Actual source code: lu.c

      1: /*
      2:    Defines a direct factorization preconditioner for any Mat implementation
      3:    Note: this need not be considered a preconditioner since it supplies
      4:          a direct solver.
      5: */

      7: #include <../src/ksp/pc/impls/factor/lu/lu.h>

      9: static PetscErrorCode PCFactorReorderForNonzeroDiagonal_LU(PC pc, PetscReal z)
     10: {
     11:   PC_LU *lu = (PC_LU *)pc->data;

     13:   PetscFunctionBegin;
     14:   lu->nonzerosalongdiagonal = PETSC_TRUE;
     15:   if (z == (PetscReal)PETSC_DECIDE) lu->nonzerosalongdiagonaltol = 1.e-10;
     16:   else lu->nonzerosalongdiagonaltol = z;
     17:   PetscFunctionReturn(PETSC_SUCCESS);
     18: }

     20: static PetscErrorCode PCSetFromOptions_LU(PC pc, PetscOptionItems *PetscOptionsObject)
     21: {
     22:   PC_LU    *lu  = (PC_LU *)pc->data;
     23:   PetscBool flg = PETSC_FALSE;
     24:   PetscReal tol;

     26:   PetscFunctionBegin;
     27:   PetscOptionsHeadBegin(PetscOptionsObject, "LU options");
     28:   PetscCall(PCSetFromOptions_Factor(pc, PetscOptionsObject));

     30:   PetscCall(PetscOptionsName("-pc_factor_nonzeros_along_diagonal", "Reorder to remove zeros from diagonal", "PCFactorReorderForNonzeroDiagonal", &flg));
     31:   if (flg) {
     32:     tol = PETSC_DECIDE;
     33:     PetscCall(PetscOptionsReal("-pc_factor_nonzeros_along_diagonal", "Reorder to remove zeros from diagonal", "PCFactorReorderForNonzeroDiagonal", lu->nonzerosalongdiagonaltol, &tol, NULL));
     34:     PetscCall(PCFactorReorderForNonzeroDiagonal(pc, tol));
     35:   }
     36:   PetscOptionsHeadEnd();
     37:   PetscFunctionReturn(PETSC_SUCCESS);
     38: }

     40: static PetscErrorCode PCSetUp_LU(PC pc)
     41: {
     42:   PC_LU         *dir = (PC_LU *)pc->data;
     43:   MatSolverType  stype;
     44:   MatFactorError err;
     45:   const char    *prefix;

     47:   PetscFunctionBegin;
     48:   pc->failedreason = PC_NOERROR;
     49:   if (dir->hdr.reusefill && pc->setupcalled) ((PC_Factor *)dir)->info.fill = dir->hdr.actualfill;

     51:   PetscCall(PCGetOptionsPrefix(pc, &prefix));
     52:   PetscCall(MatSetOptionsPrefixFactor(pc->pmat, prefix));

     54:   PetscCall(MatSetErrorIfFailure(pc->pmat, pc->erroriffailure));
     55:   if (dir->hdr.inplace) {
     56:     MatFactorType ftype;

     58:     PetscCall(MatGetFactorType(pc->pmat, &ftype));
     59:     if (ftype == MAT_FACTOR_NONE) {
     60:       if (dir->row && dir->col && dir->row != dir->col) PetscCall(ISDestroy(&dir->row));
     61:       PetscCall(ISDestroy(&dir->col));
     62:       /* This should only get the ordering if needed, but since MatGetFactor() is not called we can't know if it is needed */
     63:       PetscCall(PCFactorSetDefaultOrdering_Factor(pc));
     64:       PetscCall(MatGetOrdering(pc->pmat, ((PC_Factor *)dir)->ordering, &dir->row, &dir->col));
     65:       if (dir->row) { }
     66:       PetscCall(MatLUFactor(pc->pmat, dir->row, dir->col, &((PC_Factor *)dir)->info));
     67:       PetscCall(MatFactorGetError(pc->pmat, &err));
     68:       if (err) { /* Factor() fails */
     69:         pc->failedreason = (PCFailedReason)err;
     70:         PetscFunctionReturn(PETSC_SUCCESS);
     71:       }
     72:     }
     73:     ((PC_Factor *)dir)->fact = pc->pmat;
     74:   } else {
     75:     MatInfo info;

     77:     if (!pc->setupcalled) {
     78:       PetscBool canuseordering;

     80:       PetscCall(PCFactorSetUpMatSolverType(pc));
     81:       PetscCall(MatFactorGetCanUseOrdering(((PC_Factor *)dir)->fact, &canuseordering));
     82:       if (canuseordering) {
     83:         PetscCall(PCFactorSetDefaultOrdering_Factor(pc));
     84:         PetscCall(MatGetOrdering(pc->pmat, ((PC_Factor *)dir)->ordering, &dir->row, &dir->col));
     85:         if (dir->nonzerosalongdiagonal) PetscCall(MatReorderForNonzeroDiagonal(pc->pmat, dir->nonzerosalongdiagonaltol, dir->row, dir->col));
     86:       }
     87:       PetscCall(MatLUFactorSymbolic(((PC_Factor *)dir)->fact, pc->pmat, dir->row, dir->col, &((PC_Factor *)dir)->info));
     88:       PetscCall(MatGetInfo(((PC_Factor *)dir)->fact, MAT_LOCAL, &info));
     89:       dir->hdr.actualfill = info.fill_ratio_needed;
     90:     } else if (pc->flag != SAME_NONZERO_PATTERN) {
     91:       PetscBool canuseordering;

     93:       if (!dir->hdr.reuseordering) {
     94:         PetscCall(MatDestroy(&((PC_Factor *)dir)->fact));
     95:         PetscCall(PCFactorSetUpMatSolverType(pc));
     96:         PetscCall(MatFactorGetCanUseOrdering(((PC_Factor *)dir)->fact, &canuseordering));
     97:         if (canuseordering) {
     98:           if (dir->row && dir->col && dir->row != dir->col) PetscCall(ISDestroy(&dir->row));
     99:           PetscCall(ISDestroy(&dir->col));
    100:           PetscCall(PCFactorSetDefaultOrdering_Factor(pc));
    101:           PetscCall(MatGetOrdering(pc->pmat, ((PC_Factor *)dir)->ordering, &dir->row, &dir->col));
    102:           if (dir->nonzerosalongdiagonal) PetscCall(MatReorderForNonzeroDiagonal(pc->pmat, dir->nonzerosalongdiagonaltol, dir->row, dir->col));
    103:         }
    104:       }
    105:       PetscCall(MatLUFactorSymbolic(((PC_Factor *)dir)->fact, pc->pmat, dir->row, dir->col, &((PC_Factor *)dir)->info));
    106:       PetscCall(MatGetInfo(((PC_Factor *)dir)->fact, MAT_LOCAL, &info));
    107:       dir->hdr.actualfill = info.fill_ratio_needed;
    108:     } else {
    109:       PetscCall(MatFactorGetError(((PC_Factor *)dir)->fact, &err));
    110:       if (err == MAT_FACTOR_NUMERIC_ZEROPIVOT) {
    111:         PetscCall(MatFactorClearError(((PC_Factor *)dir)->fact));
    112:         pc->failedreason = PC_NOERROR;
    113:       }
    114:     }
    115:     PetscCall(MatFactorGetError(((PC_Factor *)dir)->fact, &err));
    116:     if (err) { /* FactorSymbolic() fails */
    117:       pc->failedreason = (PCFailedReason)err;
    118:       PetscFunctionReturn(PETSC_SUCCESS);
    119:     }

    121:     PetscCall(MatLUFactorNumeric(((PC_Factor *)dir)->fact, pc->pmat, &((PC_Factor *)dir)->info));
    122:     PetscCall(MatFactorGetError(((PC_Factor *)dir)->fact, &err));
    123:     if (err) { /* FactorNumeric() fails */
    124:       pc->failedreason = (PCFailedReason)err;
    125:     }
    126:   }

    128:   PetscCall(PCFactorGetMatSolverType(pc, &stype));
    129:   if (!stype) {
    130:     MatSolverType solverpackage;
    131:     PetscCall(MatFactorGetSolverType(((PC_Factor *)dir)->fact, &solverpackage));
    132:     PetscCall(PCFactorSetMatSolverType(pc, solverpackage));
    133:   }
    134:   PetscFunctionReturn(PETSC_SUCCESS);
    135: }

    137: static PetscErrorCode PCReset_LU(PC pc)
    138: {
    139:   PC_LU *dir = (PC_LU *)pc->data;

    141:   PetscFunctionBegin;
    142:   if (!dir->hdr.inplace && ((PC_Factor *)dir)->fact) PetscCall(MatDestroy(&((PC_Factor *)dir)->fact));
    143:   if (dir->row && dir->col && dir->row != dir->col) PetscCall(ISDestroy(&dir->row));
    144:   PetscCall(ISDestroy(&dir->col));
    145:   PetscFunctionReturn(PETSC_SUCCESS);
    146: }

    148: static PetscErrorCode PCDestroy_LU(PC pc)
    149: {
    150:   PC_LU *dir = (PC_LU *)pc->data;

    152:   PetscFunctionBegin;
    153:   PetscCall(PCReset_LU(pc));
    154:   PetscCall(PetscFree(((PC_Factor *)dir)->ordering));
    155:   PetscCall(PetscFree(((PC_Factor *)dir)->solvertype));
    156:   PetscCall(PCFactorClearComposedFunctions(pc));
    157:   PetscCall(PetscFree(pc->data));
    158:   PetscFunctionReturn(PETSC_SUCCESS);
    159: }

    161: static PetscErrorCode PCApply_LU(PC pc, Vec x, Vec y)
    162: {
    163:   PC_LU *dir = (PC_LU *)pc->data;

    165:   PetscFunctionBegin;
    166:   if (dir->hdr.inplace) {
    167:     PetscCall(MatSolve(pc->pmat, x, y));
    168:   } else {
    169:     PetscCall(MatSolve(((PC_Factor *)dir)->fact, x, y));
    170:   }
    171:   PetscFunctionReturn(PETSC_SUCCESS);
    172: }

    174: static PetscErrorCode PCMatApply_LU(PC pc, Mat X, Mat Y)
    175: {
    176:   PC_LU *dir = (PC_LU *)pc->data;

    178:   PetscFunctionBegin;
    179:   if (dir->hdr.inplace) {
    180:     PetscCall(MatMatSolve(pc->pmat, X, Y));
    181:   } else {
    182:     PetscCall(MatMatSolve(((PC_Factor *)dir)->fact, X, Y));
    183:   }
    184:   PetscFunctionReturn(PETSC_SUCCESS);
    185: }

    187: static PetscErrorCode PCApplyTranspose_LU(PC pc, Vec x, Vec y)
    188: {
    189:   PC_LU *dir = (PC_LU *)pc->data;

    191:   PetscFunctionBegin;
    192:   if (dir->hdr.inplace) {
    193:     PetscCall(MatSolveTranspose(pc->pmat, x, y));
    194:   } else {
    195:     PetscCall(MatSolveTranspose(((PC_Factor *)dir)->fact, x, y));
    196:   }
    197:   PetscFunctionReturn(PETSC_SUCCESS);
    198: }

    200: /*MC
    201:    PCLU - Uses a direct solver, based on LU factorization, as a preconditioner

    203:    Options Database Keys:
    204: +  -pc_factor_reuse_ordering - Activate `PCFactorSetReuseOrdering()`
    205: .  -pc_factor_mat_solver_type - Actives `PCFactorSetMatSolverType()` to choose the direct solver, like superlu
    206: .  -pc_factor_reuse_fill - Activates `PCFactorSetReuseFill()`
    207: .  -pc_factor_fill <fill> - Sets fill amount
    208: .  -pc_factor_in_place - Activates in-place factorization
    209: .  -pc_factor_mat_ordering_type <nd,rcm,...> - Sets ordering routine
    210: .  -pc_factor_pivot_in_blocks <true,false> - allow pivoting within the small blocks during factorization (may increase
    211:                                          stability of factorization.
    212: .  -pc_factor_shift_type <shifttype> - Sets shift type or -1 for the default; use '-help' for a list of available types
    213: .  -pc_factor_shift_amount <shiftamount> - Sets shift amount or -1 for the default
    214: .  -pc_factor_nonzeros_along_diagonal - permutes the rows and columns to try to put nonzero value along the diagonal.
    215: .  -pc_factor_mat_solver_type <packagename> - use an external package for the solve, see `MatSolverType` for possibilities
    216: -  -mat_solvertype_optionname - options for a specific solver package, for example -mat_mumps_cntl_1

    218:    Level: beginner

    220:    Notes:
    221:    Not all options work for all matrix formats

    223:    Run with `-help` to see additional options for particular matrix formats or factorization algorithms

    225:    The Cholesky factorization direct solver, `PCCHOLESKY` will be more efficient than `PCLU` for symmetric positive-definite (SPD) matrices

    227:    Usually this will compute an "exact" solution in one iteration and does
    228:    not need a Krylov method (i.e. you can use -ksp_type preonly, or
    229:    `KSPSetType`(ksp,`KSPPREONLY`) for the Krylov method.

    231: .seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `MatSolverType`, `MatGetFactor()`, `PCQR`, `PCSVD`,
    232:           `PCILU`, `PCCHOLESKY`, `PCICC`, `PCFactorSetReuseOrdering()`, `PCFactorSetReuseFill()`, `PCFactorGetMatrix()`,
    233:           `PCFactorSetFill()`, `PCFactorSetUseInPlace()`, `PCFactorSetMatOrderingType()`, `PCFactorSetColumnPivot()`,
    234:           `PCFactorSetPivotInBlocks()`, `PCFactorSetShiftType()`, `PCFactorSetShiftAmount()`
    235:           `PCFactorReorderForNonzeroDiagonal()`
    236: M*/

    238: PETSC_EXTERN PetscErrorCode PCCreate_LU(PC pc)
    239: {
    240:   PC_LU *dir;

    242:   PetscFunctionBegin;
    243:   PetscCall(PetscNew(&dir));
    244:   pc->data = (void *)dir;
    245:   PetscCall(PCFactorInitialize(pc, MAT_FACTOR_LU));
    246:   dir->nonzerosalongdiagonal = PETSC_FALSE;

    248:   ((PC_Factor *)dir)->info.fill      = 5.0;
    249:   ((PC_Factor *)dir)->info.dtcol     = 1.e-6; /* default to pivoting; this is only thing PETSc LU supports */
    250:   ((PC_Factor *)dir)->info.shifttype = (PetscReal)MAT_SHIFT_NONE;
    251:   dir->col                           = NULL;
    252:   dir->row                           = NULL;

    254:   pc->ops->reset           = PCReset_LU;
    255:   pc->ops->destroy         = PCDestroy_LU;
    256:   pc->ops->apply           = PCApply_LU;
    257:   pc->ops->matapply        = PCMatApply_LU;
    258:   pc->ops->applytranspose  = PCApplyTranspose_LU;
    259:   pc->ops->setup           = PCSetUp_LU;
    260:   pc->ops->setfromoptions  = PCSetFromOptions_LU;
    261:   pc->ops->view            = PCView_Factor;
    262:   pc->ops->applyrichardson = NULL;
    263:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFactorReorderForNonzeroDiagonal_C", PCFactorReorderForNonzeroDiagonal_LU));
    264:   PetscFunctionReturn(PETSC_SUCCESS);
    265: }