Date: 2022-03-31T04:47:57+00:00

Actual source code: eisen.c

      2: /*
      3:    Defines a  Eisenstat trick SSOR  preconditioner. This uses about
      4:  %50 of the usual amount of floating point ops used for SSOR + Krylov
      5:  method. But it requires actually solving the preconditioned problem
      6:  with both left and right preconditioning.
      7: */
      8: #include <petsc/private/pcimpl.h>

     10: typedef struct {
     11:   Mat       shell,A;
     12:   Vec       b[2],diag;   /* temporary storage for true right hand side */
     13:   PetscReal omega;
     14:   PetscBool usediag;     /* indicates preconditioner should include diagonal scaling*/
     15: } PC_Eisenstat;

     17: static PetscErrorCode PCMult_Eisenstat(Mat mat,Vec b,Vec x)
     18: {
     19:   PC             pc;
     20:   PC_Eisenstat   *eis;

     22:   MatShellGetContext(mat,&pc);
     23:   eis  = (PC_Eisenstat*)pc->data;
     24:   MatSOR(eis->A,b,eis->omega,SOR_EISENSTAT,0.0,1,1,x);
     25:   return 0;
     26: }

     28: static PetscErrorCode PCApply_Eisenstat(PC pc,Vec x,Vec y)
     29: {
     30:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;
     31:   PetscBool      hasop;

     33:   if (eis->usediag) {
     34:     MatHasOperation(pc->pmat,MATOP_MULT_DIAGONAL_BLOCK,&hasop);
     35:     if (hasop) {
     36:       MatMultDiagonalBlock(pc->pmat,x,y);
     37:     } else {
     38:       VecPointwiseMult(y,x,eis->diag);
     39:     }
     40:   } else VecCopy(x,y);
     41:   return 0;
     42: }

     44: static PetscErrorCode PCPreSolve_Eisenstat(PC pc,KSP ksp,Vec b,Vec x)
     45: {
     46:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;
     47:   PetscBool      nonzero;

     49:   if (pc->presolvedone < 2) {
     51:     /* swap shell matrix and true matrix */
     52:     eis->A  = pc->mat;
     53:     pc->mat = eis->shell;
     54:   }

     56:   if (!eis->b[pc->presolvedone-1]) {
     57:     VecDuplicate(b,&eis->b[pc->presolvedone-1]);
     58:     PetscLogObjectParent((PetscObject)pc,(PetscObject)eis->b[pc->presolvedone-1]);
     59:   }

     61:   /* if nonzero initial guess, modify x */
     62:   KSPGetInitialGuessNonzero(ksp,&nonzero);
     63:   if (nonzero) {
     64:     VecCopy(x,eis->b[pc->presolvedone-1]);
     65:     MatSOR(eis->A,eis->b[pc->presolvedone-1],eis->omega,SOR_APPLY_UPPER,0.0,1,1,x);
     66:   }

     68:   /* save true b, other option is to swap pointers */
     69:   VecCopy(b,eis->b[pc->presolvedone-1]);

     71:   /* modify b by (L + D/omega)^{-1} */
     72:   MatSOR(eis->A,eis->b[pc->presolvedone-1],eis->omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),0.0,1,1,b);
     73:   return 0;
     74: }

     76: static PetscErrorCode PCPostSolve_Eisenstat(PC pc,KSP ksp,Vec b,Vec x)
     77: {
     78:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;

     80:   /* get back true b */
     81:   VecCopy(eis->b[pc->presolvedone],b);

     83:   /* modify x by (U + D/omega)^{-1} */
     84:   VecCopy(x,eis->b[pc->presolvedone]);
     85:   MatSOR(eis->A,eis->b[pc->presolvedone],eis->omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),0.0,1,1,x);
     86:   if (!pc->presolvedone) pc->mat = eis->A;
     87:   return 0;
     88: }

     90: static PetscErrorCode PCReset_Eisenstat(PC pc)
     91: {
     92:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;

     94:   VecDestroy(&eis->b[0]);
     95:   VecDestroy(&eis->b[1]);
     96:   MatDestroy(&eis->shell);
     97:   VecDestroy(&eis->diag);
     98:   return 0;
     99: }

    101: static PetscErrorCode PCDestroy_Eisenstat(PC pc)
    102: {
    103:   PCReset_Eisenstat(pc);
    104:   PetscFree(pc->data);
    105:   return 0;
    106: }

    108: static PetscErrorCode PCSetFromOptions_Eisenstat(PetscOptionItems *PetscOptionsObject,PC pc)
    109: {
    110:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;
    111:   PetscBool      set,flg;

    113:   PetscOptionsHead(PetscOptionsObject,"Eisenstat SSOR options");
    114:   PetscOptionsReal("-pc_eisenstat_omega","Relaxation factor 0 < omega < 2","PCEisenstatSetOmega",eis->omega,&eis->omega,NULL);
    115:   PetscOptionsBool("-pc_eisenstat_no_diagonal_scaling","Do not use standard diagonal scaling","PCEisenstatSetNoDiagonalScaling",eis->usediag ? PETSC_FALSE : PETSC_TRUE,&flg,&set);
    116:   if (set) {
    117:     PCEisenstatSetNoDiagonalScaling(pc,flg);
    118:   }
    119:   PetscOptionsTail();
    120:   return 0;
    121: }

    123: static PetscErrorCode PCView_Eisenstat(PC pc,PetscViewer viewer)
    124: {
    125:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;
    126:   PetscBool      iascii;

    128:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    129:   if (iascii) {
    130:     PetscViewerASCIIPrintf(viewer,"  omega = %g\n",(double)eis->omega);
    131:     if (eis->usediag) {
    132:       PetscViewerASCIIPrintf(viewer,"  Using diagonal scaling (default)\n");
    133:     } else {
    134:       PetscViewerASCIIPrintf(viewer,"  Not using diagonal scaling\n");
    135:     }
    136:   }
    137:   return 0;
    138: }

    140: static PetscErrorCode PCSetUp_Eisenstat(PC pc)
    141: {
    142:   PetscInt       M,N,m,n;
    143:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;

    145:   if (!pc->setupcalled) {
    146:     MatGetSize(pc->mat,&M,&N);
    147:     MatGetLocalSize(pc->mat,&m,&n);
    148:     MatCreate(PetscObjectComm((PetscObject)pc),&eis->shell);
    149:     MatSetSizes(eis->shell,m,n,M,N);
    150:     MatSetType(eis->shell,MATSHELL);
    151:     MatSetUp(eis->shell);
    152:     MatShellSetContext(eis->shell,pc);
    153:     PetscLogObjectParent((PetscObject)pc,(PetscObject)eis->shell);
    154:     MatShellSetOperation(eis->shell,MATOP_MULT,(void (*)(void))PCMult_Eisenstat);
    155:   }
    156:   if (!eis->usediag) return 0;
    157:   if (!pc->setupcalled) {
    158:     MatCreateVecs(pc->pmat,&eis->diag,NULL);
    159:     PetscLogObjectParent((PetscObject)pc,(PetscObject)eis->diag);
    160:   }
    161:   MatGetDiagonal(pc->pmat,eis->diag);
    162:   return 0;
    163: }

    165: /* --------------------------------------------------------------------*/

    167: static PetscErrorCode  PCEisenstatSetOmega_Eisenstat(PC pc,PetscReal omega)
    168: {
    169:   PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;

    172:   eis->omega = omega;
    173:   return 0;
    174: }

    176: static PetscErrorCode  PCEisenstatSetNoDiagonalScaling_Eisenstat(PC pc,PetscBool flg)
    177: {
    178:   PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;

    180:   eis->usediag = flg;
    181:   return 0;
    182: }

    184: static PetscErrorCode  PCEisenstatGetOmega_Eisenstat(PC pc,PetscReal *omega)
    185: {
    186:   PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;

    188:   *omega = eis->omega;
    189:   return 0;
    190: }

    192: static PetscErrorCode  PCEisenstatGetNoDiagonalScaling_Eisenstat(PC pc,PetscBool *flg)
    193: {
    194:   PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;

    196:   *flg = eis->usediag;
    197:   return 0;
    198: }

    200: /*@
    201:    PCEisenstatSetOmega - Sets the SSOR relaxation coefficient, omega,
    202:    to use with Eisenstat's trick (where omega = 1.0 by default).

    204:    Logically Collective on PC

    206:    Input Parameters:
    207: +  pc - the preconditioner context
    208: -  omega - relaxation coefficient (0 < omega < 2)

    210:    Options Database Key:
    211: .  -pc_eisenstat_omega <omega> - Sets omega

    213:    Notes:
    214:    The Eisenstat trick implementation of SSOR requires about 50% of the
    215:    usual amount of floating point operations used for SSOR + Krylov method;
    216:    however, the preconditioned problem must be solved with both left
    217:    and right preconditioning.

    219:    To use SSOR without the Eisenstat trick, employ the PCSOR preconditioner,
    220:    which can be chosen with the database options
    221: $    -pc_type  sor  -pc_sor_symmetric

    223:    Level: intermediate

    225: .seealso: PCSORSetOmega()
    226: @*/
    227: PetscErrorCode  PCEisenstatSetOmega(PC pc,PetscReal omega)
    228: {
    231:   PetscTryMethod(pc,"PCEisenstatSetOmega_C",(PC,PetscReal),(pc,omega));
    232:   return 0;
    233: }

    235: /*@
    236:    PCEisenstatSetNoDiagonalScaling - Causes the Eisenstat preconditioner
    237:    not to do additional diagonal preconditioning. For matrices with a constant
    238:    along the diagonal, this may save a small amount of work.

    240:    Logically Collective on PC

    242:    Input Parameters:
    243: +  pc - the preconditioner context
    244: -  flg - PETSC_TRUE turns off diagonal scaling inside the algorithm

    246:    Options Database Key:
    247: .  -pc_eisenstat_no_diagonal_scaling - Activates PCEisenstatSetNoDiagonalScaling()

    249:    Level: intermediate

    251:    Note:
    252:      If you use the KSPSetDiagonalScaling() or -ksp_diagonal_scale option then you will
    253:    likley want to use this routine since it will save you some unneeded flops.

    255: .seealso: PCEisenstatSetOmega()
    256: @*/
    257: PetscErrorCode  PCEisenstatSetNoDiagonalScaling(PC pc,PetscBool flg)
    258: {
    260:   PetscTryMethod(pc,"PCEisenstatSetNoDiagonalScaling_C",(PC,PetscBool),(pc,flg));
    261:   return 0;
    262: }

    264: /*@
    265:    PCEisenstatGetOmega - Gets the SSOR relaxation coefficient, omega,
    266:    to use with Eisenstat's trick (where omega = 1.0 by default).

    268:    Logically Collective on PC

    270:    Input Parameter:
    271: .  pc - the preconditioner context

    273:    Output Parameter:
    274: .  omega - relaxation coefficient (0 < omega < 2)

    276:    Options Database Key:
    277: .  -pc_eisenstat_omega <omega> - Sets omega

    279:    Notes:
    280:    The Eisenstat trick implementation of SSOR requires about 50% of the
    281:    usual amount of floating point operations used for SSOR + Krylov method;
    282:    however, the preconditioned problem must be solved with both left
    283:    and right preconditioning.

    285:    To use SSOR without the Eisenstat trick, employ the PCSOR preconditioner,
    286:    which can be chosen with the database options
    287: $    -pc_type  sor  -pc_sor_symmetric

    289:    Level: intermediate

    291: .seealso: PCSORGetOmega(), PCEisenstatSetOmega()
    292: @*/
    293: PetscErrorCode  PCEisenstatGetOmega(PC pc,PetscReal *omega)
    294: {
    296:   PetscUseMethod(pc,"PCEisenstatGetOmega_C",(PC,PetscReal*),(pc,omega));
    297:   return 0;
    298: }

    300: /*@
    301:    PCEisenstatGetNoDiagonalScaling - Tells if the Eisenstat preconditioner
    302:    not to do additional diagonal preconditioning. For matrices with a constant
    303:    along the diagonal, this may save a small amount of work.

    305:    Logically Collective on PC

    307:    Input Parameter:
    308: .  pc - the preconditioner context

    310:    Output Parameter:
    311: .  flg - PETSC_TRUE means there is no diagonal scaling applied

    313:    Options Database Key:
    314: .  -pc_eisenstat_no_diagonal_scaling - Activates PCEisenstatSetNoDiagonalScaling()

    316:    Level: intermediate

    318:    Note:
    319:      If you use the KSPSetDiagonalScaling() or -ksp_diagonal_scale option then you will
    320:    likley want to use this routine since it will save you some unneeded flops.

    322: .seealso: PCEisenstatGetOmega()
    323: @*/
    324: PetscErrorCode  PCEisenstatGetNoDiagonalScaling(PC pc,PetscBool *flg)
    325: {
    327:   PetscUseMethod(pc,"PCEisenstatGetNoDiagonalScaling_C",(PC,PetscBool*),(pc,flg));
    328:   return 0;
    329: }

    331: static PetscErrorCode PCPreSolveChangeRHS_Eisenstat(PC pc, PetscBool* change)
    332: {
    333:   *change = PETSC_TRUE;
    334:   return 0;
    335: }

    337: /* --------------------------------------------------------------------*/

    339: /*MC
    340:      PCEISENSTAT - An implementation of SSOR (symmetric successive over relaxation, symmetric Gauss-Seidel)
    341:            preconditioning that incorporates Eisenstat's trick to reduce the amount of computation needed.

    343:    Options Database Keys:
    344: +  -pc_eisenstat_omega <omega> - Sets omega
    345: -  -pc_eisenstat_no_diagonal_scaling - Activates PCEisenstatSetNoDiagonalScaling()

    347:    Level: beginner

    349:    Notes:
    350:     Only implemented for the SeqAIJ matrix format.
    351:           Not a true parallel SOR, in parallel this implementation corresponds to block
    352:           Jacobi with SOR on each block.

    354: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
    355:            PCEisenstatSetNoDiagonalScaling(), PCEisenstatSetOmega(), PCSOR
    356: M*/

    358: PETSC_EXTERN PetscErrorCode PCCreate_Eisenstat(PC pc)
    359: {
    360:   PC_Eisenstat   *eis;

    362:   PetscNewLog(pc,&eis);

    364:   pc->ops->apply           = PCApply_Eisenstat;
    365:   pc->ops->presolve        = PCPreSolve_Eisenstat;
    366:   pc->ops->postsolve       = PCPostSolve_Eisenstat;
    367:   pc->ops->applyrichardson = NULL;
    368:   pc->ops->setfromoptions  = PCSetFromOptions_Eisenstat;
    369:   pc->ops->destroy         = PCDestroy_Eisenstat;
    370:   pc->ops->reset           = PCReset_Eisenstat;
    371:   pc->ops->view            = PCView_Eisenstat;
    372:   pc->ops->setup           = PCSetUp_Eisenstat;

    374:   pc->data     = eis;
    375:   eis->omega   = 1.0;
    376:   eis->b[0]    = NULL;
    377:   eis->b[1]    = NULL;
    378:   eis->diag    = NULL;
    379:   eis->usediag = PETSC_TRUE;

    381:   PetscObjectComposeFunction((PetscObject)pc,"PCEisenstatSetOmega_C",PCEisenstatSetOmega_Eisenstat);
    382:   PetscObjectComposeFunction((PetscObject)pc,"PCEisenstatSetNoDiagonalScaling_C",PCEisenstatSetNoDiagonalScaling_Eisenstat);
    383:   PetscObjectComposeFunction((PetscObject)pc,"PCEisenstatGetOmega_C",PCEisenstatGetOmega_Eisenstat);
    384:   PetscObjectComposeFunction((PetscObject)pc,"PCEisenstatGetNoDiagonalScaling_C",PCEisenstatGetNoDiagonalScaling_Eisenstat);
    385:   PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_Eisenstat);
    386:   return 0;
    387: }