Date: 2016-07-24T17:09:21+00:00

Actual source code: snesncg.c
petsc-3.7.3 2016-07-24
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      1: #include <../src/snes/impls/ncg/snesncgimpl.h> /*I "petscsnes.h" I*/
      2: const char *const SNESNCGTypes[] = {"FR","PRP","HS","DY","CD","SNESNCGType","SNES_NCG_",0};

      6: PetscErrorCode SNESReset_NCG(SNES snes)
      7: {
      9:   return(0);
     10: }

     12: #define SNESLINESEARCHNCGLINEAR "ncglinear"

     14: /*
     15:   SNESDestroy_NCG - Destroys the private SNES_NCG context that was created with SNESCreate_NCG().

     17:   Input Parameter:
     18: . snes - the SNES context

     20:   Application Interface Routine: SNESDestroy()
     21: */
     24: PetscErrorCode SNESDestroy_NCG(SNES snes)
     25: {

     29:   PetscFree(snes->data);
     30:   return(0);
     31: }

     33: /*
     34:    SNESSetUp_NCG - Sets up the internal data structures for the later use
     35:    of the SNESNCG nonlinear solver.

     37:    Input Parameters:
     38: +  snes - the SNES context
     39: -  x - the solution vector

     41:    Application Interface Routine: SNESSetUp()
     42:  */

     44: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch);

     48: PetscErrorCode SNESSetUp_NCG(SNES snes)
     49: {

     53:   SNESSetWorkVecs(snes,2);
     54:   if (snes->pcside == PC_RIGHT) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNESNCG only supports left preconditioning");
     55:   if (snes->functype == SNES_FUNCTION_DEFAULT) snes->functype = SNES_FUNCTION_UNPRECONDITIONED;
     56:   return(0);
     57: }
     58: /*
     59:   SNESSetFromOptions_NCG - Sets various parameters for the SNESNCG method.

     61:   Input Parameter:
     62: . snes - the SNES context

     64:   Application Interface Routine: SNESSetFromOptions()
     65: */
     68: static PetscErrorCode SNESSetFromOptions_NCG(PetscOptionItems *PetscOptionsObject,SNES snes)
     69: {
     70:   SNES_NCG       *ncg = (SNES_NCG*)snes->data;
     72:   PetscBool      debug = PETSC_FALSE;
     73:   SNESLineSearch linesearch;
     74:   SNESNCGType    ncgtype=ncg->type;

     77:   PetscOptionsHead(PetscOptionsObject,"SNES NCG options");
     78:   PetscOptionsBool("-snes_ncg_monitor","Monitor NCG iterations","SNES",ncg->monitor ? PETSC_TRUE : PETSC_FALSE, &debug, NULL);
     79:   if (debug) {
     80:     ncg->monitor = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)snes));
     81:   }
     82:   PetscOptionsEnum("-snes_ncg_type","NCG Beta type used","SNESNCGSetType",SNESNCGTypes,(PetscEnum)ncg->type,(PetscEnum*)&ncgtype,NULL);
     83:   SNESNCGSetType(snes, ncgtype);
     84:   PetscOptionsTail();
     85:   if (!snes->linesearch) {
     86:     SNESGetLineSearch(snes, &linesearch);
     87:     if (!snes->pc) {
     88:       SNESLineSearchSetType(linesearch, SNESLINESEARCHCP);
     89:     } else {
     90:       SNESLineSearchSetType(linesearch, SNESLINESEARCHL2);
     91:     }
     92:   }
     93:   SNESLineSearchRegister(SNESLINESEARCHNCGLINEAR, SNESLineSearchCreate_NCGLinear);
     94:   return(0);
     95: }

     97: /*
     98:   SNESView_NCG - Prints info from the SNESNCG data structure.

    100:   Input Parameters:
    101: + SNES - the SNES context
    102: - viewer - visualization context

    104:   Application Interface Routine: SNESView()
    105: */
    108: static PetscErrorCode SNESView_NCG(SNES snes, PetscViewer viewer)
    109: {
    110:   SNES_NCG      *ncg = (SNES_NCG *) snes->data;
    111:   PetscBool      iascii;

    115:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    116:   if (iascii) {
    117:     PetscViewerASCIIPrintf(viewer, "ncg type: %s\n", SNESNCGTypes[ncg->type]);
    118:   }
    119:   return(0);
    120: }

    124: PetscErrorCode SNESLineSearchApply_NCGLinear(SNESLineSearch linesearch)
    125: {
    126:   PetscScalar    alpha, ptAp;
    127:   Vec            X, Y, F, W;
    128:   SNES           snes;
    130:   PetscReal      *fnorm, *xnorm, *ynorm;

    133:   SNESLineSearchGetSNES(linesearch, &snes);
    134:   X     = linesearch->vec_sol;
    135:   W     = linesearch->vec_sol_new;
    136:   F     = linesearch->vec_func;
    137:   Y     = linesearch->vec_update;
    138:   fnorm = &linesearch->fnorm;
    139:   xnorm = &linesearch->xnorm;
    140:   ynorm = &linesearch->ynorm;

    142:   if (!snes->jacobian) {
    143:     SNESSetUpMatrices(snes);
    144:   }

    146:   /*

    148:    The exact step size for unpreconditioned linear CG is just:
    149:    alpha = (r, r) / (p, Ap) = (f, f) / (y, Jy)
    150:    */
    151:   SNESComputeJacobian(snes, X, snes->jacobian, snes->jacobian_pre);
    152:   VecDot(F, F, &alpha);
    153:   MatMult(snes->jacobian, Y, W);
    154:   VecDot(Y, W, &ptAp);
    155:   alpha = alpha / ptAp;
    156:   VecAXPY(X,-alpha,Y);
    157:   SNESComputeFunction(snes,X,F);

    159:   VecNorm(F,NORM_2,fnorm);
    160:   VecNorm(X,NORM_2,xnorm);
    161:   VecNorm(Y,NORM_2,ynorm);
    162:   return(0);
    163: }

    167: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_NCGLinear(SNESLineSearch linesearch)
    168: {
    170:   linesearch->ops->apply          = SNESLineSearchApply_NCGLinear;
    171:   linesearch->ops->destroy        = NULL;
    172:   linesearch->ops->setfromoptions = NULL;
    173:   linesearch->ops->reset          = NULL;
    174:   linesearch->ops->view           = NULL;
    175:   linesearch->ops->setup          = NULL;
    176:   return(0);
    177: }

    181: /*

    183:  Assuming F = SNESComputeFunction(X) compute Y^tJ^tF using a simple secant approximation of the jacobian.

    185:  */
    186: PetscErrorCode SNESNCGComputeYtJtF_Private(SNES snes, Vec X, Vec F, Vec Y, Vec W, Vec G, PetscScalar * ytJtf)
    187: {
    189:   PetscScalar    ftf, ftg, fty, h;

    192:   VecDot(F, F, &ftf);
    193:   VecDot(F, Y, &fty);
    194:   h      = 1e-5*fty / fty;
    195:   VecCopy(X, W);
    196:   VecAXPY(W, -h, Y);          /* this is arbitrary */
    197:   SNESComputeFunction(snes, W, G);
    198:   VecDot(G, F, &ftg);
    199:   *ytJtf = (ftg - ftf) / h;
    200:   return(0);
    201: }

    205: /*@
    206:     SNESNCGSetType - Sets the conjugate update type for SNESNCG.

    208:     Logically Collective on SNES

    210:     Input Parameters:
    211: +   snes - the iterative context
    212: -   btype - update type

    214:     Options Database:
    215: .   -snes_ncg_type<prp,fr,hs,dy,cd>

    217:     Level: intermediate

    219:     SNESNCGSelectTypes:
    220: +   SNES_NCG_FR - Fletcher-Reeves update
    221: .   SNES_NCG_PRP - Polak-Ribiere-Polyak update
    222: .   SNES_NCG_HS - Hestenes-Steifel update
    223: .   SNES_NCG_DY - Dai-Yuan update
    224: -   SNES_NCG_CD - Conjugate Descent update

    226:    Notes:
    227:    PRP is the default, and the only one that tolerates generalized search directions.

    229: .keywords: SNES, SNESNCG, selection, type, set
    230: @*/
    231: PetscErrorCode SNESNCGSetType(SNES snes, SNESNCGType btype)
    232: {

    237:   PetscTryMethod(snes,"SNESNCGSetType_C",(SNES,SNESNCGType),(snes,btype));
    238:   return(0);
    239: }

    243: PetscErrorCode SNESNCGSetType_NCG(SNES snes, SNESNCGType btype)
    244: {
    245:   SNES_NCG *ncg = (SNES_NCG*)snes->data;

    248:   ncg->type = btype;
    249:   return(0);
    250: }

    252: /*
    253:   SNESSolve_NCG - Solves a nonlinear system with the Nonlinear Conjugate Gradient method.

    255:   Input Parameters:
    256: . snes - the SNES context

    258:   Output Parameter:
    259: . outits - number of iterations until termination

    261:   Application Interface Routine: SNESSolve()
    262: */
    265: PetscErrorCode SNESSolve_NCG(SNES snes)
    266: {
    267:   SNES_NCG             *ncg = (SNES_NCG*)snes->data;
    268:   Vec                  X,dX,lX,F,dXold;
    269:   PetscReal            fnorm, ynorm, xnorm, beta = 0.0;
    270:   PetscScalar          dXdotdX, dXolddotdXold, dXdotdXold, lXdotdX, lXdotdXold;
    271:   PetscInt             maxits, i;
    272:   PetscErrorCode       ierr;
    273:   SNESLineSearchReason lsresult = SNES_LINESEARCH_SUCCEEDED;
    274:   SNESLineSearch       linesearch;
    275:   SNESConvergedReason  reason;

    278:   if (snes->xl || snes->xu || snes->ops->computevariablebounds) SETERRQ1(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

    280:   PetscCitationsRegister(SNESCitation,&SNEScite);
    281:   snes->reason = SNES_CONVERGED_ITERATING;

    283:   maxits = snes->max_its;            /* maximum number of iterations */
    284:   X      = snes->vec_sol;            /* X^n */
    285:   dXold  = snes->work[0];            /* The previous iterate of X */
    286:   dX     = snes->work[1];            /* the preconditioned direction */
    287:   lX     = snes->vec_sol_update;     /* the conjugate direction */
    288:   F      = snes->vec_func;           /* residual vector */

    290:   SNESGetLineSearch(snes, &linesearch);

    292:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    293:   snes->iter = 0;
    294:   snes->norm = 0.;
    295:   PetscObjectSAWsGrantAccess((PetscObject)snes);

    297:   /* compute the initial function and preconditioned update dX */

    299:   if (snes->pc && snes->functype == SNES_FUNCTION_PRECONDITIONED) {
    300:     SNESApplyNPC(snes,X,NULL,dX);
    301:     SNESGetConvergedReason(snes->pc,&reason);
    302:     if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    303:       snes->reason = SNES_DIVERGED_INNER;
    304:       return(0);
    305:     }
    306:     VecCopy(dX,F);
    307:     VecNorm(F,NORM_2,&fnorm);
    308:   } else {
    309:     if (!snes->vec_func_init_set) {
    310:       SNESComputeFunction(snes,X,F);
    311:     } else snes->vec_func_init_set = PETSC_FALSE;

    313:     /* convergence test */
    314:     VecNorm(F,NORM_2,&fnorm);
    315:     SNESCheckFunctionNorm(snes,fnorm);
    316:     VecCopy(F,dX);
    317:   }
    318:   if (snes->pc) {
    319:     if (snes->functype == SNES_FUNCTION_UNPRECONDITIONED) {
    320:       SNESApplyNPC(snes,X,F,dX);
    321:       SNESGetConvergedReason(snes->pc,&reason);
    322:       if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    323:         snes->reason = SNES_DIVERGED_INNER;
    324:         return(0);
    325:       }
    326:     }
    327:   }
    328:   VecCopy(dX,lX);
    329:   VecDot(dX, dX, &dXdotdX);

    332:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    333:   snes->norm = fnorm;
    334:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    335:   SNESLogConvergenceHistory(snes,fnorm,0);
    336:   SNESMonitor(snes,0,fnorm);

    338:   /* test convergence */
    339:   (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    340:   if (snes->reason) return(0);

    342:   /* Call general purpose update function */
    343:   if (snes->ops->update) {
    344:     (*snes->ops->update)(snes, snes->iter);
    345:   }

    347:   /* first update -- just use the (preconditioned) residual direction for the initial conjugate direction */

    349:   for (i = 1; i < maxits + 1; i++) {
    350:     /* some update types require the old update direction or conjugate direction */
    351:     if (ncg->type != SNES_NCG_FR) {
    352:       VecCopy(dX, dXold);
    353:     }
    354:     SNESLineSearchApply(linesearch,X,F,&fnorm,lX);
    355:     SNESLineSearchGetReason(linesearch, &lsresult);
    356:     SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);
    357:     if (lsresult) {
    358:       if (++snes->numFailures >= snes->maxFailures) {
    359:         snes->reason = SNES_DIVERGED_LINE_SEARCH;
    360:         return(0);
    361:       }
    362:     }
    363:     if (snes->nfuncs >= snes->max_funcs) {
    364:       snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
    365:       return(0);
    366:     }
    367:     /* Monitor convergence */
    368:     PetscObjectSAWsTakeAccess((PetscObject)snes);
    369:     snes->iter = i;
    370:     snes->norm = fnorm;
    371:     PetscObjectSAWsGrantAccess((PetscObject)snes);
    372:     SNESLogConvergenceHistory(snes,snes->norm,0);
    373:     SNESMonitor(snes,snes->iter,snes->norm);

    375:     /* Test for convergence */
    376:     (*snes->ops->converged)(snes,snes->iter,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
    377:     if (snes->reason) return(0);

    379:     /* Call general purpose update function */
    380:     if (snes->ops->update) {
    381:       (*snes->ops->update)(snes, snes->iter);
    382:     }
    383:     if (snes->pc) {
    384:       if (snes->functype == SNES_FUNCTION_PRECONDITIONED) {
    385:         SNESApplyNPC(snes,X,NULL,dX);
    386:         SNESGetConvergedReason(snes->pc,&reason);
    387:         if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    388:           snes->reason = SNES_DIVERGED_INNER;
    389:           return(0);
    390:         }
    391:         VecCopy(dX,F);
    392:       } else {
    393:         SNESApplyNPC(snes,X,F,dX);
    394:         SNESGetConvergedReason(snes->pc,&reason);
    395:         if (reason < 0  && reason != SNES_DIVERGED_MAX_IT) {
    396:           snes->reason = SNES_DIVERGED_INNER;
    397:           return(0);
    398:         }
    399:       }
    400:     } else {
    401:       VecCopy(F,dX);
    402:     }

    404:     /* compute the conjugate direction lX = dX + beta*lX with beta = ((dX, dX) / (dX_old, dX_old) (Fletcher-Reeves update)*/
    405:     switch (ncg->type) {
    406:     case SNES_NCG_FR: /* Fletcher-Reeves */
    407:       dXolddotdXold= dXdotdX;
    408:       VecDot(dX, dX, &dXdotdX);
    409:       beta         = PetscRealPart(dXdotdX / dXolddotdXold);
    410:       break;
    411:     case SNES_NCG_PRP: /* Polak-Ribiere-Poylak */
    412:       dXolddotdXold= dXdotdX;
    413:       VecDotBegin(dX, dX, &dXdotdXold);
    414:       VecDotBegin(dXold, dX, &dXdotdXold);
    415:       VecDotEnd(dX, dX, &dXdotdX);
    416:       VecDotEnd(dXold, dX, &dXdotdXold);
    417:       beta         = PetscRealPart(((dXdotdX - dXdotdXold) / dXolddotdXold));
    418:       if (beta < 0.0) beta = 0.0; /* restart */
    419:       break;
    420:     case SNES_NCG_HS: /* Hestenes-Stiefel */
    421:       VecDotBegin(dX, dX, &dXdotdX);
    422:       VecDotBegin(dX, dXold, &dXdotdXold);
    423:       VecDotBegin(lX, dX, &lXdotdX);
    424:       VecDotBegin(lX, dXold, &lXdotdXold);
    425:       VecDotEnd(dX, dX, &dXdotdX);
    426:       VecDotEnd(dX, dXold, &dXdotdXold);
    427:       VecDotEnd(lX, dX, &lXdotdX);
    428:       VecDotEnd(lX, dXold, &lXdotdXold);
    429:       beta = PetscRealPart((dXdotdX - dXdotdXold) / (lXdotdX - lXdotdXold));
    430:       break;
    431:     case SNES_NCG_DY: /* Dai-Yuan */
    432:       VecDotBegin(dX, dX, &dXdotdX);
    433:       VecDotBegin(lX, dX, &lXdotdX);
    434:       VecDotBegin(lX, dXold, &lXdotdXold);
    435:       VecDotEnd(dX, dX, &dXdotdX);
    436:       VecDotEnd(lX, dX, &lXdotdX);
    437:       VecDotEnd(lX, dXold, &lXdotdXold);
    438:       beta = PetscRealPart(dXdotdX / (lXdotdXold - lXdotdX));
    439:       break;
    440:     case SNES_NCG_CD: /* Conjugate Descent */
    441:       VecDotBegin(dX, dX, &dXdotdX);
    442:       VecDotBegin(lX, dXold, &lXdotdXold);
    443:       VecDotEnd(dX, dX, &dXdotdX);
    444:       VecDotEnd(lX, dXold, &lXdotdXold);
    445:       beta = PetscRealPart(dXdotdX / lXdotdXold);
    446:       break;
    447:     }
    448:     if (ncg->monitor) {
    449:       PetscViewerASCIIPrintf(ncg->monitor, "beta = %e\n", (double)beta);
    450:     }
    451:     VecAYPX(lX, beta, dX);
    452:   }
    453:   PetscInfo1(snes, "Maximum number of iterations has been reached: %D\n", maxits);
    454:   if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
    455:   return(0);
    456: }

    460: /*MC
    461:   SNESNCG - Nonlinear Conjugate-Gradient method for the solution of general nonlinear systems.

    463:   Level: beginner

    465:   Options Database:
    466: +   -snes_ncg_type <fr, prp, dy, hs, cd> - Choice of conjugate-gradient update parameter, default is prp.
    467: .   -snes_linesearch_type <cp,l2,basic> - Line search type.
    468: -   -snes_ncg_monitor - Print relevant information about the ncg iteration.

    470:    Notes: This solves the nonlinear system of equations F(x) = 0 using the nonlinear generalization of the conjugate
    471:           gradient method.  This may be used with a nonlinear preconditioner used to pick the new search directions, but otherwise
    472:           chooses the initial search direction as F(x) for the initial guess x.

    474:    References:
    475: .  1. -  Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu,"Composing Scalable Nonlinear Algebraic Solvers",
    476:    SIAM Review, 57(4), 2015

    479: .seealso:  SNESCreate(), SNES, SNESSetType(), SNESNEWTONLS, SNESNEWTONTR, SNESNGMRES, SNESNQN
    480: M*/
    483: PETSC_EXTERN PetscErrorCode SNESCreate_NCG(SNES snes)
    484: {
    486:   SNES_NCG       * neP;

    489:   snes->ops->destroy        = SNESDestroy_NCG;
    490:   snes->ops->setup          = SNESSetUp_NCG;
    491:   snes->ops->setfromoptions = SNESSetFromOptions_NCG;
    492:   snes->ops->view           = SNESView_NCG;
    493:   snes->ops->solve          = SNESSolve_NCG;
    494:   snes->ops->reset          = SNESReset_NCG;

    496:   snes->usesksp = PETSC_FALSE;
    497:   snes->usespc  = PETSC_TRUE;
    498:   snes->pcside  = PC_LEFT;

    500:   if (!snes->tolerancesset) {
    501:     snes->max_funcs = 30000;
    502:     snes->max_its   = 10000;
    503:     snes->stol      = 1e-20;
    504:   }

    506:   PetscNewLog(snes,&neP);
    507:   snes->data   = (void*) neP;
    508:   neP->monitor = NULL;
    509:   neP->type    = SNES_NCG_PRP;
    510:   PetscObjectComposeFunction((PetscObject)snes,"SNESNCGSetType_C", SNESNCGSetType_NCG);
    511:   return(0);
    512: }