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;

     12:   ilu->nonzerosalongdiagonal = PETSC_TRUE;
     13:   if (z == PETSC_DECIDE) ilu->nonzerosalongdiagonaltol = 1.e-10;
     14:   else ilu->nonzerosalongdiagonaltol = z;
     15:   return(0);
     16: }

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

     24:   if (!ilu->hdr.inplace) {MatDestroy(&((PC_Factor*)ilu)->fact);}
     25:   if (ilu->row && ilu->col && ilu->row != ilu->col) {ISDestroy(&ilu->row);}
     26:   ISDestroy(&ilu->col);
     27:   return(0);
     28: }

     30: PetscErrorCode  PCFactorSetDropTolerance_ILU(PC pc,PetscReal dt,PetscReal dtcol,PetscInt dtcount)
     31: {
     32:   PC_ILU *ilu = (PC_ILU*)pc->data;

     35:   if (pc->setupcalled && (((PC_Factor*)ilu)->info.dt != dt || ((PC_Factor*)ilu)->info.dtcol != dtcol || ((PC_Factor*)ilu)->info.dtcount != dtcount)) {
     36:     SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot change drop tolerance after using PC");
     37:   }
     38:   ((PC_Factor*)ilu)->info.dt      = dt;
     39:   ((PC_Factor*)ilu)->info.dtcol   = dtcol;
     40:   ((PC_Factor*)ilu)->info.dtcount = dtcount;
     41:   ((PC_Factor*)ilu)->info.usedt   = 1.0;
     42:   return(0);
     43: }

     45: static PetscErrorCode PCSetFromOptions_ILU(PetscOptionItems *PetscOptionsObject,PC pc)
     46: {
     48:   PetscInt       itmp;
     49:   PetscBool      flg,set;
     50:   PC_ILU         *ilu = (PC_ILU*)pc->data;
     51:   PetscReal      tol;

     54:   PetscOptionsHead(PetscOptionsObject,"ILU Options");
     55:   PCSetFromOptions_Factor(PetscOptionsObject,pc);

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

     60:   PetscOptionsBool("-pc_factor_diagonal_fill","Allow fill into empty diagonal entry","PCFactorSetAllowDiagonalFill",((PC_Factor*)ilu)->info.diagonal_fill ? PETSC_TRUE : PETSC_FALSE,&flg,&set);
     61:   if (set) ((PC_Factor*)ilu)->info.diagonal_fill = (PetscReal) flg;
     62:   PetscOptionsName("-pc_factor_nonzeros_along_diagonal","Reorder to remove zeros from diagonal","PCFactorReorderForNonzeroDiagonal",&flg);
     63:   if (flg) {
     64:     tol  = PETSC_DECIDE;
     65:     PetscOptionsReal("-pc_factor_nonzeros_along_diagonal","Reorder to remove zeros from diagonal","PCFactorReorderForNonzeroDiagonal",ilu->nonzerosalongdiagonaltol,&tol,NULL);
     66:     PCFactorReorderForNonzeroDiagonal(pc,tol);
     67:   }

     69:   PetscOptionsTail();
     70:   return(0);
     71: }

     73: static PetscErrorCode PCSetUp_ILU(PC pc)
     74: {
     75:   PetscErrorCode         ierr;
     76:   PC_ILU                 *ilu = (PC_ILU*)pc->data;
     77:   MatInfo                info;
     78:   PetscBool              flg;
     79:   MatSolverType          stype;
     80:   MatFactorError         err;

     83:   pc->failedreason = PC_NOERROR;
     84:   /* ugly hack to change default, since it is not support by some matrix types */
     85:   if (((PC_Factor*)ilu)->info.shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
     86:     PetscObjectTypeCompare((PetscObject)pc->pmat,MATSEQAIJ,&flg);
     87:     if (!flg) {
     88:       PetscObjectTypeCompare((PetscObject)pc->pmat,MATMPIAIJ,&flg);
     89:       if (!flg) {
     90:         ((PC_Factor*)ilu)->info.shifttype = (PetscReal)MAT_SHIFT_INBLOCKS;
     91:         PetscInfo(pc,"Changing shift type from NONZERO to INBLOCKS because block matrices do not support NONZERO\n");
     92:       }
     93:     }
     94:   }

     96:   MatSetErrorIfFailure(pc->pmat,pc->erroriffailure);
     97:   if (ilu->hdr.inplace) {
     98:     if (!pc->setupcalled) {

    100:       /* In-place factorization only makes sense with the natural ordering,
    101:          so we only need to get the ordering once, even if nonzero structure changes */
    102:       /* Should not get the ordering if the factorization routine does not use it, but do not yet have access to the factor matrix */
    103:       MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);
    104:       if (ilu->row) {PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);}
    105:       if (ilu->col) {PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);}
    106:     }

    108:     /* In place ILU only makes sense with fill factor of 1.0 because
    109:        cannot have levels of fill */
    110:     ((PC_Factor*)ilu)->info.fill          = 1.0;
    111:     ((PC_Factor*)ilu)->info.diagonal_fill = 0.0;

    113:     MatILUFactor(pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);
    114:     MatFactorGetError(pc->pmat,&err);
    115:     if (err) { /* Factor() fails */
    116:       pc->failedreason = (PCFailedReason)err;
    117:       return(0);
    118:     }

    120:     ((PC_Factor*)ilu)->fact = pc->pmat;
    121:     /* must update the pc record of the matrix state or the PC will attempt to run PCSetUp() yet again */
    122:     PetscObjectStateGet((PetscObject)pc->pmat,&pc->matstate);
    123:   } else {
    124:     if (!pc->setupcalled) {
    125:       /* first time in so compute reordering and symbolic factorization */
    126:       PetscBool useordering;
    127:       if (!((PC_Factor*)ilu)->fact) {
    128:         MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);
    129:         PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)ilu)->fact);
    130:       }
    131:       MatFactorGetUseOrdering(((PC_Factor*)ilu)->fact,&useordering);
    132:       if (useordering) {
    133:         MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);
    134:         PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);
    135:         PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);
    136:         /*  Remove zeros along diagonal?     */
    137:         if (ilu->nonzerosalongdiagonal) {
    138:           MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);
    139:         }
    140:       }
    141:       MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);
    142:       MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);
    143:       ilu->hdr.actualfill = info.fill_ratio_needed;
    144:     } else if (pc->flag != SAME_NONZERO_PATTERN) {
    145:       if (!ilu->hdr.reuseordering) {
    146:         PetscBool useordering;
    147:         MatDestroy(&((PC_Factor*)ilu)->fact);
    148:         MatGetFactor(pc->pmat,((PC_Factor*)ilu)->solvertype,MAT_FACTOR_ILU,&((PC_Factor*)ilu)->fact);
    149:         PetscLogObjectParent((PetscObject)pc,(PetscObject)((PC_Factor*)ilu)->fact);
    150:         MatFactorGetUseOrdering(((PC_Factor*)ilu)->fact,&useordering);
    151:         if (useordering) {
    152:           /* compute a new ordering for the ILU */
    153:           ISDestroy(&ilu->row);
    154:           ISDestroy(&ilu->col);
    155:           MatGetOrdering(pc->pmat,((PC_Factor*)ilu)->ordering,&ilu->row,&ilu->col);
    156:           PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->row);
    157:           PetscLogObjectParent((PetscObject)pc,(PetscObject)ilu->col);
    158:           /*  Remove zeros along diagonal?     */
    159:           if (ilu->nonzerosalongdiagonal) {
    160:             MatReorderForNonzeroDiagonal(pc->pmat,ilu->nonzerosalongdiagonaltol,ilu->row,ilu->col);
    161:           }
    162:         }
    163:       }
    164:       MatILUFactorSymbolic(((PC_Factor*)ilu)->fact,pc->pmat,ilu->row,ilu->col,&((PC_Factor*)ilu)->info);
    165:       MatGetInfo(((PC_Factor*)ilu)->fact,MAT_LOCAL,&info);
    166:       ilu->hdr.actualfill = info.fill_ratio_needed;
    167:     }
    168:     MatFactorGetError(((PC_Factor*)ilu)->fact,&err);
    169:     if (err) { /* FactorSymbolic() fails */
    170:       pc->failedreason = (PCFailedReason)err;
    171:       return(0);
    172:     }

    174:     MatLUFactorNumeric(((PC_Factor*)ilu)->fact,pc->pmat,&((PC_Factor*)ilu)->info);
    175:     MatFactorGetError(((PC_Factor*)ilu)->fact,&err);
    176:     if (err) { /* FactorNumeric() fails */
    177:       pc->failedreason = (PCFailedReason)err;
    178:     }
    179:   }

    181:   PCFactorGetMatSolverType(pc,&stype);
    182:   if (!stype) {
    183:     MatSolverType solverpackage;
    184:     MatFactorGetSolverType(((PC_Factor*)ilu)->fact,&solverpackage);
    185:     PCFactorSetMatSolverType(pc,solverpackage);
    186:   }
    187:   return(0);
    188: }

    190: static PetscErrorCode PCDestroy_ILU(PC pc)
    191: {
    192:   PC_ILU         *ilu = (PC_ILU*)pc->data;

    196:   PCReset_ILU(pc);
    197:   PetscFree(((PC_Factor*)ilu)->solvertype);
    198:   PetscFree(((PC_Factor*)ilu)->ordering);
    199:   PetscFree(pc->data);
    200:   return(0);
    201: }

    203: static PetscErrorCode PCApply_ILU(PC pc,Vec x,Vec y)
    204: {
    205:   PC_ILU         *ilu = (PC_ILU*)pc->data;

    209:   MatSolve(((PC_Factor*)ilu)->fact,x,y);
    210:   return(0);
    211: }

    213: static PetscErrorCode PCMatApply_ILU(PC pc,Mat X,Mat Y)
    214: {
    215:   PC_ILU         *ilu = (PC_ILU*)pc->data;

    219:   MatMatSolve(((PC_Factor*)ilu)->fact,X,Y);
    220:   return(0);
    221: }

    223: static PetscErrorCode PCApplyTranspose_ILU(PC pc,Vec x,Vec y)
    224: {
    225:   PC_ILU         *ilu = (PC_ILU*)pc->data;

    229:   MatSolveTranspose(((PC_Factor*)ilu)->fact,x,y);
    230:   return(0);
    231: }

    233: static PetscErrorCode PCApplySymmetricLeft_ILU(PC pc,Vec x,Vec y)
    234: {
    236:   PC_ILU         *icc = (PC_ILU*)pc->data;

    239:   MatForwardSolve(((PC_Factor*)icc)->fact,x,y);
    240:   return(0);
    241: }

    243: static PetscErrorCode PCApplySymmetricRight_ILU(PC pc,Vec x,Vec y)
    244: {
    246:   PC_ILU         *icc = (PC_ILU*)pc->data;

    249:   MatBackwardSolve(((PC_Factor*)icc)->fact,x,y);
    250:   return(0);
    251: }

    253: /*MC
    254:      PCILU - Incomplete factorization preconditioners.

    256:    Options Database Keys:
    257: +  -pc_factor_levels <k> - number of levels of fill for ILU(k)
    258: .  -pc_factor_in_place - only for ILU(0) with natural ordering, reuses the space of the matrix for
    259:                       its factorization (overwrites original matrix)
    260: .  -pc_factor_diagonal_fill - fill in a zero diagonal even if levels of fill indicate it wouldn't be fill
    261: .  -pc_factor_reuse_ordering - reuse ordering of factorized matrix from previous factorization
    262: .  -pc_factor_fill <nfill> - expected amount of fill in factored matrix compared to original matrix, nfill > 1
    263: .  -pc_factor_nonzeros_along_diagonal - reorder the matrix before factorization to remove zeros from the diagonal,
    264:                                    this decreases the chance of getting a zero pivot
    265: .  -pc_factor_mat_ordering_type <natural,nd,1wd,rcm,qmd> - set the row/column ordering of the factored matrix
    266: -  -pc_factor_pivot_in_blocks - for block ILU(k) factorization, i.e. with BAIJ matrices with block size larger
    267:                              than 1 the diagonal blocks are factored with partial pivoting (this increases the
    268:                              stability of the ILU factorization

    270:    Level: beginner

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

    275:           For BAIJ matrices this implements a point block ILU

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

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

    283:    References:
    284: +  1. - T. Dupont, R. Kendall, and H. Rachford. An approximate factorization procedure for solving
    285:    self adjoint elliptic difference equations. SIAM J. Numer. Anal., 5, 1968.
    286: .  2. -  T.A. Oliphant. An implicit numerical method for solving two dimensional timedependent diffusion problems. Quart. Appl. Math., 19, 1961.
    287: -  3. -  TONY F. CHAN AND HENK A. VAN DER VORST, APPROXIMATE AND INCOMPLETE FACTORIZATIONS,
    288:       Chapter in Parallel Numerical
    289:       Algorithms, edited by D. Keyes, A. Semah, V. Venkatakrishnan, ICASE/LaRC Interdisciplinary Series in
    290:       Science and Engineering, Kluwer.

    293: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC, PCSOR, MatOrderingType,
    294:            PCFactorSetZeroPivot(), PCFactorSetShiftSetType(), PCFactorSetAmount(),
    295:            PCFactorSetDropTolerance(),PCFactorSetFill(), PCFactorSetMatOrderingType(), PCFactorSetReuseOrdering(),
    296:            PCFactorSetLevels(), PCFactorSetUseInPlace(), PCFactorSetAllowDiagonalFill(), PCFactorSetPivotInBlocks(),
    297:            PCFactorGetAllowDiagonalFill(), PCFactorGetUseInPlace()

    299: M*/

    301: PETSC_EXTERN PetscErrorCode PCCreate_ILU(PC pc)
    302: {
    304:   PC_ILU         *ilu;

    307:   PetscNewLog(pc,&ilu);
    308:   pc->data = (void*)ilu;
    309:   PCFactorInitialize(pc);

    311:   ((PC_Factor*)ilu)->factortype         = MAT_FACTOR_ILU;
    312:   ((PC_Factor*)ilu)->info.levels        = 0.;
    313:   ((PC_Factor*)ilu)->info.fill          = 1.0;
    314:   ilu->col                              = NULL;
    315:   ilu->row                              = NULL;
    316:   PetscStrallocpy(MATORDERINGNATURAL,(char**)&((PC_Factor*)ilu)->ordering);
    317:   ((PC_Factor*)ilu)->info.dt            = PETSC_DEFAULT;
    318:   ((PC_Factor*)ilu)->info.dtcount       = PETSC_DEFAULT;
    319:   ((PC_Factor*)ilu)->info.dtcol         = PETSC_DEFAULT;

    321:   pc->ops->reset               = PCReset_ILU;
    322:   pc->ops->destroy             = PCDestroy_ILU;
    323:   pc->ops->apply               = PCApply_ILU;
    324:   pc->ops->matapply            = PCMatApply_ILU;
    325:   pc->ops->applytranspose      = PCApplyTranspose_ILU;
    326:   pc->ops->setup               = PCSetUp_ILU;
    327:   pc->ops->setfromoptions      = PCSetFromOptions_ILU;
    328:   pc->ops->view                = PCView_Factor;
    329:   pc->ops->applysymmetricleft  = PCApplySymmetricLeft_ILU;
    330:   pc->ops->applysymmetricright = PCApplySymmetricRight_ILU;
    331:   pc->ops->applyrichardson     = NULL;
    332:   PetscObjectComposeFunction((PetscObject)pc,"PCFactorSetDropTolerance_C",PCFactorSetDropTolerance_ILU);
    333:   PetscObjectComposeFunction((PetscObject)pc,"PCFactorReorderForNonzeroDiagonal_C",PCFactorReorderForNonzeroDiagonal_ILU);
    334:   return(0);
    335: }