0;
    1630:         rS_data    = NULL;
    1631:         if (S_all_inv) PetscCall(MatDenseGetArrayRead(S_all_inv, &rS_data));
    1632:         PetscCall(MatSeqAIJGetArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
    1633:         for (i = 0; i < sub_schurs->n_subs; i++) {
    1634:           PetscInt j;

    1636:           PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
    1637:           /* get (St^-1)_E */
    1638:           /* Unless we are changing the variables, I don't need to expand to upper triangular since St^-1
    1639:              will be properly accessed later during adaptive selection */
    1640:           if (rS_data) {
    1641:             if (S_lower_triangular) {
    1642:               PetscInt k;
    1643:               if (sub_schurs->change) {
    1644:                 for (k = 0; k < subset_size; k++) {
    1645:                   for (j = k; j < subset_size; j++) {
    1646:                     work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
    1647:                     work[j * subset_size + k] = work[k * subset_size + j];
    1648:                   }
    1649:                 }
    1650:               } else {
    1651:                 for (k = 0; k < subset_size; k++) {
    1652:                   for (j = k; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
    1653:                 }
    1654:               }
    1655:             } else {
    1656:               PetscInt k;
    1657:               for (k = 0; k < subset_size; k++) {
    1658:                 for (j = 0; j < subset_size; j++) work[k * subset_size + j] = rS_data[cum2 + k * size_schur + j];
    1659:               }
    1660:             }
    1661:           }
    1662:           if (sub_schurs->change) {
    1663:             Mat         change_sub, SEj, T;
    1664:             PetscScalar val = sub_schurs->gdsw ? PETSC_SMALL : 1. / PETSC_SMALL;

    1666:             /* change basis */
    1667:             PetscCall(KSPGetOperators(sub_schurs->change[i], &change_sub, NULL));
    1668:             PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, subset_size, subset_size, rS_data ? work : SEjinv_arr, &SEj));
    1669:             if (!sub_schurs->change_with_qr) { /* currently there's no support for PtAP with P SeqAIJ */
    1670:               Mat T2;
    1671:               PetscCall(MatTransposeMatMult(change_sub, SEj, MAT_INITIAL_MATRIX, 1.0, &T2));
    1672:               PetscCall(MatMatMult(T2, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
    1673:               PetscCall(MatDestroy(&T2));
    1674:               PetscCall(MatConvert(T, MATSEQDENSE, MAT_INPLACE_MATRIX, &T));
    1675:             } else {
    1676:               PetscCall(MatPtAP(SEj, change_sub, MAT_INITIAL_MATRIX, 1.0, &T));
    1677:             }
    1678:             PetscCall(MatCopy(T, SEj, SAME_NONZERO_PATTERN));
    1679:             PetscCall(MatDestroy(&T));
    1680:             PetscCall(MatZeroRowsColumnsIS(SEj, sub_schurs->change_primal_sub[i], val, NULL, NULL));
    1681:             PetscCall(MatDestroy(&SEj));
    1682:           }
    1683:           if (rS_data) PetscCall(PetscArraycpy(SEjinv_arr, work, subset_size * subset_size));
    1684:           cum += subset_size;
    1685:           cum2 += subset_size * (size_schur + 1);
    1686:           SEjinv_arr += subset_size * subset_size;
    1687:         }
    1688:         PetscCall(MatSeqAIJRestoreArrayWrite(sub_schurs->sum_S_Ej_tilda_all, &SEjinv_arr));
    1689:         if (S_all_inv) {
    1690:           PetscCall(MatDenseRestoreArrayRead(S_all_inv, &rS_data));
    1691:           if (solver_S) {
    1692:             if (schur_has_vertices) {
    1693:               PetscCall(MatFactorRestoreSchurComplement(F, &S_all_inv, MAT_FACTOR_SCHUR_FACTORED));
    1694:             } else {
    1695:               PetscCall(MatFactorRestoreSchurComplement(F, &S_all_inv, MAT_FACTOR_SCHUR_INVERTED));
    1696:             }
    1697:           }
    1698:         }
    1699:         PetscCall(MatDestroy(&S_all_inv));
    1700:       }

    1702:       /* move back factors if needed */
    1703:       if (schur_has_vertices && factor_workaround && !sub_schurs->gdsw) {
    1704:         Mat          S_tmp;
    1705:         PetscInt     nd = 0;
    1706:         PetscScalar *data;

    1708:         PetscCheck(use_potr, PETSC_COMM_SELF, PETSC_ERR_SUP, "Factor update not yet implemented for non SPD matrices");
    1709:         PetscCheck(solver_S, PETSC_COMM_SELF, PETSC_ERR_PLIB, "This should not happen");
    1710:         PetscCall(MatFactorGetSchurComplement(F, &S_tmp, NULL));
    1711:         PetscCall(MatDenseGetArray(S_tmp, &data));
    1712:         PetscCall(PetscArrayzero(data, size_schur * size_schur));

    1714:         if (S_lower_triangular) {
    1715:           cum = 0;
    1716:           for (i = 0; i < size_active_schur; i++) {
    1717:             PetscCall(PetscArraycpy(data + i * (size_schur + 1), schur_factor + cum, size_active_schur - i));
    1718:             cum += size_active_schur - i;
    1719:           }
    1720:         } else {
    1721:           PetscCall(PetscArraycpy(data, schur_factor, size_schur * size_schur));
    1722:         }
    1723:         if (sub_schurs->is_dir) {
    1724:           PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
    1725:           for (i = 0; i < nd; i++) data[(i + size_active_schur) * (size_schur + 1)] = schur_factor[cum + i];
    1726:         }
    1727:         /* workaround: since I cannot modify the matrices used inside the solvers for the forward and backward substitutions,
    1728:              set the diagonal entry of the Schur factor to a very large value */
    1729:         for (i = size_active_schur + nd; i < size_schur; i++) data[i * (size_schur + 1)] = infty;
    1730:         PetscCall(MatDenseRestoreArray(S_tmp, &data));
    1731:         PetscCall(MatFactorRestoreSchurComplement(F, &S_tmp, MAT_FACTOR_SCHUR_FACTORED));
    1732:       }
    1733:     } else if (factor_workaround && !sub_schurs->gdsw) { /* we need to eliminate any unneeded coupling */
    1734:       PetscScalar *data;
    1735:       PetscInt     nd = 0;

    1737:       if (sub_schurs->is_dir) { /* dirichlet dofs could have different scalings */
    1738:         PetscCall(ISGetLocalSize(sub_schurs->is_dir, &nd));
    1739:       }
    1740:       PetscCall(MatFactorGetSchurComplement(F, &S_all, NULL));
    1741:       PetscCall(MatDenseGetArray(S_all, &data));
    1742:       for (i = 0; i < size_active_schur; i++) PetscCall(PetscArrayzero(data + i * size_schur + size_active_schur, size_schur - size_active_schur));
    1743:       for (i = size_active_schur + nd; i < size_schur; i++) {
    1744:         PetscCall(PetscArrayzero(data + i * size_schur + size_active_schur, size_schur - size_active_schur));
    1745:         data[i * (size_schur + 1)] = infty;
    1746:       }
    1747:       PetscCall(MatDenseRestoreArray(S_all, &data));
    1748:       PetscCall(MatFactorRestoreSchurComplement(F, &S_all, MAT_FACTOR_SCHUR_UNFACTORED));
    1749:     }
    1750:     PetscCall(PetscFree(work));
    1751:     PetscCall(PetscFree(schur_factor));
    1752:     PetscCall(VecDestroy(&Dall));
    1753:   }
    1754:   PetscCall(ISDestroy(&is_I_layer));
    1755:   PetscCall(MatDestroy(&S_all));
    1756:   PetscCall(MatDestroy(&A_BB));
    1757:   PetscCall(MatDestroy(&A_IB));
    1758:   PetscCall(MatDestroy(&A_BI));
    1759:   PetscCall(MatDestroy(&F));

    1761:   PetscCall(PetscMalloc1(sub_schurs->n_subs, &nnz));
    1762:   for (i = 0; i < sub_schurs->n_subs; i++) PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &nnz[i]));
    1763:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, sub_schurs->n_subs, nnz, PETSC_OWN_POINTER, &is_I_layer));
    1764:   PetscCall(MatSetVariableBlockSizes(sub_schurs->S_Ej_all, sub_schurs->n_subs, nnz));
    1765:   PetscCall(MatAssemblyBegin(sub_schurs->S_Ej_all, MAT_FINAL_ASSEMBLY));
    1766:   PetscCall(MatAssemblyEnd(sub_schurs->S_Ej_all, MAT_FINAL_ASSEMBLY));
    1767:   if (compute_Stilda) {
    1768:     PetscCall(MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_tilda_all, sub_schurs->n_subs, nnz));
    1769:     PetscCall(MatAssemblyBegin(sub_schurs->sum_S_Ej_tilda_all, MAT_FINAL_ASSEMBLY));
    1770:     PetscCall(MatAssemblyEnd(sub_schurs->sum_S_Ej_tilda_all, MAT_FINAL_ASSEMBLY));
    1771:     if (deluxe) {
    1772:       PetscCall(MatSetVariableBlockSizes(sub_schurs->sum_S_Ej_inv_all, sub_schurs->n_subs, nnz));
    1773:       PetscCall(MatAssemblyBegin(sub_schurs->sum_S_Ej_inv_all, MAT_FINAL_ASSEMBLY));
    1774:       PetscCall(MatAssemblyEnd(sub_schurs->sum_S_Ej_inv_all, MAT_FINAL_ASSEMBLY));
    1775:     }
    1776:   }
    1777:   PetscCall(ISDestroy(&is_I_layer));

    1779:   /* Get local part of (\sum_j S_Ej) */
    1780:   if (!sub_schurs->sum_S_Ej_all) PetscCall(MatDuplicate(sub_schurs->S_Ej_all, MAT_DO_NOT_COPY_VALUES, &sub_schurs->sum_S_Ej_all));
    1781:   PetscCall(VecSet(gstash, 0.0));
    1782:   PetscCall(MatSeqAIJGetArray(sub_schurs->S_Ej_all, &stasharray));
    1783:   PetscCall(VecPlaceArray(lstash, stasharray));
    1784:   PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
    1785:   PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
    1786:   PetscCall(MatSeqAIJRestoreArray(sub_schurs->S_Ej_all, &stasharray));
    1787:   PetscCall(VecResetArray(lstash));
    1788:   PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_all, &stasharray));
    1789:   PetscCall(VecPlaceArray(lstash, stasharray));
    1790:   PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
    1791:   PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
    1792:   PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_all, &stasharray));
    1793:   PetscCall(VecResetArray(lstash));

    1795:   /* Get local part of (\sum_j S^-1_Ej) (\sum_j St^-1_Ej) */
    1796:   if (compute_Stilda) {
    1797:     PetscCall(VecSet(gstash, 0.0));
    1798:     PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &stasharray));
    1799:     PetscCall(VecPlaceArray(lstash, stasharray));
    1800:     PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
    1801:     PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
    1802:     PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
    1803:     PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
    1804:     PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &stasharray));
    1805:     PetscCall(VecResetArray(lstash));
    1806:     if (deluxe) {
    1807:       PetscCall(VecSet(gstash, 0.0));
    1808:       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_inv_all, &stasharray));
    1809:       PetscCall(VecPlaceArray(lstash, stasharray));
    1810:       PetscCall(VecScatterBegin(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
    1811:       PetscCall(VecScatterEnd(sstash, lstash, gstash, ADD_VALUES, SCATTER_FORWARD));
    1812:       PetscCall(VecScatterBegin(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
    1813:       PetscCall(VecScatterEnd(sstash, gstash, lstash, INSERT_VALUES, SCATTER_REVERSE));
    1814:       PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_inv_all, &stasharray));
    1815:       PetscCall(VecResetArray(lstash));
    1816:     } else if (!sub_schurs->gdsw) {
    1817:       PetscScalar *array;
    1818:       PetscInt     cum;

    1820:       PetscCall(MatSeqAIJGetArray(sub_schurs->sum_S_Ej_tilda_all, &array));
    1821:       cum = 0;
    1822:       for (i = 0; i < sub_schurs->n_subs; i++) {
    1823:         PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
    1824:         PetscCall(PetscBLASIntCast(subset_size, &B_N));
    1825:         PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    1826:         if (use_potr) {
    1827:           PetscCallBLAS("LAPACKpotrf", LAPACKpotrf_("L", &B_N, array + cum, &B_N, &B_ierr));
    1828:           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1829:           PetscCallBLAS("LAPACKpotri", LAPACKpotri_("L", &B_N, array + cum, &B_N, &B_ierr));
    1830:           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in POTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1831:         } else if (use_sytr) {
    1832:           PetscCallBLAS("LAPACKsytrf", LAPACKsytrf_("L", &B_N, array + cum, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
    1833:           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1834:           PetscCallBLAS("LAPACKsytri", LAPACKsytri_("L", &B_N, array + cum, &B_N, pivots, Bwork, &B_ierr));
    1835:           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in SYTRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1836:         } else {
    1837:           PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&B_N, &B_N, array + cum, &B_N, pivots, &B_ierr));
    1838:           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1839:           PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, array + cum, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
    1840:           PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
    1841:         }
    1842:         PetscCall(PetscLogFlops(1.0 * subset_size * subset_size * subset_size));
    1843:         PetscCall(PetscFPTrapPop());
    1844:         cum += subset_size * subset_size;
    1845:       }
    1846:       PetscCall(MatSeqAIJRestoreArray(sub_schurs->sum_S_Ej_tilda_all, &array));
    1847:       PetscCall(PetscObjectReference((PetscObject)sub_schurs->sum_S_Ej_all));
    1848:       PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_inv_all));
    1849:       sub_schurs->sum_S_Ej_inv_all = sub_schurs->sum_S_Ej_all;
    1850:     }
    1851:   }
    1852:   PetscCall(VecDestroy(&lstash));
    1853:   PetscCall(VecDestroy(&gstash));
    1854:   PetscCall(VecScatterDestroy(&sstash));

    1856:   if (matl_dbg_viewer) {
    1857:     if (sub_schurs->S_Ej_all) {
    1858:       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->S_Ej_all, "SE"));
    1859:       PetscCall(MatView(sub_schurs->S_Ej_all, matl_dbg_viewer));
    1860:     }
    1861:     if (sub_schurs->sum_S_Ej_all) {
    1862:       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_all, "SSE"));
    1863:       PetscCall(MatView(sub_schurs->sum_S_Ej_all, matl_dbg_viewer));
    1864:     }
    1865:     if (sub_schurs->sum_S_Ej_inv_all) {
    1866:       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_inv_all, "SSEm"));
    1867:       PetscCall(MatView(sub_schurs->sum_S_Ej_inv_all, matl_dbg_viewer));
    1868:     }
    1869:     if (sub_schurs->sum_S_Ej_tilda_all) {
    1870:       PetscCall(PetscObjectSetName((PetscObject)sub_schurs->sum_S_Ej_tilda_all, "SSEt"));
    1871:       PetscCall(MatView(sub_schurs->sum_S_Ej_tilda_all, matl_dbg_viewer));
    1872:     }
    1873:   }

    1875:   /* free workspace */
    1876:   if (matl_dbg_viewer) PetscCall(PetscViewerFlush(matl_dbg_viewer));
    1877:   if (sub_schurs->debug) PetscCallMPI(MPI_Barrier(comm_n));
    1878:   PetscCall(PetscViewerDestroy(&matl_dbg_viewer));
    1879:   PetscCall(PetscFree2(Bwork, pivots));
    1880:   PetscCall(PetscCommDestroy(&comm_n));
    1881:   PetscFunctionReturn(PETSC_SUCCESS);
    1882: }

    1884: PetscErrorCode PCBDDCSubSchursInit(PCBDDCSubSchurs sub_schurs, const char *prefix, IS is_I, IS is_B, PCBDDCGraph graph, ISLocalToGlobalMapping BtoNmap, PetscBool copycc, PetscBool gdsw)
    1885: {
    1886:   IS       *faces, *edges, *all_cc, vertices;
    1887:   PetscInt  s, i, n_faces, n_edges, n_all_cc;
    1888:   PetscBool is_sorted, ispardiso, ismumps;

    1890:   PetscFunctionBegin;
    1891:   PetscCall(ISSorted(is_I, &is_sorted));
    1892:   PetscCheck(is_sorted, PetscObjectComm((PetscObject)is_I), PETSC_ERR_PLIB, "IS for I dofs should be shorted");
    1893:   PetscCall(ISSorted(is_B, &is_sorted));
    1894:   PetscCheck(is_sorted, PetscObjectComm((PetscObject)is_B), PETSC_ERR_PLIB, "IS for B dofs should be shorted");

    1896:   /* reset any previous data */
    1897:   PetscCall(PCBDDCSubSchursReset(sub_schurs));

    1899:   sub_schurs->gdsw = gdsw;

    1901:   /* get index sets for faces and edges (already sorted by global ordering) */
    1902:   PetscCall(PCBDDCGraphGetCandidatesIS(graph, &n_faces, &faces, &n_edges, &edges, &vertices));
    1903:   n_all_cc = n_faces + n_edges;
    1904:   PetscCall(PetscBTCreate(n_all_cc, &sub_schurs->is_edge));
    1905:   PetscCall(PetscMalloc1(n_all_cc, &all_cc));
    1906:   n_all_cc = 0;
    1907:   for (i = 0; i < n_faces; i++) {
    1908:     PetscCall(ISGetSize(faces[i], &s));
    1909:     if (!s) continue;
    1910:     if (copycc) {
    1911:       PetscCall(ISDuplicate(faces[i], &all_cc[n_all_cc]));
    1912:     } else {
    1913:       PetscCall(PetscObjectReference((PetscObject)faces[i]));
    1914:       all_cc[n_all_cc] = faces[i];
    1915:     }
    1916:     n_all_cc++;
    1917:   }
    1918:   for (i = 0; i < n_edges; i++) {
    1919:     PetscCall(ISGetSize(edges[i], &s));
    1920:     if (!s) continue;
    1921:     if (copycc) {
    1922:       PetscCall(ISDuplicate(edges[i], &all_cc[n_all_cc]));
    1923:     } else {
    1924:       PetscCall(PetscObjectReference((PetscObject)edges[i]));
    1925:       all_cc[n_all_cc] = edges[i];
    1926:     }
    1927:     PetscCall(PetscBTSet(sub_schurs->is_edge, n_all_cc));
    1928:     n_all_cc++;
    1929:   }
    1930:   PetscCall(PetscObjectReference((PetscObject)vertices));
    1931:   sub_schurs->is_vertices = vertices;
    1932:   PetscCall(PCBDDCGraphRestoreCandidatesIS(graph, &n_faces, &faces, &n_edges, &edges, &vertices));
    1933:   sub_schurs->is_dir = NULL;
    1934:   PetscCall(PCBDDCGraphGetDirichletDofsB(graph, &sub_schurs->is_dir));

    1936:   /* Determine if MatFactor can be used */
    1937:   PetscCall(PetscStrallocpy(prefix, &sub_schurs->prefix));
    1938: #if defined(PETSC_HAVE_MUMPS)
    1939:   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERMUMPS, sizeof(sub_schurs->mat_solver_type)));
    1940: #elif defined(PETSC_HAVE_MKL_PARDISO)
    1941:   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERMKL_PARDISO, sizeof(sub_schurs->mat_solver_type)));
    1942: #else
    1943:   PetscCall(PetscStrncpy(sub_schurs->mat_solver_type, MATSOLVERPETSC, sizeof(sub_schurs->mat_solver_type)));
    1944: #endif
    1945: #if defined(PETSC_USE_COMPLEX)
    1946:   sub_schurs->is_hermitian = PETSC_FALSE; /* Hermitian Cholesky is not supported by PETSc and external packages */
    1947: #else
    1948:   sub_schurs->is_hermitian = PETSC_TRUE;
    1949: #endif
    1950:   sub_schurs->is_posdef     = PETSC_TRUE;
    1951:   sub_schurs->is_symmetric  = PETSC_TRUE;
    1952:   sub_schurs->debug         = PETSC_FALSE;
    1953:   sub_schurs->restrict_comm = PETSC_FALSE;
    1954:   PetscOptionsBegin(PetscObjectComm((PetscObject)graph->l2gmap), sub_schurs->prefix, "BDDC sub_schurs options", "PC");
    1955:   PetscCall(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));
    1956:   PetscCall(PetscOptionsBool("-sub_schurs_symmetric", "Symmetric problem", NULL, sub_schurs->is_symmetric, &sub_schurs->is_symmetric, NULL));
    1957:   PetscCall(PetscOptionsBool("-sub_schurs_hermitian", "Hermitian problem", NULL, sub_schurs->is_hermitian, &sub_schurs->is_hermitian, NULL));
    1958:   PetscCall(PetscOptionsBool("-sub_schurs_posdef", "Positive definite problem", NULL, sub_schurs->is_posdef, &sub_schurs->is_posdef, NULL));
    1959:   PetscCall(PetscOptionsBool("-sub_schurs_restrictcomm", "Restrict communicator on active processes only", NULL, sub_schurs->restrict_comm, &sub_schurs->restrict_comm, NULL));
    1960:   PetscCall(PetscOptionsBool("-sub_schurs_debug", "Debug output", NULL, sub_schurs->debug, &sub_schurs->debug, NULL));
    1961:   PetscOptionsEnd();
    1962:   PetscCall(PetscStrcmp(sub_schurs->mat_solver_type, MATSOLVERMUMPS, &ismumps));
    1963:   PetscCall(PetscStrcmp(sub_schurs->mat_solver_type, MATSOLVERMKL_PARDISO, &ispardiso));
    1964:   sub_schurs->schur_explicit = (PetscBool)(ispardiso || ismumps);

    1966:   /* for reals, symmetric and Hermitian are synonyms */
    1967: #if !defined(PETSC_USE_COMPLEX)
    1968:   sub_schurs->is_symmetric = (PetscBool)(sub_schurs->is_symmetric && sub_schurs->is_hermitian);
    1969:   sub_schurs->is_hermitian = sub_schurs->is_symmetric;
    1970: #endif

    1972:   PetscCall(PetscObjectReference((PetscObject)is_I));
    1973:   sub_schurs->is_I = is_I;
    1974:   PetscCall(PetscObjectReference((PetscObject)is_B));
    1975:   sub_schurs->is_B = is_B;
    1976:   PetscCall(PetscObjectReference((PetscObject)graph->l2gmap));
    1977:   sub_schurs->l2gmap = graph->l2gmap;
    1978:   PetscCall(PetscObjectReference((PetscObject)BtoNmap));
    1979:   sub_schurs->BtoNmap            = BtoNmap;
    1980:   sub_schurs->n_subs             = n_all_cc;
    1981:   sub_schurs->is_subs            = all_cc;
    1982:   sub_schurs->S_Ej_all           = NULL;
    1983:   sub_schurs->sum_S_Ej_all       = NULL;
    1984:   sub_schurs->sum_S_Ej_inv_all   = NULL;
    1985:   sub_schurs->sum_S_Ej_tilda_all = NULL;
    1986:   sub_schurs->is_Ej_all          = NULL;
    1987:   PetscFunctionReturn(PETSC_SUCCESS);
    1988: }

    1990: PetscErrorCode PCBDDCSubSchursCreate(PCBDDCSubSchurs *sub_schurs)
    1991: {
    1992:   PCBDDCSubSchurs schurs_ctx;

    1994:   PetscFunctionBegin;
    1995:   PetscCall(PetscNew(&schurs_ctx));
    1996:   schurs_ctx->n_subs = 0;
    1997:   *sub_schurs        = schurs_ctx;
    1998:   PetscFunctionReturn(PETSC_SUCCESS);
    1999: }

    2001: PetscErrorCode PCBDDCSubSchursReset(PCBDDCSubSchurs sub_schurs)
    2002: {
    2003:   PetscInt i;

    2005:   PetscFunctionBegin;
    2006:   if (!sub_schurs) PetscFunctionReturn(PETSC_SUCCESS);
    2007:   PetscCall(PetscFree(sub_schurs->prefix));
    2008:   PetscCall(MatDestroy(&sub_schurs->A));
    2009:   PetscCall(MatDestroy(&sub_schurs->S));
    2010:   PetscCall(ISDestroy(&sub_schurs->is_I));
    2011:   PetscCall(ISDestroy(&sub_schurs->is_B));
    2012:   PetscCall(ISLocalToGlobalMappingDestroy(&sub_schurs->l2gmap));
    2013:   PetscCall(ISLocalToGlobalMappingDestroy(&sub_schurs->BtoNmap));
    2014:   PetscCall(MatDestroy(&sub_schurs->S_Ej_all));
    2015:   PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_all));
    2016:   PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_inv_all));
    2017:   PetscCall(MatDestroy(&sub_schurs->sum_S_Ej_tilda_all));
    2018:   PetscCall(ISDestroy(&sub_schurs->is_Ej_all));
    2019:   PetscCall(ISDestroy(&sub_schurs->is_vertices));
    2020:   PetscCall(ISDestroy(&sub_schurs->is_dir));
    2021:   PetscCall(PetscBTDestroy(&sub_schurs->is_edge));
    2022:   for (i = 0; i < sub_schurs->n_subs; i++) PetscCall(ISDestroy(&sub_schurs->is_subs[i]));
    2023:   if (sub_schurs->n_subs) PetscCall(PetscFree(sub_schurs->is_subs));
    2024:   if (sub_schurs->reuse_solver) PetscCall(PCBDDCReuseSolversReset(sub_schurs->reuse_solver));
    2025:   PetscCall(PetscFree(sub_schurs->reuse_solver));
    2026:   if (sub_schurs->change) {
    2027:     for (i = 0; i < sub_schurs->n_subs; i++) {
    2028:       PetscCall(KSPDestroy(&sub_schurs->change[i]));
    2029:       PetscCall(ISDestroy(&sub_schurs->change_primal_sub[i]));
    2030:     }
    2031:   }
    2032:   PetscCall(PetscFree(sub_schurs->change));
    2033:   PetscCall(PetscFree(sub_schurs->change_primal_sub));
    2034:   sub_schurs->n_subs = 0;
    2035:   PetscFunctionReturn(PETSC_SUCCESS);
    2036: }

    2038: PetscErrorCode PCBDDCSubSchursDestroy(PCBDDCSubSchurs *sub_schurs)
    2039: {
    2040:   PetscFunctionBegin;
    2041:   PetscCall(PCBDDCSubSchursReset(*sub_schurs));
    2042:   PetscCall(PetscFree(*sub_schurs));
    2043:   PetscFunctionReturn(PETSC_SUCCESS);
    2044: }

    2046: static inline PetscErrorCode PCBDDCAdjGetNextLayer_Private(PetscInt *queue_tip, PetscInt n_prev, PetscBT touched, PetscInt *xadj, PetscInt *adjncy, PetscInt *n_added)
    2047: {
    2048:   PetscInt i, j, n;

    2050:   PetscFunctionBegin;
    2051:   n = 0;
    2052:   for (i = -n_prev; i < 0; i++) {
    2053:     PetscInt start_dof = queue_tip[i];
    2054:     for (j = xadj[start_dof]; j < xadj[start_dof + 1]; j++) {
    2055:       PetscInt dof = adjncy[j];
    2056:       if (!PetscBTLookup(touched, dof)) {
    2057:         PetscCall(PetscBTSet(touched, dof));
    2058:         queue_tip[n] = dof;
    2059:         n++;
    2060:       }
    2061:     }
    2062:   }
    2063:   *n_added = n;
    2064:   PetscFunctionReturn(PETSC_SUCCESS);
    2065: }