Date: 2022-08-02T03:14:34+00:00

Actual source code: ilu.c

      2: /*
      3:    Defines a ILU factorization preconditioner for any Mat implementation
      4: */
      5: #include <../src/ksp/pc/impls/factor/ilu/ilu.h>

      7: PetscErrorCode  PCFactorReorderForNonzeroDiagonal_ILU(PC pc,PetscReal z)
      8: {
      9:   PC_ILU *ilu = (PC_ILU*)pc->data;

     11:   ilu->nonzerosalongdiagonal = PETSC_TRUE;
     12:   if (z == PETSC_DECIDE) ilu->nonzerosalongdiagonaltol = 1.e-10;
     13:   else ilu->nonzerosalongdiagonaltol = z;
     14:   return 0;
     15: }

     17: PetscErrorCode PCReset_ILU(PC pc)
     18: {
     19:   PC_ILU         *ilu = (PC_ILU*)pc->data;

     21:   if (!ilu->hdr.inplace) MatDestroy(&((PC_Factor*)ilu)->fact);
     22:   if (ilu->row && ilu->col && ilu->row != ilu->col) ISDestroy(&ilu->row);
     23:   ISDestroy(&ilu->col);
     24:   return 0;
     25: }

     27: PetscErrorCode  PCFactorSetDropTolerance_ILU(PC pc,PetscReal dt,PetscReal dtcol,PetscInt dtcount)
     28: {
     29:   PC_ILU *ilu = (PC_ILU*)pc->data;

     31:   if (pc->setupcalled && (((PC_Factor*)ilu)->info.dt != dt || ((PC_Factor*)ilu)->info.dtcol != dtcol || ((PC_Factor*)ilu)->info.dtcount != dtcount)) {
     32:     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot change drop tolerance after using PC");
     33:   }
     34:   ((PC_Factor*)ilu)->info.dt      = dt;
     35:   ((PC_Factor*)ilu)->info.dtcol   = dtcol;
     36:   ((PC_Factor*)ilu)->info.dtcount = dtcount;
     37:   ((PC_Factor*)ilu)->info.usedt   = 1.0;
     38:   return 0;
     39: }

     41: static PetscErrorCode PCSetFromOptions_ILU(PetscOptionItems *PetscOptionsObject,PC pc)
     42: {
     43:   PetscInt       itmp;
     44:   PetscBool      flg,set;
     45:   PC_ILU         *ilu = (PC_ILU*)pc->data;
     46:   PetscReal      tol;

     48:   PetscOptionsHead(PetscOptionsObject,"ILU Options");
     49:   PCSetFromOptions_Factor(PetscOptionsObject,pc);

     51:   PetscOptionsInt("-pc_factor_levels","levels of fill","PCFactorSetLevels",(PetscInt)((PC_Factor*)ilu)->info.levels,&itmp,&flg);
     52:   if (flg) ((PC_Factor*)ilu)->info.levels = itmp;

     54:   PetscOptionsBool("-pc_factor_diagonal_fill","Allow fill into empty diagonal entry","PCFactorSetAllowDiagonalFill",((PC_Factor*)ilu)->info.diagonal_fill ? PETSC_TRUE : PETSC_FALSE,&flg,&set);
     55:   if (set) ((PC_Factor*)ilu)->info.diagonal_fill = (PetscReal) flg;
     56:   PetscOptionsName("-pc_factor_nonzeros_along_diagonal","Reorder to remove zeros from diagonal","PCFactorReorderForNonzeroDiagonal",&flg);
     57:   if (flg) {
     58:     tol  = PETSC_DECIDE;
     59:     PetscOptionsReal("-pc_factor_nonzeros_along_diagonal","Reorder to remove zeros from diagonal","PCFactorReorderForNonzeroDiagonal",ilu->nonzerosalongdiagonaltol,&tol,NULL);
     60:     PCFactorReorderForNonzeroDiagonal(pc,tol);
     61:   }

     63:   PetscOptionsTail();
     64:   return 0;
     65: }

     67: static PetscErrorCode PCSetUp_ILU(PC pc)
     68: {
     69:   PC_ILU                 *ilu = (PC_ILU*)pc->data;
     70:   MatInfo                info;
     71:   PetscBool              flg;
     72:   MatSolverType          stype;
     73:   MatFactorError         err;

     75:   pc->failedreason = PC_NOERROR;
     76:   /* ugly hack to change default, since it is not support by some matrix types */
     77:   if (((PC_Factor*)ilu)->info.shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
     78:     PetscObjectTypeCompare((PetscObject)pc->pmat,MATSEQAIJ,&flg);
     79:     if (!flg) {
     80:       PetscObjectTypeCompare((PetscObject)pc->pmat,MATMPIAIJ,&flg);
     81:       if (!flg) {
     82:         ((PC_Factor*)ilu)->info.shifttype = (PetscReal)MAT_SHIFT_INBLOCKS;
     83:         PetscInfo(pc,"Changing shift type from NONZERO to INBLOCKS because block matrices do not support NONZERO\n");
     84:       }
     85:     }
     86:   }

     88:   MatSetErrorIfFailure(pc->pmat,pc->erroriffailure);
     89:   if (ilu->hdr.inplace) {
     90:     if (!pc->setupcalled) {

     92:       /* In-place factorization only makes sense with the natural ordering,
     93:          so we only need to get the ordering once, even if nonzero structure changes */
     94:       /* Should not get the ordering if the factorization routine does not use it, but do not yet have access to the factor matrix */
     95:       PCFactorSetDefaultOrdering_Factor(pc);
     96:       MatDestroy(&((PC_Factor*)ilu)->fact);
     97:       MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);
     98:       if (ilu->row) PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);
     99:       if (ilu->col) PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);
    100:     }

    102:     /* In place ILU only makes sense with fill factor of 1.0 because
    103:        cannot have levels of fill */
    104:     ((PC_Factor*)ilu)->info.fill          = 1.0;
    105:     ((PC_Factor*)ilu)->info.diagonal_fill = 0.0;

    107:     MatILUFactor(pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);
    108:     MatFactorGetError(pc->pmat,&err);
    109:     if (err) { /* Factor() fails */
    110:       pc->failedreason = (PCFailedReason)err;
    111:       return 0;
    112:     }

    114:     ((PC_Factor*)ilu)->fact = pc->pmat;
    115:     /* must update the pc record of the matrix state or the PC will attempt to run PCSetUp() yet again */
    116:     PetscObjectStateGet((PetscObject)pc->pmat,&pc->matstate);
    117:   } else {
    118:     if (!pc->setupcalled) {
    119:       /* first time in so compute reordering and symbolic factorization */
    120:       PetscBool canuseordering;
    121:       if (!((PC_Factor*)ilu)->fact) {
    122:         MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);
    123:         PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)ilu)->fact);
    124:       }
    125:       MatFactorGetCanUseOrdering(((PC_Factor*)ilu)->fact,&canuseordering);
    126:       if (canuseordering) {
    127:         PCFactorSetDefaultOrdering_Factor(pc);
    128:         MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);
    129:         PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);
    130:         PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);
    131:         /*  Remove zeros along diagonal?     */
    132:         if (ilu->nonzerosalongdiagonal) {
    133:           MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);
    134:         }
    135:       }
    136:       MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);
    137:       MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);
    138:       ilu->hdr.actualfill = info.fill_ratio_needed;
    139:     } else if (pc->flag != SAME_NONZERO_PATTERN) {
    140:       if (!ilu->hdr.reuseordering) {
    141:         PetscBool canuseordering;
    142:         MatDestroy(&((PC_Factor*)ilu)->fact);
    143:         MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);
    144:         PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)ilu)->fact);
    145:         MatFactorGetCanUseOrdering(((PC_Factor*)ilu)->fact,&canuseordering);
    146:         if (canuseordering) {
    147:           /* compute a new ordering for the ILU */
    148:           ISDestroy(&ilu->row);
    149:           ISDestroy(&ilu->col);
    150:           PCFactorSetDefaultOrdering_Factor(pc);
    151:           MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);
    152:           PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);
    153:           PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);
    154:           /*  Remove zeros along diagonal?     */
    155:           if (ilu->nonzerosalongdiagonal) {
    156:             MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);
    157:           }
    158:         }
    159:       }
    160:       MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);
    161:       MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);
    162:       ilu->hdr.actualfill = info.fill_ratio_needed;
    163:     }
    164:     MatFactorGetError(((PC_Factor*)ilu)->fact,&err);
    165:     if (err) { /* FactorSymbolic() fails */
    166:       pc->failedreason = (PCFailedReason)err;
    167:       return 0;
    168:     }

    170:     MatLUFactorNumeric(((PC_Factor*)ilu)->fact,pc->pmat,&((PC_Factor*)ilu)->info);
    171:     MatFactorGetError(((PC_Factor*)ilu)->fact,&err);
    172:     if (err) { /* FactorNumeric() fails */
    173:       pc->failedreason = (PCFailedReason)err;
    174:     }
    175:   }

    177:   PCFactorGetMatSolverType(pc,&stype);
    178:   if (!stype) {
    179:     MatSolverType solverpackage;
    180:     MatFactorGetSolverType(((PC_Factor*)ilu)->fact,&solverpackage);
    181:     PCFactorSetMatSolverType(pc,solverpackage);
    182:   }
    183:   return 0;
    184: }

    186: static PetscErrorCode PCDestroy_ILU(PC pc)
    187: {
    188:   PC_ILU         *ilu = (PC_ILU*)pc->data;

    190:   PCReset_ILU(pc);
    191:   PetscFree(((PC_Factor*)ilu)->solvertype);
    192:   PetscFree(((PC_Factor*)ilu)->ordering);
    193:   PetscFree(pc->data);
    194:   return 0;
    195: }

    197: static PetscErrorCode PCApply_ILU(PC pc,Vec x,Vec y)
    198: {
    199:   PC_ILU         *ilu = (PC_ILU*)pc->data;

    201:   MatSolve(((PC_Factor*)ilu)->fact,x,y);
    202:   return 0;
    203: }

    205: static PetscErrorCode PCMatApply_ILU(PC pc,Mat X,Mat Y)
    206: {
    207:   PC_ILU         *ilu = (PC_ILU*)pc->data;

    209:   MatMatSolve(((PC_Factor*)ilu)->fact,X,Y);
    210:   return 0;
    211: }

    213: static PetscErrorCode PCApplyTranspose_ILU(PC pc,Vec x,Vec y)
    214: {
    215:   PC_ILU         *ilu = (PC_ILU*)pc->data;

    217:   MatSolveTranspose(((PC_Factor*)ilu)->fact,x,y);
    218:   return 0;
    219: }

    221: static PetscErrorCode PCApplySymmetricLeft_ILU(PC pc,Vec x,Vec y)
    222: {
    223:   PC_ILU         *icc = (PC_ILU*)pc->data;

    225:   MatForwardSolve(((PC_Factor*)icc)->fact,x,y);
    226:   return 0;
    227: }

    229: static PetscErrorCode PCApplySymmetricRight_ILU(PC pc,Vec x,Vec y)
    230: {
    231:   PC_ILU         *icc = (PC_ILU*)pc->data;

    233:   MatBackwardSolve(((PC_Factor*)icc)->fact,x,y);
    234:   return 0;
    235: }

    237: /*MC
    238:      PCILU - Incomplete factorization preconditioners.

    240:    Options Database Keys:
    241: +  -pc_factor_levels <k> - number of levels of fill for ILU(k)
    242: .  -pc_factor_in_place - only for ILU(0) with natural ordering, reuses the space of the matrix for
    243:                       its factorization (overwrites original matrix)
    244: .  -pc_factor_diagonal_fill - fill in a zero diagonal even if levels of fill indicate it wouldn't be fill
    245: .  -pc_factor_reuse_ordering - reuse ordering of factorized matrix from previous factorization
    246: .  -pc_factor_fill <nfill> - expected amount of fill in factored matrix compared to original matrix, nfill > 1
    247: .  -pc_factor_nonzeros_along_diagonal - reorder the matrix before factorization to remove zeros from the diagonal,
    248:                                    this decreases the chance of getting a zero pivot
    249: .  -pc_factor_mat_ordering_type <natural,nd,1wd,rcm,qmd> - set the row/column ordering of the factored matrix
    250: -  -pc_factor_pivot_in_blocks - for block ILU(k) factorization, i.e. with BAIJ matrices with block size larger
    251:                              than 1 the diagonal blocks are factored with partial pivoting (this increases the
    252:                              stability of the ILU factorization

    254:    Level: beginner

    256:    Notes:
    257:     Only implemented for some matrix formats. (for parallel see PCHYPRE for hypre's ILU)

    259:           For BAIJ matrices this implements a point block ILU

    261:           The "symmetric" application of this preconditioner is not actually symmetric since L is not transpose(U)
    262:           even when the matrix is not symmetric since the U stores the diagonals of the factorization.

    264:           If you are using MATSEQAIJCUSPARSE matrices (or MATMPIAIJCUSPARSE matrices with block Jacobi), factorization
    265:           is never done on the GPU).

    267:    References:
    268: +  * - T. Dupont, R. Kendall, and H. Rachford. An approximate factorization procedure for solving
    269:    self adjoint elliptic difference equations. SIAM J. Numer. Anal., 5, 1968.
    270: .  * -  T.A. Oliphant. An implicit numerical method for solving two dimensional timedependent diffusion problems. Quart. Appl. Math., 19, 1961.
    271: -  * -  TONY F. CHAN AND HENK A. VAN DER VORST, APPROXIMATE AND INCOMPLETE FACTORIZATIONS,
    272:       Chapter in Parallel Numerical
    273:       Algorithms, edited by D. Keyes, A. Semah, V. Venkatakrishnan, ICASE/LaRC Interdisciplinary Series in
    274:       Science and Engineering, Kluwer.

    276: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC, PCSOR, MatOrderingType,
    277:            PCFactorSetZeroPivot(), PCFactorSetShiftSetType(), PCFactorSetAmount(),
    278:            PCFactorSetDropTolerance(),PCFactorSetFill(), PCFactorSetMatOrderingType(), PCFactorSetReuseOrdering(),
    279:            PCFactorSetLevels(), PCFactorSetUseInPlace(), PCFactorSetAllowDiagonalFill(), PCFactorSetPivotInBlocks(),
    280:            PCFactorGetAllowDiagonalFill(), PCFactorGetUseInPlace()

    282: M*/

    284: PETSC_EXTERN PetscErrorCode PCCreate_ILU(PC pc)
    285: {
    286:   PC_ILU         *ilu;

    288:   PetscNewLog(pc,&ilu);
    289:   pc->data = (void*)ilu;
    290:   PCFactorInitialize(pc,MAT_FACTOR_ILU);

    292:   ((PC_Factor*)ilu)->info.levels        = 0.;
    293:   ((PC_Factor*)ilu)->info.fill          = 1.0;
    294:   ilu->col                              = NULL;
    295:   ilu->row                              = NULL;
    296:   ((PC_Factor*)ilu)->info.dt            = PETSC_DEFAULT;
    297:   ((PC_Factor*)ilu)->info.dtcount       = PETSC_DEFAULT;
    298:   ((PC_Factor*)ilu)->info.dtcol         = PETSC_DEFAULT;

    300:   pc->ops->reset               = PCReset_ILU;
    301:   pc->ops->destroy             = PCDestroy_ILU;
    302:   pc->ops->apply               = PCApply_ILU;
    303:   pc->ops->matapply            = PCMatApply_ILU;
    304:   pc->ops->applytranspose      = PCApplyTranspose_ILU;
    305:   pc->ops->setup               = PCSetUp_ILU;
    306:   pc->ops->setfromoptions      = PCSetFromOptions_ILU;
    307:   pc->ops->view                = PCView_Factor;
    308:   pc->ops->applysymmetricleft  = PCApplySymmetricLeft_ILU;
    309:   pc->ops->applysymmetricright = PCApplySymmetricRight_ILU;
    310:   pc->ops->applyrichardson     = NULL;
    311:   PetscObjectComposeFunction((PetscObject)pc,"PCFactorSetDropTolerance_C",PCFactorSetDropTolerance_ILU);
    312:   PetscObjectComposeFunction((PetscObject)pc,"PCFactorReorderForNonzeroDiagonal_C",PCFactorReorderForNonzeroDiagonal_ILU);
    313:   return 0;
    314: }