Date: 2021-03-03T22:27:11+00:00

Actual source code: eisen.c
petsc-3.14.5 2021-03-03
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      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;

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

     25:   MatShellGetContext(mat,(void**)&pc);
     26:   eis  = (PC_Eisenstat*)pc->data;
     27:   MatSOR(eis->A,b,eis->omega,SOR_EISENSTAT,0.0,1,1,x);
     28:   return(0);
     29: }

     31: static PetscErrorCode PCApply_Eisenstat(PC pc,Vec x,Vec y)
     32: {
     33:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;
     35:   PetscBool      hasop;

     38:   if (eis->usediag) {
     39:     MatHasOperation(pc->pmat,MATOP_MULT_DIAGONAL_BLOCK,&hasop);
     40:     if (hasop) {
     41:       MatMultDiagonalBlock(pc->pmat,x,y);
     42:     } else {
     43:       VecPointwiseMult(y,x,eis->diag);
     44:     }
     45:   } else {VecCopy(x,y);}
     46:   return(0);
     47: }

     49: static PetscErrorCode PCPreSolve_Eisenstat(PC pc,KSP ksp,Vec b,Vec x)
     50: {
     51:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;
     52:   PetscBool      nonzero;

     56:   if (pc->presolvedone < 2) {
     57:     if (pc->mat != pc->pmat) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot have different mat and pmat");
     58:     /* swap shell matrix and true matrix */
     59:     eis->A  = pc->mat;
     60:     pc->mat = eis->shell;
     61:   }

     63:   if (!eis->b[pc->presolvedone-1]) {
     64:     VecDuplicate(b,&eis->b[pc->presolvedone-1]);
     65:     PetscLogObjectParent((PetscObject)pc,(PetscObject)eis->b[pc->presolvedone-1]);
     66:   }

     68:   /* if nonzero initial guess, modify x */
     69:   KSPGetInitialGuessNonzero(ksp,&nonzero);
     70:   if (nonzero) {
     71:     VecCopy(x,eis->b[pc->presolvedone-1]);
     72:     MatSOR(eis->A,eis->b[pc->presolvedone-1],eis->omega,SOR_APPLY_UPPER,0.0,1,1,x);
     73:   }

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

     78:   /* modify b by (L + D/omega)^{-1} */
     79:     MatSOR(eis->A,eis->b[pc->presolvedone-1],eis->omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),0.0,1,1,b);
     80:   return(0);
     81: }

     83: static PetscErrorCode PCPostSolve_Eisenstat(PC pc,KSP ksp,Vec b,Vec x)
     84: {
     85:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;

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

     92:   /* modify x by (U + D/omega)^{-1} */
     93:   VecCopy(x,eis->b[pc->presolvedone]);
     94:   MatSOR(eis->A,eis->b[pc->presolvedone],eis->omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),0.0,1,1,x);
     95:   if (!pc->presolvedone) pc->mat = eis->A;
     96:   return(0);
     97: }

     99: static PetscErrorCode PCReset_Eisenstat(PC pc)
    100: {
    101:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;

    105:   VecDestroy(&eis->b[0]);
    106:   VecDestroy(&eis->b[1]);
    107:   MatDestroy(&eis->shell);
    108:   VecDestroy(&eis->diag);
    109:   return(0);
    110: }

    112: static PetscErrorCode PCDestroy_Eisenstat(PC pc)
    113: {

    117:   PCReset_Eisenstat(pc);
    118:   PetscFree(pc->data);
    119:   return(0);
    120: }

    122: static PetscErrorCode PCSetFromOptions_Eisenstat(PetscOptionItems *PetscOptionsObject,PC pc)
    123: {
    124:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;
    126:   PetscBool      set,flg;

    129:   PetscOptionsHead(PetscOptionsObject,"Eisenstat SSOR options");
    130:   PetscOptionsReal("-pc_eisenstat_omega","Relaxation factor 0 < omega < 2","PCEisenstatSetOmega",eis->omega,&eis->omega,NULL);
    131:   PetscOptionsBool("-pc_eisenstat_no_diagonal_scaling","Do not use standard diagonal scaling","PCEisenstatSetNoDiagonalScaling",eis->usediag ? PETSC_FALSE : PETSC_TRUE,&flg,&set);
    132:   if (set) {
    133:     PCEisenstatSetNoDiagonalScaling(pc,flg);
    134:   }
    135:   PetscOptionsTail();
    136:   return(0);
    137: }

    139: static PetscErrorCode PCView_Eisenstat(PC pc,PetscViewer viewer)
    140: {
    141:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;
    143:   PetscBool      iascii;

    146:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    147:   if (iascii) {
    148:     PetscViewerASCIIPrintf(viewer,"  omega = %g\n",(double)eis->omega);
    149:     if (eis->usediag) {
    150:       PetscViewerASCIIPrintf(viewer,"  Using diagonal scaling (default)\n");
    151:     } else {
    152:       PetscViewerASCIIPrintf(viewer,"  Not using diagonal scaling\n");
    153:     }
    154:   }
    155:   return(0);
    156: }

    158: static PetscErrorCode PCSetUp_Eisenstat(PC pc)
    159: {
    161:   PetscInt       M,N,m,n;
    162:   PC_Eisenstat   *eis = (PC_Eisenstat*)pc->data;

    165:   if (!pc->setupcalled) {
    166:     MatGetSize(pc->mat,&M,&N);
    167:     MatGetLocalSize(pc->mat,&m,&n);
    168:     MatCreate(PetscObjectComm((PetscObject)pc),&eis->shell);
    169:     MatSetSizes(eis->shell,m,n,M,N);
    170:     MatSetType(eis->shell,MATSHELL);
    171:     MatSetUp(eis->shell);
    172:     MatShellSetContext(eis->shell,(void*)pc);
    173:     PetscLogObjectParent((PetscObject)pc,(PetscObject)eis->shell);
    174:     MatShellSetOperation(eis->shell,MATOP_MULT,(void (*)(void))PCMult_Eisenstat);
    175:   }
    176:   if (!eis->usediag) return(0);
    177:   if (!pc->setupcalled) {
    178:     MatCreateVecs(pc->pmat,&eis->diag,NULL);
    179:     PetscLogObjectParent((PetscObject)pc,(PetscObject)eis->diag);
    180:   }
    181:   MatGetDiagonal(pc->pmat,eis->diag);
    182:   return(0);
    183: }

    185: /* --------------------------------------------------------------------*/

    187: static PetscErrorCode  PCEisenstatSetOmega_Eisenstat(PC pc,PetscReal omega)
    188: {
    189:   PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;

    192:   if (omega >= 2.0 || omega <= 0.0) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Relaxation out of range");
    193:   eis->omega = omega;
    194:   return(0);
    195: }

    197: static PetscErrorCode  PCEisenstatSetNoDiagonalScaling_Eisenstat(PC pc,PetscBool flg)
    198: {
    199:   PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;

    202:   eis->usediag = flg;
    203:   return(0);
    204: }

    206: static PetscErrorCode  PCEisenstatGetOmega_Eisenstat(PC pc,PetscReal *omega)
    207: {
    208:   PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;

    211:   *omega = eis->omega;
    212:   return(0);
    213: }

    215: static PetscErrorCode  PCEisenstatGetNoDiagonalScaling_Eisenstat(PC pc,PetscBool *flg)
    216: {
    217:   PC_Eisenstat *eis = (PC_Eisenstat*)pc->data;

    220:   *flg = eis->usediag;
    221:   return(0);
    222: }

    224: /*@
    225:    PCEisenstatSetOmega - Sets the SSOR relaxation coefficient, omega,
    226:    to use with Eisenstat's trick (where omega = 1.0 by default).

    228:    Logically Collective on PC

    230:    Input Parameters:
    231: +  pc - the preconditioner context
    232: -  omega - relaxation coefficient (0 < omega < 2)

    234:    Options Database Key:
    235: .  -pc_eisenstat_omega <omega> - Sets omega

    237:    Notes:
    238:    The Eisenstat trick implementation of SSOR requires about 50% of the
    239:    usual amount of floating point operations used for SSOR + Krylov method;
    240:    however, the preconditioned problem must be solved with both left
    241:    and right preconditioning.

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

    247:    Level: intermediate

    249: .seealso: PCSORSetOmega()
    250: @*/
    251: PetscErrorCode  PCEisenstatSetOmega(PC pc,PetscReal omega)
    252: {

    258:   PetscTryMethod(pc,"PCEisenstatSetOmega_C",(PC,PetscReal),(pc,omega));
    259:   return(0);
    260: }

    262: /*@
    263:    PCEisenstatSetNoDiagonalScaling - Causes the Eisenstat preconditioner
    264:    not to do additional diagonal preconditioning. For matrices with a constant
    265:    along the diagonal, this may save a small amount of work.

    267:    Logically Collective on PC

    269:    Input Parameters:
    270: +  pc - the preconditioner context
    271: -  flg - PETSC_TRUE turns off diagonal scaling inside the algorithm

    273:    Options Database Key:
    274: .  -pc_eisenstat_no_diagonal_scaling - Activates PCEisenstatSetNoDiagonalScaling()

    276:    Level: intermediate

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

    282: .seealso: PCEisenstatSetOmega()
    283: @*/
    284: PetscErrorCode  PCEisenstatSetNoDiagonalScaling(PC pc,PetscBool flg)
    285: {

    290:   PetscTryMethod(pc,"PCEisenstatSetNoDiagonalScaling_C",(PC,PetscBool),(pc,flg));
    291:   return(0);
    292: }

    294: /*@
    295:    PCEisenstatGetOmega - Gets the SSOR relaxation coefficient, omega,
    296:    to use with Eisenstat's trick (where omega = 1.0 by default).

    298:    Logically Collective on PC

    300:    Input Parameter:
    301: .  pc - the preconditioner context

    303:    Output Parameter:
    304: .  omega - relaxation coefficient (0 < omega < 2)

    306:    Options Database Key:
    307: .  -pc_eisenstat_omega <omega> - Sets omega

    309:    Notes:
    310:    The Eisenstat trick implementation of SSOR requires about 50% of the
    311:    usual amount of floating point operations used for SSOR + Krylov method;
    312:    however, the preconditioned problem must be solved with both left
    313:    and right preconditioning.

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

    319:    Level: intermediate

    321: .seealso: PCSORGetOmega(), PCEisenstatSetOmega()
    322: @*/
    323: PetscErrorCode  PCEisenstatGetOmega(PC pc,PetscReal *omega)
    324: {

    329:   PetscUseMethod(pc,"PCEisenstatGetOmega_C",(PC,PetscReal*),(pc,omega));
    330:   return(0);
    331: }

    333: /*@
    334:    PCEisenstatGetNoDiagonalScaling - Tells if the Eisenstat preconditioner
    335:    not to do additional diagonal preconditioning. For matrices with a constant
    336:    along the diagonal, this may save a small amount of work.

    338:    Logically Collective on PC

    340:    Input Parameter:
    341: .  pc - the preconditioner context

    343:    Output Parameter:
    344: .  flg - PETSC_TRUE means there is no diagonal scaling applied

    346:    Options Database Key:
    347: .  -pc_eisenstat_no_diagonal_scaling - Activates PCEisenstatSetNoDiagonalScaling()

    349:    Level: intermediate

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

    355: .seealso: PCEisenstatGetOmega()
    356: @*/
    357: PetscErrorCode  PCEisenstatGetNoDiagonalScaling(PC pc,PetscBool *flg)
    358: {

    363:   PetscUseMethod(pc,"PCEisenstatGetNoDiagonalScaling_C",(PC,PetscBool*),(pc,flg));
    364:   return(0);
    365: }

    367: static PetscErrorCode PCPreSolveChangeRHS_Eisenstat(PC pc, PetscBool* change)
    368: {
    370:   *change = PETSC_TRUE;
    371:   return(0);
    372: }

    374: /* --------------------------------------------------------------------*/

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

    380:    Options Database Keys:
    381: +  -pc_eisenstat_omega <omega> - Sets omega
    382: -  -pc_eisenstat_no_diagonal_scaling - Activates PCEisenstatSetNoDiagonalScaling()

    384:    Level: beginner

    386:    Notes:
    387:     Only implemented for the SeqAIJ matrix format.
    388:           Not a true parallel SOR, in parallel this implementation corresponds to block
    389:           Jacobi with SOR on each block.

    391: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
    392:            PCEisenstatSetNoDiagonalScaling(), PCEisenstatSetOmega(), PCSOR
    393: M*/

    395: PETSC_EXTERN PetscErrorCode PCCreate_Eisenstat(PC pc)
    396: {
    398:   PC_Eisenstat   *eis;

    401:   PetscNewLog(pc,&eis);

    403:   pc->ops->apply           = PCApply_Eisenstat;
    404:   pc->ops->presolve        = PCPreSolve_Eisenstat;
    405:   pc->ops->postsolve       = PCPostSolve_Eisenstat;
    406:   pc->ops->applyrichardson = NULL;
    407:   pc->ops->setfromoptions  = PCSetFromOptions_Eisenstat;
    408:   pc->ops->destroy         = PCDestroy_Eisenstat;
    409:   pc->ops->reset           = PCReset_Eisenstat;
    410:   pc->ops->view            = PCView_Eisenstat;
    411:   pc->ops->setup           = PCSetUp_Eisenstat;

    413:   pc->data     = (void*)eis;
    414:   eis->omega   = 1.0;
    415:   eis->b[0]    = NULL;
    416:   eis->b[1]    = NULL;
    417:   eis->diag    = NULL;
    418:   eis->usediag = PETSC_TRUE;

    420:   PetscObjectComposeFunction((PetscObject)pc,"PCEisenstatSetOmega_C",PCEisenstatSetOmega_Eisenstat);
    421:   PetscObjectComposeFunction((PetscObject)pc,"PCEisenstatSetNoDiagonalScaling_C",PCEisenstatSetNoDiagonalScaling_Eisenstat);
    422:   PetscObjectComposeFunction((PetscObject)pc,"PCEisenstatGetOmega_C",PCEisenstatGetOmega_Eisenstat);
    423:   PetscObjectComposeFunction((PetscObject)pc,"PCEisenstatGetNoDiagonalScaling_C",PCEisenstatGetNoDiagonalScaling_Eisenstat);
    424:   PetscObjectComposeFunction((PetscObject)pc,"PCPreSolveChangeRHS_C",PCPreSolveChangeRHS_Eisenstat);
    425:   return(0);
    426: }